![The forward-backward asymmetry as a function of Collins-Soper angle [88] in high-mass DY production at the LHC [89] provides enhanced sensitive to the behavior of the quark and antiquark PDFs in the large-x extrapolation region.](https://www.researchgate.net/profile/Andrei-Afanasev/publication/371684708/figure/fig1/AS:11431281168766180@1687145049711/The-forward-backward-asymmetry-as-a-function-of-Collins-Soper-angle-88-in-high-mass-DY_Q320.jpg)
![Expected accuracy on αs(M 2 z 0 ) from JLab at 22 GeV (blue), compared the EIC expectation (green) and the three most precise world data [104].](https://www.researchgate.net/profile/Andrei-Afanasev/publication/371684708/figure/fig3/AS:11431281168812686@1687145050115/Expected-accuracy-on-asM-2-z-0-from-JLab-at-22-GeV-blue-compared-the-EIC_Q320.jpg)
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JLAB-THY-23-3848
Strong Interaction Physics at the Luminosity Frontier
with 22 GeV Electrons at Jefferson Lab
A. Accardi1, P. Achenbach2, D. Adhikari3, A. Afanasev4, C.S. Akondi5, N. Akopov6,
M. Albaladejo7, H. Albataineh8, M. Albrecht2, B. Almeida-Zamora9, M. Amaryan10,
D. Androi´c11, W. Armstrong12 , D.S. Armstrong13, M. Arratia14 , J. Arrington15,
A. Asaturyan16, A. Austregesilo2, H. Avagyan2,∗, T. Averett13, C. Ayerbe Gayoso13,
A. Bacchetta17, A.B. Balantekin18, N. Baltzell2, L. Barion19, P. C. Barry2, A. Bashir20,2 ,
M. Battaglieri21, V. Bellini22 , I. Belov21, O. Benhar23, B. Benkel24, F Benmokhtar25,
W. Bentz26, V. Bertone27, H. Bhatt28 , A. Bianconi29, L. Bibrzycki30, R. Bijker31,
D. Binosi32, D. Biswas3, M. Bo¨er3, W. Boeglin33 , S.A. Bogacz2,∗, M. Boglione34, M. Bond´ı22,
E.E. Boos35, P. Bosted13 , G. Bozzi36, E.J. Brash37 , R. A. Brice˜no38, P.D. Brindza10,
W.J. Briscoe4, S.J Brodsky39 , W.K. Brooks40,41,42, V.D. Burkert2, A. Camsonne2, T. Cao2,
L.S. Cardman2, D.S. Carman2, M Carpinelli43, G.D. Cates44 , J. Caylor2, A. Celentano21,
F.G. Celiberto45, M. Cerutti17, Lei Chang46, P. Chatagnon2, C. Chen47,48 , J-P Chen2,∗,
T. Chetry33, A. Christopher1, E. Chudakov2, E. Cisbani23, I. C. Clo¨et12,
J.J. Cobos-Martinez49, E. O. Cohen50,51, P. Colangelo52, P.L. Cole53 , M. Constantinou54,
M. Contalbrigo19, G. Costantini55, W. Cosyn33, C. Cotton44, S. Covrig Dusa2, Z.-F. Cui56,
A. D’Angelo57, M. D¨oring4, M. M. Dalton2, I. Danilkin58 , M. Davydov35, D. Day44, F. De
Fazio59, M. De Napoli22, R. De Vita21, D.J. Dean2,†, M. Defurne27, M. Deur2, B. Devkota28,
S. Dhital1, P. Di Nezza60, M. Diefenthaler2, S. Diehl61,62, C. Dilks63 , M. Ding64,
C. Djalali65, S. Dobbs5, R. Dupr´e66 , D. Dutta28, R.G. Edwards2, H. Egiyan2, L. Ehinger67,
G. Eichmann68, M. Elaasar69, L. Elouadrhiri2,∗, A. El Alaoui40 , L. El Fassi28,∗,
A. Emmert44, M. Engelhardt70 , R. Ent2, D.J Ernst71, P. Eugenio5, G. Evans72, C. Fanelli13,
S. Fegan73, C. Fern´andez-Ram´ırez74,31, L.A. Fernandez20, I. P. Fernando44, A. Filippi75,
C.S. Fischer61, C. Fogler10, N. Fomin76, L. Frankfurt50, T. Frederico77, A. Freese78, Y. Fu79,
L. Gamberg80, L. Gan16,∗, F. Gao81 , H. Garcia-Tecocoatzi82, D. Gaskell2,∗, A. Gasparian83,
K Gates84, G. Gavalian2, P.K. Ghoshal2, A. Giachino85, F. Giacosa86 , F. Giannuzzi52,
G.-P. Gilfoyle87, F-X Girod2, D. I. Glazier84, C. Gleason88, S. Godfrey89, J.L. Goity2,1,
A.A. Golubenko35, S. Gonz`alez-Sol´ıs90, R.W. Gothe91,∗, Y. Gotra2, K. Griffioen13,
O. Grocholski92, B. Grube2, P. Gu`eye79, F.-K. Guo93,94, Y. Guo95, L. Guo33, T. J. Hague15,
N. Hammoud85, J.-O. Hansen2, M. Hattawy10, F. Hauenstein2, T. Hayward62, D. Heddle37 ,
N. Heinrich96, O. Hen67, D.W. Higinbotham2, I.M. Higuera-Angulo97 , A. N. Hiller Blin98,
A. Hobart66, D.E Holmberg13 , T. Horn2,99, P. Hoyer100, G.M. Huber96,∗, P. Hurck84, P. T.
P. Hutauruk101, Y. Ilieva91, I. Illari4, D.G Ireland84, E.L. Isupov35, A. Italiano22, I. Jaegle2,
N.S. Jarvis102, DJ Jenkins3, S. Jeschonnek103, C-R. Ji104 , H.S. Jo105, M. Jones2,
R.T. Jones62, D.C. Jones2, K. Joo62, M. Junaid96, T. Kageya2, N. Kalantarians106,
A. Karki28, G. Karyan6, A.T. Katramatou107, S.J.D Kay73, R. Kazimi2, C.D. Keith2,
C. Keppel2,†, A. Kerbizi108, V. Khachatryan109, A. Khanal33 , M. Khandaker110, A. Kim62,
E.R. Kinney111, M. Kohl1, A. Kotzinian6,112 , B. T. Kriesten113,2, V. Kubarovsky2,
B. Kubis114, S.E. Kuhn10 , V. Kumar96, T. Kutz67 , M. Leali115,116, R.F. Lebed117,
P. Lenisa118, L. Leskovec119, S. Li15, X. Li67, J. Liao109, H.-W. Lin79, L. Liu61, S. Liuti44,
N. Liyanage44, Y. Lu120, I.J.D. MacGregor84 , D. J. Mack2, L Maiani121, K. A. Mamo12,
1
arXiv:2306.09360v1 [nucl-ex] 13 Jun 2023
G. Mandaglio122, C. Mariani3, P. Markowitz33, H. Marukyan6, V. Mascagna29,116,
V. Mathieu123, J. Maxwell2, M. Mazouz124, M. McCaughan2, R.D. McKeown2,
B. McKinnon84, D. Meekins2, W. Melnitchouk2, C. A. Meyer102, Z.-E. Meziani12,
C. Mezrag125, R. Michaels2, G.A. Miller78, T. Mineeva40, A.S. Miramontes97, M. Mirazita60,
K. Mizutani2, H. Mkrtchyan6, A. Mkrtchyan6, B. Moffit2, P. Mohanmurthy67,
V.I. Mokeev2, P. Monaghan37 , G. Monta˜na2, R. Montgomery84, A. Moretti126,
J.M. Morgado Ch`avez125, U. Mosel61, A. Movsisyan6, P. Musico82, S.A Nadeeshani28,
S.X. Nakamura127, J. Nazeer1, A.V. Nefediev128, K. Neupane91, D. Nguyen2, S. Niccolai66,
I. Niculescu125,∗, G. Niculescu125, E.R. Nocera34, M. Nycz44, F.I. Olness129, P. G. Ortega130,
M. Osipenko21, E. Pace57, B Pandey131, P. Pandey10, Z. Papandreou96, J. Papavassiliou132 ,
L.L. Pappalardo118, G. Paredes-Torres97 , R. Paremuzyan2, S. Park2, B. Parsamyan75,112,
K.D. Paschke44,∗, B. Pasquini17, E. Passemar109,132,2, E. Pasyuk2, T. Patel1, C. Paudel33,
S.J. Paul14, J-C. Peng133, L. Pentchev2, R. Perrino52, R.J. Perry123, K. Peters134, G.
G. Petratos135, E. Piasetzky50, A. Pilloni22,122 , B. Pire136, D. Pitonyak137, M.L. Pitt3,
A.D. Polosa121, M. Pospelov138, A.C. Postuma96, J. Poudel2, L. Preet96, S. Prelovsek119,
J.W. Price139, A. Prokudin80,2 , A. J. R. Puckett62, J.R. Pybus67, S.-X. Qin140, J.-W. Qiu2,
M. Radici116, H. Rashidi141 , A.D Rathnayake44, B.A. Raue33, T. Reed33, P. E. Reimer12,
J. Reinhold33, J.-M. Richard142, M. Rinaldi143 , F. Ringer10,2, M. Ripani21 , J. Ritman134,
J. Rittenhouse West15, A. Rivero-Acosta144, C.D. Roberts56, A. Rodas2, S. Rodini136,
J. Rodr´ıguez-Quintero145, T.C. Rogers10 , J. Rojo146,147 , P. Rossi2,60,∗,†, G.C. Rossi57,
G. Salm`e23, S. N. Santiesteban148, E. Santopinto21, M. Sargsian33,∗, N. Sato2,∗,
S: Schadmand134, A. Schmidt4, S.M Schmidt64, G. Schnell149, R. A. Schumacher102,
P. Schweitzer62 , I. Scimemi150, K.C Scott1, D.A Seay44, J. Segovia151,
K. Semenov-Tian-Shansky105, A. Seryi2, A.S Sharda76, M. R. Shepherd109,∗,
E.V. Shirokov35, S. Shrestha54, U. Shrestha62, A. Signori34, K. J. Slifer148, W. A. Smith109,
A. Somov2, P. Souder152 , N. Sparveris54, F. Spizzo118, M. Spreafico21,153 , S. Stepanyan2, J.
R. Stevens13, I.I. Strakovsky4, S. Strauch91, M. Strikman154 , S. Su155, B.C.L. Sumner117 ,
E. Sun2, M. Suresh1, C. Sutera22, E.S. Swanson156, A.P Szczepaniak109 , P. Sznajder157,
H. Szumila-Vance2, L. Szymanowski157, A.-S. Tadepalli2, V. Tadevosyan6, B. Tamang28,
V.V. Tarasov158, A. Thiel114, X.-B. Tong159, R. Tyson84, M. Ungaro2, G.M. Urciuoli160,
A. Usman96, A. Valcarce130, S. Vallarino118, C.A. Vaquera-Araujo161,144,162,
L. Venturelli29,116, F. Vera33, A. Vladimirov150, A. Vossen2,63, J. Wagner157, X. Wei2,
L.B. Weinstein10, C. Weiss2,∗, R. Williams73, D. Winney163, B. Wojtsekhowski2, M.
H. Wood164 , T. Xiao165, S.-S. Xu166 , Z. Ye167, C. Yero10, M. Yurov28, N. Zachariou73,
Z. Zhang168, Z.W. Zhao63 , Y. Zhao12, X. Zheng44 , X. Zhou168, V. Ziegler2, B. Zihlmann2,
W de Paula77, and G. F. de T´eramond169
1Hampton University, Hampton, VA, 23669, USA
2Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
3Virginia Tech, Blacksburg, VA 24061 USA
4The George Washington University, Washington, D.C. 20052, USA
5Florida State University, Tallahassee, FL 32306, USA
6A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan 0036, Armenia
7Instituto de Fisica Corpuscular (IFIC), Centro Mixto CSIC-Universidad de Valencia, E-46071 Valencia, Spain
8Texas A&M University-Kingsville, Kingsville, TX 78363, USA
9Departamento de Investigaci´on en F´ısica, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, Colonia
Centro, Hermosillo, Sonora 83000, M´exico
10Old Dominion University, Norfolk, VA 23529, USA
11University of Zagreb, 10000 Croatia
2
12Argonne National Laboratory, Lemont, IL 60439, USA
13College of William and Mary, Williamsburg, VA 23187, USA
14University of California Riverside, Riverside, CA 92521, USA
15Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
16University of North Carolina Wilmington, Wilmington, NC 28403, USA
17Universit´a di Pavia and INFN, I-27100 Pavia, Italy
18University of Wisconsin, Madison, WI 53706 USA
19INFN, Sezione di Ferrara, 44122 Ferrara, Italy
20Universidad Michoacana de San Nicol´as de Hidalgo, Morelia, Michoac´an 58040, M´exico
21INFN, Sezione di Genova, Genova, 16146, Italy
22INFN, Sezione di Catania, Catania 95123, Italy
23INFN, Sezione di Roma, I-00161 Rome, Italy
24Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, 2930213 Chile
25Duquesne University, Pittsburgh. PA 15282 USA
26Department of Physics, School of Science, Tokai University, Hiratsuka-shi, Kanagawa 259-1292, Japan
27IRFU, CEA, Universit´e Paris-Saclay, 91191 Gif-sur-Yvette, France
28Mississippi State University, Mississippi State, MS 39762, USA
29Universit`a degli Studi di Brescia, Brecia I-25123, Italy
30AGH University of Krakow, al. Adama Mickiewicza 30 30-059 Krak´ow, Poland
31Instituto de Ciencias Nucleares, UNAM, A.P. 70-543, 04510 Ciudad de M´exico, M´exico
32ECT* and Fondazione Bruno Kessler, 38123 Trento, Italy
33Florida International University, Miami, FL 33199, USA
34Universit´a di Turin and INFN-Torino, 10125 Torino, Italy
35Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia
36Universit´a di Cagliari e INFN Sezione di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy
37Christopher Newport University, Newport News, VA 23606, USA
38University of California, Berkeley, CA 94720, USA
39SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
40Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, 2930213 Chile
41Center for Science and Technology of Valpara´ıso 699, Valpara´ıso, Chile
42SAPHIR Millennium Science Institute, Santiago, Chile
43Universit´a di Milano Bicocca, Milano, 20126, Italy
44University of Virginia, Charlottesville, VA 22904, USA
45Universidad de Alcal´a (UAH), Departamento de F´ısica y Matem´aticas, Campus Universitario, Alcal´a de Henares,
E-28805, Madrid, Spain
46Nankai University, Tianjin 300071, China
47Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China
48University of Science and Technology of China, Hefei, Anhui 230026, China
49Departamento de F´ısica, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, Colonia Centro,
Hermosillo, Sonora 83000, M´exico
50Tel Aviv University, Tel Aviv, 6927845, Israel
51Nuclear Research Center - Negev, 84190 Beer-Sheva, Israel
52INFN, Sezione di Bari, 70125 Bari, Italy
53Lamar University, Beaumont, TX 77710, USA
54Temple University, Philadelphia, PA 19122, USA
55Universit´a degli Studi di Brescia, 25123 Brescia, Italy and INFN, Sezione di Pavia, 27100 Pavia, Italy
56Nanjing University, Nanjing, Jiangsu 210093, China
57Universit´a di Rome Tor Vergata and INFN, 00133 Rome, Italy
58Johannes Gutenberg Universit¨at, D-55099 Mainz, Germany
59INFN Sezione di Bari, I-70126 Italy
60INFN, Laboratori Nazionali di Frascati, C.P. 13, 00044 Frascati, Italy
61II Physikalisches Institut der Universitaet Giessen, 35392 Giessen, Germany
62University of Connecticut, Storrs, CT 06269, USA
63Duke University, Durham, NC 27708, USA
64Helmholtz-Zentrum Dresden - Rossendorf, Bautzener Landstraße 400, D-01328 Dresden, Germany
65Ohio University, Athens, OH 45701, USA
66Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
67Massachusetts Institute of Technology, Cambridge, MA 02139, USA
68Institute of Physics, University of Graz, NAWI Graz, A-8010 Graz, Austria
3
69Southern University at New Orleans, New Orleans, LA 70126, USA
70New Mexico State University, Las Cruces, NM 88003, USA
71Vanderbilt University, Nashville, TN 37230,USA
72Brigham Young University, Provo, UT 84602, USA
73University of York, York YO10 5DD, UK
74Departamento de F´ısica Interdisciplinar, Universidad Nacional de Educaci´on a Distancia (UNED), Madrid
E-28040, Spain
75INFN, Sezione di Torino, I-10125 Torino, Italy
76University of Tennesse, Knoxville, TN 37996, USA
77Instituto Tecnol´ogico de Aeron´autica, S˜ao Jos´e dos Campos, 12228-900, Brazil
78University of Washington, Seattle, WA 98195, USA
79Michigan State University, East Lansing, MI 48824, USA
80Penn State University Berks, Reading, PA 19610, USA
81Beijing Institute of Technology, 100081 Beijing, China
82INFN, Sezione di Genova, 16146 Genova, Italy
83North Carolina A&T State University, Greensboro, NC 27411, USA
84University of Glasgow, Glasgow G12 8QQ, UK
85Institute of Nuclear Physics, Polish Academy of Science, Walerego Eljasza-Radzikowskiego 152, 31-342 Krakø w,
Poland
86Institute of Physics, Jan Kochanowski University, ul. Uniwersytecka 7, 25-406, Kielce, Poland
87University of Richmond, Richmond, VA 23173
88Union College, Schenectady, NY 12308, USA
89Carleton University, Ottawa, ON K2G 5V3, Canada
90Los Alamos National Laboratory, Los Alamos, NM 87545, USA
91University of South Carolina, Columbia, SC 29208, USA
92Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
93Chinese Academy of Sciences, Beijing 100190, China
94University of Chinese Academy of Sciences, Beijing 100049, China
95University of Maryland, College Park, MD 20742, USA
96University of Regina, Regina, Saskatchewan S4S 0A2, Canada
97Instituto de F´ısica y Matem´aticas, Universidad Michoacana de San Nicol´as de Hidalgo, Morelia, Michoac´an
58040, M´exico
98Institute for Theoretical Physics, T¨ubingen University, D-72076 T¨ubingen, Germany
99Catholic University of America, Washington, D.C. 20064, USA
100University of Helsinki, FIN-00014 Helsinki, Finland
101Department of Physics, Pukyong National University (PKNU), Busan 48513, Korea
102Carnegie Mellon University, Pittsburgh, PA 15213, USA
103The Ohio State University at Lima, OH 45804, USA
104North Carolina State University, Raleigh, NC 27607, USA
105Kyungpook National University, Daegu 41566, Korea
106Virginia Union University, Richmond, VA 23220, USA
107Kent State University, Kent, OH 44236, USA
108INFN, Sezione di Trieste, 34127 Trieste, Italy
109Indiana University, Bloomington, IN 47405, USA
110Sacramento City College, Sacramento, CA 95818, USA
111University of Colorado, Boulder, CO 80309, USA
112CERN, 1211 Meyrin, Switzerland
113Southeastern Universities Research Association, Washington, D.C. 20005, USA
114University of Bonn, D-53115 Bonn, Germany
115Universit`a degli Studi di Brescia, 25123 Brescia, Italy
116INFN, Sezione di Pavia, Pavia, I27100 Italy
117Arizona State University, Tempe, AZ 85281,USA
118Universit´a di Ferrara, Ferrara, 44122, Italy
119University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
120Nanjing Tech University, Nanjing 211816, China
121Sapienza University of Rome, I-00185 Rome, Italy
122Universit´a di Messina, 98166, Italy
123Departament de F´ısica Qu`antica i Astrof´ısica and Institut de Ci`encies del Cosmos, Universitat de Barcelona,
E-08028, Spain
4
124Facult´e des Sciences de Monastir, 5019 Monastir, Tunisia
125James Madison University, Harrisonburg, VA 22806, USA
126Universit´a di Trieste and INFN, 34127 Trieste. Italy
127Shandong University, Qingdao, Shandong 266237, China
128Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia
129Southern Methodist University, Dallas, TX 75205 USA
130Universidad de Salamanca, E-37008 Salamanca, Spain
131Virginia Military Institute, Lexington, VA 24450, USA
132Department of Theoretical Physics and IFIC, University of Valencia and CSIC, E-46100, Valencia, Spain
133University of Illinois at Urbana-Champaign, Urbana, IL, 61820, USA
134GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
135Kent State University, Kent, OH 44242, USA
136CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91120 Palaiseau, France
137Lebanon Valley College, Annville, PA 17003, USA
138University of Minnesota, Minneapolis, MN 55455, USA
139California State University, Dominguez Hills, Carson, CA 90747, USA
140Chongqing University, Chongqing 401331, China
141Bu-Ali Sina University, 65175 Hamedan, Iran
142Universit´
de Lyon, Institut des 2 Infinis de Lyon, UCBL-IN2P3, 4 rue Enrico Fermi, F69100 Villeurbanne, France
143INFN, Sezione di Perugia. 06123 Perugia, Italy
144Departamento de F´ısica, DCI, Campus Le´on, Universidad de Guanajuato, Loma del Bosque 103, Lomas del
Campestre C.P. 37150, Le´on, Guana juato, M´exico
145Department of Integrated Sciences and CEAFM, University of Huelva, E-21071 Huelva, Spain
146Nikhef, 1098 XG Amsterdam, The Netherlands
147Department of Physics and Astronomy, VU, 1081 HV Amsterdam, The Netherlands
148University of New Hampshire, NH 03824, USA
149University of the Basque Country UPV/EHU, 48080 Bilbao and IKERBASQUE, 48009 Bilbao, Spain
150Universidad Complutense de Madrid, Facultad de Fisica and IPARCOS, plaza de ciencias 1, 28040, Madrid,
Spain
151Departamento de Sistemas F´ısicos, Qu´ımicos y Naturales, Universidad Pablo de Olavide, E-41013 Sevilla, Spain
152Syracuse University, Syracuse, NY 13244, USA
153Universit´a degli Studi di Genova, 16126 Genova, Italy
154Pennsylvania State University, University Park, PA 16802, USA
155University of Arizona, Tucson, AZ 85721, USA
156University of Pittsburgh, Pittsburgh, PA, USA, 15206.
157National Centre for Nuclear Research, NCBJ, 02-093 Warsaw, Poland
158National Research Centre Kurchatov Institute, Moscow 123182, Russia
159The Chinese University of Hong Kong, Shenzhen, Shenzhen, Guangdong, 518172, P.R. China
160INFN Sezione di Roma, I-00185, Rome, Italy
161Consejo Nacional de Ciencia y Tecnolog´ıa, Av. Insurgentes Sur 1582. Colonia Cr´edito Constructor, Del. Benito
Ju´arez, C.P. 03940, Ciudad de M´exico, M´exico
162Dual CP Institute of High Energy Physics, C.P. 28045, Colima, M´exico
163South China Normal University, Guangzhou 510006, China
164Canisius College, Buffalo, NY 14208, USA
165University of North Texas, Denton, TX 76201, USA
166Nanjing University of Posts and Telecommunications, Nanjing 210023, China
167Tsinghua University, Beijing 100084, China
168Wuhan University, Wuhan, Hubei 430072, China
169Laboratorio de F´ısica Te´orica y Computacional, Universidad de Costa Rica, 11501 San Jos´e, Costa Rica
∗Editors
†Laboratory Management Representatives
5
Contents
1 Executive Summary 8
2 Introduction 11
3 Hadron Spectroscopy 13
3.1 Photoproduction as Tool for Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Spectroscopy of Exotic States with c¯c............................... 14
3.2.1 The X(3872) and Conventional c¯c............................. 16
3.2.2 Pentaquark PcCandidates.................................. 17
3.2.3 Tetraquark ZcCandidates.................................. 18
3.3 Light Meson Spectroscopy with 22 GeV Electrons . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Partonic Structure and Spin 21
4.1 Nucleon Light Sea in the Intermediate-xRange.......................... 21
4.2 Polarized PDFs and Strong Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 MesonStructure ........................................... 30
5 Hadronization and Transverse Momentum 32
5.1 Importance of Multi-Dimensional SIDIS Measurements . . . . . . . . . . . . . . . . . . . . . . 33
5.2 Role of Longitudinal Photon and SIDIS Structure Functions . . . . . . . . . . . . . . . . . . . 34
5.3 PhysicsOpportunities ........................................ 36
5.4 Summary ............................................... 47
6 Spatial Structure, Mechanical Properties, and Emergent Hadron Mass 48
6.1 Introduction.............................................. 48
6.2 QCDEnergy-MomentumTensor .................................. 49
6.2.1 Gluonic Mass and Momentum Distributions from Charmonium Production . . . . . . 49
6.2.2 Quark Pressure Distribution from Deeply Virtual Compton Scattering . . . . . . . . . 50
6.3 3DImagingwithGPDs ....................................... 52
6.3.1 Longitudinal/Transverse Separation in Exclusive Processes . . . . . . . . . . . . . . . 52
6.3.2 Differential Imaging with Double Deeply Virtual Compton Scattering . . . . . . . . . 54
6.3.3 Novel GPD Probes with Exclusive Diphoton Production . . . . . . . . . . . . . . . . . 55
6.3.4 Resonance Structure with N→N∗Transition GPDs . . . . . . . . . . . . . . . . . . . 56
6.3.5 Transition Distribution Amplitudes in Backward-Angle Processes . . . . . . . . . . . 58
6.4 Short-Range Electromagnetic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.1 Pion and Kaon Form Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.2 Nucleon Electromagnetic Form Factors at High Momentum Transfer . . . . . . . . . . 61
6.5 Bound Three-Quark Structure of Excited Nucleons and Emergence of Hadron Mass . . . . . . 63
6.5.1 The Emergent Hadron Mass Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6
6.5.2 Experimentally Driven Studies on N∗Structure, Emergent Hadron Mass, and Strong
QCD.............................................. 64
7 Hadron–Quark Transition and Nuclear Dynamics at Extreme Conditions 68
7.1 TheoreticalOverview......................................... 68
7.1.1 Nuclear Dynamics at Extreme Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.1.2 Hadron-QuarkTransition .................................. 70
7.1.3 Summary of Flagship Experiments at 22 GeV . . . . . . . . . . . . . . . . . . . . . . . 73
7.2 Nuclear Dynamics at Extreme Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.2.1 SuperfastQuarks....................................... 73
7.2.2 Probing Deuteron Repulsive Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.2.3 Probing3NSRCsinNuclei ................................. 77
7.3 Hadron-Quark Transition in Nuclear Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.3.1 Bound Nucleon Structure from Tagged DIS . . . . . . . . . . . . . . . . . . . . . . . . 78
7.3.2 Probing Partonic Structure with Spectator Tagging . . . . . . . . . . . . . . . . . . . 79
7.3.3 Unpolarized EMC and Antishadowing Regions . . . . . . . . . . . . . . . . . . . . . . 81
7.3.4 Spin Structure Functions in EMC, Antishadowing, and Shadowing Regions . . . . . . 82
7.3.5 Color Transparency Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.3.6 Hadronization Studies in Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.3.7 Coherent Nuclear J/ψPhotoproduction .......................... 89
8 QCD Confinement and Fundamental Symmetries 92
8.1 Precision Measurements of π0,η, and η′Decays.......................... 92
8.1.1 Primakoff Production of π0From Atomic Electrons . . . . . . . . . . . . . . . . . . . . 94
8.1.2 Primakoff Productions of ηand η′From Nuclear Targets . . . . . . . . . . . . . . . . . 96
8.2 Search for sub-GeV Dark Scalars and Pseudoscalars via the Primakoff Effect . . . . . . . . . 98
8.3 Electroweak Studies with SoLID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.4 SecondaryBeams........................................... 99
9 CEBAF Energy ‘Doubling’ - Accelerator Concept 102
10 Workshops 106
11 Acknowledgements 107
7
1 Executive Summary
The purpose of this document is to outline the developing scientific case for pursuing an energy upgrade to
22 GeV of the Continuous Electron Beam Accelerator Facility (CEBAF) at the Thomas Jefferson National
Accelerator Facility (TJNAF, or JLab). This document was developed with input from a series of workshops
held in the period between March 2022 and April 2023 that were organized by the JLab user community and
staff with guidance from JLab management (see Sec. 10). The scientific case for the 22 GeV energy upgrade
leverages existing or already planned Hall equipment and world-wide uniqueness of CEBAF high-luminosity
operations.
CEBAF delivers the world’s highest intensity and highest precision multi-GeV electron beams and has
been do so for more than 25 years. In Fall 2017, with the completion of the 12 GeV upgrade and the
start of the 12 GeV science program, a new era at the Laboratory began. The 12 GeV era is now well
underway, with many important experimental results already published, and an exciting portfolio Program
Advisory Committee approved experiments planned for at least the next 8–10 years [1]. At the same time,
the CEBAF community is looking toward its future and the science that could be obtained through a future
cost-effective upgrade to 22 GeV. The great potential to upgrade CEBAF to higher energies opens a rich
and unique experimental nuclear physics program that combines illustrious history with an exciting future,
extending the life of the facility well into the 2030s and beyond.
JLab at 22 GeV will provide unique, world-leading science with high-precision, high-luminosity experi-
ments elucidating the properties of quantum chromodynamics (QCD) in the valence regime (x≥0.1). JLab
at 22 GeV also enables researchers to probe the transition to a region of sea dominance, with access to
hadrons of larger mass and different structures. With a fixed-target program at the “luminosity frontier”,
large acceptance detection systems, as well as high-precision spectrometers, CEBAF will continue to offer
unique opportunities to shed light on the nature of QCD and the emergence of hadron structure for decades
to come. In fact, CEBAF today, and with an energy upgrade, will continue to operate with several orders
of magnitude higher luminosity than what is planned at the Electron-Ion Collider (EIC). CEBAF’s current
and envisioned capabilities enable exciting scientific opportunities that complement the EIC operational
reach, thus giving scientists the full suite of tools necessary to comprehensively understand how QCD builds
hadronic matter.
The physics program laid out in this document spans a broad range of exciting initiatives that focus
on a common theme, namely, investigations that explore different facets of the nonperturbative dynamics
that manifest in hadron structure and probe the richness of these strongly interacting systems. The central
themes of this program are reviewed in Section 2- Introduction. The main components of the research
program are highlighted in Sections 3through 8, followed by Section 9, which provides a brief overview
of the 22 GeV CEBAF energy-doubling concept. These sections outline the key measurements in different
areas of experimental studies possible at a 22 GeV CEBAF accelerator in the existing JLab experimental
end stations. They provide details on the key physics outcomes and unique aspects of the programs not
possible at other existing or planned facilities.
The 22 GeV physics program is being developed following three main principles: a) identify the flagship
measurements that can be done only with 22 GeV and their science impacts (Uniqueness); b) identify the
flagship measurements with 22 GeV that can extend and improve the 12 GeV measurements, helping the
physics interpretation through multidimensional bins in extended kinematics (Enrichment); c) identify the
measurements with 22 GeV that can set the bridge between JLab12 and EIC (Complementarity). Even if
a sharp separation among these three categories sometimes is difficult to maintain, we highlight the main
points in the following.
Uniqueness
An energy upgrade to CEBAF will dramatically enhance the discovery potential of the existing world-unique
hadron physics programs at Jefferson Lab. Several unique thrusts include:
8
•In the area of hadron spectroscopy, with real photons in Hall D and quasi-real photons in Hall B, a
unique production environment of exotic states will be probed providing cross section results, comple-
mentary to high-energy facilities. Photoproduction cross sections of exotic states could be decisive in
understanding the nature of a subset of the pentaquark and tetraquark candidates that contain charm
and anti-charm quarks. Moreover, in Hall B the high-intensity flux of quasi-real photons at high energy
will add the extra capability of studying the Q2evolution of any new state produced.
•JLab will be able to explore the proton’s gluonic structure by unique precise measurements of the
photo and electroproduction cross section near threshold of J/ψ and higher-mass charmonium states,
χcand ψ(2S). Moreover, with an increase of the polarization figure-of-merit by an order of magnitude,
GlueX will be able to measure polarization observables that are critical to disentangle the reaction
mechanism and draw conclusions about the mass properties of the proton.
•The JLab 22 GeV upgrade will enable high-precision measurements of the Primakoff production of
pseudoscalar mesons with results: to explore the chiral anomaly and the origin and dynamics of chiral
symmetry breaking; and to determine the light quark-mass ratio and the η-η′mixing angle model
independently. In particular, JLab will be able, for the first time, to perform precision measurements
of the radiative decay width of π0off an electron to reach a sub-percent precision on Γ(π0→γγ),
necessary to better understand the discrepancy between the existing experimental results and the
high-order QCD predictions, and therefore offering a stringent test of low-energy QCD.
Enrichment and Complementarity
•The 22 GeV upgrade will extend the phase space, in particular in momentum transfer Q2and hadronic
transverse momenta, for studying the momentum space tomography of nucleons and nuclei through the
transverse momentum dependent (TMDs) of parton distribution functions, offering a new complemen-
tary window between the 12 GeV program and the future EIC. Combined with the high luminosity and
precision detecting capabilities of multiparticle final state observables in a multidimensional space, it
will make JLab unique to disentangle the genuine intrinsic transverse structure of hadrons encoded in
TMDs with controlled systematics. These capabilities are critical for the interpretation of the measure-
ments carried out both at JLab and EIC and for full understanding of the complex nature of nucleon
structure properties and hadronization processes. Moreover, JLab has a uniquely fundamental role to
play in the EIC era in the realm of precision separation measurements between the longitudinal (σL)
and transverse (σT) photon contributions to the cross section, which are critical for studies of both
semi-inclusive and exclusive processes.
•The 22 GeV upgrade will be crucial for carrying out elastic and hard-exclusive process experiments.
Such measurements require sufficient energy for reaching the scaling and factorization regime, high
luminosity for measurements of low-rate processes and multivariable differential analysis, and excellent
detector resolution for cross section measurements. Essential physics applications are:
a) High-quality extraction of the D-term form factor of the QCD energy-momentum tensor and the
“pressure” distribution inside the proton.
b) Fully differential 3D imaging of the nucleon using novel processes such as Double Deeply Virtual
Compton Scattering (DDVCS) and exclusive diphoton production.
c) Exploring hadron structure with novel exclusive processes such as N→N∗transition GPDs and
N→meson transition distribution amplitudes.
d) Extending nucleon, pion, and resonance transition form factor measurements to momentum trans-
fers Q2∼30 GeV2, probing short-range hadron structure, QCD interactions, and the mechanism
of the emergence of hadron mass.
•JLab upgrade can offer critical insights for precision studies of partonic structure filling the gap in
kinematics of the combined scientific program of JLab 12 GeV and EIC. With its enhanced energy
range, the JLab 22 GeV upgrade will allow:
9
a) Precision measurements of the nucleon light sea in the intermediate to high-xrange, which can
help validate novel theoretical predictions for the intrinsic sea components in the nucleon wave
function and support Beyond Standard Model searches at colliders.
b) Precision determination of the helicity structure of the nucleon at large xand of the strong
coupling at levels well below one percent in ∆α/α.
c) Unique opportunities to explore the internal structure of mesons in the intermediate to high-x
range.
•The 22 GeV high intensity beam will create an unprecedented opportunity for Nuclear Sciences to sig-
nificantly advance our knowledge of QCD dynamics of nuclear forces at core distances. Some highlights
of the JLab 22 GeV upgrade program include:
a) Exploring nuclear forces dominated by nuclear repulsion by carrying out the first-ever direct
study of nuclear DIS structure at x > 1.25, as well as measuring deuteron structure at sub-Fermi
distances in exclusive deuteron break-up reactions with missing momenta above GeV region.
b) Providing definitive proof of three-nucleon short-range correlations by verifying the existence of
the new nuclear scaling at x > 2 and Q2= 10 - 15 GeV2in inclusive e−Ascattering;
c) Extending the reach of medium modification studies to the antishadowing region with unprece-
dentedly precise measurements using a rich variety of techniques (including tagging) and targets;
d) Proving the existence of Color Transparency phenomena in the baryonic sector.
e) Providing an unprecedented kinematic reach for studies of hadronization in the nuclear medium.
CEBAF energy upgrade will be realized taking advantage of recent novel advances in accelerator tech-
nology, which will make it possible to extend the energy reach of the CEBAF accelerator up to 22 GeV
within the existing tunnel footprint and using the existing CEBAF SRF cavity system. The proposal is to
replace the highest-energy arcs with Fixed Field Alternating Gradient (FFA) arcs and increase the number
of recirculations through the accelerating cavities. The new pair of arcs configured with an FFA lattice
would support simultaneous transport of 6 passes with energies spanning a factor of two. This novel perma-
nent magnet technology will have a big positive impact on JLab operations since it saves energy and lowers
operating cost.
CEBAF is a facility in high demand and JLab continues to invest to make optimum use of CEBAF’s
capabilities to produce high-impact science across different areas within Nuclear Physics and beyond. With
CEBAF at higher energy, some important thresholds would be crossed and an energy window that sits
between JLab at 12 GeV and EIC would be available. This, together with CEBAF capabilities to run electron
scattering experiment at the luminosity frontier, can provide unique insight into the nonperturbative QCD
dynamics and will place JLab as a unique facility capable of exploring the emergent phenomena of QCD and
its associated effective degrees of freedom.
10
2 Introduction
The proposed energy upgrade to the CEBAF accelerator at the Thomas Jefferson National Accelerator
Facility would enable the only facility worldwide, planned or foreseen, that can address the complexity at the
scientific frontier of emergent hadron structure with its high luminosity and probing precision at the hadronic
scale. While high-energy facilities will illuminate the perturbative dynamics and discover the fundamental
role of gluons in nucleons and nuclei, a medium energy electron accelerator at the luminosity frontier will be
critical to understand the rich and extraordinary variety of non-perturbative effects manifested in hadronic
structure.
Figure 1: The emergence of structure in QCD from
the perturbative regime of quarks and gluons to bound
hadrons to hadrons bound in nuclei.
The Lagrangian of QCD, which we believe governs
the dynamics of quarks and gluons, is not easily or di-
rectly connected to the complicated observables that we
measure in electron-proton and electron-nucleus scatter-
ing experiments. At one end of the spectrum, the ele-
mentary quark/gluon degrees of freedom are manifested
only at distances ≲0.1 fm, where the quark-gluon inter-
actions can be understood using methods of perturbation
theory; however, at hadronic distances ∼1 fm the dynam-
ics undergo qualitative changes, causing the appearance
of effective degrees of freedom expressed in new struc-
ture and dynamics. While these new structures develop
in the context of the underlying QCD degrees of free-
dom, their experimental interpretation remains challeng-
ing. This places strong interaction physics in the context
of “emergent phenomena”, a powerful paradigm for the
study of complex systems used in other areas of physics,
such as condensed matter, as well as biological and social
sciences. Here, the behavior of larger and complex aggre-
gates of elementary particles may not be understood in
terms of an extrapolation of the properties of a few par-
ticles. Instead, at each level of complexity, entirely new
properties appear – and the understanding of each new
behavior warrants study. This is demonstrated in Fig. 1
where the distance scale incorporates emergence.
Experimental scattering observables are shaped by certain effects rooted in the quantum and nonlinear
nature of QCD. These effects create dynamical scales not present in the original theory (see Fig. 1). One effect
is the breaking of scale invariance by quantum fluctuations at high energies beyond the range of observation,
which creates a mass/length scale that acts as the source of all other dynamical scales emerging from the
theory (the so-called trace anomaly). Another effect is the spontaneous breaking of chiral symmetry, which
generates a dynamical mass of the quarks that provides most of the mass of the light hadrons, including
the nucleon, and is therefore the source of 99% of the mass of the visible Universe. Yet another effect is
confinement, which limits the propagation of QCD color charges over hadronic distances and influences the
long-range structure of hadrons and their excitation spectrum. Understanding these nonperturbative effects
is the key to understanding the emergence of hadrons and nuclei from QCD.
Many expressions of these nonperturbative effects can be seen already in established hadron spectra,
structure, and interactions. Chiral symmetry breaking is expressed in the unnaturally small mass of the
pion, which emerges as the Goldstone boson mediating the long-range QCD interactions, and its momentum-
dependent coupling to other hadrons; confinement is visible in the spectra of heavy quarkonia. However, in
order to truly understand “how” the effective dynamics emerges from QCD, it is necessary to study the fields
of QCD through scattering processes that probe nonperturbative dynamics hadron structure and spectra.
Formulating such processes has been a priority of theoretical and experimental research in recent years.
11
Since the 2015 Long-Range Plan, several novel processes probing hadron structure and spectra have come
into focus, revealing specific aspects of nonperturbative dynamics and providing insight into the emergence
of structure from QCD. Studies of nucleon elastic electromagnetic form factors and nucleon resonance elec-
troexcitation amplitudes for many excited states of the nucleon have demonstrated the capability to explore
the emergence of hadron mass and the structure of ground and excited nucleon states at a distance scale
comparable with the hadron size. In concert, recent advances in accelerator science and technology have
made possible a promising, cost-effective extension of the energy reach of the CEBAF accelerator to 22 GeV
within the existing tunnel footprint. To map the emergence of hadronic structure from perturbative dynam-
ics, several experimental requirements must be met. One is the need for a large four-momentum transfer,
Q > 2 GeV, to have a well-controlled and localized probe (<0.1 fm). Importantly, a second momentum
scale is simultaneously needed to be sensitive to the emergent regime across the scales shown in Fig. 1. Such
two-scale experimental observables are naturally accessible at a lepton-hadron facility like CEBAF, including
exclusive electron-hadron deep virtual Compton scattering (DVCS): e(ℓ) + h(p)→e(ℓ′) + h(p′) + γwith the
hard scale Q2=−(ℓ−ℓ′)2and the second scale t= (p−p′)2, and semi-inclusive deep inelastic scattering
(SIDIS): e(ℓ) + h(p)→e(ℓ′) + h′(p′) + Xwith the momentum imbalance between ℓ′and p′as the second
scale. However, once the hadron is broken, larger momentum transfer Qleads to more collision induced ra-
diation, which could significantly shadow the structure information probed at the second (and the soft) scale
and reduce our precision to probe the emergent hadron structure. The requisite electron beam energy to
probe hadron structure is determined by the need to, for instance, reach the charm threshold in deep-virtual
processes and to separate the produced hadronic systems from the target remnants. The studies presented in
this document show that the optimal beam energy for performing such two-scale measurements is ∼20 GeV.
Another determining constraint to the measurements is the need to precisely measure small cross sections
in a multidimensional phase space, needed also for separation of different dynamical mechanisms, which
requires high luminosity and multiple devices with differing but complementary experimental capabilities.
The fixed-target experiments with the CEBAF accelerator at JLab will achieve luminosities ∼1038cm−2s−1
with the high-resolution spectrometers and SoLID, and ∼1035cm−2s−1with the CLAS12 large-acceptance
detector. The foreseen Jefferson Lab experimental equipment, including the Solenoidal Large Intensity De-
vice (SoLID) in Hall A, high luminosity CLAS12 in Hall B, precision magnetic spectrometers in Hall C,
and polarized, tagged photon beams in Hall D, matches the science need. It is a major advantage that the
measurements can be performed using the existing and well-understood JLab12 detectors, reducing cost and
minimizing technical risk to the program.
The experimental program proposed here is complementary and synergistic with both the current JLab
12 GeV program (including SoLID) and the future EIC. It provides a critical bridge between the two,
exploring fascinating and essential aspects of the emergence of hadrons that are needed for full understanding
but are not covered by either JLab 12 GeV or the EIC. The center-of-mass energies reached in these fixed-
target experiments (√s∼6 GeV) are still substantially below those reached in colliding-beam experiments
at EIC (√s > 20 GeV), while the luminosity of the fixed target facilities is ∼3−4 orders of magnitude
larger. At the same time, there is considerable synergy between the scientific programs pursued with the
upgraded CEBAF and the EIC. The experimental requirements for many of the measurements needed to
answer the myriad questions posed by the emergence of structure have been assessed in simulations, and
some highlights are described in Sections 3through 8. The experimental program at 22 GeV is based on
an energy-upgraded CEBAF facility that may be considered due to exciting and cost-effective advances in
accelerator technology that are highlighted in Section 9.
12
3 Hadron Spectroscopy
From the development of the Bohr model of the atom to the quark model of hadrons, the idea of measuring
and organizing spectra of energy states has proven to be an invaluable tool in gaining insight into the
fundamental theory that generates such states. A fascinating aspect of quantum chromodynamics (QCD)
is the broad variety of phenomena that emerge from the underlying theory and the scales at which this
emergence occurs. In the context of hadron spectroscopy, one aims to study the spectrum of semi-stable
hadrons or hadronic resonances and use this information to understand how and what types of hadrons are
generated by QCD.
The quark model originally arose from the need to explain the landscape of hadrons observed in par-
ticle collisions in the mid-twentieth century, and we now understand that QCD is the fundamental theory
underlying the model. However, the light quarks of QCD are not the same as those in the quark model,
and a detailed understanding of how QCD generates not only the spectrum predicted by the quark model
but also perhaps states with additional gluonic degrees of freedom remains an open question. Until recently,
it seemed as if almost all hadrons observed in Nature were composed of three-quark baryons or quark-
antiquark mesons. While the original quark model allows the possibility of more complex configurations of
quarks and anti-quarks, Nature appears not to prefer them. At the same time, our understanding of gluon
self-interactions in QCD motivated ideas that glueballs, with no quarks, or quark-gluon hybrids might exist.
These ideas have evolved tremendously into predictions using lattice QCD techniques about the existence
and properties of exotic hybrid mesons [2]. The experimental search for hybrid mesons is a key thrust of
the JLab 12 GeV program and complementary experiments around the world, some of which have reported
evidence of such states [3–5]. Establishing a spectrum of hybrids would further our understanding of how
the unique properties of gluons in QCD affect the emergence of the hadron spectrum.
Theoretical techniques for connecting QCD to experimental data have advanced significantly in recent
decades but new discoveries indicate our understanding of QCD dynamics is far from complete. In the last
twenty years, high-energy and high-intensity experiments have produced a mountain of discoveries in the
spectroscopy of hadrons containing heavy quarks (charm and bottom) [6–8]. For example, observation of
peaks in the invariant mass of J/ψ π−around 4 GeV [9,10] suggest new tetraquark classes of particles: being
heavy, such states must have a c¯cbut the presence of charge requires at least an additional d¯u. There are
numerous similar states, in both the bottom [11] as well as charm spectra [12], which have masses at level
where light-quark meson interactions become relevant. If these states are in fact hadron resonances, then
one would like to know their nature. For example, are these systems compact four-quark objects or more
like a meson-meson molecule? These hadrons are all instances of confinement in QCD, and it is valuable to
understand their place in the hadron landscape. Just as probing the nuclear landscape has led to a better
understanding of nuclear structure and nucleon interactions, the hadron landscape provides a path to explore
interesting features of QCD. While the 12 GeV program at JLab is able to explore light-quark systems in
isolation and can produce the lowest-mass c¯csystems, an energy upgrade is essential for JLab to contribute
unique information on photoproduction of systems with light and heavy degrees of freedom that appear to
exhibit exotic properties. Throughout this section we consider not only the final upgrade target electron
energy of 22 GeV but also demonstrate that significant new results can be obtained by interim operations
at 17 GeV if a phased upgrade strategy is adopted.
3.1 Photoproduction as Tool for Spectroscopy
An energy upgrade to CEBAF would dramatically enhance the discovery potential of the existing world-
unique hadron spectroscopy experimental programs at JLab, namely the CLAS12 experiment in Hall B [13]
and the GlueX experiment in Hall D [14]. Both experiments feature high-acceptance, multi-particle spec-
trometers that are designed to detect the decays of hadronic resonances and enable studies of properties
and production mechanisms of hadrons. The CLAS12 experiment uses polarized virtual photoproduction
at low Q2via electron-proton collisions, while the Hall D facility at JLab provides a real photon beam that
is partially linearly polarized through coherent bremsstrahlung scattering of the CEBAF electron beam off
13
0.8 1.0 1.2 1.4 1.6 1.8 2.0
0
5000
10000
15000
20000
25000
Total
) [GeV]M(
Yield / 40 MeV
a0(980)
a2(1320)
a2 Production
Plane
Φ
a2
γp
model production
by particle exchange
−
Δ
++
Photon Beam
Polarization Plane
π
η
spin and parity (ε)
of exchanged particle
is encoded in
the Φ distribution
a2 spin and polarization (Jm)
is encoded in the ηπ angular
distribution
Figure 2: A sketch of the polarized photoproduction of a−
2(1320) via t-channel interaction with the target.
Preliminary data from GlueX indicates that the dominant production mechanism of the spin-2 (D−wave)
peak consistent with the a2in the ηπ−spectrum is by exchange of an unnatural parity particle (ϵ=−).
of a diamond radiator. With Hall D, the recoil electron momentum is measured, which provides an energy
determination of each photon incident on the proton target at the center of the GlueX spectrometer, while for
CLAS12, detection of the scattered electron provides energy and (linear) polarization of the virtual photon.
The future high-energy and high-luminosity spectroscopy program leverages existing experience with these
two facilities and their complementary photoproduction mechanisms.
Photoproduction of mesons by linearly polarized photons provides an opportunity to extract information
about the production mechanisms and how these mechanisms vary with kinematics. Figure 2illustrates a
typical model for production of ηπ−by linearly polarized photons where the beam photon interacts with a
particle emitted by the target, i.e., at-channel production. Preliminary results from the GlueX experiment
illustrate that a−
2(1320) can be identified in the ηπ−mass spectrum using the angular distribution of the
ηπ−. By analyzing the angle between the production and polarization planes, one learns that the dominant
production mechanism of a−
2is by exchange of a particle with unnatural parity (JP= 0−,1+, . . .) like a
pion (JP= 0−). This is consistent with expectations: the photon beam can be considered a virtual ρmeson
that scatters off of a π−emitted by the target to produce the a−
2via its well-known ρπ coupling. The
use of linearly polarized photons enables this additional angular analysis that sheds light on the production
coupling of the hadronic resonance in addition to the decay coupling.
An advantage of using photoproduction to study hadronic resonances is the variety of different production
mechanisms that are available – many virtual particles can be exchanged between the beam and the target
over a broad kinematic range. In contrast, when studying resonances in Bmeson decays or e+e−collisions,
the quantum numbers and kinematics of the initial state are fixed. These well-known initial conditions in
the latter case simplifies the analysis and interpretation of experimental data, but can also constrain the
opportunities for exploring resonance production. The use of linearly polarized real or virtual photoproduc-
tion relaxes production constraints at a cost of increasing analysis complexity, and provides a unique and
complementary tool to study hadronic resonances. In addition, the GlueX and CLAS12 experiments offer
the opportunity to cross-check results over a wide range of kinematics and final states using two similar but
complementary photoproduction mechanisms.
3.2 Spectroscopy of Exotic States with c¯c
The last two decades have produced numerous discoveries of new particles in the charm and bottom sectors
by experiments like BaBar, BESIII, and Belle at e+e−machines, as well as LHCb at the LHC. All of these
14
8 10 12 14 16 18 20 22
Eγ [GeV]
1−
10
1
10
2
10
γp Cross Section [nb]
Pc
+ Predictions
Zc
+ (3900) Prediction
J/ψ Data (12 GeV)
J/ψ Projection (17 GeV)
χc1 Projection (22 GeV)
ψ(2S) Projection (22 GeV)
γ
p
γ
p
J/ψJ/ψ
nπ+
π+
p
c
c
u
u
d
c
d
u
c
Zc
+ ?
Pc
+ ?
Figure 3: Photoproduction cross sections
of states containing c¯cas a function
of photon beam energy. The points
are GlueX data [19] The colored boxes
are projections of statistical precision
using the GlueX detector with differ-
ent assumptions about the electron en-
ergy. The collection of dashed and dotted
curves indicate how pentaquark Pc[20]
or tetraquark Zc[21] candidates might
appear.
experiments have pushed the luminosity frontier and as a result have the ability to discover new hadrons
that are rarely produced. Some of these new discoveries, like the observation of excited states of the Ωb
(bss) [15], extend our knowledge of conventional hadrons containing heavy quarks, while many others, like
the charged Zctetraquark candidates [9,10,12,16,17], have forced a reconsideration of long-standing ideas
about the valence quark content of hadrons generated by QCD. Extensive reviews of these new particles
can be found in Refs. [6–8,18]. While these particles are colloquially referred to as the XY Z states, the
community has yet to agree on a naming scheme, let alone an underlying theoretical interpretation, for the
numerous new additions to the hadron landscape.
The XY Z states are exotic because they have properties that are inconsistent with the well-understood
heavy q¯qmesons. Some exotic features are clear: a meson with non-zero electric charge cannot be a c¯cstate.
Other states are unusual because they have masses, quantum numbers, or decay properties that do not align
with expectation based on our understanding of heavy-quark systems. A common feature to all of the X Y Z
states is that they have masses where both heavy and light quarks play a key role in their structure and
decays, that is, the path to understanding these particles involves QCD in the strongly interacting regime.
A peculiar feature of the XY Z states is that, with the exception of the X(3872), none so far have been
observed in multiple production mechanisms [22]. Most observations of XY Z states come from analysis of
e+e−collisions or the decay of hadrons containing bquarks, but these two production mechanisms seem to
have generated a non-overlapping set of exotic candidates. The reason why some states appear in certain
production environments but not others is not understood. A feature of both production mechanisms is
that they require exotic candidates to be produced in conjunction with other hadrons. For example, if one
wants to produce a charged tetraquark candidate Zcin an e+e−collision, another charged hadron must be
present in the final state. The fact that most XY Z states appear as a peak in the mass spectrum of two
particles in a three-body system has led to the suggestion that some of the states are not hadronic resonances
but kinematic effects known as triangle singularities [23–26]. These effects arise when relatively long-lived
particles, like Dmesons, are produced with kinematic conditions that are favorable for rescattering into
some final state of interest. A peak in the invariant mass of the final state is then an indicator of meeting
the criteria for rescattering and not the signal of a resonance. In these three-body decays, separating the
signature of a new type of hadron from a kinematic effect, a question of utmost importance to understanding
the spectrum of hadrons generated by QCD, requires precise measurement and theoretical understanding of
the lineshape [27].
With an energy upgrade, JLab is capable of providing unique and complementary information that could
be decisive in understanding the nature of a subset of the XY Z states. Those states that are particularly well
15
3.3 3.4 3.5 3.6 3.7
0
2
4
6
8
10
12
14
N(χc1) = 55.3 ± 8.2
N(χc2) = 13.6 ± 4.7
Events / 5 MeV
γp → J/ψγp
M(J/ψγ) [GeV]
M(χc2)M(χc1)
Yield [Events]:
Figure 4: Preliminary results from the
GlueX Collaboration showing evidence for
exclusive photoproduction of χc1. The χc1
candidates are reconstructed in the γJ/ψ
decay mode with J/ψ →e+e−. These pre-
liminary results use the entire photon beam
energy range available to GlueX and come
from a subset of about 3 ×1011 events col-
lected over 100 days of beam on target. The
PDG [31] values for the masses of the χc1
and χc2are given by the green arrows.
suited for exploration at JLab are the ones that are candidates for resonances in J/ψ p,J/ψ π, and ψ(2S)π
systems. Since the photon has the same quantum numbers as the J/ψ or ψ(2S), photoproduction can be
viewed as a mechanism to scatter a virtual J/ψ directly off of a proton or off the charged pion cloud around
a proton. In such production mechanisms, sketched at the top of Fig. 3, the production vertex is directly
related to the decay vertex. These clean two-to-two scattering processes are free from triangle singularities
that can complicate the interpretation of existing data from e+e−collisions and Bdecay.
3.2.1 The X(3872) and Conventional c¯c
The discovery of the X(3872) by Belle in 2003 [28] marked the start of what continues today as a very exciting
investigation into the spectroscopy of systems containing a heavy q¯qcomponent. The X(3872) is the most
robust and most extensively studied of all of the XY Z states. It has been observed by numerous experiments
and in numerous production environments. Its quantum numbers are determined: JP C = 1++ [29] and as
such the PDG has designated the state χc1(3872). The state has a very narrow width of about 1 MeV, a mass
that is consistent with the D0D∗0threshold, and exhibits large isospin violation in its decays. Explanations
of its underlying structure include conventional χc1(2P), DD∗molecule, and compact tetraquark. Because
of its robustness, it serves as an interesting standard candle in photoproduction investigations with an
upgraded CEBAF. Virtual photoproduction of the X(3872) with a muon beam was recently explored by
COMPASS [30], but interestingly, the state observed, while having a mass consistent with the X(3872),
exhibited different decay properties than established by other experiments. The COMPASS observations are
based on a total of 13.2±5.2 events. A follow-up investigation in electroproduction or photoproduction with
a high-luminosity CEBAF is warranted.
By looking to the edge of the capability of the current machine, one can see potential for new explorations
of charmonium production. The CEBAF configuration is such that the GlueX experiment receives one
additional pass through the north accelerating LINAC than the other halls. Therefore, the highest energy
photons in the JLab 12 GeV machine are impinging on the GlueX target. Figure 4shows the J/ψ γ invariant
mass in the reaction γp →J/ψ γp where a preliminary signal of about 50 events consistent with γp →χc1p
is observed. This result, which uses 100 days of beam on the GlueX target, will yield the first measurement
of the photoproduction cross section of the χc1(1P). An upgrade of the electron energy to 22 GeV is
projected to increase the χc1yield by two orders of magnitude, which would enable a measurement of the
cross section dependence on energy. The X(3872) has some similarities to the χc1(2P) state of the c¯csystem.
If the X(3872) is observed in photoproduction at an energy-upgraded CEBAF, then JLab can contribute
unique information that may provide insight to the nature of the X(3872) by conducting a comparison of
photoproduction mechanisms of the χc1and X(3872).
16
9 10 11 12 13 14 15 16 17
0
5
10
15
20
25
Polarization Figure of Merit [pb-1/45 MeV]
Eγ [GeV]
17 GeV
22 GeV
Electron Beam Energy
12 GeV
J/ψχc1 ψ(2S)
Figure 5: The polarization figure of merit
(P2(dNγ/dE)) as a function of photon beam en-
ergy Eγfor the existing 12 GeV GlueX configu-
ration assuming 100 days of beam on target (yel-
low). Figures of merit assuming equal beam time
are shown for 17 GeV and 22 GeV electrons, both
of which are drawn for the same diamond ori-
entation. Various c¯cproduction thresholds are
shown.
3.2.2 Pentaquark PcCandidates
In 2015, the LHCb Collaboration reported the observation of two pentaquark candidates in the decay of
Λb→J ψ p K−[32]. The states appear as peaks in the J/ψ p mass spectrum around 4.4 GeV and have
minimum quark content of c¯cuud. In 2019, using a significantly larger dataset, LHCb was able to further
resolve three narrow peaks in the mass spectrum known as the Pc(4312)+,Pc(4440)+, and Pc(4457)+[33].
Like some other XY Z candidates, the three-body final state, as well as the presence of charm baryon and
meson mass thresholds, invites an explanation for some of the peaks as triangle singularities. If the states
are true J/ψ p resonances, then they should be produced in photon-proton collisions, with the photon acting
like a virtual J/ψ, as pictured at the top of Fig. 3. One would expect the J/ψ production cross section to
peak at photon beam energies that excite the pentaquark resonance [20].
Figure 3shows data from the GlueX experiment for the J/ψ cross section as a function of photon beam
energy. While the cross section shows some structure, discussed extensively in Refs. [19,34], it is not evident
that this structure is a result of a pentaquark resonance. The shape of the cross section at threshold is
thought to be linked to the gluonic structure of the proton (see Section 6). The orange boxes in Fig. 3show
the projections for the statistical precision on the J/ψ cross section assuming a similar amount of integrated
luminosity on the GlueX target but with an electron beam energy of 17 GeV. One can define a polarization
figure-of-merit as P2I, where Pis the beam polarization and Iis the beam intensity. (The statistical
uncertainty on polarized observables scales like the inverse square-root of the figure of merit.) Figure 5shows
the polarization figure-of-merit for a typical 12 GeV configuration of the GlueX beamline and a configuration
that uses 17 GeV electrons incident on the GlueX radiator. The 17 GeV beam increases the polarization
figure of merit by an order of magnitude near J/ψ production threshold. A precision measurement of J/ψ
polarization would inform our understanding of the production mechanism and potentially validate the
use of such data to draw conclusions about the proton structure. An upgrade to 22 GeV would permit
measurements of the χc1and ψ(2S) cross sections with similar precision. To probe the c¯cthreshold region,
these investigations must be conducted with photon beam energies in the 8-20 GeV region, making them
well-suited for the energy and luminosity planned for the upgrade.
If a positive signal for any of the Pcstates can be established in photoproduction, then this eliminates the
possibility that the corresponding peak observed in Λbdecay is due to a kinematic effect and solidifies the
interpretation as a resonance. Signals in photoproduction open the door for new measurements, for example,
an analysis of the J/ψ p angular distributions would provide information about the quantum numbers of the
corresponding Pcstate. A stringent upper-limit on the photoproduction cross section further constrains the
interpretation of Λbdecay results. In the near future, combined analyses of J/ψ,χcJ , and open charm final
states using data from existing facilities are expected to put severe constraints on models that describe the
LHCb signals as a consequence of kinematic effects. This is important, as no rescattering model is able to
17
quantitatively reproduce the pentaquark signals so far, and the information of other channels is needed to
improve this description. If an independent observation of any of the Pcstates becomes available in a different
production mechanism, then the null result in photoproduction is informative of the internal structure of
the pentaquark, as one must explain why the underlying structure causes a suppression in photoproduction.
3.2.3 Tetraquark ZcCandidates
Studies of e+e−collisions at center-of-mass energies at both the c¯cand b¯
bscales, as well as studies of B
meson decay, have uncovered a large collection of tetraquark candidates, often labeled Zcor Zb. The exotic
signature of many of these states is a peak in the invariant mass spectrum of a charged pion and a c¯c(J/ψ,
hc, or ψ(2S)) or b¯
b(Υ(nS) or hb) hadron. The mass and charge imply a minimum qq¯q¯qcontent of these
states. The pattern of exotic c¯cand b¯
bhas similarities, in particular for these charged states [9,11,12].
Let us consider as an example the Zc(3900), which has been observed by BESIII [9] and Belle [10] in
the e+e−→J/ψπ+π−reaction as an unambiguous signal in the J/ψ π invariant mass. The vicinity to
the ¯
DD∗thresholds favors an interpretation in terms of a molecule of the two open-charm mesons, but a
compact tetraquark hypothesis is not ruled out. Nontrivial rescattering of the three-body final state can also
generate a signal that mimics a resonance. The biggest obstacle to the understanding of the nature of the
Zc(3900) comes from the fact that the state has been observed in one production channel only, and most
notably it does not appear in the high-statistics Bdecay datasets available from LHCb. This casts doubts
on its very existence as a QCD resonance. In this respect, photoproduction offers an ideal setup to study
the Zc. Indeed, the coupling to photons can be related to the Zc→J/ψπ decay, as in both cases the c
and ¯cquarks must tunnel from the respective clusters (mesons for a molecule and diquarks for a tetraquark)
before forming the charmonium or annihilate into a photon. If the state actually exists, we thus expect to
see it in photoproduction, with the fine details depending on its internal structure.
As previously noted, the Zcstates that are observed to couple to a pion and a vector meson are ideal
for exploration with polarized photon beams at an upgraded JLab. As has been demonstrated with GlueX
data (Fig. 2), analysis of the production angles provides the signature for pion exchange. This, coupled
with the upgrade in energy, allows one to explore J/ψ π±and ψ(2S)π±scattering, which provides a unique
production environment that is free from rescattering triangle singularities. Figure 6shows the phase space
available for J/ψ π−∆++ and ψ(2S), π−∆++ under a variety of assumptions about the photon beam energy
in photon-proton collisions. At 17 GeV one can search for the Zc(3900) →J/ψ π in a region of phase
space that is kinematically separated from ∆πresonances. With 22 GeV photons the phase space opens
significantly and searches for states like the Zc(4430) →ψ(2S)π, a state observed in Bdecay but not in
e+e−collisions, are permitted. Both searches use the demonstrated capability of the GlueX and CLAS12
detectors for reconstructing J/ψ →e+e−and pions. In addition, the pion-exchange process is strongest at
threshold [21], making the upgraded CEBAF an ideal machine for these studies.
In parallel to this, further developments in lattice QCD will also allow us to study the state from a
different perspective. In these numerical calculations it is indeed possible to simulate the elastic scattering
of J/ψ p, which one cannot achieve in experiments because of the short lifetime of the J/ψ. Exploratory
studies performed in the past with unphysically heavy pion masses showed no evidence for a Zc(3900) [35].
However, the recent calculations of doubly charm channels highlighted a strong dependence on the pion
mass, which affects the previous studies and calls for new ones at the physical point in the future [36–38]. If
the Zcemerges from these calculations, its status as a QCD resonance be strengthened.
We expect that the same conclusions will be reached by the photoproduction searches and the lattice
results. If the state is found, that would be the final confirmation of a four-quark state, and opens a long list
of new measurements related to its internal structure, for example, the Q2dependence in electroproduction.
If both lattice and experiments agree on the nonexistence of a Zc(3900), this will teach us more on the
hadron final state interactions that generate the signal in e+e−collisions and could have implications on the
interpretation of other members of the family of Zcand Zbstates. Even more interesting, if lattice QCD and
photoproduction data find opposite conclusions, it will change our understanding of final state interactions
and of hadron structure in order to justify such an unexpected result.
18
10 15 20 25 30
2
4
6
8
10
12
14
M2(J/ψ π-) or M2(ψ(2S) π-) [GeV2]
M2(Δ++ π-) [GeV2]
Eγ = 12 GeV
Eγ = 17 GeV
Eγ = 22 GeV
Phase Space
J/ψ π- Δ++
ψ(2S) π- Δ++
Figure 6: Sketches of the available phase space
(the Dalitz plot boundary) for the J/ψ π ∆
(green) and ψ(2S)π∆ (purple) systems produced
in γp collisions under different assumptions about
the incident photon energy (indicated by line
styles). The regions of phase space that would
be populated by decays of Zc(3900) →J/ψ π and
Zc(4430) →ψ(2S)πare shaded.
3.3 Light Meson Spectroscopy with 22 GeV Electrons
An increase in electron beam energy provides enhanced capabilities to explore the spectrum of light hadrons,
thereby extending the existing 12 GeV program in hadron spectroscopy. Currently, the real photon beam
used in the GlueX experiment that is generated from the 12 GeV electrons has a peak polarization of about
35% at an energy of about 9 GeV. This configuration is obtained by a choice of orientation of the diamond
lattice with respect to the photon beam. Higher polarization can be obtained but it comes with a cost of
lowering the energy of the peak intensity. Therefore, an energy upgrade allows not only the obvious increase
in photon beam energy but also an option of producing similar energies to the current 12 GeV configuration
but with dramatic enhancements in degree of polarization and flux. The secondary coherent peak, visible
in the example in Fig. 5, can also be used. For example, using a 22 GeV electron beam it is possible to
configure the beamline such that one has 12 GeV photons with about 70% linear polarization, while at the
same time, having 15 GeV photons with about 50% linear polarization. This capability allows for exploration
of energy-dependent effects.
The increase in rate at the high-energy end of the photon spectrum is not anticipated to cause compli-
cations with increased noise or electromagnetic background in the Hall D photon beam line. Figure 7shows
photon energy spectra for three different electron beam energies. The dominant low energy portion of the
spectrum is responsible for detector backgrounds that ultimately limit the usable beam current. The spectra
in Fig. 7are normalized such that all curves have a common area above the low-energy cutoff. Therefore one
can see that increasing the electron beam energy while adjusting the diamond to keep the coherent photon
flux peak at a fixed energy results in a larger fraction of useful high-energy photons with respect to the
background-generating low energy portion of the spectrum.
The increased capabilities of an upgraded machine can be used in a variety of ways. By increasing
the polarization of real photons with GlueX, one enhances the dependence of the production amplitude
on the orientation of the decay plane with respect to production plane, the angle Φ depicted in Fig. 2.
This provides enhanced capability to discriminate between production mechanisms. Conducting meson
spectroscopy studies at higher energy also enhances the kinematic separation between the decay products
of produced mesons and excited baryons, i.e., one has much better distinction between beam fragmentation
and target excitation regimes. Finally, one has the ability to study production mechanism dependence on
energy. The CLAS12 light hadron spectroscopy program will also greatly benefit from the energy upgrade,
providing a high intensity flux of quasi-real photons at high energy and the extra capability of studying the
Q2evolution of any new state produced.
19
2 4 6 8 10 12 14 16
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
17 GeV
22 GeV
Electron Beam Energy
12 GeV
Eγ [GeV]
Photon Flux [arb.]
Figure 7: The coherent bremsstrahlung photon
spectrum shown for three different choices of elec-
tron energy and three different choices of dia-
mond radiator orientation such that the primary
peak is the same position. All three curves are
normalized such that they have equal area above
a common low energy cutoff. Note that the ver-
tical scale is truncated.
In summary, an upgraded electron beam at 22 GeV will allow the hadron spectroscopy program at
Jefferson Lab to cross the critical threshold into the region where c¯cstates can be produced in large quantities,
and with additional light quark degrees of freedom. This opens a new opportunity to study production of
exotic states and contribute with potentially decisive information about their internal structure, which would
us to understand their place in the landscape of hadrons generated by QCD. Moreover, with a 22 GeV electron
beam it will be possible to extend a large class of spectroscopic studies conducted with the 12 GeV program.
20
4 Partonic Structure and Spin
The 1970’s marked a significant turning point in the field of particle physics with the development of the
parton model. This revolutionary concept transformed our understanding of the structure of hadrons,
revealing them to be composed of quarks and gluons that interact as described by the theory of quantum
chromodynamics (QCD). Since then, there has been remarkable progress in both experimental and theoretical
research on the subject, providing us with tantalizing insights into the internal structure of protons and
neutrons. While our understanding still remains incomplete, these advancements have paved the way for
exciting new discoveries in particle physics.
The parton model introduced the fundamental quantities known as parton distribution functions (PDFs).
These functions enable the quantification of the number densities of quarks and gluons within hadrons as a
function of their momentum fraction relative to the parent hadron. The precise determination of PDFs from
experimental data has been a challenging, active area of research that requires a variety of experimental
data, ranging from low-energy reactions such as those at JLab to high-energy experiments at the LHC where
PDFs also play an important role in searches for physics beyond the standard model. This concept has
proven to be a cornerstone in the field, providing crucial insights into the nature of hadronic matter.
The field of parton physics is on the cusp of a new era of exploration, with the planned experiments
of the JLab 12 GeV program and those at the future EIC with dedicated beam polarization capabilities.
These experiments are expected to provide high-definition maps of the internal structure of hadrons, using
a range of techniques such as reactions involving polarized hadrons to access helicity-dependent PDFs, and
dedicated tagged experiments to probe the structure of mesons, among others. These cutting-edge techniques
promise to deepen our understanding of the fundamental constituents of matter and their interactions, and
represent a major step forward in our quest to unravel the emergent phenomena of QCD. However, the
combined scientific program of JLab 12 GeV and EIC has a gap in kinematics, which is where the JLab
22 GeV upgrade can offer critical insights for precision studies of partonic structure. With its enhanced
energy range, the JLab 22 GeV upgrade can provide access to a wider range of kinematic regimes, enabling
the investigation of specific partonic processes and their properties with greater precision.
In the upcoming sections, we will explore the importance of upgrading the energy capacity of the CEBAF
accelerator in significantly improving the precision and phase space coverage of experimental data. We will
discuss key measurements and physics outcomes, including:
•Precision measurements of the nucleon light sea in the intermediate to high-xrange, which can help
validate novel theoretical predictions for the intrinsic sea components in the nucleon wave function and
support BSM searches at colliders;
•Precision determination of the strong coupling and helicity structure of the nucleon;
•Unique opportunities to explore the internal structure of mesons.
An energy upgrade to 22 GeV will provide unprecedented and complementary opportunities to both existing
and planned experiments, laying the foundation for groundbreaking discoveries that will allow us understand
the emergent phenomena of QCD.
4.1 Nucleon Light Sea in the Intermediate-xRange
Nucleon Strangeness. Significant information has been accumulated on the proton’s u- and d- quark PDFs
through high-energy scattering experiments [39–41] and more recently studies have begun to shed light
on the proton’s ¯uand ¯
dcontent [42–47]. However, the quantitative understanding of the nonperturbative
strange quark sea remains elusive despite numerous investigative attempts to clarify its structure. This lack
of clarity has hampered, for example, accurate determination of the CKM matrix element Vcs and precision
measurements of the W-boson mass, both of which rely on a precise knowledge of the strange quark PDF.
21
As photons interact with dand squarks with equal strength, it becomes challenging to distinguish the
properties of strange quarks from nonstrange ones solely using inclusive Deep Inelastic Scattering (DIS)
observables. This is the case even when using proton and neutron targets, and without resorting to weak
currents for independent flavor combinations [48]. The conventional approach to ascertain the strange quark
PDF has involved inclusive charm meson production in charged current neutrino-nucleus DIS. Assessments
of the CCFR [49] and NuTeV [50] neutrino and antineutrino cross-sections from the Tevatron, along with
more recent data from the CHORUS [51] and NOMAD [52] experiments at CERN, have led to a strange to
light-antiquark ratio Rs= (s+ ¯s)/(¯u+¯
d) of approximately 0.5. However, interpreting the neutrino-nucleus
data is complicated by uncertainties in nuclear effects both in the initial and final states. These uncertainties
arise from the challenges in connecting nuclear structure functions to those of free nucleons [53] and dealing
with the charm quark energy loss and Dmeson-nucleon interactions during hadronization within the nucleus
[54,55].
A method that leverages the unique advantages of weak probes while avoiding nuclear effect complications
is inclusive W±and Zboson production in pp collisions. Recent ATLAS Collaboration data at the LHC
suggested a larger strange quark sea than traditionally obtained from neutrino scattering, with Rs≈1.13
at x= 0.023 and Q2= 1.9 GeV2[56,57]. The latest analysis combined HERA and ATLAS data and
found results consistent with the earlier enhancement, although this disagrees with the more standard ¯
d > ¯u
scenario from the Fermilab E866 Drell-Yan (DY) experiment [58,59]. Alekhin et al. argued that the strange
quark enhancement was due to the suppression of the ¯
dsea at small x[60–62]. The ATLAS Z→ℓℓ data were
found to be at odds with CMS results, which align with the ABMP16 global QCD analysis [63]. A recent
analysis by Cooper-Sarkar and Wichmann (CSKK) found no significant tension between HERA, ATLAS,
and CMS data and supported an unsuppressed strange PDF at low x[64]. However, their standard fit
contradicts the E866 DY data, although forcing ¯
d > ¯uonly reduces Rsby around 10% [64].
An alternate approach to gain insights into the strange quark PDF at lower energies involves semi-inclusive
deep-inelastic scattering (SIDIS). In this method, the detection of charged pions or kaons in the final state
serves as an indicator of the initial state PDFs. Previously, the HERMES Collaboration [65] examined the
K++K−production data from deuterons and discovered a significant increase in the extracted strange
PDF for x≲0.1 when using leading-order (LO) hard coefficients, but a notable suppression for x≳0.1.
A later analysis [66], utilizing new πand Kmultiplicity data, observed a less marked rise at small x, but
virtually zero strangeness for x > 0.1. The analysis in Ref. [66], like others, operates under the strong
assumption that the nonstrange PDFs and fragmentation functions (FFs) are well-understood, disregarding
potential correlations. However, previous analyses of polarized SIDIS data revealed that FF assumptions
can significantly influence the extracted helicity PDFs [67,68], necessitating a concurrent analysis of PDFs
and FFs for conclusive results [69]. Aschenauer et al. [70] highlighted the importance of an LO extraction as
an initial step towards a next-to-leading-order (NLO) analysis of semi-inclusive DIS data, given its current
unavailability. Borsa et al. [71] later explored how SIDIS data can constrain unpolarized proton PDFs
through an iterative reweighting procedure, advancing towards a comprehensive global analysis of PDFs
and FFs. More recently, the JAM Collaboration has carried out the combined analysis to simultaneously
determine unpolarized PDFs and FFs using DIS, SIDIS, and hadron production in e+e−reactions. The
analysis found mild trends for the kaon SIDIS data to suppress the strange quark PDF around x≳0.1 [72].
Parity Violating Deep Inelastic Scattering (PVDIS) on proton and deuteron targets offers distinctive
opportunities to elucidate the strange quark PDF [73,74]. These low-energy observables exhibit increased
sensitivity to the non-perturbative strange quark PDF, especially on deuteron targets where the sensitivity
to u−and d-quark PDFs is suppressed. However, PVDIS measurements pose a challenge due to their high-
luminosity requirements compared to other reactions, and currently, there are no PVDIS data available for
QCD global analysis. This situation is anticipated to improve in the upcoming years, thanks to the high-
luminosity capabilities of the SoLID program at JLab. Here we consider the potential impact of 22 GeV
on the strange quark PDF with simulated data at the expected kinematics from the unmodified SoLID
spectrometer, shown in Fig. 8(left), which gives access to PVDIS asymmetries approximately in the range
0.07% to 0.21%. A comparable experiment at 11 GeV would cover a similar x-range. However, operating
at 22 GeV offers several advantages: the higher Q2suppresses power corrections and expands the xregion
suitable for analysis within a joint QED+QCD factorization framework [75]. Consequently, a significant
22
0.4 0.6 0.8 1.0
x
5
10
15
20
25
30
35
Q2
w/o cuts
with cuts
W2>4.0
0.2 0.4 0.6 0.8
x
0.0
0.2
0.4
0.6
0.8
1.0
δs+/s+
µ2= 10 GeV2
JAM (current)
+JLab 22 (δuncorr.=δcorr.= 0%)
+JLab 22 (δuncorr.= 0% δcorr.= 0.5%)
Figure 8: (Left) The kinematic coverage available from a 22 GeV beam and the unmodified acceptance of
the SoLID spectrometer. (Right) The impact of 22 GeV PVDIS data on the strange quark PDF s+=s+ ¯s
in the JAM framework [76]. A high statistics measurement of AP V with realistic normalization uncertainty
measured with 22 GeV beam, the SoLID spectrometer, and the luminosity described in the text is simulated.
fraction of the higher-energy data could be incorporated into various global PDF fits. Furthermore, at the
smaller xvalues accessible at 22 GeV, PVDIS will demonstrate enhanced sensitivity to FγZ
3, which directly
probes the matter-antimatter asymmetry in the strange sector, i.e.,s−¯s. This level of sensitivity is uniquely
achievable through the JLab PVDIS programs.
Charm Content of the Proton. Employing a 22 GeV electron beam opens a sufficient phase space for the
creation of charm-anticharm pairs, significantly boosting charm production rates. If we can identify the charm
quark in the final state, charm structure function measurements at JLab22 could offer valuable insights into
charm production, especially within the intermediate to large-xrange. Such data could shed light on the
potential existence of intrinsic charm in the proton, an area recently explored by the NNPDF Collaboration
[77–79] with findings qualitatively in line with two model predictions. However, Cteq-Tea group [80] has
also examined the intrinsic charm in the nucleon finding an opposite conclusion for the evidence of intrinsic
charm, which ultimately calls for the need to access new data that can resolve the existing tensions among
the groups. While the EIC plans to measure the charm structure function to glean information on intrinsic
charm in the range of 0.001 < x < 0.6 at relatively low energies [81,82], the high-luminosity capabilities
of the proposed JLab 22 GeV upgrade could provide unprecedentedly precise data for probing the intrinsic
charm structure within protons in the mid to high-xregion. The importance of high-precision measurements
for precise calculations of charm production cannot be overstated, given their crucial role in astroparticle
physics. For instance, prompt neutrinos originating from charm decays are a dominant background for cosmic
neutrinos at IceCube and KM3Net [83]. Therefore, precise measurements of the charm structure function, as
obtainable through the JLab 22 GeV upgrade, are vital for advancing our understanding of prompt neutrino
production and reducing background uncertainties in astroparticle physics.
High-xPDFs and Synergies with HEP. In the quest for a comprehensive understanding of the unpolarized
quark and gluon structure of the proton [84,85], one of the significant advantages of boosting the JLab
lepton beam energy to 22 GeV is the ensuing ability to access the large-xregion, extending up to an
approximate value of x≃0.65. This deep dive occurs within the perturbative deep-inelastic scattering
domain, a context in which higher-twist and target-mass effects are markedly suppressed. As depicted in
Fig. 9, this enables a thorough exploration of large-xPDFs. To curb higher-twist corrections, most global
PDF fits [79,86,87] apply standard cuts at W2= (p+q)2≥12.5 GeV2and Q2=−q2>4GeV2, where
pand qrespectively denote the standard DIS kinematics of the target and the exchanged virtual photon.
Using the well-tested technique based on the PDF-mediated correlation, CTEQ-TEA group found that the
JLab 22 GeV measurements would be complementary to future LHC and EIC measurements in testing PDF
combinations, on the existing differences between the high-sea and low-sea scenarios for proton PDFs and
23
Figure 9: The kinematic coverage in the (x, Q2) plane (left) and in the (x, W 2) plane (right) of the projected
JLab measurements with a lepton beam energy of 22 GeV, compared with the corresponding coverage of
the current data taken with an 11 GeV beam. We also indicate W2= 12.5 GeV2, the usual kinematic cut
in most global PDF determinations, as well as W2= 6.5 GeV2.
provide controls over higher twist effects to constrain subleading contributions relevant for antiquark PDFs
at large-x.
In light of this, data procured from the JLab 22 GeV upgrade will uniquely augment our understanding
of the large-xproton structure, thereby influencing other physics analyses that are sensitive to this structure.
This includes high-mass New Physics searches at the LHC and high-energy astroparticle physics at neutrino
telescopes. To underscore this assertion, the region accessible up to x≃0.65 is instrumental in generating
reliable predictions for Beyond the Standard Model (BSM) searches at the LHC. To illustrate this, Fig. 10
presents predictions for the forward-backward asymmetry in high-mass DY production as a function of
Collins-Soper angle cos(θ∗) [88] at the LHC [89]. This observable has an enhanced sensitivity to the slope
of quark and anti-quark PDF in the large-xregion such that, for instance, if q= ¯q, the asymmetry AF B
is zero. At present, theory predictions for AF B give both (positive and zero) scenarios, which prevents the
use of the observable to discriminate BSM physics. In this context, measurements such as PVDIS at the 22
GeV upgrade will provide the necessary constraints on the sea PDFs in the intermediate to large-xthat can
be used to identify potential signs of New Physics in the high-energy tail of the DY rapidity and invariant
mass distributions in the context of new Effective Field Theory interactions, as developed in Ref. [90].
Intrinsic Sea in the Proton. The concept of a significant five-quark Fock state, |uudc¯c⟩, in the proton was
initially suggested by Brodsky, Hoyer, Peterson, and Sakai (BHPS) [91] to account for the observed surge
in charmed hadron production rates in the forward rapidity region. This intrinsic charm “sea” within the
|uudc¯c⟩state, distinct from the conventional extrinsic sea deriving from the g→c¯cQCD process, is theorized
to exhibit a valence-like momentum distribution with a peak at relatively large x, while the extrinsic sea is
prominent in the small xregion. The BHPS model predicts the probability for the uudQ ¯
Qfive-quark Fock
state to be approximately proportional to 1/m2
Q, where mQis the mass of the quark Q. Therefore, the light
five-quark states |uudu¯u⟩,|uudd ¯
d⟩, and |uuds¯s⟩are expected to have significantly larger probabilities than
the uudc¯cstate. This suggests that the light quark sector could potentially provide clearer evidence for the
presence of the intrinsic sea. The challenge, however, is to separate the intrinsic sea from the much more
abundant extrinsic sea. It was suggested that there exist some experimental observables that are largely free
from the contributions of the extrinsic sea [92]. In particular, ¯
d(x)−¯u(x) and ¯u(x) + ¯
d(x)−s(x)−¯s(x) are
examples of quantities largely free of the contributions from extrinsic quarks. Using the kaon SIDIS data
from HERMES on s(x) + ¯s(x) [93] and the E866 DY data on ¯
d(x)−¯u(x) [94], it was shown that the BHPS
model can describe these data well [92]. This allowed a determination of the size of intrinsic ¯uand ¯
dsea in
the proton. Moreover, the HERMES s(x) + ¯s(x) data in the x > 0.1 region allowed the determination of the
24
Figure 10: The forward-backward asymmetry as a function of Collins-Soper angle [88] in high-mass DY
production at the LHC [89] provides enhanced sensitive to the behavior of the quark and antiquark PDFs
in the large-xextrapolation region.
magnitude of intrinsic strange-quark sea [95].
The HERMES data [93] suggests a strange sea composed of two different components, each dominating
at different xvalues as shown in Fig. 11. This aligns with the expectation of both intrinsic and extrinsic
components contributing to the strange-quark sea at large and small xregions respectively. BHPS model
calculations, using specific initial scales, provide a good fit to the data, enabling extraction of the intrin-
sic strange quark sea’s probability, Ps¯s= 0.024, at µ= 0.5 GeV. Also of interest is the flavor non-singlet
¯u(x) + ¯
d(x)−s(x)−¯s(x) distribution. Leveraging HERMES and CTEQ6.6 data, the extrinsic sea contri-
bution is found to largely vanish. The distribution aligns well with BHPS model calculations, facilitating
the extraction of intrinsic light-quark sea probabilities. Consequently, values for Pd¯
d,Pu¯u, and Ps¯swere
established. Recently the HERMES Collaboration’s reassessment of the x(s(x) + ¯s(x)) distribution, using a
range of kaon fragmentation functions for their kaon SIDIS data, yielded varying outcomes for the extraction
of Ps¯sintrinsic strange quark content [96,97], as depicted in Fig. 12. This underscores the need for improved
understanding of the kaon fragmentation functions and additional kaon SIDIS data to reliably determine
s(x) + ¯s(x) and the intrinsic strange-quark sea. The enhancement of JLab to 22 GeV, in combination with
existing spectrometers and the forthcoming SoLID detector, promises to supply high-precision SIDIS kaon
production data. This will facilitate the determination of the s(x) + ¯s(x) distribution in the intermediate x
region, crucial for understanding the flavor structure of the proton’s intrinsic sea.
Nucleon’s Matter-Antimatter Asymmetry. Recent DY measurements conducted by the SeaQuest experiment
at Fermilab reported an excess of d(x) compared to u(x) over a broad kinematic range in Bjorken-x[98] with
higher statistical precision compared to the NuSea experiment [99]. These measurements have indicated a
potential nonperturbative mechanism other than gluon splitting that generates the excess. Alternatively,
by measuring the charged pion yield ratio from SIDIS, the HERMES Collaboration reported [100] results
on d(x)−u(x) with a 27.5 GeV positron beam on hydrogen and deuterium targets. These results are in
agreement with NuSea results although with modest precision, and indicated an alternative in extracting the
anti-quark flavor asymmetry of the nucleon sea with a different process (SIDIS) as compared to DY, although
in a different Q2region. More precise, complementary data from SIDIS are essential in obtaining a global
picture of of anti-quark flavor asymmetry as a function of xand Q2, especially now, after the publication of
the results on ¯
d(x)/¯u(x) from the SeaQuest experiment [98] and significant advances in extracting precise
fragmentation functions.
d(x)/u(x) and d(x)−u(x) will be measured in Hall C at JLab with a 11 GeV e−beam by using
25
x
x(s+s
−)
BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES
0
0.1
0.2
0.3
10 -1
x
x(d
−+u
−-s-s
−)
BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES+CTEQ
0
0.1
0.2
0.3
10 -2 10 -1 1
Figure 11: Comparison of the x(s(x) + ¯s(x)) data (left) and the x(¯u(x) + ¯
d(x)−s(x)−¯s(x)) distribution
(right) extracted from HERMES data with the calculations based on the BHPS model. The solid and dashed
curves are obtained by evolving the BHPS result to Q2= 2.5 GeV2using µ= 0.5 GeV and µ= 0.3 GeV,
respectively. The normalizations of the calculations for x(s(x) + ¯s(x)) are adjusted to fit the data at x > 0.1,
denoted by solid circles.
x(s+s
−)
BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES2008
CTEQ6L
(a) BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES2014-set1
CTEQ6L
(b)
BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES2014-set2
CTEQ6L
(c)
x
BHPS (µ=0.5 GeV)
BHPS (µ=0.3 GeV)
HERMES2014-set3
CTEQ6L
(d)
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
10 -1 10 -1
Figure 12: Comparison of the HERMES x(s+ ¯s) data with the calculations based on the BHPS model.
The solid black and dashed red curves are obtained by evolving the BHPS result to Q2= 2.5 GeV2using
the initial scale µat 0.5 GeV and 0.3 GeV, respectively. Different panels correspond to four different inputs
for the kaon fragmentation functions. Data at x > 0.1 are denoted by solid circles.
26
charged pion yield ratios from SIDIS reactions (e, e′π±) on hydrogen and deuterium targets in the kinematic
range 0.1< x < 0.48, 1.2< Q2<4.3 GeV2and 0.3< z < 0.7 [101]. These are key quantities that
shed light on various possible non-perturbative mechanisms that generate the nucleon sea, as well as the
anti-quark flavor asymmetry. The precise measurement of these ratios will provide data in the high-xregion
using a different process and Q2region as compared to previous DY measurements. After results from
various experiments (HERMES, NuSea, and SeaQuest), a high-statistics data sample with good control over
systematic uncertainties using SIDIS reactions will provide an independent study of the region of overlap
with previous DY measurements. These data would also allow the multi-dimensional approach used by
most global analyses. The purpose of these measurements [101] are two-fold: i) To explore the region
0.1<x<0.25 using SIDIS to establish consistency with previous DY measurements. ii) To explore the
high-x(0.25 <x<0.4) region where there is apparent tension between the NuSea and SeaQuest results. The
measurements at a higher beam energy will expand and improve our 12 GeV measurements while extending
our kinematic reach in Q2and x. These data at 22 GeV will help with a clean physics interpretation through
multidimensional bins in extended kinematics measurements, thereby giving complementary information for
the next generation of QCD global analysis of PDFs.
4.2 Polarized PDFs and Strong Coupling
The JLab accelerator, operating at 22 GeV with a high level of polarized luminosity, offers a unique oppor-
tunity to conduct precise determination of the nucleon spin structure functions. Specifically, this machine
is well-suited to investigate the deep valence quark (high-x) region and to explore the polarized sea in the
middle-xregion. Additionally, the data obtained from these experiments will be crucial for achieving a more
accurate determination of the strong coupling constant.
Polarized PDFs from JLab at 22 GeV. Inclusive structure functions of polarized nucleons have been rel-
atively well measured across a broad of DIS kinematic ranges. Particularly in the valence region, where
x > 0.5, data from JLab at 6 GeV, and 12 GeV, have yielded and will continue to provide unparalleled
insights into the nucleon’s quark helicity and flavor structure. By increasing the beam energy to 22 GeV,
we can eliminate the remaining gap in determining the asymptotic valence quark structure at the highest
achievable x, effectively cutting in half the unexplored region x= 0.8...1 inaccessible at JLab at 11 GeV
(see Fig. 13). Latest predictions indicate a significant shift in the spin carried by d-quarks from negative
values below x= 0.8 to full polarization of +1 at x= 1 [102]. The fundamental d/u quark PDFs ratio could
also be further refined in the limit x→1 beyond the current 11 GeV data. A higher beam energy would
enable access to significantly higher momentum transfer Q2and final state mass W, thereby reducing model
uncertainties stemming from resonance contributions, higher twist, and target mass effects. A pleasant side
effect of a higher beam energy is an increase in count rates for the same kinematics, enhancing statistical
precision. Beyond the extreme x→1 limit, an extended Q2range could offer opportunities to examine the
Q2evolution of PDFs, as well as production of hadrons with high transverse momentum in the moderate x
region (x= 0.1...0.6), thereby indirectly revealing the largely enigmatic “valence gluon PDFs” in this region.
By juxtaposing different beam energies at the same xand Q2, subleading structure functions such as R,
g2, and A2can be obtained, offering insights into quark-gluon correlations within the nucleon. Accessing
a higher final state invariant mass considerably widens the interpretable range for flavor tagging through
semi-inclusive production of pions, kaons, and other mesons and baryons. This opens up possibilities for
in-depth studies of sea quark PDFs in this intermediate to high-xregion, believed to be dominated by the
nucleon meson cloud.
Prospects for High-Precision Determination of αs. The strong coupling constant, denoted as αs, is a crucial
quantity in QCD and a key parameter of the Standard Model [103]. However, its experimental accuracy, with
∆αs/αs= 0.85 [104], is the least precise among all fundamental couplings. The QCD community is currently
investing significant efforts in reducing the uncertainty of αs, with active research being conducted in this
area [105]. A high-luminosity 22 GeV electron accelerator is an ideal tool for obtaining a more accurate
value of αsusing the Bjorken sum rule (BJSR) [106] defined as Γp−n
1(Q2)≡Rgp
1(x, Q2)−gn
1(x, Q2)dx. The
expected uncertainty, ∆αs/αs≃0.6%, is significantly smaller than the current world data combined. This
level of precision is achievable because 22 GeV strikes a balance between high sensitivity to αsand a small
27
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
0.6−
0.4−
0.2−
0
0.2
0.4
0.6
0.8
1
1.2
n
1
A
JLab_E99117
JLab_E06014
JLab_E12-06-110 (Proj.)
JLab 22 GeV (Proj.)
SLAC_E142
SLAC_E154
HERMES
Statistical
CQM
AdS/CFT
NJL
PQCD (w/angMom)
pQCD
DSE (realistic)
DSE (contact)
Figure 13: Neutron spin asymmetry An
1from 6 GeV experiments (black symbols) and expected precision
from the completed 11 GeV experiment E12-06-110 (blue down triangles). A possible follow-on experiment
with 30 days of 22 GeV beam and standard Hall C equipment would extend the precision and kinematic
reach of the existing data significantly (red circles). Various previous models for the x-dependence and
the expected asymptotic value at x→1 are shown in addition to a new prediction based on light-front
holographic QCD (AdS/CFT) [102].
perturbative QCD truncation uncertainty, which typically dominates high precision extractions of αs. It is
important to note that this level of accuracy cannot be reached at 11 GeV, where the missing low-xpart of
Γp−n
1is expected to become sizable as illustrated in Fig. 14 (left) where the difference between measurements
and theory is attributed to the missing low-xpart. While studying the BJSR is part of the JLab 12 GeV
program [107], precision extraction of αsis not. Similarly, the focus of the EIC is not on accurate extraction
of αs, although it can provide constraints on αsat the 1.5−2% level. However, the EIC would be important
to access low-xdata and, therefore, a 22 GeV upgrade can be seen as a synergistic effort between EIC and
JLab.
The isovector definition in BJSR has a simpler Q2-evolution and is well known to higher orders in
perturbative QCD [108,109], which helps to limit the inaccuracies in the extraction of αsin general.
Furthermore, the extraction of αsfrom the Bjorken sum rule has the advantage of having only a few non-
perturbative inputs, the most important being the precisely measured axial charge gA= 1.2762(5) [104].
Higher-twist contributions are also known to be small for Γp−n
1[110]. One can expect negligible statistical
uncertainties on Γp−n
1due to the high-luminosity of JLab at 22 GeV, which has a polarized DVCS and
TMD program that can produce sufficient statistics for an inclusive and integrated observable. In the 6 GeV
EG1-DVCS experiment, the statistical uncertainties on Γp−n
1from DVCS were below 0.1% at all Q2[110].
Therefore, for the 22 GeV experiment, we can safely project a statistical uncertainty of 0.1% for each Q2
point, with bin sizes increasing exponentially to account for the decrease in cross section with Q2. We
estimate the experimental systematic uncertainty (excluding the inaccessible low-xregion) to be around 5%
from several sources, including 3% for polarimetry (beam and target), 3% for the target dilution/purity
(NH3and 3He), 2% for the nuclear corrections (due to the extraction of the neutron data from polarized
3He, which has an uncertainty of 5% and contributes approximately one-third of Γp−n
1), 2% for the structure
function F1(required to form g1from the measured A1asymmetry), and 1% for radiative corrections. We
assign a 10% uncertainty for the low-xregion that will be covered by the EIC and a 100% uncertainty in the
extrapolation region. For the five lowest Q2-points that are not covered by the EIC, we use an uncertainty
ranging from 20% to 100%, depending on the proximity of the point to the EIC Q2-coverage. This approach
28
allows us to account for the variability in uncertainty due to the availability of PDF fits, and to provide a
comprehensive estimate for the uncertainty in the low-xpart of the project measurements at the 22 GeV.
The resulting Γp−n
1is shown in Fig. 14 (left), along with the best 6 GeV JLab DIS data [110] and the
expected results for 11 GeV and the EIC. The statistical uncertainties on Γp−n
1were found to be below 0.1%
for all Q2in the 6 GeV EG1-DVCS experiment [110]. To account for the exponential increase in bin size
as Q2increases, we use 0.1% for each Q2-point. The experimental systematic uncertainty (excluding the
missing low-xpart) is expected to be around 5%. The improved precision of the 22 GeV measurement over
previous 6 and 11 GeV measurements is evident in Fig. 14 (left), demonstrating the ideal complementarity
with the expected measurements from the EIC. To determine the value of αs(M2
z0), we fit the simulated
data using the Γp−n
1approximation at N4LO+twist-4. The fit involves determining the twist-4 coefficient
and Λsas free parameters. The pQCD approximation for αsis also at N4LO. To estimate the uncertainty
arising from pQCD truncation, we use N5LO+twist-4 with αsat N5LO [111] and take half of the difference
between N4LO and N5LO as the truncation error. In order to minimize the total uncertainty, we carefully
select the number of low-Q2points and high-Q2points used in the fit. Low-Q2points have higher αs
sensitivity and smaller systematics, but they also contribute more to the truncation error. On the other hand,
high-Q2points have lower αssensitivity and larger systematics, but they contribute less to the truncation
error. After optimization, we find that the optimal fit range is 1< Q2<8 GeV2, which leads to a value of
∆αs/αs≃6.1×10−3.
In summary, utilizing the BJSR method at JLab with a beam energy of 22 GeV can enable the measure-
ment of ∆α/α at levels well below one percent as shown in Fig. 15. The already small missing low-xissue
at moderate Q2is further improved with the addition of EIC data. In addition, the pQCD truncation error
that typically limits αs(M2
z0) extractions is reduced since the pQCD series for Γp−n
1and αshave been esti-
mated up to N5LO. The steep Q2-dependence of the BJSR method at JLab 22 GeV, which is approximately
50 times steeper than that of the EIC, provides a high level of sensitivity. Furthermore, the extraction at
moderate Q2reduces uncertainty by a factor of 5 compared to extractions near M2
z0. Overall, the BJSR
method at JLab 22 GeV can deliver a precise measurement of the strong coupling with high sensitivity and
have the potential to reduce the its current uncertainty.
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
0.225
1 10 Q2 (GeV2
Bjorken Sum
Expected JLab (< 22 GeV)
Estimate EIC
Full sum
CLAS EG1dvcs (< 6GeV)
Expected EG12 (JLab < 11 GeV)
Q (GeV)
αs(µ)
αsAdS/QCD
αsPI,Pinch
αsEC,g1, CERN, DESY,
JLab, SLAC
Expected, JLab22 GEV
0
0.5
1
1.5
2
2.5
3
10 -1 1
Figure 14: (Left) Expected Γp−n
1from 22 GeV (squares), 11 GeV (triangles), and EIC (crosses). 6 GeV
data (circles) and theory expectation (plain line) are also shown. The rectangle shows the optimal range to
extract αs. (Right) Expected accuracy on mapping αs(Q2) (squares) compared to world data [112] (rhombi)
and predictions [113,114].
29
Figure 15: Expected accuracy on αs(M2
z0) from JLab at 22 GeV (blue), compared the EIC expectation (green) and
the three most precise world data [104].
4.3 Meson Structure
Tagged deep inelastic scattering (TDIS) provides a mechanism to access meson structure via the Sullivan
process [115,116]. These measurements will be among only a few to study the essentially unknown and yet
fundamental structure of mesons with planned experiments at JLab 12 GeV and EIC. The TDIS program at
JLab a 11 GeV is expected to provide new information on pion and kaon structure in the valence regime [117,
118] specially for kaons, which has essentially no existing data for PDF analysis. In addition, it is possible to
carry out semi-inclusive measurements, by measuring low momentum final state hadrons in coincidence with
scattered electrons from hydrogen and deuterium targets. The reactions for pion TDIS will be H(e, e′p)X
and D(e, e′pp)X, and for kaon TDIS it will be H(e, e′π−p)X. The hadrons will be measured in a multiple
time projection chamber (mTPC) surrounding the target, and the electrons will be measured by the Super
Bigbite Spectrometer. The mTPC must be a high-rate capable detector and its development is one of the
driving forces of streaming readout developments at JLab. The experimental conditions to realize the TDIS
program are extremely challenging and the mTPC detector under development is expected to be capable of
tracking at one of the highest rates to date. The 11 GeV program will therefore be pivotal in establishing the
technology and experimental technique, as well as analysis methods and model development, making future
experiments at JLab 22 GeV and the Electron Ion Collider possible.
Comparing TDIS Sullivan process measurements directly with existing data from DY experiments at
CERN [119] and Fermilab [120] and upcoming DY measurements from AMBER at CERN will provide im-
portant tests of universality of the meson structures, particularly the valence quark distributions at large xπ.
However, unlike the DY experiments, the TDIS data will be almost entirely free of nuclear corrections. These
measurements will complement the low-xπcollider data taken from HERA [121,122] and future EIC [82,123].
TDIS at 11 GeV benefits from the high-luminosity capabilities of JLab and will offer much better handle on
uncertainties in the valence region, precisely where the EIC’s reach is statistically limited [123]. To perform
a reliable QCD extraction of pion (and kaon) PDFs, the observed final state invariant mass Wπmust be
large enough to avoid the expected resonances. The 11 GeV facility will be able to map out the previously
unmeasured resonance regions of the pion at low-W2
πto high precision, whereas the 22 GeV experiment will
provide a larger range of W2
πfor available PDF analysis. To assess the kinematic range where a meson PDF
analysis is realizable, we have calculated the contribution of the ρmeson (lowest-lying resonance) to the
exclusive Fπ
2structure function and find a non-negligible signal of about 20 −40% of the inclusive structure
function in the extrapolated kinematic regions of the 11 GeV experiment. Because of the width of the ρ
decay, an estimate for a minimum W2
πfor a safe PDF analysis is W2
π>1.04 GeV2. In the left panel of Fig.
16, we illustrate the phase space available for PDF analysis in a bin of t=−0.05 GeV2, the virtuality of
the scattered meson, for the 11 GeV and 22 GeV experiments using blue and red points, respectively. The
black curve represents a contour of fixed W2
πvalue at 1.04 GeV2. Points located to the right of the curve
will be eliminated, resulting in a significant reduction of available phase space for the 11 GeV experiment.
In contrast, the 22 GeV experiment offers a much larger phase space, allowing for more comprehensive PDF
analysis. In addition, due to the cut on W2
π, the range of xπsuitable for PDF analysis is greatly restricted
to 0.4< xπ<0.6 in the case of the 11 GeV experiment, while the xπcoverage is expected to be enhanced in
30
0.2 0.4 0.6 0.8xπ
1
2
3
4
5
6
Q2(GeV2)
W2
π= 1.04 GeV2
22 GeV
11 GeV
0 0.2 0.4 0.6 0.8 1
xπ
0.01
0.1
δqv/qv
JAM current
+11 GeV
+22 GeV
Figure 16: (Left) The kinematics of the 11 GeV (blue) and 22 GeV (red) points in Q2versus xπalong with
the line of W2
π= 1.04 GeV2. Multiple bins in tare on each red point. (Right) The impact on the valence
quark distribution from the JLab TDIS experiments.
the 22 GeV kinematics. We also perform an impact study on the pion PDFs with the inclusion of the 11 GeV
and 22 GeV TDIS experiments. We assume a 1.2% systematic uncertainty, with an integrated luminosity of
8.64 ×106fb−1with 100% acceptance corresponding to 200 days of data taking at dL/dt −5×1038/cm2/s.
After the cut of W2
π<1.04 GeV2, only 26 pseudodata points remained from the 11 GeV experiment, while
231 data points were permitted from the 22 GeV experiment. In the right panel of Fig. 16, we show the
relative uncertainty of the valence quark PDF in the current state (blue), and with the inclusion of the
11 GeV pseudodata (solid red) and 22 GeV pseudodata (dashed red) as a function of xπ. Notably, with the
inclusion of the 22 GeV data, we see a marked improvement in the knowledge of pion PDFs across the large
available xπrange.
To summarize, the TDIS program at the 11 and 22 GeV JLab will play a pivotal role in elucidating
the internal structure of mesons, including access to their TMDs. This exploration of the meson sector is a
significant undertaking in hadronic physics, offering a deeper understanding of QCD emergent phenomena.
As mesons provide a crucial link between fundamental quarks and the observable world, enhancing our
knowledge of their structure and dynamics promises profound insights into the fundamental principles of
the strong interaction. This includes the understanding of confinement and the dynamics of quark-gluon
interactions, which are central aspects of QCD. Furthermore, the high-precision data expected from the TDIS
program can lead to a refinement of existing theoretical models and potentially inform the development of
new ones.
31
5 Hadronization and Transverse Momentum
Semi-inclusive deep inelastic scattering (SIDIS) is a powerful tool that enables us to study the momentum
space tomography of nucleons and nuclei through a range of quantum correlation functions in QCD such as
transverse momentum dependent PDFs (TMDs). Thanks to dedicated experimental programs at HERMES
(DESY), COMPASS (CERN), and the 12-GeV program at JLab, significant progress has been made in
recent years in understanding SIDIS reactions. These experiments have provided us with intriguing glimpses
into the 3D structure of hadrons in momentum space, revealing the complex interplay between quarks and
gluons. With continued progress in this field, we can expect to gain even deeper insights into the structure of
hadrons and the nature of the strong force, with implications for both particle physics and nuclear physics.
In general, in the one-photon-exchange approximation, SIDIS reactions can be decomposed in terms of
18 structure functions (SFs) [124] stemming from multiple degrees of freedom, such as beam and target
polarizations. These objects contain various convolutions of twist-2 or higher-twist PDFs and fragmentation
functions that are multiplied by specific kinematic pre-factors [124] and they offer unique information about
quark-gluon dynamics in the nucleon. In addition to standard DIS kinematic variables xand Q2, the
SFs responsible for different azimuthal modulations in ϕh(azimuthal angle between hadronic and leptonic
planes), and ϕS(azimuthal angle of the transverse spin), depend also on the fraction of the virtual photon
energy carried by the final state hadron, z, and its transverse momentum with respect to the virtual photon,
PT.
The complexity of the SIDIS reaction poses significant experimental challenges to isolate each SFs from
cross sections/asymmetries since SFs have intricate kinematic dependencies, such as x,Q2, and PT. In
particular, measuring each of these requires the full ϕdependence of the reaction and, in some cases, the
ϵdependence, which defines the relative cross section contributions from longitudinal (σL) and transverse
photons (σT). Moreover, their determination becomes increasingly difficult in the high-energy valence re-
gion where certain SFs, such as helicity-dependent SFs sensitive to longitudinal spin-dependent TMDs, are
suppressed due to kinematic factors.
Most of the current SIDIS programs have mainly focused on studying SFs related to transversely polarized
virtual photons. Unfortunately, longitudinal SFs have not received much attention, and their contribution
to TMD phenomenology remains largely unexplored. This lack of understanding of longitudinal photon
contributions introduces systematic uncertainties that can only be evaluated through direct measurements.
Therefore, it is crucial to expand our program by measuring the wide range of SFs across an enhanced
multidimensional phase space. This will help to validate and improve ultimately our understanding of
parton dynamics in SIDIS reactions.
In addition, the interpretation of SIDIS data in terms of TMDs has been a significant challenge in
recent years, as it involves multiple physical mechanisms that contribute to the production of hadrons in
the final state [125–128] in addition to the complexity of the reactions in terms of structure functions. The
connection between SIDIS data and TMDs is only established within the TMD current region, which overlaps
with other mechanisms such as target, central, and hard collinear fragmentation regions depending on the
overall collision energy [127,129].
The 22 GeV upgrade, with its extended Q2coverage, offers a new complementary window between the
12 GeV program and the future Electron Ion Collider (EIC). In addition, this new energy range makes
JLab unique to disentangle the genuine intrinsic transverse structure of hadrons encoded in TMDs with
controlled systematics. The availability of two energies or in-between energy ranges also allows us to identify
the scaling properties of the SIDIS reaction, validate the measurements of leading contributions, and explore
sub-leading contributions associated with multi-parton dynamics of QCD. A combined 11 GeV and 22 GeV
SIDIS program is therefore needed to address these issues.
The importance of separating the structure functions cannot be overstated and a potential JLab 22 GeV
upgrade could provide a significant boost to the Q2and PTrange, enabling us to access more accurate
measurements of these structure functions with the following benefits:
32
•High-luminosity measurements over an enhanced multidimensional phase space without the need of
averaging or marginalization of the SIDIS phase space, e.g., will allow access to the Q2dependence of
structure functions at fixed xor fixed PTand validate the expectations from theoretical frameworks
in QCD;
•Large acceptance for existing JLab spectrometers that allows precise determination of the ϕdependence
of the cross section, allowing unambiguous identification of the relevant structure functions;
•Finally, the high energy and luminosity, combined with well-understood magnetic focusing spectrom-
eters, will provide the ability to make measurements of the ϵ-dependent terms over a large region of
(x, Q2) phase space, allowing the measurement of R=σL/σTin SIDIS.
In the following we will discuss how the CEBAF upgrade will be essential to boost the scientific reach of
the SIDIS program, enabling us to make new discoveries about the fundamental nature of hadronic matter.
With this upgrade, we will be able to explore new frontiers in the study of quarks and gluons, and to gain
a deeper understanding of QCD’s emergent phenomena.
5.1 Importance of Multi-Dimensional SIDIS Measurements
SIDIS cross sections, hadron multiplicities, and polarization independent azimuthal asymmetries are multi-
differential in nature. Therefore a Multi-Dimensional (Multi-D) analysis is mandatory to disentangle the
intricate dependencies on the kinematical variables x,Q2,PT,z. Comparing results obtained by different
SIDIS experiments operating with different beam energies and phase-space coverage is often impractical and
error-prone if the comparisons are done on a one-dimensional basis. Looking at single-dimensional kine-
matic dependencies of cross sections or asymmetries obtained from different experiments while integrating
over other dimensions of non-equal phase space contours, may result in significant discrepancies. Precision
measurements in Multi-D for all variables are also critical to understand effects induced by phase space
limitations. It was suggested that even at COMPASS energies the phase space available for single-hadron
production in deep-inelastic scattering should be taken into account to describe data in the standard pQCD
formalism.
Another class of effects that Multi-D measurements can help is to understand the systematics associated
with initial and final state hadron mass corrections in SIDIS. The HERMES experiments provided pioneering
measurements at a similar energy as the proposed 22 GeV upgrade but with limited integrated luminosity.
JLab22, in contrast, will enable detailed Multi-D measurements that will answer open questions from the
HERMES program, confront the factorized description of hadron production in SIDIS with a wealth of
precision data bridging the sub-asymptotic and Bjorken regimes. Increasing JLab’s beam energy from 6-
12 GeV to 22 GeV will allow one to measure SIDIS events at higher values of Q2than previously possible,
and further allowing to study subleading power corrections originating from higher-twist parton correlations.
Multi-D measurements play a crucial role in the investigation of helicity-dependent TMD PDFs, specif-
ically the relatively unknown g1(x, kT), where kTis the transverse momentum of the quark. However,
obtaining measurements of helicity TMDs at higher energies is challenging due to the suppression of the
kinematic factor √1−ϵ2. In the valence region and at high energies, this factor becomes relatively small,
making it difficult to extract the double spin asymmetries needed for the determination of g1(x, kT) in the
multidimensional space. Recent measurements of the PT-dependence in double spin asymmetries (DSAs),
conducted for the first time across different x-bins, have revealed interesting insights. These measurements
suggest the existence of different average transverse momenta for quarks aligned or anti-aligned with the
nucleon spin [130,131], consistent with findings from LQCD simulations [132]. The extended range of PT
accessible at the JLab 22 GeV kinematics will allow for exploration of the PT-range where contributions
from vector mesons are expected to be negligible [133] and shed light on the nature of g1(x, kT).
In order to understand the systematics involved in extracting helicity TMD-PDFs from DSAs, it is
necessary to conduct thorough investigations into the PTand Q2dependencies. In addition, it is crucial to
examine the potential backgrounds arising from other SFs that contribute to various azimuthal modulations.
33
Figure 17: The double spin asymmetry as a function of PTin ep →e′π+Xin a given bin in x(left) and
the Q2-dependence of the double spin asymmetry in a given bin in xfor ep →e′pX (right). The projections
for 100 days, use the existing simulation and reconstruction chain, and the luminosity currently used for the
CLAS12 detector (see Fig. 18). The curves correspond to different widths in kTof g1(x, kT) compared to
f1(x, kT).
Figure 17 illustrates projected measurements of the kinematic dependencies of DSAs for a 22 GeV beam
utilizing the existing CLAS12 detector. Expanding the range of Q2would enable precision tests of the
evolution properties of g1(x, kT), thereby facilitating the validation of different phenomenological approaches.
In summary, the utilization of multi-dimensional analysis approaches carries numerous implications and
benefits. The intricate nature of nucleon structure properties and hadronization processes necessitates precise
multi-dimensional measurements for a comprehensive understanding of SIDIS reactions. Such measurements
will be delivered by the JLab 22 GeV program in fine 4D bins as shown in Fig. 18 as projected by simu-
lations of the existing CLAS12 detector. The combined measurements at the upgraded machine with high
luminosity and extended phase space coverage across all JLab Halls involved in the SIDIS program, will
provide unprecedented measurements of SIDIS reactions for the hadronic physics community.
5.2 Role of Longitudinal Photon and SIDIS Structure Functions
One of the key features to understand hard reactions with virtual photons like in DIS and SIDIS reactions is
the distinction between the longitudinal (σL) and transverse (σT) photons contributions. Such distinctions
at Q2above 10 GeV will be only possible at JLab with an upgraded 22 GeV beam, delivering high-luminosity
data. With well-understood magnetic focusing spectrometers, the new experiments will be able to measure
the most precise ratios of the longitudinal to transverse cross sections R=σL/σT. While moderately accurate
measurements of this ratio have been made for inclusive deep inelastic scattering [134–136], there are hardly
any measurements of RSIDIS for the SIDIS process. Therefore, it is imperative to address this limitation, as
modern measurements of SIDIS at HERMES, COMPASS, and JLab have relied on RSIDIS =RDIS , which
is necessarily independent of z,PT,ϕ, and hadron and target nucleon types.
In TMD phenomenology it is often assumed that FUU,L is negligible at low transverse momentum.
However, recent investigations from Refs. [137,138] have indicated that such assumptions might not be valid
as also indicated in Fig. 19 where predictions for the ratio R=FUU,L /FU U,T , display sizable contributions
reaching up to 30% [139]. These findings demonstrate that the contribution of FUU,L cannot be disregarded,
as it can be substantial and essential for an accurate interpretation of FUU,T , which is associated with
standard leading-twist TMDs. The empirical separation of the transverse and longitudinal components of
cross sections is typically achieved through the measurement of the photo-hadron cross section under various
kinematic conditions. These measurements correspond to the same photon 4-momentum Q2and xvalues
34
Figure 18: Multi-D phase space of SIDIS at 22 GeV kinematics. The color range shows the expected relative
uncertainties for SIDIS cross sections in 4D bins, using the existing CLAS12 simulation/reconstruction chain
for 100 days of running with 1035 cm−2s−1luminosity.
but differ in the virtual photon polarization parameter ϵ. In order to acquire these essential measurements,
experiments must be conducted at different kinematic combinations, including varying incident electron
energies. To facilitate such experiments and fully realize the next generation of SIDIS measurements, the
CEBAF accelerator is therefore required to be running higher energies beyond the existing 12 GeV program.
As zapproaches 1 (i.e., exclusive scattering), the Q2dependence of RSIDIS =FUU,L/FUU,T is expected
to change from 1/Q2to Q2. Experimental measurements at COMPASS on the deuteron [140] and the
proton [141], at HERMES [142] and CLAS/CLAS12 [143,144] have shown that the Fcos 2ϕh
UU related in
the perturbative limit to FUU,L [137], and the Fcos ϕh
UU arising from the interference between longitudinal
and transverse photons can be very significant, with cos ϕh-modulations as high as 30% [140–144], and
unexpectedly getting higher at large Q2, which can potentially indicate the dominant role of longitudinal
35
HOW LARGE COULD IT BE @JLAB24?
FUU,L
?
=M2
Q2Ch4k2
T
M2f1D1i
<latexit sha1_base64="+olfVIM9fRE9h4w3b8gTiOtfG+4=">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</latexit>
similar approach as Anselmino et al., hep-ph/0501196
Q2=4. GeV2
Q2=5.5 GeV2
Q2=7. GeV2
Q2=8.5 GeV2
Q2=10. GeV2
0.0 0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
Ph⟂[GeV]
R
x = 0.3, z = 0.5
Large size, even at small transverse momentum. Decreases less than 1/Q2
Preliminary
Ph⟂=0.02 GeV
Ph⟂=0.2 GeV
Ph⟂=0.5 GeV
2.0 2.2 2.4 2.6 2.8 3.0
0.0
0.1
0.2
0.3
0.4
0.5
Q[GeV]
R
Preliminary
Figure 19: Estimate of RSIDIS =FUU,L/FU U,T versus the hadron transverse momentum PT(PhT ) at fixed
values of xand zand for different values of Q2, compatible with JLab22 kinematics, using MAP22 TMD
analysis [139].
photons in certain kinematics. Similarly, a strong signal for the SF FsinϕS
UT at large zhas been observed by
both the HERMES and COMPASS Collaborations, which can be attributed to the unsuppressed nature of
longitudinal photons cross sections. The longitudinal cross sections and its associated structures functions
play a prominent role in SIDIS reactions, in particular for unpolarized and transversely polarized targets [124].
The existing uncertainty surrounding the experimental knowledge of RSIDIS raises doubts about the
reliability of using current SIDIS data to infer quark flavor and spin distributions in hadrons. While, a new
experiment in Hall C is expected to provide precise measurements of RSIDIS using the Rosenbluth technique
in the next few years, these measurements will have limited kinematic space due to the 11 GeV maximum
beam energy, but will enable the extraction of the transverse SIDIS cross section without any uncontrolled
assumptions about R. Extension of the beam energy to 22 GeV would significantly expand the kinematic
phase space that is critical to accurately interpret the data in QCD. In Fig. 20 we present projections for
measuring RSIDIS by combining multiple energies from 11 GeV up to 22 GeV using simulated SIDIS data
with pions in the final state. The results were obtained with the existing Hall C spectrometers, assuming 3
months of nominal beam time, a beam current of 40 µA, and measurement of both π+and π−for LH2 and
LD2 targets. The projections assume a difference in ϵvalues of at least 0.2, and point-to-point systematic
uncertainties of 1.4%, consistent with other Hall C experiments. Note that the projections for the PT
dependence assume that information about the ϕ-dependent interference terms in the cross section will be
constrained by other experiments (e.g. Hall B), since the Hall C spectrometers provide full ϕcoverage only
up to PT=0.4 to 0.5 GeV.
In summary, with high energy and luminosity, along with well-characterized magnetic focusing spec-
trometers, it becomes feasible to make measurements of the ϵ-dependent terms over a wide range of the
(x, Q2, z, PT) phase space enabling the most precise measurements of R=σL/σTin SIDIS.
5.3 Physics Opportunities
Quark-Spin Dependence of Hadronization and Correlations of Hadrons in CFR. The measurement of the
Collins asymmetries [145] in SIDIS off a transversely polarized target is a unique opportunity to access simul-
taneously the partonic transverse spin structure of the nucleons and the spin-dependence of the hadronization
36
0
0.5
4 6 8 10 12 14
0
0.5
0.3 0.4 0.5 0.6 0.7 0.8
Q2
R
RDIS
x=0.6
x
R
Q2=9
PT
R
x=0.3, Q2=5.5
0
0.5
0 0.2 0.4 0.6 0.8 1
11 GeV
14 GeV
18 GeV
22 GeV
x
Q2 (GeV2)
11 GeV
22 GeV
0
10
20
30
0 0.2 0.4 0.6 0.8 1
Figure 20: Projections for measurements of RSIDIS =σL,SIDIS/σT ,SIDIS with electron beam energies up to
22 GeV. The left panel shows the available kinematic space in Hall C using the existing HMS and SHMS
spectrometers. The right three panels demonstrate the accuracy achievable with 3 months of nominal 40 µA
current on LH2 and LD2 targets, collecting both π+and π−SIDIS data for a measurement of the Q2
dependence, the xdependence, and the PhT dependence. The black curves indicate the measured value of
RDI S .
process. These asymmetries can be written [124] as a convolution of the chiral-odd transversity TMD PDF
hq
1and the chiral-odd and T-odd spin-dependent TMD fragmentation function (FF) H⊥h
1q[145], referred
to as the Collins function. While the transversity TMD PDF hq
1describes the transverse polarization of a
quark with flavor qin a transversely polarized nucleon, the spin-dependent FF describes the fragmentation
of a transversely polarized quark qinto the unpolarized hadron h. The structure function can depend on
the Bjorken x,Q2, the fractional energy zcarried by h, and on the transverse momentum PTof h.
The Collins FF offers a unique opportunity of studying the quark-spin dependence of the hadronization
process, which is a still poorly understood non-perturbative phenomenon in QCD. A wider knowledge of this
function would bring very useful input information to build the models of the polarized hadronization, e.g.
models inspired to the string fragmentation model [146] or field-theoretical models [147], which in turn will
help to understand hadronization process that correlates with quark-spin.
To date the Collins FF has been extracted for the production of pseudoscalar (PS) mesons, but not for
heavier hadron species. Contributions from vector mesons (VMs) to the Collins asymmetry due to correlation
of hadrons produced in the current fragmentation region (CFR), is one of the important sources of systematics
involved in TMD extraction, so far completely ignored in phenomenology. Dihadron production in the
Current Fragmentation (CFR) Region, in general, plays a crucial role in this regard, as it provides access to
intricate details of QCD dynamics that are not readily accessible through single-hadron SIDIS measurements.
Furthermore, dihadron production becomes essential in understanding the systematics arising from various
simplifying assumptions (such as independent fragmentation and isospin symmetry) used in the extraction
of TMD PDFs from single-hadron SIDIS. The data from polarized SIDIS experiments, such as HERMES,
COMPASS, and more recently CLAS, have enabled access to multiparton correlations. Given the current
state-of-the-art in extracting PDFs within the realm of pQCD, it is crucial to undertake a comprehensive
37
1−
10 x
0.05−
0
0.05
0.1
)π-
S
φ+
h
φsin(
UT
A
StringSpinner
+
ρ 0
ρ−
ρ
0.2 0.4 0.6 0.8
z
0.05−
0
0.05
0.1
h+X→ ↑u
a
0.2 0.4 0.6 0.8 1
)/c (GeV
T
P
0.05−
0
0.05
0.1
h+X→↑u
a
1−
10 x
0.1−
0.05−
0
0.05
0.1
)π-
S
φ+
h
φsin(
UT
A
+
πStringSpinner,
Final
Direct
Decays
0.2 0.4 0.6 0.8
z
0.1−
0.05−
0
0.05
0.1
h+X→ ↑u
a
0.2 0.4 0.6 0.8 1
)/c (GeV
T
P
0.1−
0.05−
0
0.05
0.1
h+X→↑u
a
Figure 21: Prediction for the Collins asymmetries for ρ+(circles), ρ0(squares) and ρ−(triangles) in SIDIS
off transversely polarized protons in the JLab22 kinematics and the impact of VMs on the inclusive pion
Collins SSA. The simulations are carried using the StringSpinner package [148] and the PYTHIA 8.2 [149]
event generator.
analysis of the Q2behavior of different relevant observables needed for validation of underlying frameworks
for analysis of single hadron SIDIS, neglecting hadronic correlations, and separation of different contributions
to relevant SFs, such as the SF describing the hadronization of transversely polarized quarks. For dihadron
observables, the spectra in (z, Mh), where zis the fragmentation variable and Mhis the invariant mass of
the hadron pair, could provide insights into contributions beyond the expected two-pion mass distribution
as illustrated in Fig. 22. Measured Single-Spin Asymmetries (SSAs) [150] clearly demonstrate a dependence
on the invariant mass of the pion pair, indicating significant correlation effects in hadron production in the
Current Fragmentation Region (CFR).
In the context of the recently developed “string+3P0model” [151] of polarized hadronization [151], it
was shown that a deeper insight into the spin dependence of hadronization is encoded in the Collins FF
associated with the production of vector mesons (VMs), more in particular for the case of ρmesons (see also
Ref. [152]). Since the contamination of the ρmeson sample from decays of heavier resonances is expected to
be negligible according to simulations, the produced VMs are mostly sensitive to the direct mechanisms of
quark fragmentation. Therefore, measurements of the Collins asymmetries for VMs is relevant to constrain
the free parameters of the hadronization models, which in turn will shed new light on the mechanisms of
quark fragmentation. However, the experimental information on the Collins asymmetries for VMs is presently
38
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
[GeV]
h
M
0
0.005
0.01
0.015
0.02
0.025
distribution
h
M
data
0
ρ
ω0
S
K
η
'η
φ
string
cluster
undefined parent
Figure 22: Invariant mass Mhdistribution for π+π−dihadrons from CLAS22 Monte Carlo data (black
points). The colored distributions represent dihadrons where one or both of the hadrons are produced from
the indicated parent. The dominant contributions are from ρ0and ωdecays. One histogram entry is filled
for each single pion.
limited because a) the high combinatorial background that must be subtracted when constructing the VM
candidates in experimental data, and b) the low statistics of VMs as compared to the final state mesons.
The only existing measurement is the asymmetry for ρ0mesons measured by the COMPASS experiment in
SIDIS off transversely polarized protons [153]. This pioneering work shows that the measurement of Collins
asymmetries for ρmesons is feasible and can be done with higher precision at future facilities.
An upgraded CEBAF accelerator running at 22 GeV provides a unique opportunity to study Collins
asymmetries with VMs since it is expected to lead to a lower combinatorial background from non-resonant
hadron pairs in the invariant mass regions of the ρmesons, e.g. as compared to the EIC operating at much
higher energies. The high luminosity design of JLab22 favors the collection of a sizeable number of ρmeson-
candidates and of pion pairs in the invariant mass regions before and after the ρregion, needed for a reliable
background estimation to cleanly extract the Collins asymmetries with VMs in the ρregion.
Using the simulation framework of the “string+3P0model” in the PYTHIA 8.2 Monte Carlo event
generator [149] via the StringSpinner package [148], sizable Collins asymmetries for VMs up to 10% for the
case of ρ+have been projected in the kinematic regions available at the JLab22 GeV as shown in Fig. 21.
The large values of the asymmetries stems from the behavior of the transversity PDF in the valence region
which (see e.g. Ref. [154]). The intriguing dependencies of the asymmetry as a function of zand PTare a
genuine prediction of the model which can be confronted with measurements at the JLab 22 GeV. Similar
studies performed for kaons may give a hint on the origin of kaon SSAs observed in SIDIS which are typically
higher that SSAs on pions. While the expected relative fractions of vector mesons vs. scalar mesons in the
strange sector may be higher, the relative fractions of decay particles in the kaon samples are less. The
measurement of the Collins asymmetries for ρand K∗mesons at JLab22 will thus serve as a benchmark for
the “string+3P0model” of hadronization, and in general for the models of hadronization aiming at explaining
the experimentally observed spin effects. The developed models can then be used for the systematic inclusion
of spin effects in present Monte Carlo event generators, which are needed for the future experiments such as
the EIC.
39
Figure 23: Conceptual separation of SIDIS regions and preliminary CLAS12 beam-spin asymmetry for the
inclusive ep →e′pX sample with a 10.6 GeV longitudinally polarized electron beam incident on a liquid-
hydrogen target as a function of xF, and the missing mass of the epX system (left)
Correlations of Hadrons in the Current and Target Fragmentation Regions. In order to conduct detailed
studies of the correlations in hadron production, it is necessary to detect additional hadrons produced either
in the CFR, or in the Target Fragmentation Region (TFR), where observed hadrons are generated from
the hadronization of spectator partons that did not interact with the virtual photon. In the TFR, hadrons
are not described by factorization into PDFs and FFs. Instead, the theoretical framework to study these
reactions is based on the concept of Fracture Functions (FrFs), originally established in Ref. [155] and later
extended to the spin- and transverse-momentum-dependent case [156]. Similar to PDFs and FFs, FrFs
describe the conditional probability of forming a specific final state hadron after the ejection of a particular
quark. Studies of the TFR [157] are not only interesting in their own right but are also critical for properly
interpreting many CFR measurements, which have been the driving force behind numerous experiments
over the past few decades. For instance, while it is sometimes possible to kinematically separate the TFR
and CFR (e.g., in high-energy Drell-Yan processes), it is not always clear where this demarcation occurs,
particularly in fixed-target experiments.
In the absence of a comprehensive understanding of the signals anticipated from target fragmentation,
there exists a potential risk of misinterpreting results that are erroneously attributed to current fragmenta-
tion. Therefore, studying the TFR is crucial for a comprehensive interpretation of SIDIS measurements and
to avoid potential misattributions in the analysis of experimental data.
In the literature, various methods have been proposed to differentiate between contributions from CFR
and TFR in SIDIS experiments. The commonly used variables for this purposes are the hadron rapidity,
defined as η=1
2log hEh+pz
Eh−pzi, and the x-Feynman variable, denoted as xF=2p·q
|q|W. Recently, new phenomeno-
logical ideas have emerged [127], offering additional tools to quantify the likelihood of a given kinematic bin
in SIDIS to be controlled by a particular physical production mechanisms as illustrated in Fig. 23 (left).
However, it is important to note that no exact experimental observable exists that can precisely separate the
TFR from the CFR. One possible approach to discriminate between the two regions is by leveraging the fact
that although the form of the inclusive cross sections remains the same in both regions [156], the structure
functions governing the kinematic dependence of individual modulations have distinct origins. For instance,
in Fig. 23, the CLAS12 beam-spin asymmetry from inclusive proton production is presented as a function
of xF. In the negative xFregion, where the reconstructed proton moves opposite to the virtual photon, a
negative 2% asymmetry is observed. As the asymmetry transitions to the positive xFregion, the sign flips,
40
and it levels out at around positive 2%. The magnitude of the asymmetry in the intermediate transition
region, when compared to both edge cases, can provide indications about the relative composition of CFR
and TFR events. Accurately tracking this transition and appropriately accounting for background events
originating from the opposite kinematic region to the one of interest are crucial components in fixed-target
experiments, such as JLab22. Moreover, such considerations could even impact the interpretation of TMD
studies at the EIC.
Tagged SIDIS Measurements. Tagged measurements refer to processes where a hadron is detected with
momenta of the order of zero up to several 100 MeV (relative to the target center-of-mass) in the target
fragmentation region. For SIDIS a tagged measurement means a hadron detected both in the current
and fragmentation region, giving access to parton interactions and correlations [158], see Fig. 24a. Both
correlations in kinematic variables (longitudinal momentum, transverse momentum PT, azimuthal angles)
as well as in quantum numbers (flavor, spin, charge) could be studied. The PTcorrelations in particular
could shed light on the origin of the intrinsic quark transverse momentum and discriminate that from other
possible sources such as final-state interactions and soft radiation [158]. Even without detection of a current
fragmentation hadron, the tagged DIS measurement would yield information on the dynamics of target
fragmentation [155] and hadronization, which is an area with few available measurements.
correlations
a) b)
constrain initial
nuclear state
Figure 24: Schematic diagram of tagged SIDIS processes where we illustrate the interaction between the tar-
get and the virtual photon. a) Detection of a hadron in both the current fragmentation region (top line) and
target fragmentation region (bottom line) gives access to partonic interactions and correlations. b) Tagged
measurements on light nuclei with tagged nuclear fragments constrain the initial nuclear configuration.
On light nuclei such as 2H, 3He and 4He, nuclear fragments (so-called spectator nucleon(s) or an A−1
nucleus) can be tagged. The momenta of the detected fragments then result in an additional handle on
the configuration of the initial nuclear state (see Fig. 24b), to be contrasted with non-tagged measurements
where one averages over all possible nuclear configurations. For the deuteron with proton spectator tagging,
measurements at small spectator momenta (∼100 MeV) can be used to perform on-shell extrapolation,
which probes free neutron structure [159,160]. In the case of tagged SIDIS, this would allow the extraction
of neutron TMDs free from nuclear effects and corrections, an essential ingredient to perform TMD flavor
decompositions. At larger spectator momenta, a differential study of medium modifications or non-nucleonic
components of the nuclear wave function belongs to the possibilities.
Tagged measurements are in general challenging in fixed-target experiments, since they need dedicated
detectors to detect the low-momentum tagged particles. JLab will have the necessary equipment and expe-
rience from the 12 GeV era measurements with the BONUS12 [161] and ALERT [162] detectors. Moreover,
JLab will have a monopoly on these data in the very high Bjorken-xregion and the tagged measurements –
which invite highly differential studies in the measured variables – will benefit from the very high luminosity
of the proposed upgrade.
Independent Fragmentation and Role of Charge Symmetry. At leading order in perturbative QCD, the as-
sumption of independent fragmentation allows us to utilize the ratios of semi-inclusive π+and π−production
to investigate potential charge symmetry violation (CSV) effects in quark PDFs. Recently, Experiment E12-
09-002 was conducted in Hall C, which collected SIDIS data for π+and π−production from deuterium. The
aim of this experiment was to explore CSV effects using the formalism proposed in Ref. [163]. Additional
41
data were also obtained from hydrogen to assess the validity of the assumption of independent fragmentation.
By studying the zdependence and magnitude of various charge and target ratios, such as the “difference
ratio” H(π+−π−)/D(π+−π−), it is possible to examine the dependence on the valence quark distributions.
Any deviation from the expected behavior of these ratios would indicate violations of charge symmetry or
inconsistencies in the independent fragmentation assumption.
The extraction of CSV from SIDIS pion production requires knowledge of the ratio of unfavored to
favored fragmentation functions, Dunfav/Df av . This ratio can either come from existing parameterizations
or can be fit to the data from the experiment. A multiparameter fit performed on the Hall C data revealed
a determination of the charge symmetry violating quark Parton Distribution Functions (PDFs) consistent
with the upper limit derived from a previous global fit of quark PDFs [164]. Unlike most PDF fits that do
not consider quark charge symmetry violation as a free parameter, this earlier fit allowed for the inclusion
of quark CSV as a degree of freedom. However, the quality of the fit of the Hall C data is not ideal
indicating some tension between the experimental data and the assumed leading order form. On the other
hand, if fragmentation functions that incorporate some degree of charge symmetry violation are assumed
(for example, using the fragmentation function fit from Ref. [165]), the quality of the fit is much improved.
These preliminary results are intriguing, and it is difficult to disentangle charge symmetry violating
effects in the quark PDFs and fragmentation functions from the possible lack of validity of the leading order
fragmentation assumption. Better understanding of the PT-dependence of fragmentation functions, and the
impact of vector mesons discussed above, will certainly help in quantifying the systematics of the CSV and
the assumption of independent fragmentation in general. The large Q2range allowed by 22 GeV would be of
enormous benefit in that the expected Q2behavior of the SIDIS cross sections as well as the ratios discussed
above could be explored with high precision. For example, the unexpected Q2dependence would suggest
that the leading-order assumption and CSV extractions from SIDIS data will require proper evaluation of
the systematics. Conversely, if the expected Q2dependence is observed, one would have greater confidence
that any observed CSV effects are valid.
Precision TMD Studies. From the perspective of phenomenological applications, the JLab 22 GeV upgrade
is expected to provide unprecedented accuracy in the measurement of SIDIS cross sections in the large-x
region, which will help to determine the TMD nucleon structure with greater precision than ever before.
The impact of the JLab22 data on reducing uncertainties is estimated to be about two orders of magnitude
for x= 0.1, as demonstrated in Fig. 26. This estimation is based on the MAP22TMD [139] extraction as
the baseline. A similar impact is expected when using the SV19 extraction [166].
It is crucial to acknowledge that the impact studies conducted with the current generation of TMD
fits have limitations. The main factor behind this is that the available data does not have the resolution
required to capture the finer details of the TMD distributions, which leads to the use of simplified ansatzes
in the extractions that may be biased. Notably, none of the current fits account for flavor dependence or
PDF uncertainty. The unaccounted uncertainties from these factors could potentially be significant [167].
The energy range of JLab22 measurements, Q2<20 GeV2, is also a critical aspect to consider. At these
energies, power corrections to the factorization theorems are not negligible. The effects of power corrections
have been shown to be significant in existing SIDIS measurements, such as those at COMPASS or HERMES,
but are often neglected due to insufficient precision and resolution. This is particularly true for polarized
measurements. With the high precision of JLab22, the impact of power correction effects can be explored
with great accuracy, providing valuable input for theoretical studies.
The precision and resolution expected from JLab22 present an opportunity to directly study TMD physics
in position space. One promising avenue is the direct determination of the Collins-Soper (CS) kernel, a
critical element of the theory which relates the TMD-PDFs at different energy scales, by combining SIDIS
measurements at different Q, thus avoiding parametric bias [168]. The high precision of JLab22 will allow
for a very accurate exploration of the CS kernel, including power corrections, and provide valuable input for
theoretical studies. Similar studies are also possible at the EIC. Figure 27 shows the estimated uncertainties
for JLab22 and EIC, with the baseline being the SV19 value of the CS kernel [166]. The results demonstrate
the complementary nature of EIC and JLab22 for such studies, with JLab22 capable of accessing larger
values of bdue to finer resolution at small PT, while EIC provides more accurate values at small bdue to
42
Figure 25: The qTdistribution of the SIDIS cross section can be divided in different regions according to
the size of qTwith respect to Q. Large qTs correspond to the collinear region, where we expect pQCD to
be at work. Small qTs correspond to the TMD region, where non-perturbative effects become dominant. A
smooth matching is supposed to happen in the intermediate region, the so-called matching region.
wider coverage in PTand higher Q.
As previously mentioned, the measurements of SIDIS at JLab22 will be affected by power corrections.
Consequently, the extraction of the CS kernel will take the form illustrated in Fig. 27 (right). At small b, the
value of the CS kernel is purely perturbative, and the difference between the left and right panels in Fig. 27
demonstrates the effect of power corrections. By comparing extractions at different Q,x, and z, it will be
possible to reconstruct the shape of power corrections with great precision and without any modeling. This
presents a unique opportunity that can only be realized with high-luminosity ep machines such as JLab22
and EIC.
The Matching Region in SIDIS. The theoretical study of SIDIS is based on factorization theorems which,
in principle, allow for the description of the qT(qT=PT/z) distribution of the SIDIS cross section over
the full qTrange. More specifically, TMD factorization allows for the description of the small qTregion,
where qT≪Q, but fails at larger values of qT. In turn, collinear factorization describes the cross section
at large qT, where qT≫Q, but becomes divergent at small qT. As shown in the left panel of Fig. 25, the
region where the two schemes are supposed to match is called “matching region”. Usually the matching
procedure is devised to work on the basis of the Yterm contribution, which corrects for the misbehavior
of the non-perturbative contribution (W) as qTbecomes large, providing a consistent (and positive) qT
differential cross section, σ=W+Y. The Y-term should provide an effective smooth transition to large
qT, where fixed-order perturbative calculations are expected to apply. For this scheme to work four distinct
kinematic regions, large enough and well separated between one another, have to be clearly identified. A
pictorial representation of these regions is shown in the right panel of Fig. 25. Given the major part of the
polarized SIDIS data is in the range of 0.2< z < 0.8 the “matching region” will be for PT∼0.5−1.5 GeV.
Serious issues, however, affect the practical implementation of this scheme. In fact, comparison with
existing SIDIS experiments like HERMES, COMPASS, and JLab12 have shown large discrepancies with the
cross section computed in the collinear formalism, which is expected to be valid at large qT, as shown in
Ref. [125]. Moreover, matching through the Yterm often fails as Yis very large (as large as the cross section
itself) even at low qTand it is affected by very large theoretical uncertainties, see for example the study of
Ref. [169]. The issues described above lead to some fundamental questions, which urgently need answering:
How does QCD manifest itself in the matching region? Is it just a transition region or does it need a new
theoretical approach of its own?
In order to gain a thorough understanding of the transition region between different kinematic regimes in
SIDIS, it is crucial to have high-statistics data that precisely cover the relevant kinematics. This transition
region represents intervals where competing processes, production mechanisms, and even exclusive diffractive
processes contribute to the SIDIS reaction. These intervals can be referred to as “matching regions” where
different mechanisms coexist and complement each other. The relative contribution of TMD and collinear
factorization regions in these matching regions strongly depends on the specific kinematic sector being probed
43
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Figure 26: Impact on the error bands of the TMD in k⊥space (left) and its Fourier-conjugate b⊥(right)
at two values of xand at Q= 2 GeV, based on the MAP22TMD analysis [139]. Purple bands: current
situation. Red bands: after the inclusion of JLab22 data.
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Figure 27: Comparison of uncertainty bands for the Collins-Soper (CS) kernel versus b⊥(b=b⊥), directly
extracted from the data using the method proposed in [168], for both EIC and JLab22. The extractions
consider only a single ratio of two bins in Q, integrated over xand z. In the left figure, the CS kernels are
normalized to the SV19 value [166] for better visibility of the uncertainty bands. The right figure shows a
more realistic picture of the extracted CS kernel, including the effects of power corrections.
in the multi-dimensional phase space. Similarly, the correlations between hadrons produced in the CFR and
TFR, as well as other competing processes, are intricately linked to the dynamics of these transitions.
To effectively separate and study these transitions, it becomes crucial to have precise and high-quality
experimental measurements in the multi-dimensional phase space. Such measurements will provide valuable
information on the dependencies of various observables on Q2, which are expected to differ for different
contributing mechanisms. This enables the validation and proper separation of these distinct mechanisms.
A unique feature of JLab22 is that it will offer an unprecedented insight into the matching region, a region
that cannot be explored with similar resolution in any other SIDIS experiment. The upgraded JLab22, with
its amazing statistics, will be a magnifying glass on the central region and will allow us to explore an energy
and transverse momentum range that is crucial to improve our current understanding of QCD in terms of
factorization theorems. With its fine resolution and largely extended reach in x, JLab22 will acquire an
unprecedented ability to perform multiple binning analyses as shown in Fig. 18, which will provide high
precision information on the TMD region.
Role of LQCD. In addition to experimental efforts in SIDIS, significant progress has been made in recent
years to calculate TMD-PDFs inside a nucleon from lattice QCD. One direction is the computation of ratios of
TMD x-moments in the b⊥space [170], and the other is large-momentum effective theory (LaMET) [171,172]
44
Figure 28: Transverse momentum dependence of sea and valence quarks [158] (left) and extension of the
transverse momentum coverage with JLab22 (open circles) for a given bin in xand z(0.25 <x<0.3,0.35 <
z < 0.45) at Q2>3 GeV2.
Figure 29: Left panel: Polarized gluon distribution x∆g(x) at Q2= 10 GeV2from JAM [181], showing
separately ∆g > 0 (red lines) and ∆g < 0 (blue lines) and contrasted to ±the unpolarized gluon distribution,
x|g(x)|(green lines). Right panel: double longitudinal spin asymmetry Aπ+
LL for semi-inclusive π+production
from a proton, for a selected kinematics at JLab with 22 GeV electron beam. Note that the heights of the
colored boxes give a 1σuncertainty in the asymmetry from the PDF replicas, while the error bars give the
expected statistical uncertainty with 100% acceptance.
that allows for the extraction of the Collins-Soper kernel [173] as well as the full (x, b⊥) dependence of
the TMD-PDFs [174]. So far, there have been several lattice calculations of the CS kernel at unphysical
quark masses [175–179], where the systematic uncertainties are gradually being understood and improved.
Besides, the first exploratory calculation of the unpolarized proton TMD-PDF with lattice renormalization
and one-loop perturbative matching has also been carried out [180]. The lattice results are currently in
qualitative agreement with phenomenological results and exhibit similar behaviors in the Fourier-conjugate
position space b⊥, with uncertainties increasing gradually as b⊥increases. This highlights the importance of
experimental studies at large b⊥, which requires fine binning of experimental data in the PTof hadrons. On
the lattice side, with the improvement of statistical and systematic errors in the large b⊥region, there will
be a more precise comparison between theory and experiment on these TMD observables, and JLab data
can be critical to test the theory.
Mapping out the Large-xSea. Understanding the dynamics of partons, including the non-perturbative sea
quarks, is crucial for gaining insights into strong interactions. The correlations between the spin of the
target and/or the momentum and spin of quarks, along with final state interactions, determine the azimuthal
distributions of produced particles. Measurements of flavor asymmetries in sea quark distributions, carried
45
out in Drell-Yan experiments, have revealed substantial non-perturbative effects at large Bjorken-x, where
valence quarks dominate [182]. Earlier measurements by the NMC experiment indicated that the integrated
¯
ddistribution is larger than the integrated ¯udistribution [183]. The E866 and SeaQuest Collaborations have
provided more recent measurements suggesting a significantly larger ¯
ddistribution compared to ¯uacross
the accessible range of x[44,184]. Non-perturbative q¯qpairs, which are also correlated with spins, play a
crucial role in spin-orbit correlations and the measurement of single-spin asymmetries observed in various
experiments over the past few decades.
Predictions indicate that the distribution of unpolarized sea quarks exhibits a power-like tail, approxi-
mately proportional to 1/P 2
T, extending up to the chiral symmetry-breaking scale [158]. A similar behavior
is observed in the flavor-nonsinglet polarized sea. The transverse momentum distributions of valence and
sea quarks are predicted to have distinct shapes, particularly at large values of PT. The effect of dynamical
chiral symmetry breaking on the partonic structure of nucleons has important implications for the transverse
momentum distributions of particles produced in hard scattering processes. With the significant increase in
phase space provided by 22 GeV experiments, a much wider range of transverse momenta can be accessed,
which is critical for studying TMDPDFs.
Gluon Polarization. For the past thirty years [185], the nuclear physics community has been driven by
the pursuit of understanding the proton spin puzzle - the breakdown of the proton’s spin into its quark
and gluon helicity and orbital angular momentum components. Experimental programs around the world
have been dedicated to this effort, and we now have a relatively comprehensive understanding of the total
fraction of helicity carried by quarks. However, questions remain about the specific flavor decomposition of
the sea quark contributions. A significant breakthrough was achieved when double spin asymmetries were
observed in inclusive jet production in polarized proton-proton collisions at RHIC [186], allowing for the first
detection of a polarized gluon distribution. Follow-up data from the STAR [187–189] and PHENIX [190]
Collaborations have reinforced these findings, giving us greater confidence in our understanding of both the
quark and gluon helicity content of the proton.
The JAM Collaboration [181] recently conducted a review of the analysis of jet data to assess the degree
to which the results rely on the theoretical assumptions made in the analysis, such as SU(3) flavor symmetry
for the axial vector charges that govern non-singlet combinations of spin-dependent PDFs [191,192], and
the positivity constraints for unpolarized PDFs. Their analysis revealed that a second set of solutions could
be possible without the PDF positivity constraints [193,194], which are not technically necessary based on
theoretical grounds. As illustrated in Fig. 29, this set of solutions could lead to ∆g < 0, contrary to the
traditional small and positive ∆gand positive quark polarization ∆qthat combine to produce a positive
asymmetry, as observed in the STAR data. The data suggest that negative ∆gcould also be feasible, with
a greater magnitude, which, when paired with positive ∆q, can generate a cancellation between the positive
contribution from the gluon-gluon channel and the negative contribution from the quark-gluon channel,
producing equally valid explanations for the inclusive jet data.
In a previous study, J¨ager et al. [195] explored potential constraints on the sign of ∆gby examining
inclusive pion production in polarized pp collisions using the PHENIX data [196] for neutral pions. They were
able to derive a small but negative lower limit for the double spin asymmetry that corresponds to negative
gluon helicity PDF comparable to those observed in the JAM analysis [181]. Furthermore, the sign of ∆ghas
been investigated through a comparison of PHENIX data on inclusive charged pion production [197,198].
The comparison of predictions based on recent JAM analysis [181] for π+and π−asymmetries at pp
center of mass energies √s= 200 GeV and 510 GeV as a function of xT= 2pT/√s, where pTis the
transverse momentum of the final state pion in the laboratory frame, indicate the uncertainties on these
data are still too large to exclude either a positive or negative value of ∆g, even though the π+asymmetry
has the potential to differentiate between the different solutions for ∆g.
Although EIC might provide the definitive resolution on ∆gand its sign via scaling violation in DIS,
an alternative possibility to resolve this problem on a comparable time scale can be found in the context
of double spin asymmetries (DSAs) in SIDIS. Specifically, longitudinally polarized lepton-nucleon reactions
with large transverse momentum hadrons produced in the final state have direct sensitivity on polarized
46
gluons inside the initial state nucleons because the corresponding hard scattering matrix elements are at
the same order of magnitude in the strong coupling constant αsas the quark scattering contributions. The
feasibility to discriminate the sign of gluon polarization with this process was recently studied at Ref. [199]
with an analysis that compared the discriminatory capabilities at JLab 12 GeV and the potential upgrade to
the 22 GeV with the projected Aπ+
LL asymmetries. The statistical uncertainties for the JLab projections were
based on a luminosity of dL/dt = 10−35 cm−2s−1. The asymmetries at JLab 12 GeV have relatively large
values and small statistical uncertainties. However, for most kinematics, the asymmetry bands with positive
and negative polarized gluons overlap significantly, making it difficult to differentiate between the positive
and negative ∆gsolutions. The upgraded 22 GeV electron beam allows access to a larger portion of the
intermediate and low-xregion and provides better discrimination between the two possible scenarios for ∆g
(see Fig. 29). We stress that this analysis did not included acceptance effects nor systematic effects stemming
from depolarization. The analysis in Ref. [199] concludes that a high luminosity JLab with a ≈20 GeV
beam is well-suited for differentiating between positive and negative solutions due to the asymmetry’s scaling
behavior with √s.
5.4 Summary
The energy upgrade at JLab presents a unique opportunity to extend measurements to a wider range in
x,Q2, and PT. This will be crucial for advancing our understanding of QCD dynamics, including the
evolution properties and transverse momentum dependences of PDFs. To achieve a detailed understanding
of the contributions to measured cross sections and asymmetries in SIDIS with controlled systematics,
it is necessary to consider all involved kinematical variables (x,Q2,z,PT, and ϕ). JLab is the only
facility capable of separating different structure functions involved in polarized SIDIS, including longitudinal
photon contributions. By performing precision Multi-D measurements of single and dihadron SIDIS with an
upgraded CEBAF accelerator, and by studying the Q2dependences of observables, we can test the impact
of several theoretical assumptions used in TMD phenomenology. This will also provide validation of the
extraction frameworks, which is critical for proper evaluation of systematic uncertainties. Additionally, the
detection of multiparticle final states and the study of multiplicities and asymmetries of dihadrons and vector
mesons will offer crucial insights into the source of single spin asymmetries and the dynamics of the polarized
quark hadronization process.
47
6 Spatial Structure, Mechanical Properties, and Emergent Hadron
Mass
6.1 Introduction
The extended spatial structure of hadrons is one of the basic expressions of their emergence from QCD. It
attests to their composite nature and reveals the dynamical scales created by the non-perturbative phenomena
of chiral symmetry breaking and confinement (see Sec. 2). It also reveals the mechanical properties (internal
motion, forces) and allows one to discuss hadron structure in terms similar to those used for nonrelativistic
systems such as atoms or nuclei. The study of the spatial structure of hadrons is a rapidly expanding field
of science, with experimental programs ongoing at JLab12 and planned at EIC, and many theoretical and
experimental developments and opportunities reaching further into the future.
One source of information on the spatial structure are the hadron form factors of operators measuring lo-
cal physical quantities. Originally, the concept of form factors was developed for the electromagnetic currents
operators, and extensive efforts have been devoted mapping the distributions of charge and magnetization in
hadrons and nuclei. Recently, the concept of form factors has been extended to a much larger class of local
QCD operators composed from quark and gluon fields. The form factors of the QCD energy-momentum
tensor (spin-2 quark and gluon operators) describe the spatial distributions of momentum, angular momen-
tum, and forces in the nucleon and quantify the mechanical properties of the dynamical system [200,201].
The form factor of the trace anomaly (spin-0 gluon operator) describes the spatial distribution of the gluonic
fields involved in scale symmetry breaking and plays an important role in the proton mass decomposition
[202–204].
Another source of information on the spatial structure of hadrons are the generalized parton distributions
(GPDs) [205–207], which describe the spatial distributions of quarks and gluons in the transverse plane seen
by a high-energy probe sampling field components with given longitudinal momentum. They allow one to
create “tomographic images” of the hadron in terms of quark/gluon degrees of freedom and bring them to
life as 3D objects in space. Extensive efforts are under way to extract the GPDs from experimental data and
lattice QCD calculations and construct the tomographic images. While essential progress will be made with
the data from JLab12 and EIC, there remain significant challenges to hadron imaging that can be overcome
with new theoretical and experimental developments beyond these programs.
Form factors and GPDs are measured in exclusive electro/photoproduction processes, where the initial
hadron emerges intact in the final state, and the momentum transfer is conjugate to the spatial structure
investigated. Such measurements generally require high luminosity because of low rates and the need for
differential measurements. At the same time, they require collision energies allowing for energy and momen-
tum transfers significantly above the hadronic scale ∼1 GeV (high-Q2electroproduction, heavy quarkonium
production). The proposed high-intensity 22 GeV facility would provide the necessary combination of both
capabilities and substantially expand the possibilities for exploring the spatial structure of hadrons in both
gluon and quark degrees of freedom. Qualitatively new applications are the measurement of gluonic form
factors of hadrons through exclusive charmonium production, and fully differential 3D imaging of the nucleon
using dilepton/diphoton production. In addition, the new facility would offer essential quantitative advances
in the study of electromagnetic form factors, GPDs with exclusive photon/meson production, and the study
of meson form factors and GPDs.
The emergence of hadronic mass from the massless theory of QCD is certainly the most fundamental
phenomenon of strong interaction physics. It gives rise to more than 90% of the visible mass of the Universe
residing in the protons and neutrons in atomic nuclei. The question “how” this happens is essential for
understanding the structure of matter. Hadronic mass is generated by nonperturbative interactions between
quarks and gluons associated with mass scales significantly larger than the QCD scale parameter ΛQCD ≈
200 MeV (or distance scales significantly smaller than 1 fm). For quarks the mass generation is associated
with the well-known phenomenon of dynamical chiral symmetry breaking, which converts the nearly massless
QCD quarks into constituent quarks with a dynamical mass. The same nonperturbative interactions mediate
48
high-momentum scattering processes on hadrons such as N→Nelastic form factors or N→N∗transition
form factors at momentum transfers Q2∼few GeV2. This connection can be made explicit in approaches
such as continuum Schwinger methods, which describe quark/gluon mass generation and baryon three-quark
structure in a unified framework. In this context only measurements at JLab - after a 22 GeV energy upgrade
- of electromagnetic ground state and N→N∗transition form factors would allow us to continuously map
out the transition from the strongly coupled to the perturbative QCD regime and hence to explore the full
range of distances where the dominant part of hadron mass and bound three-quark structures emerge from
QCD [208].
6.2 QCD Energy-Momentum Tensor
6.2.1 Gluonic Mass and Momentum Distributions from Charmonium Production
Explaining the origin of the nucleon mass is essential for understand the structure of all visible matter in the
Universe. The uand dquark masses in the QCD Lagrangian account only for a tiny fraction of the nucleon
mass, and most of it is generated by gluon fields through the effect of dynamical chiral symmetry breaking.
The mass distribution in the nucleon is encoded in the form factors of the gluonic energy-momentum tensor
(so-called gravitational form factors) and can be quantified in this way [202–204]. They include the spin-0
gluon operator describing the trace anomaly, and the spin-2 gluon operator measuring the gluon momentum
distribution. Theoretical studies have shown that these form factors can be extracted from measurements of
exclusive J/ψ photo/electroproduction near the threshold (W−Wthr ∼2-4 GeV), by analyzing the combined
Wand tdependence of the differential cross section [209–214]. This opens the prospect of exploring the
mass, pressure, and force distributions of gluons in the proton. Such measurements are complementary to
J/ψ production at EIC energies (W≳10 GeV), which probe the gluon GPDs at x≲0.1 [82].
0.4
0.3
0.2
0.1
J/ using
l
g
QCD
J/ using G
PDs
kAl {Gel}
Figure 30: The gluonic form factors A(k2=−t) (left) and D(k2)=4C(k2) (right) extracted from the
two-dimensional cross section data of J/ψ −007 Collaboration [214] using the holographic QCD approach
[211,212] (dash-dot curve) and the GPD approach [213] (green solid curve), compared to the recent lattice
calculation [215] (blue dotted curve).
Recent experimental results from JLab12 show the feasibility of extracting gluonic structure from near-
threshold J/ψ production [214]. Figure 30 shows the gluonic form factors A(t) and D(t) of the proton,
extracted from the exclusive J/ψ photoproduction differential cross section measured in the JLab Hall C
experiment E12-16-007 [214] using two different theoretical descriptions of the reaction mechanism: a GPD-
based model implementing collinear factorization [213], and a holographic QCD model based on gauge-string
duality [211,212]. The analyses have also extracted the gluonic radii of the nucleon, which can be compared
with the electric charge radius. The results suggest that the gluonic mass distribution of the proton resides
49
Figure 31: Left: Dq(t) vs. −tfrom 6 GeV DVCS data compared to theoretical predictions. Right: Black line
is the pressure distribution versus distance from the proton center employing a Fourier transform of Dq(t)
in t. The light-green band shows the estimated systematic uncertainty of the fit.
within the electric charge distribution. Further measurements of J/ψ photo/electroproduction at 11 GeV are
planned with the future SoLID detector at JLab [216]. The theoretical interpretation of these measurements
is a matter of on-going research and raises several questions which cannot be definitively answered with the
present 12 GeV data and require a broader kinematic range.
The JLab 22 GeV upgrade will be crucial to realizing the potential of this program. The extended
energy range will make it possible to measure the interplay of Wand tdependence over a range sufficient
for separating the spin-0 and 2 contributions and testing/improving the proposed models of the reaction
mechanism. The 22 GeV fixed-target energy covers exactly the region where the differences between different
reaction models are maximal and can be distinguished by the data. The luminosity ∼1037 cm−2s−1will be
critical for these low-rate differential measurements. For near-threshold J/ψ production the JLab 22 GeV
facility would be unique. Complementary measurements of near-threshold Υ production would be possible
with the EIC at 100 fb−1luminosity with suitable detectors [82]. This field of research is evolving rapidly,
and significant progress in theory is expected over the next 10 years.
6.2.2 Quark Pressure Distribution from Deeply Virtual Compton Scattering
The form factors of the energy-momentum tensor are at the center of modern nucleon structure physics.
Of particular interest is the D-term [217], which describes aspects of the distribution of QCD forces on
the quarks in the nucleon (“pressure”) [218] and has become the subject of numerous theoretical studies of
the “mechanical properties” of the nucleon [200,201]. The D-term form factor appears as the subtraction
constant in a dispersion relation of the amplitude of the deeply-virtual Compton scattering (DVCS) process
and be extracted from the experimental data on ep →e′γp with minimal model dependence. First empirical
extractions of the D-term form factor and the “pressure” distribution have been performed with the JLab 6
GeV data (see Fig. 31) [219,220]; see also discussion and results in Refs. [221,222]. The restricted kinematic
range covered by the 6 GeV data resulted in very large uncertainties in extracting the distribution of pressure
and shear stress. The main limitations are the small range of energies (or longitudinal momentum fraction
ξ) available for evaluating the dispersion integral, small range of t(limited by a condition on t/Q2) available
for computing the Fourier transform of the form factor.
A high quality extraction of the D(t) form factor would be possible with the proposed 22 GeV facility.
The available energy would improve the convergence of dispersion integral and permit tests of the stability
of the subtraction. It would also allow one to extend the measurements to significantly higher values of t,
while keeping t/Q2at values such that power corrections are under control. Projections of the form factor
measurements and extraction of the pressure distribution at various energies are shown in Fig. 32.
50
Figure 32: Left: The D-term form factor of the QCD energy-momentum tensor, Dq(t), as a function of the
momentum transfer −t, as extracted from DVCS experiments. The arrows indicate the −tranges covered at
different beam energies with the constraint −t/Q2<0.2. Right: Quark pressure distribution in the proton,
p(r), as a function of the distance from the proton center, r, obtained as the Fourier transform of Dq(t).
Figure 33: Left: The CLAS12 detector system. Right: Response to exclusive DVCS + Bethe-Heitler events
at 22 GeV beam energy: (a) Scattered electron kinematics in Q2vs. xB. (b) DVCS-BH photon kinematics
in polar angle vs. momentum, (c) proton kinematics in polar angle vs. momentum, (d) event distribution
in −tvs. azimuthal angle ϕ.
The CLAS12 detector [13] shown in Fig. 33 has been designed with measurements of GPD-related pro-
cesses in mind. It has demonstrated with data published recently [223] that CLAS12 is well suited for
measurements of the DVCS-BH process in large connected kinematic domains in Q2, xB,−tand azimuthal
angle ϕto measure cross sections and polarized and polarized target processes simultaneously at the currently
available maximum beam energy of 10.6 GeV. Simulations of the same processes at 22 GeV shown in Fig. 33
demonstrate that CLAS12 is also well matched to measure the response to DVCS and BH events at an up-
graded JLab beam energy of 22 GeV. Connected kinematic ranges in 1.5< Q2<20 GeV2, 0.05 < xB<0.6,
0.1<−t < 2.5 GeV2, and azimuthal angle 0 <ϕ<360◦will be simultaneously measured. The large ranges
in xBand −tare essential as applying the dispersion relation requires the full integration in ξ=xB/(2−xB).
51
6.3 3D Imaging with GPDs
6.3.1 Longitudinal/Transverse Separation in Exclusive Processes
The past few decades have been ripe with progress in our understanding of the QCD structure of strongly
interacting systems, from unraveling the spin structure of the proton in terms of the quark and gluon spin
and orbital angular momentum, to developing a microscopic definition of pressure and mass while giving a
detailed description of the spatial distributions of quarks and gluons. The key objects that made it possible
to perform quantitative detailed studies, and that connect all of these physical properties are the GPDs
([224,225] for reviews, see Refs. [205–207,226]). GPDs are measurable through deeply virtual exclusive
scattering (DVES) processes, in particular DVCS, where they appear embedded in the Compton Form
Factors (CFFs), which are convolutions over the longitudinal partonic momentum fraction, x, with known
perturbative kernels. In DVES the electron scatters off the proton or nucleus with momentum, p, at high
four-momentum transfer squared, Q2. A high momentum photon or a meson is produced, leaving a proton
with momentum p′=p−∆, in the final state. By Fourier transforming the GPDs in the variable ∆T, the
transverse momentum transfer between the initial and final proton, one can access the impact parameter
dependent parton distribution functions, ρq,g (x, b) [227,228], which simultaneously define the distributions
in longitudinal momentum fraction, x, of a quark/gluon positioned at a transverse distance, b, from the
hadron’s center of mass (CoM). Measuring CFFs and GPDs allows us, therefore, to extend the grasp on the
physics information contained in the nucleon elastic form factors, providing a unique probe of QCD at the
amplitude level.
Extracting 3D images of the proton’s interior from experimental data while pinning down the origin of
it’s mass and spin are defining goals of the nuclear and particle physics experimental programs at JLab
and the upcoming EIC. While the EIC is mostly focused at low Bjorken xB, where gluonic components
are dominant, JLab above 12 GeV allows us to explore in detail the valence quark region. By expanding
the xBand Q2domain, a JLab upgrade to 22 GeV would allow us to explore the emergence of antiquarks
in exclusive reactions. Despite two decades long efforts of DVES measurements pioneered by experiments
at the HERA collider, and subsequently carried out in dedicated programs at JLab and at the COMPASS
experiment at CERN, CFFs and GPDs remain elusive quantities to extract from data. A major obstacle
affecting all analyses has been posed, so far, by the rather involved expressions for the cross section in
both the unpolarized and polarized configurations, which do not allow us to associate a given GPD in
a specific polarization configuration with a polarization measurement for the corresponding configuration
[229,230]. While, on one side, this prevents us from using previous experience on inclusive and semi-
inclusive experiments, which are characterized by a more transparent structure of the cross section for
various polarization configurations (see e.g. the analysis in Ref. [124] and references therein), it has now
become clear that the DVCS cross section tracks the one for electron-nucleon elastic scattering experiments
determining the nucleon electromagnetic and weak form factors.
The analyses presented in Refs. [231–233] performed along these lines show, in fact, that a Rosenbluth
separation of data from an unpolarized target allow us to simultaneously determine two of the GPDs entering
the cross section for the interference term between DVCS and the Bethe-Heitler (BH) process. Together with
the more efficient reformulation of the cross section for the ep →e′p′γ(M) process presented in Refs. [231,
233,234], refined statistical analyses such as the ones afforded by machine learning (ML) techniques can
decisively improve the extraction of physical observables form data. Several analyses using ML tools to
extract CFFs from data were already presented in Refs. [222,235–238].
A program for extracting meaningful information from data can be continued with more precise data
taking with dedicated experiments beyond JLab12 GeV. An extensive analysis using precision data in the
valence and emerging sea quarks region would allow us, to separate the leading twist component from
the O(1/Q)/power corrections dependent effects arising from both dynamical higher twists, and kinematic
corrections. Furthermore, the onset of the scaling regime of QCD will be ultimately confirmed by the
comparison of DVCS and Timelike Compton Scattering (TCS) data over a sufficiently large range of four-
momentum transfer, Q2. Other outstanding questions to be addressed in this program will be: 1) separating
the twist two and three components through meaningful Rosenbluth separations; 2) separating out the
52
Figure 34: Longitudinal to transverse virtual photon polarization parameter for the DVCS process, ϵDV C S .
The L/T separation of the DVCS term can be accomplished at the kinematic points shown on (left) Ee=
6,11,18,24 GeV and fixed xB= 0.2, t=−0.2 GeV2; (right) EIC configurations are given as √s= 74 GeV
corresponds to Ee= 5 GeV, Ep= 275 GeV; and √s= 104 GeV corresponds to Ee= 10 GeV, Ep= 275 GeV
at kinematics xB= 0.01, t=−0.2 GeV2(work in progress with Brandon Kriesten)
Figure 35: Flavor separated and gluon contributions to the CFF plotted as a function of xBat JLab
kinematics typical of a 22 GeV upgrade. Notice the role of the valence component in the evaluation of the
CFF given that q+ ¯q=qv+ 2¯q. (work in progress with Brandon Kriesten)
various flavor GPDs; 3) zooming into the onset of gluon components.
Figure 34 shows the longitudinal to transverse virtual photon polarization parameter for the DVCS
process at JLab and EIC kinematics, respectively. The advantage of the JLab setting can be clearly seen.
Figure 35 addresses the issue of the separation of various quark flavors contributions to the ep →e′p′γ
cross section. On the right we also present the gluon contribution through its effect on perturbative QCD
evolution at NLO. All curves were calculated in the model of Ref. [234].
In conclusion, the JLab higher energy upgrade will be uniquely important to perform the Rosenbluth
separations that allow us to separate out twist-2 from twist-3 components proportional to OAM [231], and
to perform in depth studies of the scale dependence of GPDs centered on the valence contribution and the
emergence of sea quark effects.
53
Figure 36: Comparison of SoLID DDVCS kinematic coverage between 11 GeV (black) and 22 GeV (color)
electron beams. They both use the same running conditions and detect the scattered electron and decay
muon pair at forward and large angle. xBis Bjorken-x,Q2is the negative four momentum transfer squared,
and Q′2is the invariant mass of muon pair squared. 22 GeV electron beam will allow access to substantially
higher xB,Q2, and Q′2.
6.3.2 Differential Imaging with Double Deeply Virtual Compton Scattering
The program of “tomographic imaging” of the nucleon with GPDs requires the full information on their de-
pendence on the longitudinal momentum variables — the parton momentum fraction x, and the longitudinal
momentum transfer ξ. Conventional exclusive processes such as DVCS cannot fully disentangle the xand ξ
dependence, because the observables sample the GPDs only in the special kinematics of x=ξor as integrals
over x. Novel processes such as dilepton production
e+p→e′+ (l+l−) + p, l =eor µ(1)
(Double Deeply Virtual Compton Scattering, or DDVCS) can disentangle the longitudinal momentum vari-
ables in the GPDs by varying the dilepton mass in the process [239,240]. By measuring the t-dependence
in this configuration, they could provide fully differential tomographic images of nucleon structure.
These next-generation measurements are challenging, and exploratory studies with JLab 12 GeV are
under way [241]. The focus is on the production of muon pairs, which eliminates the additional complexity
of mixing electron from the pair with the scattered electron. Muons also go through larger amount of
materials allowing to improve signal to noise by using large amounts of shielding. Letters of Intent for
exploratory measurements of DDVCS at 11 GeV have been submitted to the JLab PAC, one using the the
SoLID spectrometer and another the CLAS12 setup.
The proposed 22 GeV facility would be ideally suited for this program. The high luminosity is essential
because the DDVCS cross section is suppressed by a factor αem ∼10−2compared to DVCS. The energy is
needed for reaching dilepton masses M(l+l−)∼few GeV in electroproduction with Q2∼few GeV2, where
one can perform scaling studies and apply the GPD-based reaction mechanism based on QCD factorization.
Figure 36 shows the kinematical coverage of the SoLID and CLAS setups at 22 GeV. For both, the range in
Q2and Q′2≡M2(µ+µ−) is much enlarged compared to 11 GeV. The cross section estimates were obtained
using the GRAPE and VGG models, and indicate a reduction of cross section at 22 GeV by about a factor of
3 compared to 11 GeV. The beam spin asymmetries expected in 22 GeV kinematics are sizable, of the order
of several per cent, as in the 11 GeV kinematics, and can be measured reliably with the proposed setups.
54
Figure 37: The lowest order hard amplitude for the photoproduction of a large mass diphoton (complemen-
tary diagrams with k1↔k2are not shown).
10
SγN[GeV2]
0
0.5
1
1.5
20.1
ξ
[pb/GeV6]
d3σ
dtdu'dMγγ2
20 30
0.20.30.4
Figure 38: Differential cross section as a function of
SγN (bottom axis) and the corresponding ξ(top axis)
for M2
γγ = 4 GeV2,t=tmin, and u′=−1 GeV2. The
leading order result is denoted by the solid (dashed)
red line, while the next-to-leading order one by the
dotted (dash-dotted) blue line for the GK (MMS)
GPD model.
6.3.3 Novel GPD Probes with Exclusive Diphoton Production
The quest for nucleon tomography in terms of GPDs necessitates the study of as many exclusive processes
as possible. Processes with 2 →3 hard amplitudes have been shown to provide many examples of interesting
reactions [242–244]. The quasi-real photoproduction of a large invariant mass photon pair [245,246]:
γ(k, ϵ) + N(p1, s1)→γ(k1, ϵ1) + γ(k2, ϵ2) + N(p2, s2),(2)
is the simplest among them since it is purely electromagnetic at the Born order level, as shown in Fig. 37. It
has been proven to factorize [247,248] into a hard amplitude and quark GPDs. Because of the symmetries
of the process, the contributing GPDs are the charge conjugation odd parts of quark GPDs,
H+(x, ξ, t) = H(x, ξ , t)−H(−x, ξ, t),(3)
˜
H+(x, ξ, t) = ˜
H(x, ξ, t) + ˜
H(−x, ξ, t),(4)
and similar equations for E+and ˜
E+, which are decoupled from the DVCS, TCS, and DDVCS reactions.
Gluonic GPDs do not contribute for the same reason.
The hard scale of this reaction is the diphoton invariant squared mass, M2
γγ = (k1+k2)2, while the
skewness variable, ξ, similarly as in the TCS case, is related to τ= (M2
γγ )/(SγN −M2) with SγN = (k+p1)2
through ξ≈τ/(2−τ). The estimated cross section is shown in Fig. 38 as a function of SγN (bottom axis) and
the corresponding ξ(top axis) for M2
γγ = 4 GeV2,−t=−(p2−p1)2=−tmin , and u′= (k−k2)2=−1 GeV2.
55
This energy range for a quasi-real photon beam will be easily accessible with the JLab22 facility. We show
the leading-order and next-to-leading order results for two GPD models [249,250]. The electroproduction
reaction, which receives contributions from two Bethe-Heitler like processes is discussed in detail in Ref. [251].
The presented estimation of cross sections shows that the experiment is feasible with a high-luminosity
facility in the JLab22 energy range. The CLAS12 detector looks adequate for observing and measuring this
process. Dedicated experiments may be prepared in Hall A or Hall C. The difference between our results
with two different GPD models shows that this process is discriminative and will induce severe constraints
on our understanding of the quite badly known charge conjugation even part of quark GPDs. Note that the
process is available in both the PARTONS framework [252] and EpIC Monte Carlo generator [253], making
impact and measurability studies convenient for the experimental community. Since the diphoton process
is insensitive to the gluon and sea quark GPDs, there is no enhancement of the amplitude at small ξ. This
is the reason why in Fig. 38 the cross section drops in the sea region. Therefore, contrarily to the DVCS
or TCS cases, the large photon energy reached by the future EIC does not help to have larger scattering
amplitudes.
6.3.4 Resonance Structure with N→N∗Transition GPDs
While measurements of exclusive processes have already provided much insight into the 3D structure of
the ground state nucleon, little is known about the 3D structure of resonances so far. This information is
encoded in so-called transition GPDs [205,207], which can be accessed in exclusive processes with a N→N∗
transition [254–256]. The simplest such reaction is the N→N∗DVCS process,
γ∗+N−→ γ+N∗−→ γ+ (Nmeson),(5)
where a real photon is produced in addition to a nucleon resonance, which then decays into a ground state
nucleon and a meson. Another reaction is N→N∗pseudoscalar meson electroproduction,
γ∗+N−→ M+N∗−→ M+ (Nmeson).(6)
For both reactions, a QCD factorization theorem holds in the Bjorken limit: −t/Q2≪1 and xBfixed, with
an additional condition on Q2in relation to the resonance mass: Q2≫m2
N∗[254,255].
The theory and interpretation of transition GPDs has made substantial progress in recent years and has
become a field of study in its own right. For the simplest case of the N→∆ transition, the structural
decomposition of the matrix elements has been studied for the chiral-even (quark helicity-conserving) [205]
and chiral-odd (quark helicity-flipping, or transversity) GPDs [254]. The first moments of the chiral-even
N→∆ GPDs are related to the Jones-Scadron electromagnetic form factors [205,257] and the Adler axial
form factors [205,258,259] of the N→∆ transition. The second moments of the chiral-even GPDs give
access to the N→∆ transition matrix elements of the QCD energy-momentum tensor [260], including
the QCD angular momentum of the N→∆ transition [261], and possess a rich mechanical structure. Of
particular interest is the possibility of connecting the N→Nand N→∆ GPDs through the 1/Ncexpansion
of QCD, using the emergent spin-flavor symmetry in the large-Nclimit, which enables a unified analysis of
ground state and transition GPDs [205,254,262,263].
The chiral-even transition GPDs are probed in DVCS with N→∆ transitions. The process has been
described theoretically in detail in Ref. [255], and with a special focus on CLAS12 kinematics in Ref. [256].
The first experimental study of p→∆+DVCS beam spin asymmetries and cross sections is currently ongoing
based on CLAS12 data. The chiral-odd transition GPDs are probed in hard exclusive pion electroproduction
with N→∆ transitions. Such processes have been studied theoretically in Ref. [254], using predictions for
the transition GPDs based on the large-Nclimit of QCD. On the experimental side, no publications of
observables sensitive to transition GPDs were available for a long time, since either statistics or the beam
energy were not sufficient to study the high Q2regime of such N→N∗reactions and to have enough
phase space to suppress the dominant backgrounds. With the structure function ratio σLT ′/σ0of the hard
exclusive π−∆++ electroproduction process, the first observable sensitive to transition GPDs was recently
56
Figure 39: Preliminary results for the structure func-
tion ratio σLT ′/σ0for π−∆++ (black) [264] in com-
parison to results from π+n(red) [265] and π0p
(blue) [266]. The gray histogram shows the system-
atic uncertainty of the π−∆++ measurement.
Figure 40: Comparison of the available phase space, accessible with the present CLAS12 setup, in Q2−
xBor the π−∆++ process under forward kinematics (−t < 1.5 GeV2) (left) and for the π+π−invariant
mass of the same process, which is used to suppress the dominant ρproduction background by the cut on
M(π+π−)>1.1 GeV, indicated by the yellow line (right) for a 10.6 GeV, 18 GeV and 22 GeV electron
beam.
submitted for publication by the CLAS Collaboration [264]. Figure 39 shows a comparison of preliminary
results for the structure function ratio σLT ′/σ0for π−∆++ in comparison to results from π+n[265] and
π0p[266]. The large absolute magnitude for π−∆++, compared to π+ncan be seen as a clear effect of the
excitation process [264].
The N→N∗DVCS, as well as the N→N∗DVMP processes, will both strongly profit from an energy
and luminosity upgrade of JLab/CLAS12. From the statistics point of view, the low efficiency for the
detection of the multi-particle final states, in combination with the background suppression cuts, strongly
limit the available statistics of the final sample. From the beam energy point of view, the currently available
beam energy of 10.6 GeV allows a study of the lower lying nucleon and ∆ resonances in a limited Q2range.
However, especially for higher mass resonances, the factorization requirement Q2≫m2
N∗strongly limits the
option based on a 10.6 GeV electron beam. Here, a 22 GeV upgrade of JLab will enable the investigation
of higher-mass resonances and extend the accessible Q2range for the lower-mass resonances. Based on this
extended range, a detailed study of the scaling behavior of the different observables will become possible.
Figure 40 shows the available phase space, accessible with the present CLAS12 setup, in Q2−xBfor the
π−∆++ process under forward kinematics and the π+π−invariant mass of the same process for a 10.6 GeV,
18 GeV, and 22 GeV electron beam. The distributions of the N→∆ DVCS process show similar charac-
teristics. It can be seen that a 22 GeV upgrade of JLab will provide a significantly increased Q2range for a
fixed value of xB. This will provide a big advantage for the study of these processes, since the factorization
57
of the N→N∗DVCS and DVMP processes requires a high virtuality Q2to be above the resonance mass
squared. While this condition can be already fulfilled with a 10.6 GeV electron beam for lower-mass reso-
nances, such as the ∆(1232), an energy upgrade to 22 GeV will be essential ensure the factorization of the
process for higher-mass resonances and to study the scaling behavior of the observables. As shown in the
right part of Fig. 40, the increase of the phase space for the different invariant mass combinations will al-
low a more efficient suppression of non-resonant background from exclusive meson production and also from
other (differently charged) nucleon resonance production channels, which is mostly expected at lower masses.
Higher beam energies will, therefore, also provide a more efficient event selection and a better suppression
of the non-resonant background. The 22 GeV upgrade of JLab, in combination with a luminosity upgrade
of CLAS12, will thus provide ideal conditions for the study of the 3D structure of nucleon resonances via
transition GPDs.
6.3.5 Transition Distribution Amplitudes in Backward-Angle Processes
pNpM
γ∗
u
s
CF
N DA
p′
N
q2=−Q2
t
MNTDA
pNpγ
γ∗
u
s
CF
N DA
p′
N
q2=−Q2
t
γN TDA
Figure 41: The factorized amplitude for backward electroproduction of a meson (left) or a photon (right).
CF denotes the perturbatively calculable coefficient function.
While the pronounced forward peak of exclusive electroproduction cross sections has been investigated
extensively in the last two decades, revealing the backward-angle peak was quite delayed (for a review, see
Ref. [267]), although several theoretical predictions [268,269] advocated for its study in the framework of
the collinear factorization approach of perturbative QCD. In a nutshell, the argument relies on the fact that
a deeply virtual photon is able to resolve the partonic structure of the nucleon in a quite similar way in
the backward as in the forward regimes. It thus seems legitimate to assume the extension of the validity
of collinear factorization in near-backward kinematics. The scattering amplitude is then presented as a
convolution of non-perturbative hadronic matrix elements of the light-cone three quark operators, with a
hard subprocess amplitude describing the interaction of partons with the hard electromagnetic probe.
The reaction mechanism for electroproduction of a backward meson off a nucleon, and backward electro-
production of a real photon off a nucleon (backward DVCS, bDVCS) is presented, respectively, in Figs. 5
and 11 of Ref. [270]. Apart from familiar nucleon distribution amplitudes (DAs), this description involves a
new class of non-perturbative non-diagonal objects: nucleon-to-meson (MN) and nucleon-to-photon (γN )
transition distribution amplitudes (TDAs). The concept of transition distribution amplitudes (TDAs) [270]
naturally extends both the concept of nucleon DAs and nucleon GPDs. To leading twist-3 accuracy, TDAs
are defined as matrix elements of the same three quark light cone operator occurring in the definition of
nucleon DAs, with color structure εc1c2c3qc1(z1)qc2(z2)qc3(z3). However, these matrix elements are taken be-
tween two states of different baryonic charges (a nucleon and a meson, or a nucleon and a photon). Moreover,
similarly to the case of GPDs, the non-zero transfer of longitudinal momenta is characterized by a skewness
variable ξdefined with respect to the u-channel momentum transfer pM,γ −pN. As in the forward case, ξis
related to the Bjorken variable xBas ξ≈xB
2−xB. Nucleon-to-meson and nucleon-to-photon TDAs quantify
58
0.10 0.15 0.20 0.25 0.30 0.35 0.40
1
5
10
50
100
xB
d2σ/dΩπ[nb/sr]
γ*pπ0p; Q2=3,5GeV2; u=u0;
0.10 0.15 0.20 0.25 0.30 0.35 0.40
1
2
5
10
20
50
xB
d2σ/dΩγ[nb/sr]
γ*pγp; Q2=3,5GeV2; u=u0;
Figure 42: An estimate of d2σ
dΩcross sections for (left) backward electroproduction of a π0meson, (right) or
of a photon, as a function of xBfor Q2= 3, 5 GeV2. The xBrange is representative of the kinematics that
may be accessed by a JLab22 experiment.
partonic correlations inside hadrons; they give access to the baryon charge distribution in the transverse
plane and provide new tools to study the shape of nucleon’s mesonic and electromagnetic clouds.
The first experimental studies of near-backward hard exclusive reactions at JLab have been recently
presented in Refs. [271–273]. A dedicated study of the exclusive backward electroproduction of a π0above
the resonance region has recently been approved with JLab Hall C [274]. The goal of this experiment is
to perform cross section measurements at several different Q2values with complete σL,σT,σLT , and σT T
separation to verify the σTdominance, revealed in Ref. [272], for near-backward ω-meson electroproduction.
Challenging the validity of the collinear factorized description of hard backward meson and photon
electroproduction reactions is of primary importance to elaborate a unified and consistent approach for
physics of hard exclusive reactions both in the forward and in the backward regions with non-trivial cross
channel baryon number exchange. The improved luminosity and perfect angular coverage after the suggested
22 GeV upgrade makes JLab a unique experimental facility to probe hadron dynamics in the vicinity of the
backward peak, to confirm or disprove the validity of factorized description, discriminate between different
TDA models, and recover the hadronic structural information encoded in TDAs.
In order to examine the prospects of experimental studies of backward reactions at the kinematical condi-
tions of JLab22, we present theoretical predictions for the cross section of hard backward electroproduction
of pions and photons in the (Q2, xB) range appropriate to this facility. In Fig. 42 are shown the differential
cross sections d2σ
dΩof γ∗N→πN ′(left) and γ∗N→γN′(right) as a function of the Bjorken variable xBfor
the two values of Q2= 3, 5 GeV2. For the case of backward pion production these cross section estimates
are based on the cross-channel nucleon exchange model for πN TDAs suggested in Ref. [275]. For the case
of backward DVCS [276], we rely on the nucleon-to-photon TDA model [277,278] with adjustable normal-
ization devised in to account for the recent backward J/ψ photoproduction data presented by the Hall D
Collaboration [279]. The current model TDAs are still quite primitive and the results must be taken only as
very rough order of magnitude estimates. However, taken at face value, these predictions clearly show that
the corresponding cross sections are accessible with JLab22. The higher electron energy will allow to extend
in a crucial way the results obtained up to now at JLab [271,272], as well as those expected in the near
future [274] and help to get a detailed understanding of hadron dynamics in the vicinity of the backward
peak. Note that, contrarily to the forward electroproduction (DVCS, DVMP, or TCS) processes, backward
amplitudes do not benefit from small ξenhancement since TDAs mostly probe the valence quark content of
nucleons. Very high energy processes at EIC are thus not the favored channels for their study.
As a final comment, let us stress that experiments with nuclear targets can be used to explore the
phenomenon of color transparency [280] for backward hard reactions [281], which is a crucial prediction of
the short distance nature of the underlying mechanism.
59
6.4 Short-Range Electromagnetic Structure
6.4.1 Pion and Kaon Form Factors
Measurement of the π+electromagnetic form factor for Q2>0.3 GeV2can be accomplished at by the
detection of the exclusive reaction p(e, e′π+)nat low −t. This is best described as quasi-elastic (t-channel)
scattering of the electron from the virtual π+cloud of the proton, where t= (pp−pn)2is the Mandelstam
momentum transfer to the target nucleon. Scattering from the π+cloud dominates the longitudinal photon
cross section (dσL/dt), when |t| ≪ m2
p. To reduce background contributions, one preferably separates the
components of the cross section due to longitudinal (L) and transverse (T) virtual photons (and the LT, TT
interference contributions), via a Rosenbluth separation. The value of Fπ(Q2) is determined by comparing
the measured σLvalues at small −tto the best available electroproduction model. The obtained Fπvalues
are in principle dependent upon the model used, but one anticipates this dependence to be reduced at
sufficiently small −t.
Hall C has a uniquely important role to play in the EIC era, particularly in the realm of precision
L/T-separation measurements. Conventional Rosenbluth separations are impractical at the EIC, because
statistical and random systematic uncertainties in σLare magnified by 1/δϵ, where δϵ is the difference in the
virtual photon polarization parameters at high and low beam energies. To keep the uncertainties in σLto
an acceptable level, δϵ > 0.2 is typically required, i.e. an uncertainty magnification no more than 5. This is
not feasible at the EIC, so physicists will need to rely on an extrapolation of L/T-separated data from Hall
C for the interpretation of EIC data.
We consider a two phase program. In phase 1, only measurements with the existing HMS+SHMS
instrumentation were explored, to see what can be accomplished in a “cost-effective phased-approach”. In
this phase, a higher energy JLab electron beam, in concert with the existing HMS+SHMS spectrometers in
Hall C will enable important Deep Exclusive Meson Production (DEMP) measurements which significantly
extend the kinematic range of the 11 GeV physics measurements and improve the range of overlap between
JLab L/T-separated measurements and the unseparated measurements of the EIC. This improved overlap
will greatly ease the interpretability of the higher Q2EIC data and be a significant scientific contribution.
Several programs of measurement are significantly enhanced. The pion form factor is a key observable to
study in our understanding the physics of color confinement, i.e. understanding the transition of the behavior
of QCD from long distance scales (low Q2, where confinement dominates and the interaction is very strong)
to short distance scales (high Q2, where the quarks act as if they are free). The pion is one of the simplest
QCD systems available for study, and the measurement of its elastic form factor is the best hope for seeing
this transition experimentally. This is possible via high resolution measurements of the p(e, e′π+)nreaction.
18 GeV electron beam will allow the π+form factor to determined to Q2= 10 GeV2with small uncertainties,
and up to 11.5 GeV2with somewhat larger model uncertainties, a significant advance over the 12 GeV data.
Similarly, assuming the extracted σLare sufficiently sensitive to the K+ pole, high resolution measurements
of the p(e, e′K+)Λ reaction may allow the K+form factor to be determined up to Q2= 7.0 GeV2with small
uncertainties, and to 9.0 GeV2with larger uncertainties.
A separate program with broad significance is the study of hard-soft factorization in exclusive meson
production. To access the physics contained in GPDs, one is limited to the kinematic regime where the
hard-soft factorization theorem applies. There is no single criterion for the kinematic region of applicability,
but tests of necessary conditions can provide evidence that the factorization regime has been reached. One
of the most stringent tests is the Q2-dependence of the π,Kexclusive electroproduction cross sections, i.e.
σLscales to leading order as Q−6;σTdoes not, with the expectation of Q−8scaling; and σL≫σT. The
experimental validation of the onset of the hard scattering regime is essential for the reliable interpretation of
JLab GPD program results. One question that can be addressed is whether the onset of scaling is different for
kaons than pions. Furthermore, by studying both K+and π+, a quasi-model-independent study of hard-soft
factorization can be performed. Such a program is already underway with E12-09-011 [282] and E12-19-006
[283]. Electron beams up to 18 GeV with the HMS+SHMS nearly double the Q−nscaling test range of these
experiments, greatly reducing uncertainties and extending the range of these measurements over a wider x
range. A related issue is the study of hard-soft factorization in backward angle DEMP reactions, which can
60
Figure 43: Existing data (blue,
black, yellow, green) and projected
uncertainties for future data on the
pion form factor from JLab (Pio-
nLT: cyan; 22 GeV VHMS+SHMS:
red) and EIC (black), in compari-
son to a variety of hadronic struc-
ture models. JLab 22 GeV with an
upgraded VHMS will dramatically
improve the overlap between the Fπ
from true L/T-separations at JLab
and non-L/T-separated data from
the EIC.
be described in Sec. 6.3.5. An 18 GeV beam will enable a significant improvement in the Q−nscaling test
in these reactions as well.
A phase 2 set of measurements replaces the HMS with a new spectrometer we dub VHMS, to enable
measurements utilizing the full 22 GeV electron beam energy. For pion form factor measurements, the scat-
tered electron would be detected in the SHMS and the high-momentum, forward-going π+in the upgraded
VHMS. In this scenario, assuming similar p(e, e′π+)nstatistics to the recently completed PionLT experiment
[283], we project 22 GeV electron beam and an upgraded VHMS will extend the region of high quality F+π
values from Q2=6.0 GeV2(PionLT) to Q2=13.0 GeV2, and with somewhat larger errors to Q2=15 GeV2
(see Fig. 43. Here the error bars are calculated, but y-positions of the projected data are arbitrary. The
22 GeV upgrade will provide greatly improved overlap between the FπJLab and EIC datasets. As the
interpretation of some EIC data (e.g. GPD extraction from DEMP data) will depend on an extrapolation of
Hall C L/T-separated data, maximizing the overlap between the Hall C and EIC datasets are a high priority.
6.4.2 Nucleon Electromagnetic Form Factors at High Momentum Transfer
The elastic electromagnetic form factors of hadrons are among the simplest measurable quantities for probing
the spatial distributions and interactions of their elementary quark-gluon constituents. The precise polar-
ization transfer measurements of the proton form factor ratio µpGp
E/Gp
Mfrom JLab’s Halls A [284,285] and
C [286], that revealed the unexpected decrease of this ratio for momentum transfers Q2≳1 GeV2, are among
the best-known and most widely cited experimental results from JLab [287]. Measurements of hadron elastic
form factors at large momentum transfers Q2are sensitive to the interesting and theoretically challenging
region of transition in QCD between the non-perturbative regime of strong coupling and confinement and
the perturbative regime of weak coupling and asymptotic freedom [288,289].
The nucleon form factors are accessible experimentally through measurements of differential cross sec-
tions and double-polarization observables. A summary of the current state of knowledge of the nucleon
electromagnetic form factors can be found in Ref. [289]. A future energy upgrade of CEBAF would fa-
cilitate extending these measurements to Q2of at least 20-30 GeV2for the magnetic form factors, and at
least 15-20 GeV2for the electric form factors. Due to the approximate Q−12 dependence of the elastic
eN scattering cross section at large Q2, these measurements require very high luminosities that are only
achievable in fixed-target experiments, combined with large-acceptance detectors. Moreover, measurements
of polarization observables require not merely large Q2, but also virtual photon polarization ϵmeaningfully
different from one, as the transverse asymmetry/recoil polarization At=Ptthat is sensitive to the form
61
0 5 10 15 20 25 30 35 40
)
2
(GeV
2
Q
0
10
20
30
40
50
60
(deg)
e
θ
0 5 10 15 20 25 30 35 40
)
2
(GeV
2
Q
0
10
20
30
40
50
60
(deg)
p
θ
E = 14 GeV
E = 18 GeV
E = 22 GeV
0 5 10 15 20 25 30 35 40
)
2
(GeV
2
Q
0
2
4
6
8
10
12
14
16
18
20
22
(GeV)
e
E'
0 5 10 15 20 25 30 35 40
)
2
(GeV
2
Q
0
2
4
6
8
10
12
14
16
18
20
22
(GeV)
p
p
Figure 44: Fixed target elastic eN scattering kinematics for beam energies of 14, 18, and 22 GeV. From
top left to bottom right: Q2dependence of electron and proton scattering angles θe,θp, scattered electron
energy E′
e, and scattered proton momentum pp.
factor ratio vanishes in both the forward and backward-angle limits (ϵ= 1 and ϵ= 0), and is maximum at
ϵ= 0.5 for any given Q2.
Figure 44 shows the Q2dependence of the scattering angles and momenta of the outgoing particles in
two-body eN →eN scattering for beam energies of 14, 18, and 22 GeV, representative of different numbers
of passes through an upgraded CEBAF. In the range of 10-30 GeV2, the particle angles are well-matched
to the acceptances of existing or planned large-acceptance spectrometers such as CLAS12, SBS+BigBite,
and SoLID. The outgoing particle energies are rather high, which would pose some challenges in terms of
acceptance for precision focusing spectrometers such as those in Hall C, and would be challenging in terms
of momentum resolution for medium and large-acceptance spectrometers with moderate field integral, such
as SBS+BB and/or SoLID in Hall A and CLAS12 in Hall B. Nonetheless, the measurements appear feasible
over a wide range of Q2without requiring major new detector construction.
0 10 20 30 40
)
2
(GeV
2
Q
9−
10
7−
10
5−
10
3−
10
1−
10
10
3
10
)
2
(nb/GeV
2
/dQσd
proton
0 10 20 30 40
)
2
(GeV
2
Q
9−
10
7−
10
5−
10
3−
10
1−
10
10
3
10
)
2
(nb/GeV
2
/dQσd
E = 14 GeV
E = 18 GeV
E = 22 GeV
neutron
0 10 20 30 40 )
2
(GeV
2
Q
1−
10
10
3
10
5
10
7
10
9
10
11
10
2
/GeV
-1
counts/100 fb
proton
0 10 20 30 40 )
2
(GeV
2
Q
1−
10
10
3
10
5
10
7
10
9
10
11
10
2
/GeV
-1
counts/100 fb
E = 14 GeV
E = 18 GeV
E = 22 GeV
neutron
Figure 45: Left: Differential cross section dσ/dQ2for different beam energies for proton and neutron. Right:
Same as left, expressed in terms of an event rate per unit integrated luminosity per Q2interval (assuming
2πazimuthal angle acceptance).
62
Figure 45 shows the cross section dσ/dQ2for proton and neutron, expressed in nb/GeV2and in terms
of counts per 100 fb−1per GeV2. Note that the cross section differential in Q2is independent of the beam
energy at a given Q2(in contrast to the cross section differential in electron solid angle dσ/dΩe). The cross
section dσ/dQ2assumes 2πazimuthal acceptance. While the planned Electron-Ion Collider (EIC) at BNL
should be capable of measuring elastic ep cross sections to fairly large Q2values at ϵ≈1 [290], the EIC
operating at its design luminosity will produce ≈100 fb−1per year in the best-case scenario. In contrast, a
typical CEBAF fixed-target luminosity of ≈1038 cm−2s−1(liquid hydrogen/deuterium) produces ≈10,000
fb−1per day, allowing for precision measurements of cross sections and polarization observables over a wide
range of Q2and ϵ. As such, high-Q2elastic form factor measurements are a unique worldwide capability of
CEBAF, and will remain so even in the EIC era.
6.5 Bound Three-Quark Structure of Excited Nucleons and Emergence of Hadron
Mass
6.5.1 The Emergent Hadron Mass Paradigm
The Standard Model of Particle Physics has one well-known mass-generating mechanism for the most el-
ementary constituents of Nature, viz. the Higgs boson [291,292], which is critical to the evolution of the
Universe. Yet, alone, the Higgs is responsible for just 1% of the visible mass in the Universe. Visible mat-
ter is constituted from nuclei found on Earth and the mass of each such nucleus is largely the sum of the
masses of the nucleons they contain. However, only 9 MeV of a nucleon’s mass, mN= 940 MeV, is directly
generated by Higgs boson couplings into quantum chromodynamics (QCD). Evidently, as highlighted by
Fig. 46, Nature has another, very effective, mass-generating mechanism. Often called emergent hadron mass
(EHM) [208,293–295], it is responsible for 94% of mN, with the remaining 5% generated by constructive
interference between EHM and the Higgs boson. This makes studies of the structure of ground and excited
nucleon states in experiments with electromagnetic probes a most promising avenue to gain insight into the
strong interaction dynamics that underlie the emergence of the dominant part of the visible mass in the
Universe [112,208,296–298].
Figure 46: Proton mass budget, drawn us-
ing a Poincar´e-invariant decomposition: emer-
gent hadron mass (EHM) = 94%; Higgs boson
(HB) contribution = 1%; and EHM+HB inter-
ference = 5%. (Separation at renormalization
scale ζ= 2 GeV, calculated using information
from Refs. [22,299–301]).
These experiments are key to address still open questions in contemporary hadron physics. What is the
dynamical origin of EHM; what are its connections with gluon and quark confinement, themselves seemingly
characterized by a single nonperturbative mass scale; and are these phenomena linked or even the underlying
cause of dynamical chiral symmetry breaking (DCSB)? DCSB has long been argued to provide the key to
understanding the pion, Nature’s most fundamental Nambu-Goldstone boson, with its unusually low mass
and structural peculiarities [302,303].
After the pioneering work of Schwinger in the early sixties studying nonperturbative gauge-sector dynam-
ics in Poincar´e-invariant quantum field theories [304–306], treatments of QCD using continuum Schwinger
function methods (CSMs) have delivered self-consistent calculations of the base ingredients capable of ex-
plaining EHM. The results are drawn in Fig. 47 and demonstrate that a Schwinger mechanism is active
in QCD [293,294]. The gluon vacuum polarization tensor remains four-transverse. Owing to the gluon
63
Figure 47: Momentum-dependent dressed quark and gluon masses (left) [307] and the QCD running coupling
(right) [112] deduced using CSMs from the QCD Lagrangian as a solution of the equations of motion
for the quark and gluon fields. On the left the ranges of momenta accessible for mapping the dressed
quark mass function from the results on the evolution of the γvpN∗electrocouplings with Q2from the
measurements of the 6-GeV/12-GeV eras with the CLAS/CLAS12 detectors are shown, as well as the
corresponding momentum range that will be accessible after an increase of the CEBAF energy up to 22 GeV
from the anticipated results on the γvpN∗electrocouplings at Q2from 10-30 GeV2from the measurements
with the CLAS22 detector.
self-interactions encoded in the QCD Lagrangian, the three four-transverse modes of the gluon acquire
a momentum-dependent mass. Existence of a gluon mass-scale enables the definition and calculation of
a unique QCD analog of the Gell-Mann-Low effective charge, well-known from quantum electrodynamics
(QED). This charge saturates on the infrared domain and is practically identical to the process-dependent
charge extracted in experimental studies of the Bjorken sum rule [112], as shown in the right part in Fig. 47.
The massive gluon propagator and effective charge are the principal elements in the quark gap equation
and, together, they ensure that light (even massless) quarks acquire a running mass, Mq(k), whose value at
infrared momenta matches that which is typically identified with a constituent quark mass [307, Sec. 2C].
The QCD running coupling and the momentum-dependent dressed quark and gluon masses constitute the
three pillars of EHM, about which more will be explained below. Contemporary theory is now engaged in
elucidating the huge array of their observable consequences and paths to measuring them. The challenge for
experiment is to test the predictions so that the boundaries of the Standard Model can finally be drawn.
Testing these predictions requires a paradigm shift going beyond the studies of the only stable ground state
of hadron, i.e., the proton. Just as studying the ground state of the hydrogen atom did not reveal the need
for and intricacies of QED, focusing on the ground state of only one form of hadron matter will not elucidate
the full complexity of the strong interaction dynamics in the regime where the QCD running coupling αs/π
is comparable with unity, referred to as the strong QCD (sQCD) regime. A new era is dawning, with
science poised to construct and begin operating high-luminosity, high-energy, and large acceptance facilities
that will enable precision studies of new types and excited states of hadron matter. For instance, one may
anticipate a wealth of highly precise data that will reveal the inner workings of Nature’s most fundamental
Nambu-Goldstone bosons, the πand Kmesons [302,303], and if the future is planned well, critical empirical
information on the structure of nucleon excited states (N∗s) will be extended over the full range of distances
where the dominant part of their masses and structure are anticipated to emerge from QCD [208].
6.5.2 Experimentally Driven Studies on N∗Structure, Emergent Hadron Mass, and Strong
QCD
During the last decade, crucial progress has been achieved in the exploration of the N∗electroexcitation
amplitudes, the so-called γvpN∗electrocouplings, stimulating research efforts with an emphasis on how the
64
Figure 48: Results for the p→∆(1232)3/2+magnetic transition form factor (left) and the N(1440)1/2+
A1/2(Q2) electrocoupling (middle) [327–329] from studies of πN and π+π−pelectroproduction in measure-
ments of the JLab 6-GeV era. CSM predictions with the running dressed quark mass deduced from the
QCD Lagrangian, see Fig. 47 (left), are shown as blue solid lines [298,330] and by employing a simplified
contact qq-interaction resulting in a momentum-independent (frozen) quark mass of ≈0.36 GeV as red
dotted lines [331]. Comparisons between the CSM prediction (solid line) on the A1/2(Q2) ∆(1600)3/2+
electrocoupling [318] and preliminary results from the studies of π+π−pelectroproduction with CLAS are
shown on the right. The data points with error bars have become available from independent analyses of the
cross sections in overlapping W-intervals with substantial contributions from the ∆(1600)3/2+as labeled
for Q2from 2 to 5 GeV2.
masses and properties of N∗states emerge from QCD [208,295–298]. High-quality meson electroproduction
data of the 6-GeV era at Jefferson Lab (JLab) from the CLAS detector have enabled reliable extraction of
the electrocouplings of the most prominent N∗s in the mass range up to 1.8 GeV. The data for different
N∗states expresses many facets of the strong interaction that generate N∗structure and mass in the Q2
range up to 5 GeV2[208,296–298]. This places heavy pressure on theory to deliver interpretations and
explanations.
Synergistically engaging with the JLab experimental program, a diverse collection of theoretical models
and methods have been employed in attempts to address the questions raised by the data and connect them
with QCD [298,308,309]. In the past decade, notable successes have been achieved using CSMs [310], which
have delivered numerous predictions for hadron structure observables in the meson and baryon sectors, both
for ground and excited states [295–298,311–322].
CSM analyses are characterized by the use of dressed (quasiparticle) quarks and gluons as active degrees
of freedom with momentum- and, hence, distance-dependent masses. The framework’s predictions for these
momentum-dependent mass functions (see Fig. 47 left) have been confirmed in numerical simulations of
lattice-regularized QCD [323–326]. They have also been used to define and calculate the momentum evolution
of the QCD analog of the Gell-Mann-Low running coupling in QCD [112] (see Fig. 47 right). These three
pillars of the CSM paradigm for explaining EHM – momentum dependence of the dressed quark and gluon
mass functions and the QCD running coupling – have become available from the solution of the QCD
equations of motion for the quark and gluon fields with the results shown in Fig. 47 [293–295]. The observed
ground state nucleon and N∗masses emerge mostly from the running masses of the three dressed quarks
that approach the hadron mass scale in the infrared at quark momenta k < 0.5 GeV. Consequently, the
electromagnetic elastic nucleon form factors and γvpN∗electrocouplings exhibit particular sensitivity to the
emergent part of hadron mass. Dressed gluons acquire running masses owing to the gluon self-interaction
encoded in the QCD Lagrangian [293,294]. At the distances/quark momenta where the transition from the
perturbative QCD (pQCD) to sQCD regimes is anticipated and as the QCD running coupling αs/π becomes
comparable with unity, the energy stored in the gluon field is absorbed into the running mass of the dressed
quark. A particular strength of CSMs is their ability to simultaneously treat and unify the physics of mesons
and baryons.
65
Acquiring insight into the dressed quark mass function from data on hadron structure represents a
challenge for experimental hadron physics. The amplitude of the virtual photon interaction with a dressed
quark in the process of N∗electroexcitation is sensitive to the dressed quark mass, making it possible
to map out the momentum dependence of the dressed quark mass from the results on the evolution of
the γvpN∗electrocouplings with Q2. Analyses of the JLab 6-GeV era results on the N∗electroexcitation
amplitudes have vastly improved our understanding of the momentum dependence of the dressed quark
mass function, while the running gluon mass and QCD running coupling are constrained by the results
on N∗electroexcitation [208,297,298,329]. A good description of the ∆(1232)3/2+and N(1440)1/2+
electrocouplings at Q2<5 GeV2for these resonances of different structure (see Fig. 48, left and middle),
achieved using CSMs with the same dressed quark mass function deduced from the QCD Lagrangian and
employed elsewhere in the successful description of experimental results on nucleon electroweak elastic and
transition form factors [332,333], offers sound evidence for providing insight into the momentum dependence
of the dressed quark mass. This link is strengthened by the fact that such a mass function is also a key
element in the prediction of meson electromagnetic elastic and transition form factors [311,334].
The CSM predictions made in 2019 [318] on the Q2-evolution of the ∆(1600)3/2+electrocouplings,
achieved without modifying or introducing any new parameters, were confirmed in 2022 by the preliminary
results from analysis of π+π−pelectroproduction measured with the CLAS detector (see Fig. 48 right). This
success solidifies evidence for understanding the dressed quark mass function and, consequently, EHM from
studies of the γvpN∗electrocouplings.
Most results on the γvpN∗electrocouplings from the JLab experiments of the 6-GeV era are available for
Q2<5 GeV2, allowing for the exploration of the momentum dependence of the dressed quark mass within
the range of quark momentum k < 0.75 GeV, where <30% of hadron mass is anticipated to be generated (see
Fig. 47 left). CLAS12 is the only facility capable of extending these results on the γvpN ∗electrocouplings
into the unexplored Q2range from 5 to 10 GeV2based on measurements of πN,π+π−p,KΛ, and KΣ
electroproduction [208,297], spanning the domain of quark momenta up to 1.1 GeV where ≈50% of hadron
mass is generated (see Fig. 47 left).
The already available results on the γvpN∗electrocouplings from CLAS and those foreseen from the
extension with CLAS12 will offer the information needed to facilitate the development of approaches for
the description of the structure of bound three-quark baryons based on quantities computed from the QCD
Lagrangian. These approaches will ultimately be capable of making predictions for ground state nucleon
structure observables and γvpN∗electrocouplings for Q2<10 GeV2, as was discussed at the JLab Workshop
“Strong QCD from Hadron Structure Experiments” held in 2019 [297].
Ultimately, pushing the momentum transfer squared to N∗s up to 30 GeV2will extend the coverage of
quark momenta over the domain where ≈90% of hadron mass emerges (see Fig. 47 left). At the Q2limit of
this domain, where the QCD running coupling becomes smaller, direct comparisons between nonperturbative
and perturbative QCD concepts on how hadron structure emerges from QCD can be attempted. To resolve
the challenging problem of understanding the underpinnings of EHM, Mq(k) will be mapped out over the
entire range of quark momenta from zero up to ≈2 GeV. As one progresses through this momentum scale, the
transition from strongly coupled to perturbative QCD takes place and the dressed quarks and gluons, which
emerge on the domain for which αs/π →1 (see Fig. 47), begin to reveal their inner parton-like origin. This
unique endeavor, probing QCD through detailed studies of bound three-quark states, is fully complementary
with, e.g., hard scattering off single quarks, as in deep inelastic scattering, as well as studies of pseudoscalar
and hybrid mesons, and paves the way for further extensions of the exploration of N∗structure in three
dimensions [256].
Simulations of πN,π+π−p,KΛ, and KΣ electroproduction channels with an increased CEBAF beam
energy of 22 GeV show that the γvpN∗electrocouplings can indeed be extracted up to Q2≈30 GeV2
utilizing the large acceptance CLAS12 spectrometer at luminosities L ≈ 2-5×1035 cm−2s−1(a configuration
referred to as CLAS22) as exemplified in Fig. 49 (right). A comparison of the parameters for the available and
anticipated facilities for studies of hadron structure with electromagnetic probes in this regime (see Fig. 49
left) demonstrates that, after the CEBAF energy increase, CLAS22 would be the only facility capable of
delivering results on the γvpN∗electrocouplings for Q2up to 30 GeV2. A representative example for the
66
Figure 49: (Left) Luminosity versus invariant mass coverage of the available and foreseen facilities to explore
hadron structure in experiments with electromagnetic probes. CLAS22 would be the only facility with
sufficient luminosity to determine the γvpN∗electrocouplings at Q2from 10-30 GeV2that can map out the
dressed quark mass function within the range of quark momenta k < 2 GeV where the dominant part of
hadron mass and the bound three-quark structure of N∗s emerge from QCD. (Right) Available results at
Q2up to 5 GeV2and those projected for the Q2evolution of the N(1440)1/2+A1/2electrocoupling for Q2
up to 30 GeV2for a luminosity of 5 ×1035 cm−2s−1and six months of data collection time.
anticipated accuracy in the resonance electrocoupling extraction is shown in Fig. 49 (right) for the A1/2
electrocoupling of the N(1440)1/2+.
Baryons are the most fundamental three-body systems in Nature. If we do not understand how QCD –
a Poincar´e-invariant quantum field theory – generates these bound states, then our understanding of Nature
is incomplete. Moreover, EHM is not immutable: its manifestations are manifold and growing experience is
revealing that each hadron manifests different facets. One piece – the proton – does not complete a puzzle.
Completing the QCD picture requires far more, and precise data relating to the structure of nucleon excited
states will add essential pieces. Extending the results on the γvpN ∗electrocouplings into the Q2range up to
30 GeV2, after the increase of the CEBAF energy and pushing the CLAS12 detector capabilities to measure
exclusive electroproduction to the highest possible luminosity, will offer the only foreseen opportunity to
explore how the dominant part of hadron mass and the bound three-quark structure of N∗s emerge from
QCD. These things will make CEBAF at 22 GeV a unique QCD-facility at the luminosity frontier.
67
7 Hadron–Quark Transition and Nuclear Dynamics at Extreme Con-
ditions
7.1 Theoretical Overview
One of the outstanding issues of the strong interactions physics is understanding the dynamics of the tran-
sition between hadronic and partonic (quarks and gluons) phases of matter. At high temperatures, such
transitions are relevant to the evolution of matter after the Big Bang, which have been studied experimen-
tally in heavy ion collisions. At low (near zero) temperatures and high densities (“cold dense” states), such
transitions are relevant to understanding the stability of atomic nuclei as well as dynamics of cold dense
nuclear matter that exists at the core of neutron stars and defines the limiting density for structured matter.
Two main directions of exploring “cold dense” transitions are associated with probing the dynamics
of nuclear forces at short space-time separation in nuclei (referred to hereafter as “nuclear dynamics at
extreme conditions”), and investigating nuclear medium modifications of hadronic structure for both bound
nucleons and hadrons produced in nuclear medium (referred to hereafter as “hadron-quark transition” in
nuclear medium). Overall, the research program of 22 GeV energy upgrade will be aimed at discovering the
fundamental QCD basis of short-range nuclear physics phenomena.
7.1.1 Nuclear Dynamics at Extreme Conditions
Last two decades have seen a significant progress in our understanding of the nuclear structure at short dis-
tances down to internucleon separations of ∼0.8 fm. JLab experiments at 6 GeV [335,336] and 12 GeV [337]
energies have confirmed early predictions [338] of the onset of scaling in ratios of inclusive cross sections at
large Q2and xindicating the dominance of two-nucleon short-range correlations (2N SRCs) in bound nu-
cleon momentum range of 300 −650 MeV. Several significant advances have been made in studies of 2N
SRCs affirming that (i) the latter consists of nucleonic components only [339]; (ii) the factor of 20 dominance
of proton-neutron components to that of proton-proton and neutron-neutron components [340–342], which
is due to the dominance of tensor interactions [343,344] as an indication of probing 2N SRCs at distances
as small as 0.8 fm; (iii) the prediction of momentum sharing rule [345] according to which the minority
component in asymmetric nuclei per nucleon has a larger share of high momentum component in the nuclear
ground state wave function - the effect that was confirmed experimentally at JLab [346,347].
The future of exploring the short-distance structure of nuclei is to reach the distances dominated by
practically unknown dynamics of nuclear core. The latter is one of the most fascinating subjects of the modern
Figure 50: Internucleon force reach at 22 GeV (at dis-
tances ≥1.2 fm, NN potentials contribute to the mean field
Hartree-Fock potentials, resulting in nuclear shell struc-
ture).
nuclear physics. Its existence is essential for
the stability of atomic nuclei [348] and thus
the stability of the structure in the universe.
Yet, it is very little known about dynamical
origin of nucleon-nucleon (NN ) repulsive core.
The modern phenomenological N N potentials
use the Wood-Saxon type ansatz of 1960s (see
e.g. Ref. [349]), while in effective theories the
short-range interaction is parameterized by
contact terms (see e.g. Ref. [350]). QCD gives
new perspective to dynamical origin of the
nuclear core predicting possibility of sizable
contribution from non-nucleonic components
including the hidden color [351–354]. Hid-
den color states in nuclear wave functions fol-
low from being restricted only by six-quark
color singlets in the two-baryon systems at
very short (≤0.5 fm) distances. Current con-
68
straints on such a six-quark admixture is less than few percent in overall normalization of nuclear ground state
wave function and their exploration is essential for understanding the hadron-quark transition in super-dense
nuclear matter.
Since the expected excitation energies relevant to nuclear core are in the order of several GeV (see Fig. 50),
it will require probing substantially large internal momenta in the nucleus (≳1 GeV) to be able to probe
the NN core. The repulsive nature of the interaction also indicates that the measured cross section in many
cases will be very small.
As it will be discussed in the next paragraphs, the upgraded energy and high intensity electron beam
will provide unprecedented conditions for probing very large internal momenta in nuclei. Discovering the
fundamental QCD basis for short-range nuclear physics phenomena is a primary goal for the 22 GeV energy
upgrade. This contribution builds upon two discovery proposals covered in Subsubsecs. 7.2.1 and 7.3.1 about
probing superfast quarks and bound nucleon structure with tagged deep-inelastic scattering (TDIS). Hidden
color states in nuclear wave functions and a quark-gluon basis for the European Muon Collaboration (EMC)
effect and SRCs in nuclei are examples of accessible fundamental QCD physics for JLab22. As mentioned
in the Subsubsec. 7.2.1, JLab22 probes of quark-gluon degrees of freedom in N N interactions are described
with an emphasis on the six-quark color singlets of two-nucleon system. Hidden color singlets, in contrast
to the multiple color singlet nucleons that dominate the nuclear wave function, have been suggested as a
solution to the EMC effect in A > 3 nuclei [355]. Such fundamental QCD states can be built with diquark
constituents, and a diquark bond formed with valence quarks from two different nucleons has been proposed
as the cause of SRCs in nuclei [356].
Probing Superfast Quarks in Nuclei. It is known that isolating DIS processes in nuclei at Bjorken
scaling variable x > 1 is associated with probing a bound nucleon at very large internal momenta [357–360],
which can originate from two or more nucleons being at very close proximity. For the case of deuteron
target, it corresponds to measuring preexisting state with baryonic number two that has very large internal
momenta, which could be related to very small separations. In Fig. 51 left, the kinematics of nuclear DIS is
considered responsible for producing final state mass W= 2 GeV from the bound nucleon in the deuteron.
As depicted in Fig. 51 left, the combination of high Q2and x > 1 will allow reaching internal momenta
never before measured. DIS processes in this case will proceed from scattering off nuclear quarks that carry
more momentum fraction than quarks from isolated stationary nucleons - these quarks are refereed to as
“superfast quarks” [357]. As it will be shown in Subsubsec. 7.2.1, the generation of superfast quarks in
nuclear medium is very sensitive to the dynamical origin of the nuclear core. The experimental exploration
of superfast quarks started already at 6 GeV energies [361] at JLab and currently is underway with 12 GeV
beam energies [362]. At current energies, however, inclusive cross section at x > 1 is dominated by quasielastic
(QE) scattering which has to be taken into account to evaluate the pure DIS contribution. The 22 GeV JLab
energy upgrade will allow a significant increase of the momentum transfer squared Q2at x > 1 in which case
it will allow to suppress the QE contribution (see Fig. 51 right) providing a direct access to DIS processes
in the nucleus with x > 1.
Deuteron Structure at Sub-Fermi Distances. Another rather direct way of accessing NN interactions
at core distances is to probe deuteron electrodisintegration at Q2≥4 GeV2and at very large missing
momenta, approximately above 800 MeV, for wide angular range of recoil nucleon production. In this case,
the lower limit of Q2is defined from the condition that one can clearly distinguish between struck and
recoil nucleons originating from the deuteron. For these reactions, the existence of angular anisotropy in
light-front momentum distribution will indicate the existence of non-nucleonic component in the core of the
NN interaction. The first attempt of measuring such a large internal momenta has already resulted in an
unexpected momentum distribution [363]. The increase of scattered electron energy will allow performing
systematic studies of these processes with realistic counting rates. The further extension of this program will
include the SIDIS processes tagged by baryonic resonances. The upgraded energy will significantly increase
the phase space of backward production kinematics allowing access to the preexisting non-nucleonic states
in the deuteron that produce baryonic resonances in backward kinematics.
69
1.0 1.2 1.4 1.6 1.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
x
|pz|, GeV /
c
Q2=10GeV2
15
20
30
40
Figure 51: Left: Absolute value of internal longitudinal momenta for DIS from bound nucleon with produced
final mass of W= 2 GeV at different Q2. Right: Ratio of quasielastic to DIS contribution of the nuclear
structure function F2for x= 1.5 and different Q2. No EMC effects are taken into account in this estimation.
Probing Three-Nucleon Short-Range Correlations and 3N Forces. One of the groundbreaking
results in nuclear physics with the upgraded 22 GeV energy will be the direct proof of the existence of
short-range three-nucleon (3N) SRCs in the ground state of the nuclear wave function. One of such results
could be the observation of another scaling (similar to 2N SRCs [335–338]) in the ratios of inclusive cross
sections for A > 3 and A= 3 nuclei in the domain of 3N SRCs. As discussed in Subsubsec. 7.2.3, the analysis
of existing inclusive data indicates a tantalizing signature for such a scaling [364,365].
Finally, the program of exploring nuclear forces at extreme kinematics includes the systematic study of
3N forces, irreducible to the sequence of NN interactions. Three-nucleon forces are essential in the dynamics
of high-density nuclear matter, which have predicted the existence of supermassive neutron stars (exceeding
two solar masses) that was observed in recent years. However, the dynamical origin of these forces are poorly
known. The energy upgrade will allow a systematic study of 3N forces by including both electrodisintegration
of A= 3 nuclei and probing 3N SRCs in high Q2reactions off nuclei.
7.1.2 Hadron-Quark Transition
Nuclear medium represents a unique environment to explore the QCD dynamics of hadron-quark transition.
Several phenomena are related to this transition including the ones associated with medium modifications of
quark-gluon substructure of bound nucleons. Such a modification was discovered rather accidentally for the
valence quark structure of bound nucleons by the European Muon Collaboration while studying inclusive DIS
from nuclei. It was observed that the valence parton distribution functions (PDFs) of bound nucleons are
depleted in the region of 0.3<x<0.6 beyond the level expected from the Fermi motion of bound nucleons
in nuclei. Follow up experiments have demonstrated an opposite phenomenon in which the enhancement
was observed for bound nucleon PDFs in the region of x∼0.1, the so-called antishadowing region, on the
scale of 2% for inclusive DIS. The latter has indicated possible different dynamics for medium modifications
of valence and sea quarks, including gluons, distributions.
The energy upgrade will allow systematic studies of medium modification effects both in the region of
PDFs suppression as well as antishadowing region. Such a program can be realized by mapping significantly
larger Q2and wider xkinematic ranges as well as considering semi-inclusive tagged DIS processes.
The second group of studies relevant to hadron-quark transitions is aimed at understanding the hadroniza-
tion process by considering the production of hadrons in nuclear medium. For the quasielastic channel, such
studies include experiments that probe possible color transparency (CT) phenomena while for inelastic kine-
matics, they study effects of confinement and dynamics of quark-hadron transition in the process of producing
final hadronic states.
70
Nuclear Medium Modifications (EMC Effect). Basic models of nuclear physics describe the nucleus
as a collection of unmodified nucleons moving non-relativistically under the influence of two- and three-
nucleon forces, treated approximately as a mean field. In such a picture, considering very different scale of
nuclear (tens of MeV) and baryon (hundreds of MeV) excitation energies, the partonic structure functions of
bound and free nucleons should be identical. Therefore, it was generally expected that, except for nucleon
motion effects, DIS experiments would give the same result for all nuclei.
Instead, the DIS measurements from nuclear targets [366] have observed in the valence quark region a
reduction of the structure function of nucleons bound in heavier nuclei compared to deuterium, beyond what
is expected from simple Fermi motion effects in models in which baryonic and momentum sum rules are
satisfied (the effect generally referred to as the EMC effect). Since its initial discovery, a large experimental
and theoretical efforts have been put into understanding its origin. The followup experimental advances
include the observation of the local nuclear density dependence of the EMC effects [367], as well as the
important role of SRCs in enhancing the strength of the EMC effect for A≥4 nuclei [368,369]. Currently,
there is no generally accepted theoretical interpretation of the observed EMC effects.
In general, the question of understanding the EMC effect in the valence quark domain is coupled to
understanding the very nature of confinement. The parton model interpretation of the EMC effects is that
the medium reduces the nuclear structure functions for large xvalues so that there are fewer high-momentum
quarks in a nucleus than in free space. This momentum reduction leads, via the uncertainty principle, to the
notion that quarks in nuclei are confined in a larger volume than that of a free nucleon.
Overall, the medium modification in the valence quark region is expected to be proportional to the
virtuality of bound nucleon. For example, a recent work uses the idea of holographic duality [370] to motivate
functional forms of free and medium-modified quark distribution functions [371]. This work finds that large
values of the virtuality are needed to explain the nuclear DIS data. The nuclear presence of such large values
can be be tested using the expanded tagging techniques that would be available at JLab22.
turn to the role of pionic effects on
!
Lfor nuclear and
nucleon targets. The pionic contribution to the hadronic ten-
sor is given by
"
#
W
$
%
!1
4
#
MA
!
d4
&
eiq•
&
'
P
"
J
#
$
(
&
)J
#
%
(0)
"
P
*
,(3)
where
"
P
*
represents the nucleon or nuclear target ground
state of total momentum P, and the momentum of the virtual
photon is q!(
%
,0
!,"
!
%
2#Q2). The current operator
which accounts for the effects arising from the nuclear pions
is J
#
$
(
&
):
J
#
$
!i(
+
*
,
$
+
"
+
,
$
+
*),(4)
with
+
as the complex pion field operator. The effects of the
pion charge form factor F
#
(Q2) are included below.
We are concerned with
!
L, and use the standard general
formula -27,28.
!
L!Q24
#
2
/
(Q2#
%
2)3/2 W00.(5)
We now evaluate
"
#
W00 by using J
#
0in Eq. (3). Then insert
a set of states which asymptotically contain a nucleus and a
free pion of momentum p
$
. The sum over nuclear states can
be performed using closure if one uses light front variables
(q$!q0$q3) to describe the momentum of the photon and
of the nuclear pion (k
!,k#). For large enough values of
%
the interactions of the struck pion with the residual nucleus
may be ignored, the energy of the outgoing pion may be
taken as
%
, and the effects of nonzero values of nuclear ex-
citations energies (proportional to q#/q") appearing in the
energy-momentum conserving delta function inherent in Eq.
(3)may be ignored. Then the result of a straightforward
evaluation leads to the result -29– 31.
"
#
W00(N,A)!
%
2
2Q2
2
3
f
#
/(N,A)(
&
)
MN
F
#
2(Q2),(6)
where F
#
(Q2) is taken as a monopole form consistent with
the observed mean square radius, and the factor of 2/3 ac-
counts for the fact that only charged pions enter in electron
scattering (with N!Z). Note that energy momentum conser-
vation gives the relation k#!MN
&
!Q2/q", and
&
is the
Nachtmann variable.
The pionic contribution to the longitudinal cross section
for a proton (p!N) target,
!
L
#
(p), is obtained from Eqs. (5)
and (6), and is displayed in Fig. 3. Cross sections of this size
are routinely observable. The decrease with increase of Q2is
caused by the pion form factor. The value of
!
L
#
(p) for x
!0.2, Q2!0.7 GeV2corresponds to a contribution to R
of the proton of about 0.04, small enough to avoid any con-
tradiction with existing data.
We now turn to the case of nuclear targets. The standard
general formula (5)allows us to relate
"
#
W00 to the corre-
sponding contribution (per nucleon)
"
#
!
Lto the longitudinal
cross section, so that the nuclear longitudinal cross section
(per nucleon)is given by
!
L(A)!
!
L(D)#
"
#
!
L. It is de-
sirable to present a ratio
!
L(A)/
!
L(D), or equivalently
!
L(A)/
!
T(D)RD, which allows the use of parametrizations
for F2(D) and R(D) . Thus we obtain the result
!
L(A)
!
L(D)!1#Q4
(Q2#
%
2)
%
"
#
W00
AF2
DRD
(1#RD),(7)
which may be evaluated using Eq. (6)to be
!
L(A)
!
L(D)!1#x2
3f
#
(
&
)
%
2
(Q2#
%
2)
F
#
2(Q2)
F2
DRD
(1#RD),(8)
where as usual x!Q2/2MN
%
. Note that only the pionic ef-
fects are included here. The effects of nuclear vector and
scalar mesons, so important in understanding the HERMES
FIG. 3. Pionic contribution to the photon longitudinal cross sec-
tion on the proton, as a function of Q2and x.
FIG. 4. Enhancement of longitudinal cross sections, as a func-
tion of Q2and x.
RAPID COMMUNICATIONS
REVEALING NUCLEAR PIONS USING ELECTRON SCATTERING PHYSICAL REVIEW C 64 022201(R)
022201-3
2
A
σA
L
σD
L−1
x
Figure 52: Enhancement of longitudinal
cross sections as a function of Q2and
x=Q2/2MNν, where MNis the nucleon
mass and νis the virtual photon energy.
The above discussion has been concerned with the valence
regime of large x(≥0.3). At smaller xvalues, the phenomena of
shadowing and antishadowing are present. The comprehensive re-
view of Ref. [372] shows that restricted amount of data is available
for the antishadowing region and only simple expressions based on
baryonic sum rules describe qualitatively the data. Widening the
Q2coverage as well as extending it to SIDIS processes will set a
new stage in comprehensive investigations of dynamical origin of
antishadowing.
An important extension of medium modification studies are
the exploration of the behavior of sea quarks and gluons in the
nuclear medium. One possible method for studies of sea quark
modifications that will allow to isolate pionic degrees of freedom
is to use longitudinal/transverse (L/T) separation in DIS pro-
cesses. It was shown in Ref. [373] that pionic effects with a sea
small enough to be consistent with measured nuclear dimuon pro-
duction data [374] could be large enough to predict substantial nuclear enhancement of the cross section for
longitudinally polarized virtual photons for the kinematics accessible at JLab22. Predictions are shown in
Fig. 52.
In regards to possible medium modifications of sea quarks, the analysis of the SeaQuest Collaboration [98]
data, which studied the Drell-Yan process off nuclei, suggests the presence of an EMC-like modification of
nuclear PDFs [375]. Also, the forward dijet production data in pA collisions at the Large Hadron Collider
are consistent with the models which assume gluon PDFs modifications analogous EMC effects [376]. At
22 GeV beam energy, the one unique feature of high-intensity beam will be the possibility to study gluon
modification at large x(≥0.5). This can be achieved by considering open charm production channels such
as γ+N→Λc+D+Xat W2>(MΛ+Md+MN)2and J/ψ production in γ+N→J/ψ +Xreactions.
71
To this end, larger energies of JLab22 would allow to perform a detailed analysis of the EMC ratio for a
broad range of x, including the ranges in which the EMC ratio is not a linear function of x. Additionally, it
would extend the experience gained in current pioneering experiments exploring EMC effects in tagged DIS
processes to the high energy domain and thus emphasize their important signature for such an investigation.
Color Transparency Phenomena. CT is a fundamental prediction of QCD stating that one can observe
reduced initial or/and final state interactions (FSIs) in coherent production of hadrons in the nuclear medium
at high-momentum transfer [377]. The basic idea follows from just two points: 1) high-momentum transfer
reactions may make point-like color singlet states known as point-like configurations (PLC)1; 2) small color
neutral objects have small cross sections for strong interactions. CT experiments need to have well controlled
kinematics, such as the QE knockout of protons from nuclei.
CT effects have been observed [378] in the 500 GeV reaction of π+A→A+jj, where the notation jj
refers to two jets at high relative momenta. Tantalizing indications of the onset of CT have been reported
at JLab energies in the A(e, e′)π+[379] and A(e, e′)ρ[380,381] reactions. The putative signature is a rise
of the nuclear transparency (defined as a ratio of a measured cross section to a cross section expected in
the absence of final state interactions) with increasing values of Q2that is proportional to p. However, the
present range is not quite large enough to provide an utterly convincing evidence for CT effects. Higher
energy measurements would add a great value.
The lingering concern for the baryonic sector is that the observation of CT effects is as elusive as ever.
The results of the recent JLab experiment [382] probing CT effects in the QE 12C(e, e′p) reaction up to
Q2of 14 GeV2have claimed no reduction of FSIs which essentially suggests a flat dependence of nuclear
transparency with increasing Q2. There are two possible explanations of this observation: i) it is very difficult
to form PLC in color single three-quark systems that require significantly large Q2, and/or ii) the expansion
of the three-quark PLC is so fast and thus it quickly hadronizes before escaping the nucleus.
The above two scenarios can be cross-checked and verified at JLab22 for CT studies with baryon produc-
tion by either increasing the Q2and thus slowing down the QCD expansion [383], or employing a comple-
mentary logic in which case one measures only events that are products of a struck nucleon rescattering off
the spectator nucleon in the nucleus on the so-called double-scattering processes [384–386]. The uniqueness
in searching for CT effects in these processes is that one can use lightest nuclei such as deuteron and reach
considerable sensitivity to possible modifications of the cross section of PLC interactions with the spectator
nucleon and thus keeping expansion effects essentially under control (see Subsubsec. 7.3.5).
Hadronization in Nuclei. The confinement of quarks inside hadrons is conceivably one of the most
remarkable feature of QCD. The quest to quantitatively understand the confinement dynamics in terms
of experimentally measured quantities is an essential goal of modern nuclear physics. Much experimental
attention has been focused on understanding confinement through hadron spectroscopy. Alternatively, the
subject is often introduced through the string-breaking mechanism. This picture is confirmed by lattice
calculations using static quarks depicting the gluon field concentrated in a flux-tube (or string) [387,388],
which extends over a space-time region. The string has a “tension” κof a magnitude in the order of 1 GeV/fm
that is predicted by the Lund string model to be the rate of the propagating quark’s energy loss in the
analyzing nuclei [389,390].
Due to the great success of DIS studies in probing the internal structure of the nucleon since early 1970s
at SLAC [391], DIS off nuclei has been considered the pioneering process in investigating quark propagation,
hadron formation, and medium modifications of observable characterizing these transitions [54,391–393].
The description of the hadronization process is denoted then by two space-time scales categorizing its two
stages. In the first stage following the virtual photon hard scattering, the struck quark propagates in the
target nucleus, during the production time (τp), and undergoes medium-stimulated gluon bremsstrahlung
prior to becoming a color-neutral object, known as prehadron. The latter evolves in the second stage into a
fully dressed hadron with its own gluonic field within the formation time (τf). The hadronization studies are
1In the literature, they are also called small size configurations (SSC), and both terms are used interchangeably.
72
thus performed to provide information on the dynamics scales of the process, and to constrain the existing
models with various predictions of its time characteristics either in vacuum or in nuclei [389,394–398].
The fundamental focus of the broad JLab program of 6 GeV and 12 GeV era, which is extended here
to 22 GeV (see Subsubsec. 7.3.6), is to determine the mechanisms of confinement in forming hadrons.
The essential experimental technique that enables these studies is to employ nuclei as space analyzers of
hadronization processes. In this approach, hadrons are formed from energetic quarks over distance scales
ranging from 0-10 fm, which are perfectly matching the dimensions of atomic nuclei. For example, a recent
simple geometrical model has found a strong dependence behavior on observed hadron energy fraction, z, for
the partonic phase, ranging from 2 fm at high zto 8 fm at smaller zfor HERMES data [398], in quantitative
agreement with existing predictions of the Lund string model [389,390].
7.1.3 Summary of Flagship Experiments at 22 GeV
The list of flagship experiments are chosen based on the current progress of nuclear physics and nuclear
QCD studies at JLab and elsewhere, emphasizing the kinematic reach that 22 GeV energy will achieve. The
uniqueness of the suggested upgrade is that, in addition to the increased energy, the high intensity of the
beam will allow to perform measurements of increasingly small cross sections with unprecedented accuracy.
Additionally, many impeding effects that currently need to be accounted or subtracted theoretically become
corrections and thus grant access to unique phenomena relevant to nuclear structure at small distances and
hadronization effects.
For nuclear dynamics at extreme conditions, the experiments highlighting the study of superfast quarks in
nuclei, repulsive core in the deuteron, and 3N SRCs in nuclei are discussed, respectively, in Subsubsecs. 7.2.1,
7.2.2, and 7.2.3. While the highlighted experiments for hadron-quark transition in nuclear medium are i)
probing bound nucleon and partonic structures via tagged processes (see Subsubsecs. 7.3.1 and 7.3.2); ii)
investigating unpolarized and polarized EMC effects as well as antishadowing and shadowing regions (see
Subsubsecs. 7.3.3 and 7.3.4); iii) CT studies (see Subsubsec. 7.3.5); iv) hadronization studies in nuclei (see
Subsubsec. 7.3.6), and v) coherent nuclear J/Ψ photoproduction (see Subsubsec. 7.3.7).
All aforementioned experiments have established research groups who will perform similar measurements
at 12 GeV. The progress achieved in conducting these experiments at 12 GeV will be significant for further
refining and extending the scope of the measurements that can be accessed only with upgraded 22 GeV
beam energy.
7.2 Nuclear Dynamics at Extreme Conditions
7.2.1 Superfast Quarks
The origin of the nuclear repulsive core is one of biggest unknowns in nuclear physics. The phenomenology
of NN interaction indicates that the repulsive core dominates at internucleon distances <
∼0.5 fm. These are
also the distances where one expects the onset of quark-gluon degrees of freedom in hadronic interaction.
Therefore, it is very likely that the solution of the nuclear core problem lies in understanding QCD dynamics
of the nuclear forces at short distances. QCD introduces additional intrigue in grasping the repulsive core of
NN interactions. For example, when considering the six-quark color-singlet cluster as the limiting case of
NN system, one expects as much as 80% of the components of the NN wave function to consist of hidden
color states such as two-color octet “nucleons” [352]. In such a picture, hidden colors may play a significant
role in the dynamics of the core.
One way of exploring the dynamics of the NN core is the consideration of exclusive N N scattering at
large momentum transfer −t. The current observations have indicated a qualitative change of the dynamics of
hadronic interaction once relevant distances (∼1
√−t) become comparable to the range of the N N core [399],
but the complexity of theoretical interpretations of hadronic processes limited the ability to interpret these
73
results in terms of hidden color or other quark-level structure at short distances.
Currently, the most promising direction in exploring the physics of the core is high energy electro-nuclear
processes in which the virtual photon scatters from highly correlated bound nucleonic systems at small
space-time separations. That such correlations can be isolated and investigated in high energy nuclear
processes was one of the achievements of the experimental program of the investigation of high energy
electro-nuclear processes [400]. The scaling observed in the ratios of inclusive e−Ato e−2H cross sections
in QE kinematics at Bjorken x > 1 [337,401] has indicated the possibility of isolating 2N SRCs [400,402].
Subsequent experiments comparing the strengths of the proton-proton and proton-neutron SRCs [341] have
demonstrated the tensor nature of 2N SRCs and provided input on the momentum structure of SRCs [403].
While these measurements focused on QE scattering and did not probe the partonic structure of these
short-distance nucleons, extension of inclusive studies to high Q2offer the possibility to combine the kinematic
isolation of short-range structures in nuclei at x > 1 with the extraction of parton distributions via DIS
processes. The extraction of the distribution of these superfast quarks, which carry more longitudinal
momentum than is possible in a single, stationary nucleon, is sensitive to the partonic structure of the SRCs
that dominate scattering in this regime. In a simple convolution model, the PDFs at x > 1 arise from the
convolution of the nucleon PDFs and the nuclear momentum distributions, with the superfast quarks coming
from this highest-xquarks in the highest-momentum nucleons. This leads to a distribution which falls off
rapidly with x. However, modifications of the SRC internal structure can significantly change this picture. In
pictures where the overlap of the nucleons in the SRC allows for direct quark exchange between the nucleons,
there can be a dramatic enhancement in the distribution of these superfast quarks, as illustrated by two
models shown in Fig. 53 left. The models that are based only on nucleonic degrees of freedom predict larger
suppression of the distribution of superfast quarks [400,406], as illustrated in Fig. 53 right.
There are two major challenges to making DIS measurements at x > 1. First, reaching the DIS regime
for x > 1 requires extremely high Q2values, and it is not clear exactly what Q2is required to cleanly isolate
the parton distributions. On top of this, the inclusive cross section is very low due to the simultaneous
requirement of reaching very large xvalues and extremely high Q2. Because the typical cuts used to define
Figure 53: Left: Deuteron valence quark distribution based on a simple convolution model (dashed red
line [404]), compared to a deuteron with a 5% component based on the 6q-bag model of Ref. [405]. In the
EMC effect region, the impact is extremely small, while the six-quark bag contribution enhances the PDF
for x > 1, dominating the PDFs above x= 1.1. Right: Deuteron structure function for unmodified deuteron
and modified deuteron based on the color screening model [400]. In this case, the deuteron PDF is suppressed
at large xand Q2, rather than enhanced. The left figure is adapted from Ref. [404], and the right figure is
reproduced from Ref. [400].
74
DIS are not appropriate for the x > 1 region, the goal is to aim for Q2values where the underlying e−N
scattering is dominated by DIS. Momenta of bound nucleon that can kinematically generate a quark with
x≥1 in deep-inelastic scattering can be evaluated from the relation:
(q+pN) = W2
N,(7)
where qand pNare four-momenta of virtual photon and bound nucleon and WNis the final mass produced
on the bound nucleon. For the case of the deuteron target pN=pd−ps, where pdand psare on-shell
momenta of deuteron target and spectator nucleon, respectively. As demonstrated in Fig. 51 left, DIS
processes considering WN= 2 GeV results in very large initial momenta for bound nucleon at x > 1.
In taking the convolution of the e−Ncross section with the distribution of bound nucleons, the fraction
of scattering for which W2
N, the invariant mass of the e−Nsystem, is in the DIS region and taken to be
W2
N>4 GeV2for large Q2, can be determined.
Calculations suggest that the cross section is DIS dominated over a range in x(x > 1) for scattering with
12 GeV beam energies [400], but with significant contributions from the resonance region as well. Duality
of the proton and neutron PDFs [407,408] implies that the average cross section in the resonance region
closely follows that predicated from the DIS structure function, with resonances yielding additional structure
in W2(and thus x) on top of this. In nuclei, the Fermi smearing leads to this structure being washed out,
yielding scaling behavior even at modest Q2over most of the resonance region [409]. As such, the resonance
contributions are expected to yield modest deviations from the DIS expectation. Data taken at 6 GeV
already demonstrate that the x > 1 structure functions are consistent with expected scaling behavior and
can be well reproduced using a QCD scaling inspired fit [361], even where the cross section is dominated by
resonance contributions. While data recently taken at 12 GeV [362] at x > 1 and high Q2will not be free of
resonance region contributions, the greatly enhance DIS contribution will allow for a much more precise study
of scaling in this region, allowing us to make conclusions about the underlying superfast quark distribution,
with modest uncertainties associated with non-DIS contributions. Given the size of the effects predicted by
some models, this could be sufficient to have a first indication, if not quantitative measurement, of what
sort of PDF modification occurs in SRC-dominated scattering. However, the quantitative conclusions will be
limited by these non-DIS contributions, and we will have only the xdependence and a limited Adependence
to differentiate between different effects.
Figure 54 shows the kinematics of existing measurements at JLab6 (open) and JLab12 (solid) black circles,
Figure 54: Kinematic domain accessible for 22 GeV electron beam. Colorful points are the 22 GeV projections
while the open (solid) black circles are the 6 (12) GeV measurements.
75
along with projections for 22 GeV. The red (blue) points indicate the x-Q2region that yields >1 count/hr
(>10 counts/hr) for a 50 µA beam on a ∼2% carbon target. This will provide high-statistics tests of scaling
for xvalues up to x= 1.1-1.2, allowing the quantification of non-DIS contributions. In addition, it will allow
to map out both Q2and Adependencies up to x= 1.3 for Q2≥30 GeV2, while allowing for measurements
Q2>40 GeV2and pushing to x > 1.4 for a limited subset of targets.
7.2.2 Probing Deuteron Repulsive Core
Exclusive quasielastic electrodisintegration of the deuteron d(e, e′Nf)Nrat high Q2, in which Nrcan be
identified as a recoil nucleon, is expected to provide most direct access to the short-range nuclear structure
of the deuteron at very large missing momenta [410]. The d(e, e′p)nmeasurements up to missing momenta
of ∼550 MeV and Q2= 3.5 GeV2, which were carried out in Hall A [411], have verified that FSIs are
highly anisotropic with respect to the neutron recoil angle, θnq , as theoretically predicted. The data were
reproduced very well by the theoretical calculations of Refs. [412–414], where the kinematic window at θnq ∼
35◦to 45◦was found to have reduced FSIs and therefore providing an access to the ground state deuteron
wave function at internal momenta up to ∼550 MeV, see Fig. 55 left.
The existence of a kinematic window of the ground sate wave function at large internal momenta was
exploited further in recent Hall C [363] study, which has extended the previous measurement up to missing
momenta of 950 MeV while selecting kinematics where FSIs are reduced. The results are in good agreement
with theoretical calculations of M. Sargsian [412] up to missing momenta of ∼700 MeV, however, none of the
existing theoretical calculations were able to describe the data above these momenta, see Fig. 55 right. These
are very unexpected and surprising results indicating the possible onset of a new regime in the dynamics of
the p−nstate [415,416].
Taking into account the fact that starting at missing momenta of ∼750 MeV ∆∆ excitation threshold is
crossed in the p−nsystem, one expects that reaching such large missing momenta will open up new venue in
probing non-nucleonic components in the deuteron, including possible hidden-color states. At JLab22, it will
be possible to carry out systematic studies of d(e, e′Nf)Nrprocesses for up to unprecedented high values
of recoil nucleon momenta (∼1.5 GeV). These measurements can be performed in Hall C by measuring
scattered electron and struck proton in coincidence [417], or in Hall B by measuring the recoil proton in
coincidence with scattered electron.
FSI max
FSI min
R=σexp/σPWIA
Pm= 500 MeV/c Q2= 3.5 (GeV/c)2
projected data (2023)
Hall A data
(Boeglin et al. 2011)
Hall C data
(Yero et al. 2020)
R=σexp/σPWIA
r > ~ 2 fm
(long-range) r < ~1 fm
(repulsive hard-core)
~1.0 < r < ~2 fm
(intermediate)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Missing Momenta,pm(GeV/c)
100
σred (fm3)
10−2
10−4
10−6
θnq (deg)
Q2= 4.5 (GeV/c)2
θnq = 35±5∘
30 60 90 120
θnq (deg)
FSI max
FSI min
R=σexp/σPWIA
Pm= 500 MeV/c Q2= 3.5 (GeV/c)2
projected data (2023)
Hall A data
(Boeglin et al. 2011)
Hall C data
(Yero et al. 2020)
R=σexp/σPWIA
r > ~ 2 fm
(long-range) r < ~1 fm
(repulsive hard-core)
~1.0 < r < ~2 fm
(intermediate)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Missing Momenta,pm(GeV/c)
100
σred (fm3)
10−2
10−4
10−6
θnq (deg)
Q2= 4.5 (GeV/c)2
θnq = 35±5∘
Missing Momenta,pm(GeV/c)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(GeV)
Figure 55: Left: Angular distribution ratio R(θnq) = σexp/σP W I A for pm= 0.5 GeV [411], where PWIA
stands for the plane wave impulse approximation. Right: Reduced cross sections for the neutron recoil angle
θnq = 35 ±5◦[363].
76
7.2.3 Probing 3N SRCs in Nuclei
Three nucleon short-range correlations, in which three nucleons come close together, are unique arrange-
ments in the strong interaction physics. Unlike 2N SRCs, 3N SRCs have never been directly probed.
p
p
p
m
r3
r2
qp
p
p
m
r3
r2
q
(a) (b)
Figure 56: (a) Type-I 3N SRCs in which the fast
probed nucleon is balanced by two recoil nucle-
ons. (b) Type-II 3N SRCs in which all tree nu-
cleons have equal momenta with relative angles
of ∼120◦.
It is expected that 3N-SRCs, which dominate the high
momentum component of nuclear wave function at in-
ternal momenta of ≳700 MeV [339,353], being almost
universal up to a scale factor (see e.g. Refs. [353,418]).
The dynamics of three-nucleon short-range configura-
tions reside at the borderline of our knowledge of nuclear
forces making their exploration a testing ground for “be-
yond the standard nuclear physics” phenomena such as ir-
reducible three-nucleon forces, inelastic transitions in 3N
systems as well as the transition from hadronic to quark
degrees of freedom. Their strength is expected to grow
faster with the local nuclear density than the strength
of 2N SRCs [339,353]. As a result, their contribution
will be essential for the understanding of the dynamics of
super-dense nuclear matter (see e.g. Ref. [419]).
Theoretical studies of electrodisintegration of A= 3 system [343,420] indicate the dominance of two types
of 3N SRCs: type-I in which the high momentum of probed nucleon is balanced by two spectator nucleons
each carrying approximately half of the probed nucleon momentum, see Fig. 56 (a), and type-II in which
all three nucleons have equal momenta with relative angles of ∼120◦, see Fig. 56 (b). These configurations
dominate at different missing energy values of the reaction indicating different electroproduction processes
that can probe 3N SRCs.
Recent studies [364,365] have demonstrated that the type-I 3N-SRCs can be probed unambiguously in
inclusive scattering at α3N>2, where α3Nis the light front momentum fraction of 3N SRCs carried by the
interacting nucleon. A spectacular signature of the onset of 3N SRCs in this case will be the appearance
of a new scaling in the ratio of inclusive cross sections of nuclei with A > 3 to A= 3 nucleus (similar to
what was observed in JLab for 2N SRCs in the region of 1.3≤α2N≤1.5 [402,421]). Currently, there
is no data for α3N>2. Based on the phenomenological point-of-view that 2N SRCs should be suppressed
already at internal momenta above 700 MeV, it was predicted in Refs. [364,365] that 3N SRC scaling could
be set at that values and thus observed at α3N≥1.6. Currently, there is a very restricted number of data
satisfying this condition which demonstrates tantalizing signatures for the onset of nuclear scaling relevant
for 3N SRCs, see Fig. 57 left. An unambiguous verification of type-I 3N SRCs require kinematic conditions
0
1
2
3
4
5
6
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
4He/3He*(3/4)
α3N
JLAB
SLAC 3He
Avg 2N
[a2(4He)/a2(3He)]2
Figure 57: Left: The α3Ndependence of inclusive cross section ratios for 4He to 3He. The data are from
JLab [337] and SLAC [422,423] experiments. The horizontal line at 1.3≤α3N<1.5 identifies the magnitude
of the 2N SRC plateau [364,365]. Right: The Q2range necessary to isolate 3N SRCs for JLab 22 GeV. Also
shown are the ranges that will be accessed in the 12 GeV experiments.
77
that will cover sufficiently a wide range of α3N>2 for a great variety of nuclei. As depicted in Fig. 57 right,
this will require reaching the range of Q2≥10 −15 GeV2which is accessible only at JLab22.
The main concerns for experimental studies of type-II 3N SRCs is that they require measurements with
large removal energies of Em≥300 MeV. Such reactions can be probed in a new generation of high Q2
exclusive disintegration of A= 3 nuclei in which a large missing energy Emand at least one large recoil
momentum of spectator nucleons can be measured simultaneously. As it is demonstrated in Refs. [343,420],
these processes are very sensitive to the presence of irreducible 3N forces resulting in predictions of cross
section differing by one order of magnitude.
7.3 Hadron-Quark Transition in Nuclear Medium
7.3.1 Bound Nucleon Structure from Tagged DIS
Nucleons in the nucleus are densely packed, strongly interacting, and composite objects. It would be surpris-
ing if nucleons in the nucleus did not distort or modify the structure of their neighboring nucleons. However,
there is little evidence for this modification beyond the neutron lifetime and the ∼1% binding energy. The
EMC Effect is one of the few pieces of evidence for bound nucleon modifications [406,424–426].
Inclusive measurements detect only the scattered lepton. In order to select DIS scattering from individual
nucleons, we need to “tag” them, by detecting the spectator nucleons. For example, if an electron scatters
from a proton in 4He, we would need to detect the scattered electron and the recoil 3H. If the recoil
Figure 58: The TDIS reaction. An elec-
tron with four-momentum kexchanges a
virtual photon with a nucleon in a deuteron
with momentum pi. The scattered electron
has four-momentum k′. The spectator back-
ward nucleon is detected with momentum
prec, thus tagging the struck nucleon. The
four-momentum transfer is Q2=−(k−k′)2
and the Bjorken scaling variable is xB=x=
Q2/2MNν.
A−1 nucleus is a spectator to the reaction (i.e., if it does not
rescatter), then it recoils with momentum equal to and opposite
the initial momentum of the struck nucleon, prec ≈ −pi, see
Fig. 58. In fixed-target experiments, this is best done with
very light nuclei, such as the deuteron, to enable the detection
of the relatively low-momentum recoil nucleus.
These experiments need to boost their kinematics into the
rest frame of the struck nucleon, using x′and W′rather than
xand W, the invariant mass of final-state hadrons. They min-
imize rescattering of the spectator nucleon by detecting back-
angle spectators.
By measuring nucleon structure over a range of prec, TDIS
measurements can distinguish between slight modification of all
nucleons and significant modification of SRC nucleons. Slight
modification of all nucleons implies a small pi-independent
modification. Large modification of SRC nucleons implies a
strongly pi-dependent modification, with large modification at
large pi.
Previous tagged DIS measurements at 6 GeV have either
focused on almost-free nucleon structure by measuring low-
momentum recoil protons from deuterium using the barely off
shell nucleon structure (BONuS) detector plus CLAS [427–429]
or they have measured higher momentum recoils 300 ≤prec ≤
600 MeV and suffered from a lack of statistics and kinematic
range [430]. Current and near-future 12 GeV measurements in-
clude low-momentum recoils measured with a low energy radial
tracker (ALERT) or BONuS and higher-momentum recoils measured with backward angle neutron detector
(BAND) or Large Angle Detector.
However, the existence of a possible high-intensity 22 GeV electron beam at JLab, even with the ex-
78
Figure 59: Expected tagged DIS d(e, e′ns) statistics for 22 GeV, the CLAS12 and BAND detectors and
180 fb−1of luminosity for four bins in αs(the light cone momentum fraction) as a function of x′.
isting CLAS12 and BAND detectors, could dramatically increase the statistical and kinematic reach of the
experiments. As can be seen in Fig. 59, the expected statistical precision over a wide range of αsand x′
is remarkable. This is a dramatic increase over the statistics and kinematic range of existing and planned
12 GeV experiments.
7.3.2 Probing Partonic Structure with Spectator Tagging
The origin of the EMC effect continues to evade a clear explanation, which is often hampered by theoretical
or experimental complications that frequently cloud the interpretation. In quasielastic electron scattering,
quenching of the Coulomb sum rule has been difficult to interpret for different models [431,432], and exper-
iments with a recoil polarimeter to measure polarization transfer or induced polarization observables need
model calculations to describe the data, but provide little insight into the substructure of the nucleon [433–
436]. Unlike the EMC effect, these quasielastic measurements lack a direct partonic interpretation. On the
other hand, spectator-tagged deeply virtual Compton scattering (DVCS) provides a partonic interpretation,
and through a fully exclusive measurement, yields a separate handle for studying final state interactions
much like induced polarization measurements.
Recent DVCS results on light nuclei from the CLAS Collaboration have sparked interest in the so-
called generalized EMC effect [437]. Predictions for this off-forward beam spin asymmetry ratio of the sin ϕ
harmonic in nuclei over the free nucleon are in general agreement with the data [438,439]. The harmonic of
the beam spin asymmetry (BSA) is
Asin ϕ
LU =1
πZπ
−π
dϕ sin ϕALU (ϕ),(8)
where ALU (ϕ) is the measured DVCS beam spin asymmetry binned in x, the momentum transfer square t,
and Q2. This harmonic is proportional to the following combination of Compton form factors (CFFs) [440]
Asin ϕ
LU ∝Im(F1H − t
4M2F2E+xB
2(F1+F2)˜
H),(9)
79
which, in the case of the proton, is dominated by Im(H), and for the neutron, it is mostly sensitive to Im(E)
and Im( ˜
H).
Figure 60: The ALERT detector.
There are two tagged DVCS generalized
EMC ratios planned for the upcoming 11 GeV
CLAS12 ALERT experiment, which will use
both 4He and 2H targets [441]. The off-forward
proton and neutron ratios are Rp=Ap∗
LU /Ap
LU
and Rn=An∗
LU /An
LU , where the “∗” indicates
the in-medium (4He) BSA, the denominators
will use the free proton BSA from the accumu-
lated CLAS12 liquid-hydrogen data sets and a
quasi-free neutron from 2H with ALERT de-
tector depicted in Fig. 60. The latter is built
around a 30-cm-long gaseous 4He target straw
and consists of a small drift chamber sur-
rounded by a time-of-flight hodoscope, which is roughly 20 cm in diameter and 30 cm in length.
Additionally, the measurement of the beam spin asymmetry (BSA) in coherent DVCS is part of the broad
ALERT scientific program [162]. BSA offers a way to explore partonic spatial distributions leading then to
3-D tomography of nuclei. Combining this coherent nuclear BSA with the free proton DVCS ALU results
will allow for discerning among the several competing explanations of the nuclear medium effects. The 4He
nucleus is a spin-0 object and therefore at twist-2 its partonic structure can be parameterized by only one
chiral even GPD [HA(x, ξ, t)]. Thus, proposed asymmetry measurements allow for a significantly simplified
extraction of the real and imaginary parts of the Compton form factor HAin a model independent way. This
azimuthal asymmetry arises from the interference between the DVCS and the Bethe-Heitler (BH) amplitudes.
The BH process, in which the real photon is emitted by the scattering electron rather than the hadron, and
DVCS have identical final states. The BH amplitude depends on the electromagnetic form factors, which is
well known. The resulting asymmetry expression is given by
ALU =α0(ϕh)ℑA
α1(ϕh) + α2(ϕh)ℜA+α3(ϕh)(ℜA+ℑA),(10)
where ℜA=Re{HA}and ℑA=Im{HA}are the real and imaginary parts of the desired CFF, respectively,
ϕhis the azimuthal angle between leptonic and hadronic planes, and αi(ϕh)’s are ϕh-dependent kinematical
terms. The experimentally observed asymmetries are calculated in each kinematic bin using DVCS event
yields for positive (+) and negative (−) helicity states as
ALU =1
Pb
N+−N−
N++N−,(11)
where Pbis the polarization of the incident electron beam, and N+(N−) denotes the DVCS yield for
positive (negative) helicity. For the coherent channel, the target 4He remains intact and recoils as a whole.
The exclusivity is achieved by detecting the scattered electron and real photon in the forward CLAS12
detector and tag the back-scattered low-momentum 4He nucleus in ALERT.
The 22 GeV simulation of nuclear DVCS reactions off 4He has been performed using the Monte Carlo
(MC) event generator TOPEG (The Orsay Perugia Event Generator) [442], developed by R. Dupr´e et al., and
the CLAS12 GEANT4 MC (GEMC) package, which includes the full geometry and material specifications
of ALERT detector. The CLAS12 Forward Tagger (FT) has been considered in this simulation to improve
the acceptance of very forward real photons produced at much lower angles up to about 2 degrees.
The extracted BSA statistical precision from the 22 GeV simulation was scaled to correspond to a
luminosity of 1035 cm−2s−1for 55 PAC days. The analyzed bins for xand −twere chosen as the ones
planned for the 11 GeV ALERT experiment [162]. For the BSA, ALU , the simulated data were integrated
over the full range of Q2. The assumed beam polarization was taken in the range of 80%. Figure 61 shows
ALU projections for selected set of bins along with the anticipated 22 GeV kinematic coverage. The 22 GeV
80
Figure 61: The 22 GeV kinematic coverage of xvs. −tphase-space along with the expected ALU for selected
set of bins. The shown asymmetry bins correspond to a fixed 0.12 <−t < 0.17 GeV2range, and to
0.05 <x<0.17, 0.17 <x<0.23, and 0.23 < xB<0.50 from top to bottom in the right panel.
JLab upgrade will significantly extend the Q2reach of the measurements (up to 12 GeV) and elevates the
statistics of the lower xregion, 0.08 < x < 0.15, which would allow for more detailed xdependence studies
with optimized bins. The FT inclusion leads to a more than four-fold increase of the DVCS acceptance due
to the improved lower angular coverage, which significantly improves the expected BSA statistical precision,
as depicted in Fig. 61 right panel.
7.3.3 Unpolarized EMC and Antishadowing Regions
While tremendous experimentally and theoretically efforts have been put into understanding the EMC effect,
much fewer efforts have been invested in studying the antishadowing xregion (x∼0.1) in the medium. In
the inclusive DIS measurement, the DIS cross section of a heavy nucleus indicates enhancements near x∼
0.1 compared with one of a deuteron target. On the other hand, the Drell-Yan experiments reveal no such
enhancement, indicating that the sea quarks may not suffer from the antishadowing effect [374].
SIDIS is a powerful tool for studying the quark distributions in nucleons and nuclei. Using high-energy
electrons scattering off a nucleon, the virtual photon knocks out a quark in the nucleons. Then the quark has
to undergo a complicated hadronization process due to the color confinement. Out of many colorless final
state hadrons generated in the hadronization process, the leading hadron will be measured in coincidence
with the scattered electron. Under the factorization framework, the SIDIS structure functions of electron-
nucleus scattering can be factorized into the convolution of the colinear PDFs and the colinear fragmentation
functions (FFs) for all quark flavors and gluons, in the colinear framework. When the transverse momentum
of the leading hadron is measured, the structure function becomes the convolution of TMDs and the 3-D
FFs. One of the biggest advantages of using SIDIS to measure PDFs is the “flavor-tagging” feature where
the different detected leading hadrons are uniquely sensitive to the knocked-out quarks.
One can measure the SIDIS via electron-nucleus scattering and get access to the nuclear PDF (nPDF)
of individual quarks by tagging different hadrons and directly study the flavor-dependence of the EMC
81
Figure 62: Kaon-SIDIS projection in 4-D binning (Q2,z,x,pT) for 3He at 1035 cm−2s−1luminosity and
beam time of 100 days. Out of totally 38 (Q2,z) bins, only three bins are shown here to illustrate the
comparison of statistical uncertainties and coverage of pTand xbetween 11 GeV (red circles) and 22 GeV
(blue squares) beam energies for three different Q2bins and one fixed zvalue.
effect and antishadowing effect in nuclei. However, the SIDIS cross sections measure not only the medium
modification of PDFs but also the nuclear effect of the nuclear FFs (nFFs) which are small for light nuclei
but significant for heavy nuclei [443]. A systematic global analysis of high-precision nuclear-SIDIS data with
extensive kinematic coverage and multiple hadron productions is essential to decouple the nPDFs and nFFs
for different quark flavors.
With a 22 GeV electron beam, one can enforce the SIDIS reaction in the current fragmentation re-
gion where the cross sections can be factorized as the convolution of nPDFs and nFFs. Theory suggests
that at 11 GeV only 70% of pion-SIDIS data and 20% of kaon-SIDIS data are in the current fragmen-
tation region [127]. The higher energy also allows for the measurement of heavy mesons such as kaons,
protons/antiproton, and lambda which are impossible to be measured with an 11 GeV beam. Broader Q2
and pTdistributions also enable theoretical corrections. Figure 62 show the projection of the k+-SIDIS data
in 4-D (Q2,z,x,pT) with 3He at 1035 cm−2s−1luminosity and 100 days of running. The same projections
at 11 GeV are also given as a comparison. Doubling the beam energy not only largely extends the Q2and
pTcoverage but also pushes the xdown to the medium region with great precision.
Without going through the complicated global analysis, one fixed (Q2,z) range can be picked; e.g.,
3< Q2<4 GeV2and 0.3 < z < 0.35, to compare the variation of SIDIS cross section with xbetween a heavy
nucleus and deuteron. Figure 63 shows the sensitivities of super-ratios R(σh+
A/σh−
A
σh+
D/σh−
D
) with different hadron final
states to different nPDF global fits for lead, where EPPS21 [444] nPDFs assumes flavor-independence and
TUJU21 [445] nPDFs allows flavor-dependence. Note that in the collinear framework, the pTdistribution is
integrated when extracting the cross sections. The distributions near x∼0.1 have great statistical precision
to determine if there is any indication of flavor-dependence of the EMC and antishadowing effects. There
are a total of 36 similar (Q2,z) bins allowing for sophisticated global extraction of individual nPDF for
different quark flavors in light to heavy nuclei to systematically study their EMC and antishadowing effects
in the valance and sea regions.
7.3.4 Spin Structure Functions in EMC, Antishadowing, and Shadowing Regions
Medium-Modified Spin Structure. As detailed in Subsubsec. 7.3.1, the experimental study of structure
modifications of bound nucleons has been carried out for decades. Yet, despite much theoretical work, there
is not consensus on what causes them. There is an approved 11 GeV JLab experiment to measure spin
82
10−210−1
xbj
0.95
1.00
1.05
1.10
1.15
1.20
1.25
Rπ
Pb/D = (σπ−
Pb /σπ+
Pb )/(σπ−
D/σπ+
D)
EPPS21
TUJU21
SIDIS Projection (22GeV)
10−210−1
xbj
0.96
0.98
1.00
1.02
1.04
RK
Pb/D = (σK−
Pb /σK+
Pb )/(σK−
D/σK+
D)
EPPS21
TUJU21
SIDIS Projection (22GeV)
10−210−1
xbj
1.00
1.02
1.04
1.06
1.08
1.10
1.12
Rp
Pb/D = (σ¯
p
Pb /σp
Pb )/(σ¯
p
D/σp
D)
EPPS21
TUJU21
SIDIS Projection (22GeV)
Figure 63: SIDIS super-ratios, R=σh+
A/σh−
A
σh+
D/σh−
D
, between lead and deuteron for pion (left panel), kaon (middle
panel), and proton (right panel) production for 3 < Q2<4 GeV2and 0.3 < z < 0.35 after integrating over
pT. The curves are EPPS21 [444] global nPDF fits (assuming flavor independence) and TUJU21 [445] nPDF
fits (allowing flavor dependence).
structure function modifications for the first time, primarily in the EMC and antishadowing regions, for
a bound polarized proton embedded in a polarized 7Li nucleus [446,447]. The same technique, if used at
22 GeV, would push for the first time into the shadowing region, and with sufficient reach in four momentum
transfer Q2to give confidence in the validity of theoretical assumptions. The JLab22 uniquely gives access
to the shadowing region for spin structure functions, measured at high luminosities enabled by fixed target
experiments.
This is very interesting physics because the shadowing and antishadowing regions are characterized at
least partially by the onset of multi-step diffractive processes which allow constructive and destructive in-
terferences. These are thought in some models to cause enhancement and suppression in the antishadowing
and shadowing region, respectively [448], while other models have different approaches [449–454]. Theoret-
ical work that includes these regions for polarized 7Li range from predicting a 10% suppression to a 50%
enhancement in spin structure function ratios. It is very clear this is terra incognita and further progress in
understanding these crucially important kinematic regimes of x <0.3 without new data is improbable.
Anticipated Results and Coverage. Following the above discussion of the approved 12 GeV JLab
experiment, the goal now is to produce the 22 GeV projections for one of the main observables, denominated
as R1, which is defined as
R1=[dσ+−dσ−]7Li
[dσ+−dσ−]p
,(12)
where the positive and negative signs indicate the relative beam and target polarization. In Fig. 64, predicted
R1results are shown for fifty days of beam time in the upgraded CLAS22. For the assumed luminosity of
2x1035 cm−2s−1, the uncertainties are dominated by systematic uncertainties except for a few bins at high x.
This luminosity has been nearly achieved in present-day CLAS for light nuclear targets such as deuterium.
In comparison to the 11 GeV experiment, the 22 GeV measurement will feature much higher four-
momentum transfer for each bin in x, assuring that we can have full confidence in the interpretation of the
results. For example, for a minimum xof 0.08, the momentum transfer will be 3.2 GeV2at 22 GeV compared
to 1.2 GeV2at 11 GeV. Furthermore, for 22 GeV, we can reach Q2of 10 GeV2at x= 0.3 compared to x= 0.75
at 11 GeV, where the statistical information will be much poorer and the Fermi momentum effects begin
to encroach. While the Q2range will be superior for the 22 GeV study, there is also very much value in
intercomparison of the results from the two energies and thus being able to study several aspects such as
scaling behavior, higher twist, contribution from the unmeasured A2, and target mass effects. As a result,
83
x
R1(x, Q2)
Q2: 2.4-4 GeV2, 4-6 GeV2, 6-10 GeV2, > 10 GeV2
Calculated for 50 days of running in CLAS22
Uncertainties shown are statistical, and total in quadrature
Figure 64: Anticipated results for observable R1(see text). The assumed luminosity for this prediction is
2x1035 cm−2s−1, which has been nearly demonstrated in present-day CLAS for light nuclear targets.
the two beam energy measurements will complement each other in important ways.
7.3.5 Color Transparency Studies
QCD uniquely predicts the existence of hadrons with their constituent quarks in a small-sized color singlet,
thus suppressing interactions between the singlet and the surrounding color field in the nuclear medium [381,
455–458]. This QCD phenomenon, dubbed as CT, can be observed experimentally in exclusive processes
with sufficiently high momentum transfer leading to a significant reduction in FSIs [455].
The experimental observable commonly used to search for CT effects is the nuclear transparency, T,
taken as a ratio of the cross section per nucleon for a process on a bound nucleon to that of a free nucleon.
Thus, the signature of CT is measured as an increase in the nuclear transparency with increasing momentum
transfer squared, Q2(or momentum of the final state hadron). In complete CT, FSIs vanish and Tplateaus.
In the absence of CT, the nuclear transparency is not expected to change, following the same relative energy
independence of the N N cross section.
Meson experiments in both 6 and 12 GeV era of JLab have explored the onset of CT through the hard
exclusive electroproduction of ρand πmesons off nuclei. Pion production measurements in Hall C measured
the transparency for e+A→e′+π++A∗using the HMS and SOS spectrometers. The results have
indicated both an energy and Adependence of the nuclear transparency consistent with models inclusive
of CT effects [459] for Q2from 1.1 to 4.7 GeV2. The CLAS Collaboration experiment measured ρ-meson
production on carbon and iron targets relative to 2H in the range of 0.8 to 2.2 GeV2[381,460]. The extracted
nuclear transparencies showed a Q2and Adependence consistent with the very same models of CT and at
a lower onset than that measured for the pion [461–463].
While the onset of CT is anticipated to be at a lower energy regime in mesons than baryons, the pre-
cise kinematic regime for protons is not known. Intriguing results from large angle A(p, 2p) scattering at
Brookhaven National Laboratory (BNL) [464–467] indicated a region of interest for A(e, e′p) experiments
at JLab. The measured A(e, e′p) cross section was compared to calculations in the plane wave impulse
approximation which excludes FSIs. Experiments were conducted at SLAC [468,469], and JLab [470–472]
measuring Q2up to 14.2 GeV2and the highest proton momentum of ∼8.5 GeV ruling out the observation
84
of the onset of CT in this regime for protons. In light of these most recent proton results, new ideas for
exploring the onset of CT in different kinematics have become increasingly significant.
An increase of the JLab beam energy is crucial for fully evaluating the QCD signature of CT in nuclei.
The increased beam energy enables measurements of the entire range, from nearly the onset to full CT, for
mesons such as the ρand pion. The extended reach in Q2and the improved rates that accompany the increase
of beam energy enable a robust program for exploring the onset of CT in protons in various kinematics to
be detailed in the next section.
The 22 GeV beam energy upgrade at JLab increases the maximum attainable Q2and improves the rates
at otherwise slow-counting kinematics. The possibilities of extending meson measurements for ρin Hall B
and pion in Hall C are presented here as a proof of capability.
For the ρ-meson exclusive diffractive measurement using the CLAS12 spectrometer in Hall B, the Q2
can be extended up to 14 GeV2(with the highest bin upper limit is 16 GeV2). The 22 GeV simulation is
performed by assuming the same CLAS12 nominal per-nucleon luminosity of 1035cm−2s−1, 7 PAC days as
the 11 GeV projections, and the Hall B flag assembly where the solid-target foils are mounted in series (see
Fig. 4in Ref. [381]). The obtained pro jections for copper are shown in Fig. 65 left for a fixed coherence
length representing the lifetime of the q¯qfluctuation of the virtual photon. In the region where the 11 and
22 GeV beam energy projections overlap, the statistical uncertainties are reduced by almost a factor of 3,
except for the 3 GeV2case at 22 GeV because it is at the lower edge of the CLAS12 acceptance.
Similarly, one can extend the π+measurements in Hall C with a higher beam energy, but the maximum
Q2is approximately 12.5 GeV2due to spectrometer limitations and to maintain t < 1 GeV2to reduce FSIs.
Assuming a similar experimental setup as that in the 12 GeV era with electrons in the HMS and π+in the
SHMS, one can take measurements at Q2= 9.5,11,and 12.5 GeV2with a 17.6 GeV beam energy on targets
of H, 2H, 12C and 63 Cu. Assuming 80 µA beam current on hydrogen and a 3% statistical uncertainty for each
kinematic, the full experiment could be completed with 200 hours of beam on target with the projections
shown in Fig. 65 right. Note that the assumption made here is the beam dump power limitations would be
increased with the increased beam energy.
0.4
0.5
0.6
0.7
0.8
0.9
246810121416
Q2 (GeV2)
Nuclear Transparency
63Cu
Theory: FMS CT Model
Theory: FMS NO CT Model
5 GeV 56Fe CT Result
Exp: Hall B, 11 GeV
Exp: Hall B, 22 GeV
2 4 6 8 10 12 ]
2
[GeV
2
Q
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Nuclear Transparency
C
12
Cu
63
Glauber + CT(I)
JLab 6 GeV result
JLab 12 GeV
JLab 22 GeV
Figure 65: Left: the nuclear transparency for the ρ-meson experiment in Hall B, where the solid cir-
cles correspond to the already published 5 GeV CLAS6 results on 56Fe [460], and the open squares
(triangles) correspond to the projections with 11 GeV (22 GeV) beam energy on 63Cu. The Frank-
furt–Miller–Strikman (FMS) [461] curve is a linear extrapolation of the 11 GeV predictions. Right: the
nuclear transparency for the π+-meson in Hall C on carbon and copper targets, where the solid points
correspond to results already published [470–472], and the open points correspond to the projections with
11 GeV and 17.6 GeV beam energies.
85
Figure 66: Projections for D(e, e′p) in rescattering kinematics. The curves are from Ref. [473] corresponding
to 3 possible values of the CT model parameter, ∆M2.
Likewise, one can extend the measurements for the proton in parallel kinematics as in [472] in Hall C.
While the maximum momenta of the SHMS and HMS spectrometers and minimum angles limit the extended
reach in Q2, the increase in beam energy significantly improves the rates at the high Q2. An increase
in the beam energy to 13 GeV improves the rates by a factor of three at the previously highest Q2=
14.2 GeV2. Assuming a beam energy of 13 GeV, one can measure additional Q2= 14.2,15.8,and 17.4 GeV2
at 2.2% statistical uncertainty on 12C in 160 hours of 80 µA beam on target. An increase in the beam energy
can provide a strong test for light-front holographic QCD (LFHQCD) predictions (see Ref. [458]). Eventual
upgrades to the spectrometer momenta would improve the reach in attainable Q2in Hall C.
New measurements are accessible with the increase in beam energy for exploring the onset of CT in the
proton in non-traditional kinematics with high FSIs. This would make it possible to explore the loophole left
from previous measurements if the apparent lack of observed CT is due to limitations in parallel kinematics.
For example, D(e, e′p)nhas well-known FSI contributions from double scattering that is strongly determined
by the recoiling neutron angle and momentum. In this way, it is feasible to measure the D(e, e′p)nreaction
in the Hall C spectrometers accessing high Q2up to 17 GeV2(see discussion in Ref. [473]). A scan in
Q2= 8,10,12,14,15,and 17 GeV2using the HMS and SHMS in coincidence with a 13 GeV beam could be
accomplished with a 3% statistical uncertainty and 3 months of beam on target, as shown in Fig. 66.
7.3.6 Hadronization Studies in Nuclei
With the emergence of the hadronization concept in the late 1970s [474] to explain the limited transverse
momenta of hadrons in jets produced in e+e−and pp collisions, many theoretical models were developed
with the objective to offer an explanation to the experimental data as well as a theoretical framework for
the dynamics of the hadronization process.
Similarly to the EMC effect [475], it is expected that the hadron production from hard reactions, in the
presence of hot dense QCD matter or cold nuclear medium, would be different from its equivalent in vacuum.
This was confirmed by the PHENIX [476] and STAR [477] experiments at RHIC, as well as SLAC [391],
HERMES and EMC Collaborations [392,478–480]. The observed hadron attenuation could be attributed to
many effects such as: quark energy loss due to induced gluon radiation and quark multiple rescattering with
the surrounding medium, and to FSIs of the produced hadron (or prehadron) with the nucleus. Those effects
were widely studied in many models such as: Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport
model, Lund string model, Rescaling model, Quark energy loss model, Quantitative model, Higher-twist
pQCD model, etc. Despite the existence of a large number of phenomenological models, that in general
reproduce qualitatively the global features of the data, a clear understanding of the hadronization mechanism
is still a challenge and a moderate success in describing the data was achieved. Inputs from experimental data
are crucial to test and calibrate these models and also to check the validity of many theoretical calculations.
To establish a detailed picture of the time-space development of the hadronization mechanism in SIDIS
production, the two time-distance scales τpand τfneed to be studied. Simple calculations based on pQCD
and the Lund string model showed that the length of the first stage, Lp≈ν(1−zh)/κ, depends on the energy
of the virtual photon transferred to the struck quark(s), ν, the fraction z=Eh/ν, where Ehis the energy
transferred to the final hadron, and on the string tension κ. In the hadron rest frame, the length of the second
stage, Lf, is approximated by the hadron radius, 0.5−0.8 fm. Taking into account time dilation, Lf, in the
86
lab frame, can range up to distances that exceed the size of the nucleus. The above estimations demonstrate
that the hadronization occurs at small time and length scales. Consequently, the hadrons detected at very
large distances from the origin of the reaction do not provide detailed information that is sensitive to the
production and formation times. These facts clarify the importance of using a nuclear media in the study of
hadronization. The scattering centers (nucleons) inside the nuclei act like miniscule detectors placed within
distances comparable to the length scales associated with the hadronization. Therefore, measurements of the
effects induced by these scattering centers on the propagating quark, prehadron and hadron would provide
a unique opportunity to study the hadronization mechanism at its early stages.
Another important topic in hadronization is the study of two hadron production from lepton-nucleus
deep-inelastic scattering. Depending on the evolution of the fragmentation process with time and space,
the observed signal might either be dominated by in-medium prehadronic interactions or by partonic energy
loss. This could be investigated through the two hadron production in SIDIS off nuclei. If quark energy
loss were the dominant mechanism, then one would expect that the hadron attenuation would not depend
significantly on the number of hadrons involved, and the double-hadron to single-hadron ratio for a nuclear
target should not depend strongly on the atomic mass number A. If, on the other hand, hadron absorption
were the dominant process, then requiring an additional slow hadron would suppress the two-hadron yield
from heavier nuclei. Therefore, the double-hadron to single hadron ratio would decrease with the size of
the nuclear medium. Measurements from HERMES [481] showed a slight dependence on the atomic mass
number. The data were confronted to three models based on different assumptions and, interestingly, none
of them was able to describe the observed double-to single hadron yields.
In the end, the study of hadronization using SIDIS processes off nuclei offers the possibility to address
some challenging questions, such as i) what are the dynamics leading to color confinement?; ii) what are
the effects of the nuclear medium on the fragmentation functions?; iii) how long does it take to form the
colorless object (prehadron)?; and iv) how long does it take to form the color field of a fully dressed hadron?
Answers to those questions would enhance our understanding of hadronization which is one of the exciting
frontier subjects in QCD.
Proposed Measurements and Results. The SIDIS experimental observables needed to explore the two
time-scales associated with the hadronization process are:
i) The transverse momentum, pT, broadening related to the production time of the struck color-neutralized
objects, which is defined as
∆⟨p2
T⟩A
h(Q2, ν, z) = ⟨p2
T⟩A
h− ⟨p2
T⟩D
h(Q2, ν, z),(13)
where ⟨p2
T⟩A
his the mean pTsquared obtained for a nucleus Aand hadron hwhile Q2is the four-
momentum transfer squared, and
ii) The hadron multiplicity ratio related to the hadron formation time and defined as:
RA
h(Q2, z, ν, pT) = NA
h(Q2, z, ν, pT)/NA
e(ν, Q2)
(ND
h(Q2, z, ν, pT)/ND
e(ν, Q2),(14)
where, NA
eand NA
hare, respectively, the yield of DIS electrons and SIDIS hadrons produced on a
nucleus Afor a given kinematic bin.
Additionally, the double-to-single hadron multiplicity ratio is defined as:
R2h(x, Q2, z2, p2
T,2,∆ϕ) = (Nh1,h2(x, Q2, z1, p2
T,1, ϕ1, z2, p2
T,2,∆ϕ)/Nh1(x, Q2, z1, p2
T,1, ϕ1))A
z1>0.5
(Nh1,h2(x, Q2, z1, p2
T,1, ϕ1, z2, p2
T,2,∆ϕ)/Nh1(x, Q2, z1, p2
T,1, ϕ1))D
z1>0.5
,(15)
where NA,z1>0.5
h1,h2is the number of events containing at least two hadrons, z1is the energy fraction of the
first (leading) hadron, and z2is the energy fraction of the second (subleading) hadron. NA
h1is the yield of
87
one leading hadron, and ϕis the angle between the leptonic and hadronic planes. Instead of binning in ϕ2,
the convention of Ref. [482] is adopted by binning on ∆ϕ≡ϕ1−ϕ2.
The pT-broadening is related to the path travelled by the struck quark in the nucleus. Its measurement is
very important because it reveals whether or not the hadronization is occurring inside or outside the nuclear
medium. Therefore, the hadron multiplicity ratio is the appropriate observable to experimentally measure
the hadron formation time. It is normalized by DIS electrons to cancel out initial state nuclear effects, such
as nuclear modified partonic distributions, and to isolate final state nuclear modifications. A decrease of the
ratio with the mass number Aand an increase with the energy νis expected because the attenuation has to
be larger for large nuclei and the nuclear effects have to weaken with increasing struck quark(s) energy.
Those observables were previously studied by the HERMES and CLAS Collaborations for various hadron
channels such as pions [478,481–484], kaons [485], proton [479,486], and lambda [487]. The proposal here
is to measure these observables using CLAS12 at 22 GeV for many reasons. First, it will allow to cover a
wide phase-space including both the valence and sea quark regions. The upgraded detection capability as
well as luminosity will allow the study of hadronization for a large variety of hadron species. It is expected
to perform these measurements with an unprecedented precision, which will help understand some of the
HERMES data taken with limited statistics. Furthermore, the combination of CLAS6 and CLAS12 datasets
taken at 5 GeV and 11 GeV then 22 GeV will make CLAS the unique place to study hadronization using a
wider kinematical coverage.
Figure 67: Three-fold z(z2)-binned projections of RA
h(left column), ∆⟨p2
T⟩(middle column), and R2h
(right column) for various hadrons production off carbon target represented with different colors and for a
combination of xand Q2bins that are outside the 11 GeV coverage on both rows. Error bars represent the
statistical precision of the simulated sample from GiBUU assuming a per-nucleon luminosity of 1035 cm−2s−1
and 15 PAC days.
88
In Fig. 67, the three-fold differential projections of all three observables are shown for various hadrons
production off carbon target. Since systematic uncertainties for similar measurements at CLAS6 and HER-
MES have had more than 1% systematic uncertainties, the study of channels listed here will be also limited
by systematic uncertainties. By running for 60 PAC days with a deuterium target in series with one of the
heavy nuclei such as carbon, copper, tin, and lead, and assuming the nominal CLAS12 per-nucleon lumi-
nosity of 1035 cm−2s−1, one can make a variety of measurements of several hadron species to much higher
precision than ever achieved. A larger run period may be needed for precise measurements for rare hadron
channels, particularly those with charm quarks.
7.3.7 Coherent Nuclear J/ψPhotoproduction
Coherent production of heavy vector mesons (VM) from nuclei is considered a critical measurement for
understanding the gluon distribution in nuclei [488], allowing access both to the xdependence and the
spatial distribution of the gluons. The J/ψ meson is particularly promising for such a measurement; as the
lightest heavy vector meson, higher-twist and sea-quark effects are suppressed in its production in favor
of two-gluon exchange, while its relatively low mass allows phase space for its production at much lower
energies than heavier mesons such as the Υ.
Photoproduction of VM in Heavy-Ion ultraperipheral collisions (UPC) has been used at the Large Hadron
Collider to study the gluon distributions in heavy nuclei such as 208Pb, using the electromagnetic field of
the ions as a source of photons for photon-nucleus interactions [489–493]. One study at BNL used UPC
production of J/ψ to examine the gluon structure of the deuteron [494], including the first observation of
coherent J/ψ photoproduction from such a light nucleus. However, UPC interactions are limited for a few
reasons, including ambiguity in which nucleus is being probed and the lack of exclusivity in measuring the
event. Experiments with electron beams and real photon beams, in the case of Hall D, are necessary to
provide both complementarity and more detailed measurements of these processes.
Photoproduction of J/ψ from proton targets has previously been measured in Hall D [495] at 12 GeV,
providing the first detailed measurements of the proton’s gluon distribution in the threshold region of high
x=m2
J/ψ
2mpEγ. Similar measurements in nuclei, however, are limited by the sharply falling nuclear form
factor. The large mass of the J/ψ requires a high four-momentum transfer −t=−(pγ−pJ/ψ)2near the
production threshold, heavily suppressing the coherent production of J/ψ with low-energy photons. The
minimum momentum transfer decreases with increasing energy of the incident photon, allowing access to
the phase space dominated by coherent production. A consequence of this is that while the photoproduction
cross section of J/ψ from protons increases slowly with the photon energy, nuclear coherent production
cross sections increase much more dramatically as the kinematics grow more favorable, as shown in Fig. 68.
For this reason, while coherent J/ψ photoproduction off nuclei remains challenging at current 12 GeV
energies, the tagged photon energies enabled by a 22 GeV electron beam would enable such a measurement.
10 15 20 25
E
[GeV]
10 2
10 1
100
101
tot
[nb]
p J
/
p
2
H
J
/2
H
4
He
J
/4
He
Figure 68: Coherent J/ψ photoproduction cross
section from different nuclei, including free pro-
ton, deuterium, and 4He, as a function of the
photon energy.
This would provide the first measurement of the nuclear
gluon distributions at x > 0.23 and would be complemen-
tary to UPC measurements in heavy ion collisions and
diffractive VM production at the EIC, each of which has
limited ability to resolve nuclear gluon dynamics in this
near-threshold region.
Two observables are of particular interest in measur-
ing exclusive VM production. The first is the beam pho-
ton energy Eγ, which controls the longitudinal momen-
tum xof the gluons being probed. The second is the
momentum transfer , which is conjugate to the impact
parameter; performing a Fourier transform of the mea-
sured nuclear form factor gives access to the transverse
position distribution of the gluons [496]. One relation
this provides us is the extraction of the gluonic RMS ra-
89
dius of the nucleus, in a manner equivalent to the extraction of the charge radius from the form factor
slope:
⟨r2
g⟩=6
FA(0)
dFA
dt t=0
.(16)
This observable would be directly comparable to current UPC measurements, allowing validation of the
extracted deuteron properties.
The 22 GeV electron beam would enable a much higher-energy flux of real photons in Hall D as compared
with the current 12 GeV beam. We perform the following projections assuming an electron-tagged photon
luminosity of 200 pb−1in the energy range spanning 87.5−97.5% of the beam energy, or 19.25 < Eγ<
20.9 GeV. This corresponds to a kinematic region of x∼0.25. We similarly examine the case for a 17 GeV
beam, corresponding to x∼0.33. In each of these cases, lower photon energies, or higher values of x, can
be reached by reducing the coherent peak of the photon energy spectrum. We note for completeness that
the GlueX spectrometer was recently used successfully to measure photonuclear interactions off nuclei for
the study of short-range correlations, supporting the ability to perform measurements with nuclear targets
such as deuterium, helium and even lead [497].
The projections shown here were calculated by fitting previous measurements of the photoproduction
cross section from the proton [495,498], assuming the dipole form factor for the proton extracted from the
GlueX measurements in order to extrapolate the forward t= 0 photoproduction cross section as a function
of x, scaling this forward cross section by the appropriate factor A2for each nucleus, and replacing the
proton form factor with nuclear form factors obtained by Fourier transforming single-nucleon densities [499]
calculated using the AV18 [349] interaction. This provides a data-driven model of the differential cross
section for coherent photoproduction as a function of photon energy Eγand momentum transfer t. We have
considered here the light nuclei 2H and 4He; heavier nuclei can also be measured, but would result in events
concentrated closer to t= 0, decreasing our ability to resolve the transverse structure.
Figure 69 shows the projected statistical precision that can be achieved in the measurement of this
differential cross section. Here we have considered only the decay channel J/ψ →e+e−, with a branching
ratio of 5.97%, and conservatively assume a 50% efficiency for detecting the J/ψ and selecting the event. We
find that a substantial number of coherent events can be measured in the region of lower momentum-transfer,
but statistics do not allow mapping the form factor beyond |t|>0.5 GeV2; more complex features of the
form factor such as the node structure at higher |t|would require much higher statistics or beam energy.
We note that a major complication comes from the substantial incoherent background γA →J/ψX, in
0.0 0.2 0.4 0.6 0.8 1.0
t
[GeV
2
]
10 4
10 2
100
102
d
/
dt
[nb/GeV
2
]
(
Ee
= 17
GeV
) × 10 1
(
Ee
= 22
GeV
)
Incoherent
2
H
J
/2
H
GlueX 200 pb
1
0.0 0.2 0.4 0.6 0.8
t
[GeV
2
]
10 6
10 4
10 2
100
102
d
/
dt
[nb/GeV
2
]
(
Ee
= 17
GeV
) × 10 1
(
Ee
= 22
GeV
)
Incoherent
4
He
J
/4
He
GlueX 200 pb
1
Figure 69: Expected nuclear coherent J/ψ measurement statistics for deuterium (left) and Helium-4 (right).
Calculations were performed at electron energies of 17 GeV (scaled down by a factor of 10) and 22 GeV,
assuming an integrated luminosity of 200 pb−1for photons carrying between 87.5−97.5% of the beam
energy. Also included are projections for the incoherent background (dotted line), which dominate over the
coherent signal at these kinematics.
90
which the nucleus does not remain intact but breaks up into constituent nucleons. This process, the cross
sections for which were estimated by scaling the cross section from a free proton, is increasingly dominant
over coherent production at higher |t|, likely limiting the feasible measurement region to low-momentum-
transfer kinematics, and does not give insight to the average gluon structure of the nucleus; rather, it is
sensitive to fluctuations in the nuclear state. It is possible to reject this background by detecting final-state
particles resulting from nuclear breakup, such as relatively low-momentum protons or neutrons. Such event
rejection would likely require target engineering to ensure that incoherent nucleons are able to reliably exit
the target. Similar targets have previously been used in JLab experiments requiring low-momentum particle
tagging [427].
91
8 QCD Confinement and Fundamental Symmetries
The JLab 22 GeV upgrade will enable high-precision measurements of the Primakoff production of pseu-
doscalar mesons with results to explore the chiral anomaly and the origin and dynamics of chiral symmetry
breaking, allow model-independent determinations of the light quark mass ratio and the η-η′mixing angle,
and provide critical input to the hadronic light-by-light corrections to the anomalous magnetic moment of
the muon. The higher beam energy will also greatly improve the reach of direct searches for light (sub-GeV)
dark matter scalars and pseudoscalers through Primakoff production, add to the reach and robustness of
Standard Model tests using parity-violation in deep inelastic scattering (PVDIS), and expand opportunities
for studies with secondary beams.
Figure 70: The QCD symmetries at low-energy and the properties of light pseudoscalar meson π0,η, and η′.
8.1 Precision Measurements of π0,η, and η′Decays
Three lightest neutral self-conjugated pseudoscalar mesons, π0,η, and η′, are manifestation of fundamental
symmetries of the nonperturbative QCD ground state. They provide a rich laboratory for tests of the
fundamental symmetries in the Standard Model and beyond [500].
In the chiral limit where the quark masses are set to zero, as shown in the left-hand side of Fig. 70, the
QCD Lagrangian LQCD is invariant under the global symmetry group of SU (3)L×SU(3)R×U(1)A×U(1)B.
These symmetries, however, appear in nature differently. The condensation of quark–antiquark pairs in
the QCD vacuum spontaneously breaks the chiral symmetry SU (3)L×S U (3)Rdown to the flavor SU(3)V
symmetry. Each broken generator results in a massless Nambu–Goldstone boson, corresponding to the octet
of pseudoscalar mesons (π0,π±,K±,K0,¯
K0, and η8). The U(1)Asymmetry is explicitly broken by the
quantum fluctuations of the quarks coupling to the gauge fields, known as the chiral anomaly [501,502].
Such anomalous symmetry breaking has a purely quantum-mechanical origin, representing one of the most
profound symmetry breaking phenomena. The anomaly associated with quarks coupling to the gluon fields
prevents η0from being a Goldstone boson; the same anomaly is also related to so called “the θterm” in
the strong PC problem. Consequently, the singlet η0acquires a nonvanishing mass in the chiral limit [503].
This axial anomaly is proportional to 1/Nc, where Ncis the number of colors. Therefore η0does become a
Goldstone boson [504] at the large Nclimit. On the other hand, the anomaly associated with the coupling
of quarks to the electromagnetic field, is primarily responsible for the two-photon decays of π0,η, and η′.
If the quark masses are turned on (which are small compared to the chiral symmetry breaking scale
92
∼1 GeV), as shown in the right-hand side of Fig. 70, the chiral symmetry is explicitly broken and thereby
generates masses for the Nambu–Goldstone bosons, following the mechanism discovered by Gell-Mann,
Oakes, and Renner [505]. Furthermore, the unequal quark masses break the SU (3)Vflavor symmetry
(and, to a lesser extent, isospin), leading to mixing between the chiral limit states. The mixing of π0and
ηis proportional to mu−md, and the mixing of ηand η′is proportional to ms−ˆm( ˆm= (mu+md)/2).
In addition, the isospin symmetry breaking gives rise to hadronic decays of η→π+π−π0and η→3π0,
where their partial decay widths are normalized to the partial decay width of η→γγ experimentally. These
decays constitute one of the relatively rare isospin-breaking hadronic observables that the electromagnetic
effects are strongly suppressed [506,507], offering clean experimental access to the light quark mass difference
mu−md. Lastly, U(1)Bbaryon number symmetry is also broken explicitly by the axial anomaly associated
with electroweak gauge fields, however, this effect is negligible except in the very early Universe [508].
π0, η, η′
µ
Figure 71: Pseudoscalar pole contributions
to hadronic light-by-light scattering in the
anomalous magnetic moment of the muon;
crossed diagrams are not shown. The red
blobs denote the pseudoscalar transition
form factors. Figure taken from Ref. [500].
A study of π0,η, and η′also plays a critical role in search-
ing for new physics beyond the Standard Model. The un-
certainty in the Standard Model prediction of the anoma-
lous magnetic moment of the muon (aµ) is dominated by
hadronic effects [509]. Next to hadronic vacuum polarization,
the second-most-important contribution is given by a loop
topology dubbed hadronic light-by-light scattering (HLbL),
which in turn is dominated by pole contributions of the lightest
flavor-neutral pseudoscalars π0,η, and η′, as shown in Fig. 71.
The strength of these contributions is determined by the singly
and doubly virtual transition form factors (TFFs).
For the largest individual HLbL contribution, the π0pole
term, a data-driven, dispersion-theoretical determination of the
TFF has been performed [510,511]. It is based on the incorpo-
ration of the lowest-lying singularities due to 2πand 3πintermediate states, information on the asymptotic
behavior in QCD, and experimental data for the π0→γγ decay width as well as the spacelike singly vir-
tual TFF available at high energies. The result allows for a precise assessment of the different sources of
uncertainty,
aπ0
µ= 63.0(0.9)Fπγγ (1.1)disp 2.2
1.4BL(0.6)asym ×10−11 = 63.02.7
2.1×10−11 ,(17)
where the individual uncertainties refer to the form factor normalization, dispersive input, experimental
uncertainty in the singly virtual data, and the onset of the asymptotic contribution, in order. Here, the
normalization uncertainty has already been reduced from the original publications [510,511] to the value in
Eq. (17) given in the White Paper [509], thanks to the improved value for the π0radiative width obtained
by the PrimEx Collaboration [512] (shown as a solid blue point in Fig. 72). The result in Eq. (17) is in good
agreement with the lattice QCD calculation [513], however, mainly after readjusting the TFF normalization
to the PrimEx experimental value [512]. Remarkably, while the chiral corrections [514–516] increase the π0
width about 4% compared to the prediction based on the chiral anomaly alone (see Fig. 72) that is in slight
tension with the PrimEx result, the lattice calculation [513] points toward to a form factor normalization that
is on the small side. Further independent studies of the π0TFF in lattice QCD are in progress [517,518].
An experimental opportunity enabled by an energy upgrade to 22 GeV to produce π0off an atomic electron
target (described below) to further improve the experimental precision for both decay width and TFF of π0,
will be clearly important.
Beyond the normalization, a precise measurement of the slope of the π0TFF provides an important
constraint on the calculation of aµ. The sum rule [510,511]
m2
π0
Fπγγ
∂
∂q2Fπ0γ∗γ∗(q2,0)q2=0
= 31.5(2)Fπγγ (8)disp (3)BL ×10−3= 31.5(9) ×10−3(18)
is more sensitive to the dispersive input and allows for an important cross-check on the matching to the
high-energy asymptotics [519].
93
While significant work on dispersion-theoretical analyses of the ηand η′TFFs has already been per-
formed [500,520–523], a fully data-driven determination of the corresponding aµcontributions in analogy
to π0has not yet been completed. The numbers in Ref. [509] are based on a phenomenological data-driven
approach using rational approximants [524],
aη
µ= 16.3(1.4) ×10−11 , aη′
µ= 14.5(1.9) ×10−11 ,(19)
where the uncertainties could be further improved and be decomposed in terms of individual sources of input
in the manner of Eq. (17) by the future experimental data. Both ηand η′TFF normalizations and (singly
virtual) high-energy asymptotics therein are closely linked to η–η′mixing [525]. For η, a recent lattice-QCD
calculation of aη
µ[526] (with a further one in progress [518]) suggests fair agreement with Eq. (19), but
again demonstrates quite some tension with the phenomenological low-energy parameters, normalization
and slope, of the corresponding TFF. Interestingly, once again the radiative width for η→γγ is relatively
small compared to the Particle Data Group average [31] that includes only the results from the e+e−collision
measurements, and much closer to a Primakoff result by the Cornell Collaboration [527] published in 1974.
Clearly, high-precision experimental determinations of the decay widths for π0,η, η′→γγ and their space-
like singly virtual TFF’s at small Q2within the modern JLab Primakoff program would be most valuable
in this respect.
In summary, a study of π0,η, and η′will have great potential to shed light on some fundamental questions
in the Standard Model and beyond: testing the chiral anomaly and probing the origin and dynamics of chiral
symmetry breaking; offering a clean path for model independent determinations of the light quark-mass ratio
and the η-η′mixing angle; and providing critical inputs to the theoretical calculations of the hadronic light-
by-light contributions to the anomalous magnetic moment of the muon [500].
In the past two decades, the PrimEx Collaboration has successfully developed a comprehensive Primakoff
experimental program at JLab 6 and 12 GeV with nuclear targets. The Primakoff effect [528] is a process of
high-energy photo- or electroproduction of mesons in the Coulomb field of a target. This program includes
high-precision measurements of the two-photon decay widths Γ(P→γγ) and the spacelike transition form
factors FP γ∗γ∗(−Q2,0) at four-momentum transfers Q2= 0.001 . . . 0.3 GeV2, where Prepresents π0,η, and
η′[529]. The JLab 22 GeV upgrade will enable such measurements with experimental sensitivities not
previously achievable.
8.1.1 Primakoff Production of π0From Atomic Electrons
As the lightest hadron, π0plays a special role in our understand of QCD confinement. Its radiative decay
width is one of very rare parameters in low-energy QCD that can be predicted at ≈1% precision, offering an
important test of QCD confinement. The chiral anomaly drives the decay of the π0meson into two photons
with no adjustable parameters in the predicted decay width [501,502,530]:
Γ(π0→γγ) = m3
π0α2N2
c
576π3F2
π0
= 7.750 ±0.016 eV,(20)
where αis the fine-structure constant, mπ0is the π0mass, Nc= 3 is the number of colors in QCD. This
prediction, shown as a dark red band in Fig. 72, is exact in the chiral limit (except for an experimental uncer-
tainty contributed from the pion decay constant, Fπ0= 92.277±0.095 MeV, extracted from the charged pion
weak decay [531]). Due to the small mass of the π0, higher order corrections to this prediction induced by
the non-vanishing quark masses are small (∼4%) and can be calculated with percent accuracy. Several inde-
pendent theoretical calculations are shown as color bands in Fig. 72. These calculations are performed either
in the framework of chiral perturbation theory (ChPT) up to O(p6) (NLO) [514,515] (NNLO corrections
are considered in Ref. [516]) or based on QCD sum rules [532].
The two most recent experiments (PrimEx-I and PrimEx-II) on π0were carried out with nuclear targets
(12C, 28 Si, and 208Pb) during the JLab 6 GeV era. The weighted average of PrimEx I and II results is
Γ(π0→γγ) = 7.802(052)stat(105)syst eV [512]. This result with a 1.50% total uncertainty, shown as a solid
94
Figure 72: The projected precision on Γ(π0→γγ) with an atomic electron target (the red point) and
the previous published results (the blue points) listed in PDG [31]. Theoretical predictions are: chiral
anomaly [501,502] (dark red band); IO, QCD sum rule [532] (gray band); KM, ChPT NNLO [516] (ma-
genta band); AM, ChPT NLO [515] (blue band); GBH, ChPT NLO [514] (green band).
blue point in Fig. 72, represents the most accurate measurement of this fundamental parameter to date. Its
central value agrees to the leading-order chiral anomaly prediction [530] and is 2σbelow the theoretical
calculations [514–516,532] based on higher-order corrections to the anomaly. This is clearly a significant
result calling for further investigations. An experimental opportunity enabled by a JLab 22 GeV upgrade
to produce π0off an atomic electron target to reach a sub-percent precision on Γ(π0→γγ), as shown in
Fig. 72, is necessary to better understand the discrepancy between the existing experimental result and the
high-order QCD predictions.
The biggest challenge for using a nuclear target is that the Primakoff effect is not the only mechanism
for the production of mesons, as shown Fig. 73 (left). There is nuclear coherent background from strong
production, an interference between the strong and Primakoff production amplitudes, and the incoherent
nuclear process. The classical method of extracting the Primakoff amplitude is to fit the measured total
differential cross section in the forward direction based on the different characteristic behaviors of the pro-
duction mechanisms with respect to the production angles. If using an electron target, all these nuclear
backgrounds can be eliminated.
The threshold for photo- or electroproduction of π0off an electron target is 18 GeV. An energy upgrade
of the electron beam at JLab to 22 GeV will thus enable precision measurements of radiative decay width
(using photo-production) and transition form factor (using electroproduction) of π0off an electron for the
first time. The Primakoff production off an atomic electron has significant advantages over a nucleus in the
following areas:
•Elimination of all nuclear backgrounds. The largest systematic uncertainty in the previous PrimEx I
and II experiments [512] with nuclear targets (12C, 28Si, and 208Pb) is due to yield extraction (∼1 %)
to separate Primakoff events from the nuclear backgrounds, as shown in Fig. 73 (left). With an electron
95
0
10
20
30
40
50
60
70
0 0.5 1 1.5 2 2.5
28Si
production angle, (deg)
dσ / dθ, (μbarn / rad)
Total
Primakoff
Nuclear Coherent
Interference
Incoherent
0 0.2 0.4 0.6 0.8
]
o
[
lab
0
π
θ
0
100
200
300
]
o
[nb/0.001
lab
0
π
θ
d/
σ
d
JLab 22 GeV
Figure 73: Left: The measured cross section of γ+Si→π0+Si from the PrimEx II experiment [512] (with
Eγof 4.45–5.30 GeV). Right: The projected cross section of γ+e→π0+eat JLab 22 GeV (with Eγof
20–22 GeV and without smearing of the experimental resolutions).
target, all nuclear backgrounds will be eliminated, see Fig. 73 (right).
•Elimination of uncertainties due to nuclear effects. Extracting Γ(π0→γγ) from the measured Pri-
makoff cross section off a nucleus requires knowing the nuclear charge form factor, corrected for the
initial-state interaction of the incoming photon (or electron in the case of TFF measurement) and
the final-state interaction of the outgoing mesons in the nuclear medium. Using an electron target (a
point-like particle) eliminates all uncertainties related to these nuclear effects.
•Enabling recoil detection. For the case of a nuclear target, the momentum of the recoil nucleus in the
Primakoff process is too small to measure. Primakoff production off an electron target will enable
detection of the recoil electron to suppress backgrounds, such as those from the beam line, offering a
cleaner Primakoff signal.
The projected precision on Γ(π0→γγ) with an atomic electron target is ≈0.95% (the red point
in Fig. 72), a one-third reduction of uncertainty from the previous PrimEx I and II (the blue point in
Fig. 72) [512]. It will independently verify the observed discrepancy between the previous PrimEx result [512]
and the high-order QCD predictions, offering a stringent test of low-energy QCD.
8.1.2 Primakoff Productions of ηand η′From Nuclear Targets
In addition, the 22 GeV upgrade will greatly enhance the Primakoff measurements of the two-photon decay
widths and the transition form factors of ηand η′off nuclear targets. As shown in Fig. 73 (left), the
Primakoff cross section is peaked at a small polar angle, θP r ∼m2
2E2, and increases with the beam energy,
[dσP r
dΩ]max ∼Z2E4
m3, where E,m, and Zare the beam energy, the meson mass and the charge of target,
respectively. The nuclear coherent cross section has a broader distribution peaked at a relatively larger
angle, θNC ∼2
EA1/3. A higher beam energy will help better separating the Primakoff from the nuclear
backgrounds, as well as increasing the Primakoff cross section, which is more important for massive mesons,
such as η′, as demonstrated in Fig 75.
96
Figure 74: Light quark mass ratio Qdetermined by two different methods. The left-hand side are calculated
from the η→3πdecay determined by using the Cornell Primakoff [527], the collider average [531] exper-
imental results, and the projected Primakoff measurement at JLab 22 GeV for Γ(η→γγ) as input. The
right-hand side shows the results of Qobtained from the kaon mass difference with different theoretical esti-
mates for the electromagnetic corrections based on Dashen’s theorem, Ref. [533] (KN), and the lattice [534].
This figure is taken from Ref. [500] with modifications.
' angle (deg)η
0 0.5 1 1.5 2 2.5 3
barn / rad)µ (θ / dσd
0
0.2
0.4
0.6
0.8
1
' angle (deg)η
0 0.5 1 1.5 2 2.5 3
barn / rad)µ (θ / dσd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Total
Primakoff
Coherent
Incoherent
Interference
Figure 75: Differential cross sections of γ+4H e →η′+4He as a function of the η′production angles for the
beam energy of 10 GeV (left) and of 20 GeV (right).
The PrimEx-eta experiment [535] on the ηradiative decay width, Γ(η→γγ), was recently completed for
data collection in 2022 with JLab 12 GeV. The data analysis is in progress with an anticipated precision of 4-
6% (based on the current preliminary assessment). With a JLab 22 GeV upgrade, the projected precision for
Γ(η→γγ) will be at level of 2%. The existing published results on this parameter were performed using two
photon interactions either via the Primakoff effect or through e+e−collisions (e+e−→γ∗γ∗e+e−→ηe+e−).
The collider results listed in PDG [31] have individual experimental uncertainty ranging from 4.6% to 25%.
They are consistent within the experimental uncertainties, however, their average value is about ∼4σlarger
than the previous Primakoff result [527] (with 14% precision) published by the Cornell Collaboration in
1974. New precision Primakoff result from JLab at 22 GeV (or even at the current 12 GeV potentially) will
help resolving this long-standing puzzle.
All other ηpartial decay widths listed in the PDG [31] are normalized to the two-photon decay width. A
precision measurement of Γ(η→γγ) will improve all other partial decay widths in the ηsector, thus offering a
broader impact. One of such examples is to determine the light quark mass ratio, Q ≡ (m2
s−ˆm2)/(m2
d−m2
u),
by improving the accuracy of the η→3πdecay width [536]. The fundamental parameter Qdrives isospin
violation in the Standard Model. In most cases, however, the isospin-violating observables are also affected
97
by electromagnetic effects. In order to extract information on Q, one must first calculate and disentangle
the contribution due to electromagnetic interactions. For example, in the case of K+–K0mass difference
as shown in Fig. 74 (right), the extracted Qfrom such observable is sensitive to the theoretical calculations
of the electromagnetic correction. By contrast, the η→3πdecay is caused almost exclusively by the
isospin symmetry breaking part of the Hamiltonian ∼(mu−md)(u¯u−d¯
d)/2. Moreover, Sutherland’s
theorem [506,507] forbids electromagnetic contributions in the chiral limit; and contributions of order α
are also suppressed by (mu+md)/ΛQCD. These single out η→3πto be the best path for an accurate
determination of Q[500,536]. As shown in Fig. 74 (left), the largest systematic uncertainty for the current
value of Qdetermined from η→3πis dominated by the experimental discrepancy between the Cornell
Primakoff result [527] and the collider average [31] for Γ(η→γγ). The projected Primakoff measurement of
Γ(η→γγ) at JLab 22 GeV upgrade will offer a more precise determination of Qby resolving this discrepancy,
shown as a red point in Fig. 74 (left).
All existing measurements of Γ(η′→γγ) were carried out by using e+e−collisions, shown as the blue
points in Fig. 76, with experimental uncertainty for each individual experiment in the range of 7.3%–27% [31].
The JLab energy upgrade will be essential to perform the first Primakoff measurement on Γ(η′→γγ) by
helping a clean separation of the Primakoff signal from the nuclear backgrounds, as demonstrated in Fig 75.
The projected precision of ∼3.5% for Γ(η′→γγ) at JLab 22 GeV, the red point in Fig. 76, will help our
understanding of the U(1)Aanomaly coupling to the gluon field. The precision measurements of ηand η′,
coupled with theory, will provide further input for global analyses of the η–η′system to determine their
mixing angles and decay constants. Moreover, it will further pin down the contributions of ηand η′to the
light-by-light scattering in (g−2)µ.
8.2 Search for sub-GeV Dark Scalars and Pseudoscalars via the Primakoff Ef-
fect
The Primakoff cross section, σP r ∼Z2
m3log(E), will increase with a higher beam energy and a higher Z
target. The proposed high-energy and high-luminosity upgrade at JLab will offer opportunities to directly
search for sub-GeV dark scalars and pseudoscalars via the Primakoff production off a heavy target (such as
Pb), probing two out of four the most motivated portals coupling the Standard Model sector to the dark
sector. The distinguishable characteristics of Primakoff mechanism will serve as filters to suppress the QCD
backgrounds. The candidates of scalar and pseudoscalar can be explored by hunting for resonant peaks of
γγ,e+e−,µ+µ−,ππ, and πππ in the forward angles where the Primakoff production dominates.
The Dark Matter (DM) constitutes about 85% of the matter in the Universe. Very little knowledge
about the nature of DM is known, except its gravitational property. There is a strong consensus among the
physics community about the vital importance of broadening the scope of new physics searches [537–539],
both in parameter space and in experimental approaches. Recently, sub-GeV dark matter or mediators have
gained strong motivation, driven partly by several observed anomalies. The reported excesses in high-energy
cosmic rays could be explained by dark matter annihilation [540,541]. The muonic anomaly [542–544] and
an anomalous e+e−resonance observed in 8Be decay [545,546] can be resolved with new gauge bosons.
In addition, the scalar and pseudoscalar-mediated dark forces can solve small scale structure anomalies in
dwarf galaxies and subhalos, while satisfying constraints on larger galaxy and cluster scales [547–549]. If
these phenomena are interpreted in terms of new physics, all point toward DM or mediators in the MeV–
GeV mass range. A 22 GeV upgrade will greatly advance searches for such scalars and pseudoscalars via the
Primakoff effect.
As an example, we considered a hypothetical Axion-Like Particle (ALP) [550,551], a, produced from
the Primakoff process, γ+P b →a+P b with a→γγ, using the GlueX apparatus with an upgraded
forward calorimeter (FCAL-II) that is currently underinstallation. The cross section for this process is
dσ
dΩ= Γa→γγ 8αZ 2
m3
a
β3E4
Q4|Fe.m. (Q)|2sin2θlab
a[551]. The ALP radiative decay width is Γa→γγ =c2
γm3
a
64πΛ2,
where cγ
Λis the coupling of axion to the photon as described in Ref. [550,551]. Assuming the space between
the P b target (∼5% R.L.) and FCAL-II has a distance of 10.5 m and is filled with the He gas only, one
98
Figure 76: The existing experimental results (the blue points) of the η′→γγ decay width by the collider
experiments [31] and the projected measurement at JLab 22 GeV (the red point) via the Primakoff effect.
searches for the ALP that decays either inside of the target (prompt) or after the target (displaced). As
shown in Fig. 77, the projected GlueX reach at JLab 22 GeV for a 2σsignificance (see orange band) with
1 pb−1integrated luminosity (corresponding to ∼120 days of beam time for a photon flux of ∼108γ/s) is
competitive to the reaches by the Belle II with 50 ab−1integrated luminosity [552] that is equivalent to
about 7 years of running.
8.3 Electroweak Studies with SoLID
Parity-violation in deep inelastic scattering (PVDIS) provides a sensitivity to Beyond Standard Model (BSM)
couplings. The parity-violating asymmetry APV is generated from the interference of electromagnetic and
weak neutral currents and measured experimentally by scattering a longitudinally polarized electron beam
on an unpolarized target. Measuring the the parity-violating asymmetry from electron-deuteron scattering
allows for the measurement the effective electron-quark coupling constants (2Ciu −Cid) with i= 1,2 which,
under the Standard Model, can be expressed as a function of the weak mixing angle sin2θW.
An experimental program for measurements of AP V is planned to run at JLab, utilizing the planned
Solenoidal Large Intensity Device (SoLID) [557] spectrometer. The large acceptance and high luminosity
capability of SoLID makes it ideal for a precision measurement of the parity-violating asymmetry. Upgrading
CEBAF to 22 GeV and using SoLID will extend the Q2and xrange beyond what is possible at 11 GeV.
As described in Section 4.1, a program of measurements with SoLID at 22 GeV will significantly improve
knowledge of quark parton distribution functions over a broad range of x. Additionally, measurements at
22 GeV of AD
P V from the deuteron will also provide an improvement in the overall uncertainty on the effective
electron-quark coupling constants (2Ciu −Cid) of about 15%, as compared to the expected uncertainty from
the 11 GeV experiment.
8.4 Secondary Beams
The stopping of the high-energy beam will produce a shower of radiation, most of which will be contained in
the thick beam dump, while deeply penetrating muons and neutrinos will continue to propagate, producing
99
2−
10 1−
10 1
]
2
c [GeV/
a
m
6−
10
5−
10
4−
10
3−
10
2−
10
]
-1
[GeVΛ /
γ
c
, prompt
-1
GlueX@22GeV, Pb, 1pb , prompt & displaced
-1
GlueX@22GeV, Pb, 1pb
-1
Belle II (a), 50 ab-1
Belle II (b), 50 ab , prompt & displaced
-1
GlueX@12GeV, Pb, 1pb
Figure 77: The experimental reaches for the ALP-photon coupling vs. the ALP mass. The pro jected
reaches for GlueX at JLab 22 GeV (in yellow and orange) are estimated for a P b target with 1 pb−1
integrated luminosity. The reach at GlueX 12 GeV (in blue) is from [551]. The projected Belle II [552] (a:
prompt decay and b: displaced vertex) reaches (in pink) are for 50 ab−1integrated luminosity. The existing
limits [553–556] are shown in gray.
high-intensity secondary beams. Simulations have shown that the neutrino flux above the dump is character-
ized by a decay-at-rest (DAR) spectrum. It is expected that the intense neutrino flux of ∼9·1017 expected to
be available at 10 GeV, a flux that is comparable to flagship DAR-neutrino facilities such as the Spallation
Neutron Source at Oak Ridge National Lab, would be doubled by the increase in beam energy to 22 GeV.
Such a neutrino facility would enable studies of coherent elastic neutrino-nucleus scattering (CEνNS), with
count rates up to 40 times more than the recently published COHERENT measurement [558]. As the
CEνNS cross section is a clean, tree-level prediction of the Standard Model, such measurements would be
provide a means to search for BSM signals that might arise from non-standard interactions such as dark
matter, new mediators, or a large neutrino magnetic moment. In addition, CEνNS provides a different and
complementary way to measure Standard Model parameters such as the neutron radius of nuclei and weak
mixing angle sin2θW.
Further opportunities would be gained with the addition of a secondary beamline, such as is envisioned
for the approved BDX experiment [559]. Muons are produced in the electron beamdump primarily by Bethe-
Heitler radiation. A high-intensity flux of ∼3·108µ/s (∼2·109µ/s) is expected at the exit of the concrete
vault, produced by and mainly collinear with a a 10GeV (20 GeV) primary e-beam. Figure 78 compares the
simulated Bremsstrahlung-like energy distribution for 10GeV and 20 GeV primary e-beams. Such a muon
beam would offer the possibility to search for muon-coupling light dark scalars that may explain the (g−2)µ
anomaly [560]. A similar enhancement due to higher energy is also be expected for the production of light
dark matter (through A′-sstralhung, resonant and non-resonant annihilation) that will be searched for by
the BDX experiment [559,561], as shown in Fig. 79.
100
3E8 μ/s
2E9 μ/s
e- beam @ 10 GeV
e- beam @ 20 GeV
Figure 78: Muon energy distribution produced by interactions of a 10 GeV (20 GeV) electron beam with
the beam dump in Hall A.
Figure 79: The BDX sensitivity at 90% CL (green curve) by using a 22GeV electron beam. The limit is
given for the scaling parameter y, proportional to the LDM-SM interaction cross section, as a function of the
LDM mass mχ. The curve refers to the ideal case of a zero-background measurement, assuming a 300 MeV
energy threshold and an overall 20% signal efficiency.
101
9 CEBAF Energy ‘Doubling’ - Accelerator Concept
The previous energy upgrade of CEBAF, from 6 to 12 GeV, was achieved by installing additional SRF
cavities in the North and South LINACs, increasing the energy gain per pass, while leaving the maximum
number of passes unchanged. Recent advances in accelerator technology have made it possible to further
extend the energy reach of the CEBAF accelerator up to 22 GeV within the existing tunnel footprint. In the
proposed energy upgrade, the energy gain per pass remains unchanged, while the number of recirculations
through the accelerating cavities is nearly doubled. Encouraged by the recent success of the CBETA project
(Cornell Brookhaven Electron Test Accelerator) [562]), a proposal was formulated to increase the CEBAF
energy from the present 12 GeV to about 22 GeV by replacing the highest-energy arcs with Fixed Field
Alternating Gradient (FFA) arcs [563], as illustrated schematically in Fig. 80).
Figure 80: Sketch of the CEBAF accelerator with the two highest energy arcs, Arc 9 and Arc A, replaced
with a pair of FFA arcs (green).
The design is based on an exciting new approach to accelerate electrons efficiently with multiple LINAC
passes and transporting them through a single FFA beamline, as was successfully demonstrated by CBETA
project. The Non-Scaling FFA approach allows beam acceleration within a small beam pipe as in syn-
chrotrons, but without varying the magnetic field. These recirculating 180◦FFA arcs are made up of 86
repeating cells. The arc’s building block is a compact, 2.8-m-long, FODO cell composed with two magnets
and two drifts. Each of the magnets is a multi-function Halbach magnet [564], [565] with dominant dipole
and quadrupole fields. One magnet per cell bends and focuses the electron beam, and the other bends
and de-focuses in the same plane. As illustrated in Fig. 81, different energy beams may be transported
through a narrow beam pipe, since the transverse orbit offsets are confined to small aperture of about 5 cm.
Closely spaced orbits and low betas (5 m) result from very strong focusing, reducing the horizontal dispersion
function from meters in conventional separate functions arcs down to a few cm in the FFA arc.
The new pair of arcs configured with an FFA lattice would support simultaneous transport of 6 passes with
energies spanning a factor of two. This wide energy bandwidth could be achieved using the non-scaling FFA
principle implemented with Halbach-style permanent magnets. As illustrated in Fig. 82, the magnet design
features an open mid-plane geometry, in order for the synchrotron radiation to pass through the magnets,
while minimizing radiation damage to the permanent magnet material. This novel magnet technology saves
energy and lowers operating costs.
102
Figure 81: Compact FODO cell configured with two combined function magnets featuring closely spaced
orbits and small Twiss functions for six different energy beams.
Figure 82: The cross section and field specs of the open mid-plane magnets consisting of 24 wedge-shaped
pieces of NdFeB. The outer wedges are symmetrical, while the top and bottom wedges have two edges parallel
to the horizontal axis.
In addition to the spreaders, one must design the time-of-flight horizontal ‘Splitters’ for each of the
energies that pass through the FFA arcs. These will be located along the new FFA arcs, downstream of the
spreaders (shown as purple boxes in in Fig. 80) Conceptually, they will be similar to those at CBETA. They
103
will need to fit in the space currently occupied by the highest-energy passes in the CEBAF recirculating
arcs. This would necessitate a pair of time-of-flight splitters, which are capable of adjusting the momentum
compaction, M56, at both East and West FFA arc.
One of the challenges of the multi-pass LINAC optics is to provide uniform focusing in a vast range of
energies, using fixed field lattice. The current CEBAF is configured with a 123 MeV injector feeding into a
racetrack Recirculating Linear Accelerator (RLA) with a 1.1 GeV LINAC on each side. Increasing number
of LINAC passes to 10+ makes optical matching virtually impossible due to extremely high energy span
ratio (1:175).
The proposed new building block of LINAC optics is configured as a sequence of triplet cells flanking two
cryomodules. Initial triplets, based on 45 Tesla/m quads, are scaled with increasing momentum along the
LINAC. This style LINAC focusing provides a stable multi-pass optics compatible with much smaller beta
functions in the FFA arcs and it is capable of covering energy ratio of 1:33. This sets the minimum injection
energy at 650 MeV. In the current concept, it is proposed to replace old 123 MeV injector with a 650 MeV
3-pass recirculating injector based on the existing LERF facility augmented by three C-70 cryomodules. The
upgraded 650 MeV injector is schematically illustrated in Fig. 83. The beam is then transferred from the
LERF vault through a dedicated fixed energy 650 MeV transport line and injected into the North LINAC
Figure 83: Schematic view of 650 MeV recirculating injector (3-pass) based on LERF.
Staying within the CEBAF footprint, while transporting high energy beams (10-22 GeV) calls for special
mitigation of synchrotron radiation effects. One of them is to increase the bend radius at the arc dipoles
(packing factor of the FFA arcs increased to about 92%). Arc optics was designed to ease individual
adjustment of momentum compaction and the horizontal emittance dispersion, H, in each arc to suppress
adverse effects of the synchrotron radiation on beam quality: dilution of the transverse and longitudinal
emittance due to quantum excitations Table 1lists arc-by-arc cumulative dilution of the transverse, ∆ϵN,
and longitudinal, ∆σ∆E
E, emittances due to quantum excitations calculated using the following analytic
formulas:
∆ϵN=2π
3Cqr0< H > γ6
ρ2,(21)
∆ϵ2
E
E2=2π
3Cqr0
γ5
ρ2,(22)
Here, ∆ϵ2
Eis an increment of energy square variance, r0is the classical electron radius, γis the Lorentz
boost and Cq=55
32√3
ℏ
mc ≈3.832 ·10−13 m for electrons (or positrons). The horizontal emittance dispersion
in Eq. 21, is given by the following formula: H= (1 + α2)/β ·D2+ 2α DD′+β·D′2where D, D′are the
bending plane dispersion and its derivative, with averaging over bends defined as: < ... > =1
πRbends ... dθ.
In summary, the proposed 22 GeV, 10-pass, design would promise to deliver a normalized emittance of
61 mm·mrad with a relative energy spread of 1.2·10−3. Further recirculation beyond 22 GeV is limited
by large, 0.9 GeV per electron, energy loss due to synchrotron radiation, which depends on energy to the
104
Pass number Beam Energy ϵx
Nσ∆E
E
[GeV] [mm mrad] [%]
1 2.8 1.0 0.01
2 5.0 2 0.02
3 7.2 4 0.02
4 9.4 12 0.03
5 11.5 20 0.03
6 13.7 21 0.04
7 15.8 23 0.05
8 17.9 26 0.06
9 19.9 34 0.08
10 21.9 49 0.11
10.5 22.9 61 0.12
Table 1: The horizontal and longitudinal emittances diluted by synchrotron radiation as delivered at various
passes. Here, σ∆E
E=q∆ϵ2
E
E2.
fourth power. The net energy loss is comparable to the energy gain per LINAC, which clearly sets the limit
of reasonable number of recirculations.
Finally, given the greater total energies expected with this upgrade, we are also investigating the impact
this will have on our extraction system and beam delivery to the experimental halls. For the extraction
system, this will depend partly on the needs of the experimental program, and partly on how we choose to
extract the beam. For the beam delivery to the halls, the hall beamlines are currently under investigation.
Improvements to the magnetic septa are expected to be required, and the dipoles to the hall lines will need
to be strengthened and improved as well. The overall optics will require some adjustments, but should be
manageable.
One of the more challenging aspects of this design is the method of beam extraction. Multiple methods
are under consideration, each with associated limitations on the flexibility of beam delivery – the resulting
scheme has to balance the needs of the users, technical feasibility, and cost.
To conclude, significant progress has been made in the design of the energy upgrade for CEBAF using
FFA transport. Over the last year, we have settled on a design concept, developed more detailed designs of
various machine sections, and iterated some sections as simulations were performed. While the full design
is not yet completed, we are working toward that goal as we begin to consider other aspects of this upgrade
concept.
105
10 Workshops
This White Paper is a culmination of several dedicated workshops conducted since the spring of 2022. These
workshops led up to the final event, the mini-symposium held at the annual APS April meeting 2023. We
are pleased to provide access to the presentations from these workshops through the following links:
J-FUTURE, March 28–30, 2022 Jefferson Lab and Messina University (Italy). Organizers: Marco
Battaglieri, Alessandro Pilloni, Adam Szczepaniak, Eric Voutier.
High Energy Workshop Series 2022, Jefferson Lab
–Hadron Spectroscopy with a CEBAF Energy Upgrade, June 16-17, 2022. Organizers: Marco
Battaglieri, Sean Dobbs, Derek Glazier, Alessandro Pilloni, Justin Stevens, Adam Szczepaniak,
Alaina Vaughn.
–The Next Generation of 3D Imaging, July 7-8, 2022. Organizers: Harut Avagyan, Carlos Munoz
Camacho, Jian-Ping Chen, Xiangdong Ji, Jianwei Qiu, Patrizia Rossi.
–Science at Mid-x: Anti-shadowing and the Role of the Sea, July 22-23, 2022. Organizers: John
Arrington, Mark Dalton, Cynthia Keppel, Wally Melnitchouk, Jianwei Qiu.
–Physics Beyond the Standard Model, Aug. 1, 2022. Organizers: Marco Battaglieri, Bob McKe-
own, Xiaochao Zheng.
–J/Psi and Beyond, Aug. 16-17, 2022. Organizers: Ed Brash, Ian Clo¨et, Zein-Eddine Meziani,
Jianwei Qiu, Patrizia Rossi.
APCTP Focus Program on Nuclear Physics 2022: Hadron Physics Opportunities with JLab Energy
and Luminosity Upgrade, July 18-23, 2022, Korea. Organizers: Harut Avagyan, Chueng-Ryong Ji,
Kyungseon Joo, Victor Mokeev, Yongseok Oh, A. Vladimirov.
ECT*: Opportunities with JLab Energy and Luminosity Upgrade, Sep. 26-30, 2022, Italy. Organizers:
Moskov Amaryan, John Arrington, Harut Avagyan, Alessandro Bacchetta, Marco Battaglieri, Lamiaa
El Fassi, Ralf Gothe, Or Hen, Xiangdong Ji, Kyungseon Joo, Xiaochao Zheng.
Science at the Luminosity Frontier: Jefferson Lab at 22 GeV, Jan. 23-25, 2023, Jefferson Lab. Organiz-
ers: “Spectra and Structure of Heavy and Light Hadrons as Probes of QCD”: Ralf Gothe, Matt Shep-
herd; “Sea and Valence Partonic Structure and Spin”: Jian-Ping Chen, Ioana Niculescu, Nobuo Sato;
“Form Factors, Generalized Parton Distributions and Energy-Momentum Tensor”: Latifa Elouadrhiri,
Garth Huber, Christian Weiss; “Fragmentation, Transverse Momentum and Parton Correlations”:
Harut Avagyan, Dave Gaskell, Nobuo Sato; “Hadron-Quark Transition and Nuclear Dynamics at Ex-
treme Conditions”: Lamiaa El Fassi, Misak Sargasian; “Low-Energy Tests of the Standard Model and
Fundamental Symmetries”: Liping Gan, Kent Paschke.
APS April Meeting 2023 Mini-Symposium: Opportunies with JLab Upgrades in Energy, Luminosity,
and a Positron Beam - [Session I,Session II,Session III], April 15 and 24, 2023. Organizers: Harut
Avagyan, Jianping Chen, Liping Gan, Ashot Gasparian.
106
11 Acknowledgements
The authors would like to express their gratitude to the following colleagues, whose critical and valuable
comments contributed to the preparation of this document: Patrick Achenbach, Marco Battaglieri, Daniel
Carman, Eugene Chudakov, Bob McKeown, Mark Jones, and Viktor Mokeev.
Furthermore, the authors would also like to acknowledge the support received from the following insti-
tutions/agencies: US Department of Energy, Office of Science, Office of Nuclear Physics (contract num-
bers DE-FG02-05ER41374, DE-FG02-07ER41522, DE-FG02-01ER41172, DE-FG02-07ER41528, DE-AC05-
06OR23177) and the Early Career Program; US National Science Foundation (contract numbers PHY-
10011349, PHY-1812396, PHY-2111181, PHY 2209421); Natural Sciences and Engineering Research Council
of Canada (NSERC).
107
References
[1] J. Arrington, et al., Physics with CEBAF at 12 GeV and future opportunities, Prog. Part. Nucl. Phys.
127 (2022) 103985. arXiv:2112.00060,doi:10.1016/j.ppnp.2022.103985.
[2] J. Bulava, et al., Hadron Spectroscopy with Lattice QCD, in: Snowmass 2021, 2022. arXiv:2203.
03230.
[3] C. A. Meyer, E. S. Swanson, Hybrid Mesons, Prog. Part. Nucl. Phys. 82 (2015) 21–58. arXiv:
1502.07276,doi:10.1016/j.ppnp.2015.03.001.
[4] A. Rodas, et al., Determination of the pole position of the lightest hybrid meson candidate, Phys. Rev.
Lett. 122 (4) (2019) 042002. arXiv:1810.04171,doi:10.1103/PhysRevLett.122.042002.
[5] M. Ablikim, et al., Observation of an Isoscalar Resonance with Exotic JPC=1-+ Quantum Numbers
in J/ψ→γηη’, Phys. Rev. Lett. 129 (19) (2022) 192002, [Erratum: Phys.Rev.Lett. 130, 159901 (2023)].
arXiv:2202.00621,doi:10.1103/PhysRevLett.129.192002.
[6] S. L. Olsen, T. Skwarnicki, D. Zieminska, Nonstandard heavy mesons and baryons: Experimental
evidence, Rev. Mod. Phys. 90 (1) (2018) 015003. arXiv:1708.04012,doi:10.1103/RevModPhys.90.
015003.
[7] R. F. Lebed, R. E. Mitchell, E. S. Swanson, Heavy-Quark QCD Exotica, Prog. Part. Nucl. Phys. 93
(2017) 143–194. arXiv:1610.04528,doi:10.1016/j.ppnp.2016.11.003.
[8] R. A. Briceno, et al., Issues and Opportunities in Exotic Hadrons, Chin. Phys. C 40 (4) (2016) 042001.
arXiv:1511.06779,doi:10.1088/1674-1137/40/4/042001.
[9] M. Ablikim, et al., Observation of a Charged Charmoniumlike Structure in e+e−→π+π−J/ψ at √s
=4.26 GeV, Phys. Rev. Lett. 110 (2013) 252001. arXiv:1303.5949,doi:10.1103/PhysRevLett.110.
252001.
[10] Z. Q. Liu, et al., Study of e+e−→π+π−J/ψ and Observation of a Charged Charmoniumlike State
at Belle, Phys. Rev. Lett. 110 (2013) 252002, [Erratum: Phys.Rev.Lett. 111, 019901 (2013)]. arXiv:
1304.0121,doi:10.1103/PhysRevLett.110.252002.
[11] A. Bondar, et al., Observation of two charged bottomonium-like resonances in Y(5S) decays, Phys.
Rev. Lett. 108 (2012) 122001. arXiv:1110.2251,doi:10.1103/PhysRevLett.108.122001.
[12] M. Ablikim, et al., Observation of a Charged Charmoniumlike Structure Zc(4020) and Search for the
Zc(3900) in e+e−→π+π−hc, Phys. Rev. Lett. 111 (24) (2013) 242001. arXiv:1309.1896,doi:
10.1103/PhysRevLett.111.242001.
[13] V. D. Burkert, et al., The CLAS12 Spectrometer at Jefferson Laboratory, Nucl. Instrum. Meth. A 959
(2020) 163419. doi:10.1016/j.nima.2020.163419.
[14] S. Adhikari, et al., The GLUEX beamline and detector, Nucl. Instrum. Meth. A 987 (2021) 164807.
arXiv:2005.14272,doi:10.1016/j.nima.2020.164807.
[15] R. Aaij, et al., Observation of excited Ω0
cbaryons in Ω−
b→Ξ+
cK−π−decays, Phys. Rev. D 104 (9)
(2021) L091102. arXiv:2107.03419,doi:10.1103/PhysRevD.104.L091102.
[16] R. Aaij, et al., Observation of the resonant character of the Z(4430)−state, Phys. Rev. Lett. 112 (22)
(2014) 222002. arXiv:1404.1903,doi:10.1103/PhysRevLett.112.222002.
[17] K. Chilikin, et al., Observation of a new charged charmoniumlike state in ¯
B0→J/ψK−π+decays,
Phys. Rev. D 90 (11) (2014) 112009. arXiv:1408.6457,doi:10.1103/PhysRevD.90.112009.
[18] N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, C.-Z. Yuan,
The XY Z states: experimental and theoretical status and perspectives, Phys. Rept. 873 (2020) 1–154.
arXiv:1907.07583,doi:10.1016/j.physrep.2020.05.001.
108
[19] S. Adhikari, et al., Measurement of the J/ψphotoproduction cross section over the full near-threshold
kinematic region (4 2023). arXiv:2304.03845.
[20] A. N. Hiller Blin, C. Fern´andez-Ram´ırez, A. Jackura, V. Mathieu, V. I. Mokeev, A. Pilloni, A. P.
Szczepaniak, Studying the Pc(4450) resonance in J/ψphotoproduction off protons, Phys. Rev. D
94 (3) (2016) 034002. arXiv:1606.08912,doi:10.1103/PhysRevD.94.034002.
[21] D. Winney, A. Pilloni, V. Mathieu, A. N. Hiller Blin, M. Albaladejo, W. A. Smith, A. Szczepaniak,
XYZ spectroscopy at electron-hadron facilities. II. Semi-inclusive processes with pion exchange, Phys.
Rev. D 106 (9) (2022) 094009. arXiv:2209.05882,doi:10.1103/PhysRevD.106.094009.
[22] R. L. Workman, et al., Review of Particle Physics, PTEP 2022 (2022) 083C01.
[23] F.-K. Guo, U. G. Meißner, J. Nieves, Z. Yang, Remarks on the Pcstructures and triangle singularities,
Eur. Phys. J. A 52 (10) (2016) 318. arXiv:1605.05113,doi:10.1140/epja/i2016-16318-4.
[24] M. Bayar, F. Aceti, F.-K. Guo, E. Oset, A Discussion on Triangle Singularities in the Λb→J/ψK−p
Reaction, Phys. Rev. D 94 (7) (2016) 074039. arXiv:1609.04133,doi:10.1103/PhysRevD.94.074039.
[25] S. X. Nakamura, Pc(4312)+,Pc(4380)+, and Pc(4457)+as double triangle cusps, Phys. Rev. D 103
(2021) 111503. arXiv:2103.06817,doi:10.1103/PhysRevD.103.L111503.
[26] F.-K. Guo, X.-H. Liu, S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog.
Part. Nucl. Phys. 112 (2020) 103757. arXiv:1912.07030,doi:10.1016/j.ppnp.2020.103757.
[27] A. Pilloni, C. Fernandez-Ramirez, A. Jackura, V. Mathieu, M. Mikhasenko, J. Nys, A. P. Szczepaniak,
Amplitude analysis and the nature of the Zc(3900), Phys. Lett. B 772 (2017) 200–209. arXiv:1612.
06490,doi:10.1016/j.physletb.2017.06.030.
[28] S. K. Choi, et al., Observation of a narrow charmonium-like state in exclusive B±→K±π+π−J/ψ
decays, Phys. Rev. Lett. 91 (2003) 262001. arXiv:hep-ex/0309032,doi:10.1103/PhysRevLett.91.
262001.
[29] R. Aaij, et al., Determination of the X(3872) meson quantum numbers, Phys. Rev. Lett. 110 (2013)
222001. arXiv:1302.6269,doi:10.1103/PhysRevLett.110.222001.
[30] M. Aghasyan, et al., Search for muoproduction of X(3872) at COMPASS and indication of a new state
e
X(3872), Phys. Lett. B 783 (2018) 334–340. arXiv:1707.01796,doi:10.1016/j.physletb.2018.
07.008.
[31] R. L. Workman, et al., Review of Particle Physics, PTEP 2022 (2022) 083C01. doi:10.1093/ptep/
ptac097.
[32] R. Aaij, et al., Observation of J/ψp Resonances Consistent with Pentaquark States in Λ0
b→J/ψK−p
Decays, Phys. Rev. Lett. 115 (2015) 072001. arXiv:1507.03414,doi:10.1103/PhysRevLett.115.
072001.
[33] R. Aaij, et al., Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of the
Pc(4450)+, Phys. Rev. Lett. 122 (22) (2019) 222001. arXiv:1904.03947,doi:10.1103/PhysRevLett.
122.222001.
[34] D. Winney, et al., Dynamics in near-threshold J/ψ photoproduction (5 2023). arXiv:2305.01449.
[35] G. K. C. Cheung, C. E. Thomas, J. J. Dudek, R. G. Edwards, Tetraquark operators in lattice QCD
and exotic flavour states in the charm sector, JHEP 11 (2017) 033. arXiv:1709.01417,doi:10.1007/
JHEP11(2017)033.
[36] Y. Lyu, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, J. Meng, Doubly charmed tetraquark T+
cc from Lattice
QCD near Physical Point (2 2023). arXiv:2302.04505.
109
[37] M. Padmanath, S. Prelovsek, Signature of a Doubly Charm Tetraquark Pole in DD* Scattering on
the Lattice, Phys. Rev. Lett. 129 (3) (2022) 032002. arXiv:2202.10110,doi:10.1103/PhysRevLett.
129.032002.
[38] A. Francis, R. J. Hudspith, R. Lewis, K. Maltman, Evidence for charm-bottom tetraquarks and the
mass dependence of heavy-light tetraquark states from lattice QCD, Phys. Rev. D 99 (5) (2019) 054505.
arXiv:1810.10550,doi:10.1103/PhysRevD.99.054505.
[39] J. Blumlein, The Theory of Deeply Inelastic Scattering, Prog. Part. Nucl. Phys. 69 (2013) 28–84.
arXiv:1208.6087,doi:10.1016/j.ppnp.2012.09.006.
[40] P. Jimenez-Delgado, W. Melnitchouk, J. F. Owens, Parton momentum and helicity distributions in the
nucleon, J. Phys. G 40 (2013) 093102. arXiv:1306.6515,doi:10.1088/0954-3899/40/9/093102.
[41] S. Forte, G. Watt, Progress in the Determination of the Partonic Structure of the Proton, Ann. Rev.
Nucl. Part. Sci. 63 (2013) 291–328. arXiv:1301.6754,doi:10.1146/annurev- nucl-102212- 170607.
[42] S. Kumano, Flavor asymmetry of anti-quark distributions in the nucleon, Phys. Rept. 303 (1998)
183–257. arXiv:hep-ph/9702367,doi:10.1016/S0370-1573(98)00016-7.
[43] R. Vogt, Physics of the nucleon sea quark distributions, Prog. Part. Nucl. Phys. 45 (2000) S105–S169.
arXiv:hep-ph/0011298,doi:10.1016/S0146-6410(00)90012-7.
[44] G. T. Garvey, J.-C. Peng, Flavor asymmetry of light quarks in the nucleon sea, Prog. Part. Nucl. Phys.
47 (2001) 203–243. arXiv:nucl-ex/0109010,doi:10.1016/S0146-6410(01)00155-7.
[45] W. Melnitchouk, Insights into nucleon structure from parton distributions, PoS INPC2016 (2017) 363.
doi:10.22323/1.281.0363.
[46] C. Cocuzza, W. Melnitchouk, A. Metz, N. Sato, Bayesian Monte Carlo extraction of the sea asymmetry
with SeaQuest and STAR data, Phys. Rev. D 104 (7) (2021) 074031. arXiv:2109.00677,doi:10.
1103/PhysRevD.104.074031.
[47] A. Accardi, X. Jing, J. F. Owens, S. Park, Light quark and antiquark constraints from new electroweak
data (3 2023). arXiv:2303.11509.
[48] A. M. Cooper-Sarkar, HERA Collider Results, PoS DIS2015 (2015) 005. arXiv:1507.03849,doi:
10.22323/1.247.0005.
[49] A. O. Bazarko, et al., Determination of the strange quark content of the nucleon from a next-to-
leading order QCD analysis of neutrino charm production, Z. Phys. C 65 (1995) 189–198. arXiv:
hep-ex/9406007,doi:10.1007/BF01571875.
[50] D. Mason, et al., Measurement of the Nucleon Strange-Antistrange Asymmetry at Next-to-Leading
Order in QCD from NuTeV Dimuon Data, Phys. Rev. Lett. 99 (2007) 192001. doi:10.1103/
PhysRevLett.99.192001.
[51] A. Kayis-Topaksu, et al., Measurement of charm production in neutrino charged-current interactions,
New J. Phys. 13 (2011) 093002. arXiv:1107.0613,doi:10.1088/1367-2630/13/9/093002.
[52] O. Samoylov, et al., A Precision Measurement of Charm Dimuon Production in Neutrino Interactions
from the NOMAD Experiment, Nucl. Phys. B 876 (2013) 339–375. arXiv:1308.4750,doi:10.1016/
j.nuclphysb.2013.08.021.
[53] N. Kalantarians, C. Keppel, M. E. Christy, Comparison of the Structure Function F2 as Measured
by Charged Lepton and Neutrino Scattering from Iron Targets, Phys. Rev. C 96 (3) (2017) 032201.
arXiv:1706.02002,doi:10.1103/PhysRevC.96.032201.
[54] A. Accardi, F. Arleo, W. K. Brooks, D. D’Enterria, V. Muccifora, Parton Propagation and Frag-
mentation in QCD Matter, Riv. Nuovo Cim. 32 (9-10) (2009) 439–554. arXiv:0907.3534,doi:
10.1393/ncr/i2009-10048-0.
110
[55] A. Majumder, M. Van Leeuwen, The Theory and Phenomenology of Perturbative QCD Based Jet
Quenching, Prog. Part. Nucl. Phys. 66 (2011) 41–92. arXiv:1002.2206,doi:10.1016/j.ppnp.2010.
09.001.
[56] G. Aad, et al., Determination of the strange quark density of the proton from ATLAS measurements
of the W→ℓν and Z→ℓℓ cross sections, Phys. Rev. Lett. 109 (2012) 012001. arXiv:1203.4051,
doi:10.1103/PhysRevLett.109.012001.
[57] M. Aaboud, et al., Precision measurement and interpretation of inclusive W+,W−and Z/γ∗produc-
tion cross sections with the ATLAS detector, Eur. Phys. J. C 77 (6) (2017) 367. arXiv:1612.03016,
doi:10.1140/epjc/s10052-017-4911-9.
[58] E. A. Hawker, et al., Measurement of the light anti-quark flavor asymmetry in the nucleon sea, Phys.
Rev. Lett. 80 (1998) 3715–3718. arXiv:hep-ex/9803011,doi:10.1103/PhysRevLett.80.3715.
[59] R. S. Towell, et al., Improved measurement of the anti-d / anti-u asymmetry in the nucleon sea, Phys.
Rev. D 64 (2001) 052002. arXiv:hep-ex/0103030,doi:10.1103/PhysRevD.64.052002.
[60] S. Alekhin, S. A. Kulagin, R. Petti, Determination of Strange Sea Distributions from Neutrino-Nucleon
Deep Inelastic Scattering, Phys. Lett. B 675 (2009) 433–440. arXiv:0812.4448,doi:10.1016/j.
physletb.2009.04.033.
[61] S. Alekhin, J. Blumlein, L. Caminada, K. Lipka, K. Lohwasser, S. Moch, R. Petti, R. Placakyte,
Determination of Strange Sea Quark Distributions from Fixed-target and Collider Data, Phys. Rev. D
91 (9) (2015) 094002. arXiv:1404.6469,doi:10.1103/PhysRevD.91.094002.
[62] S. Alekhin, J. Bl¨umlein, S. Moch, Strange sea determination from collider data, Phys. Lett. B 777
(2018) 134–140. arXiv:1708.01067,doi:10.1016/j.physletb.2017.12.024.
[63] S. Alekhin, J. Bl¨umlein, S. Moch, R. Placakyte, Parton distribution functions, αs, and heavy-quark
masses for LHC Run II, Phys. Rev. D 96 (1) (2017) 014011. arXiv:1701.05838,doi:10.1103/
PhysRevD.96.014011.
[64] A. M. Cooper-Sarkar, K. Wichmann, QCD analysis of the ATLAS and CMS W±and Zcross-section
measurements and implications for the strange sea density, Phys. Rev. D 98 (1) (2018) 014027. arXiv:
1803.00968,doi:10.1103/PhysRevD.98.014027.
[65] A. Airapetian, et al., Measurement of Parton Distributions of Strange Quarks in the Nucleon from
Charged-Kaon Production in Deep-Inelastic Scattering on the Deuteron, Phys. Lett. B 666 (2008)
446–450. arXiv:0803.2993,doi:10.1016/j.physletb.2008.07.090.
[66] A. Airapetian, et al., Reevaluation of the parton distribution of strange quarks in the nucleon, Phys.
Rev. D 89 (9) (2014) 097101. arXiv:1312.7028,doi:10.1103/PhysRevD.89.097101.
[67] E. Leader, A. V. Sidorov, D. B. Stamenov, Determination of Polarized PDFs from a QCD Analysis of
Inclusive and Semi-inclusive Deep Inelastic Scattering Data, Phys. Rev. D 82 (2010) 114018. arXiv:
1010.0574,doi:10.1103/PhysRevD.82.114018.
[68] E. Leader, A. V. Sidorov, D. B. Stamenov, A Possible Resolution of the Strange Quark Polarization
Puzzle ?, Phys. Rev. D 84 (2011) 014002. arXiv:1103.5979,doi:10.1103/PhysRevD.84.014002.
[69] N. Sato, J. J. Ethier, W. Melnitchouk, M. Hirai, S. Kumano, A. Accardi, First Monte Carlo analysis of
fragmentation functions from single-inclusive e+e−annihilation, Phys. Rev. D 94 (11) (2016) 114004.
arXiv:1609.00899,doi:10.1103/PhysRevD.94.114004.
[70] E. C. Aschenauer, H. E. Jackson, S. Joosten, K. Rith, G. Schnell, C. Van Hulse, Reply to “Comment
on ‘Reevaluation of the parton distribution of strange quarks in the nucleon’”, Phys. Rev. D 92 (9)
(2015) 098102. arXiv:1508.04020,doi:10.1103/PhysRevD.92.098102.
111
[71] I. Borsa, R. Sassot, M. Stratmann, Probing the Sea Quark Content of the Proton with One-Particle-
Inclusive Processes, Phys. Rev. D 96 (9) (2017) 094020. arXiv:1708.01630,doi:10.1103/PhysRevD.
96.094020.
[72] N. Sato, C. Andres, J. J. Ethier, W. Melnitchouk, Strange quark suppression from a simultaneous
Monte Carlo analysis of parton distributions and fragmentation functions, Phys. Rev. D 101 (7) (2020)
074020. arXiv:1905.03788,doi:10.1103/PhysRevD.101.074020.
[73] L. T. Brady, A. Accardi, T. J. Hobbs, W. Melnitchouk, Next-to leading order analysis of target
mass corrections to structure functions and asymmetries, Phys. Rev. D 84 (2011) 074008, [Erratum:
Phys.Rev.D 85, 039902 (2012)]. arXiv:1108.4734,doi:10.1103/PhysRevD.84.074008.
[74] T. Hobbs, W. Melnitchouk, Finite-Q**2 corrections to parity-violating DIS, Phys. Rev. D 77 (2008)
114023. arXiv:0801.4791,doi:10.1103/PhysRevD.77.114023.
[75] T. Liu, W. Melnitchouk, J.-W. Qiu, N. Sato, Factorized approach to radiative corrections for inelastic
lepton-hadron collisions, Phys. Rev. D 104 (9) (2021) 094033. arXiv:2008.02895,doi:10.1103/
PhysRevD.104.094033.
[76] C. Cocuzza, W. Melnitchouk, A. Metz, N. Sato, Polarized antimatter in the proton from a global QCD
analysis, Phys. Rev. D 106 (3) (2022) L031502. arXiv:2202.03372,doi:10.1103/PhysRevD.106.
L031502.
[77] R. D. Ball, V. Bertone, M. Bonvini, S. Carrazza, S. Forte, A. Guffanti, N. P. Hartland, J. Rojo,
L. Rottoli, A Determination of the Charm Content of the Proton, Eur. Phys. J. C 76 (11) (2016) 647.
arXiv:1605.06515,doi:10.1140/epjc/s10052-016-4469-y.
[78] R. D. Ball, A. Candido, J. Cruz-Martinez, S. Forte, T. Giani, F. Hekhorn, K. Kudashkin, G. Magni,
J. Rojo, Evidence for intrinsic charm quarks in the proton, Nature 608 (7923) (2022) 483–487. arXiv:
2208.08372,doi:10.1038/s41586-022-04998-2.
[79] R. D. Ball, et al., The path to proton structure at 1% accuracy, Eur. Phys. J. C 82 (5) (2022) 428.
arXiv:2109.02653,doi:10.1140/epjc/s10052-022-10328-7.
[80] M. Guzzi, T. J. Hobbs, K. Xie, J. Huston, P. Nadolsky, C. P. Yuan, The persistent nonperturbative
charm enigma (11 2022). arXiv:2211.01387.
[81] M. Kelsey, R. Cruz-Torres, X. Dong, Y. Ji, S. Radhakrishnan, E. Sichtermann, Constraints on gluon
distribution functions in the nucleon and nucleus from open charm hadron production at the Electron-
Ion Collider, Phys. Rev. D 104 (5) (2021) 054002. arXiv:2107.05632,doi:10.1103/PhysRevD.104.
054002.
[82] R. Abdul Khalek, et al., Science Requirements and Detector Concepts for the Electron-Ion Col-
lider: EIC Yellow Report, Nucl. Phys. A 1026 (2022) 122447. arXiv:2103.05419,doi:10.1016/
j.nuclphysa.2022.122447.
[83] R. Gauld, J. Rojo, L. Rottoli, J. Talbert, Charm production in the forward region: constraints on
the small-x gluon and backgrounds for neutrino astronomy, JHEP 11 (2015) 009. arXiv:1506.08025,
doi:10.1007/JHEP11(2015)009.
[84] J. Gao, L. Harland-Lang, J. Rojo, The Structure of the Proton in the LHC Precision Era, Phys. Rept.
742 (2018) 1–121. arXiv:1709.04922,doi:10.1016/j.physrep.2018.03.002.
[85] R. D. Ball, et al., The PDF4LHC21 combination of global PDF fits for the LHC Run III, J. Phys. G
49 (8) (2022) 080501. arXiv:2203.05506,doi:10.1088/1361-6471/ac7216.
[86] T.-J. Hou, et al., New CTEQ global analysis of quantum chromodynamics with high-precision data
from the LHC, Phys. Rev. D 103 (1) (2021) 014013. arXiv:1912.10053,doi:10.1103/PhysRevD.
103.014013.
112
[87] S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Martin, R. S. Thorne, Parton distributions from
LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs, Eur. Phys. J. C 81 (4) (2021) 341.
arXiv:2012.04684,doi:10.1140/epjc/s10052-021-09057-0.
[88] J. C. Collins, D. E. Soper, Angular Distribution of Dileptons in High-Energy Hadron Collisions, Phys.
Rev. D 16 (1977) 2219. doi:10.1103/PhysRevD.16.2219.
[89] R. D. Ball, A. Candido, S. Forte, F. Hekhorn, E. R. Nocera, J. Rojo, C. Schwan, Parton distributions
and new physics searches: the Drell–Yan forward–backward asymmetry as a case study, Eur. Phys. J.
C 82 (12) (2022) 1160. arXiv:2209.08115,doi:10.1140/epjc/s10052-022-11133-y.
[90] A. Greljo, S. Iranipour, Z. Kassabov, M. Madigan, J. Moore, J. Ro jo, M. Ubiali, C. Voisey, Parton
distributions in the SMEFT from high-energy Drell-Yan tails, JHEP 07 (2021) 122. arXiv:2104.02723,
doi:10.1007/JHEP07(2021)122.
[91] S. J. Brodsky, P. Hoyer, C. Peterson, N. Sakai, The Intrinsic Charm of the Proton, Phys. Lett. B 93
(1980) 451–455. doi:10.1016/0370-2693(80)90364-0.
[92] W.-C. Chang, J.-C. Peng, Flavor Asymmetry of the Nucleon Sea and the Five-Quark Components of
the Nucleons, Phys. Rev. Lett. 106 (2011) 252002. arXiv:1102.5631,doi:10.1103/PhysRevLett.
106.252002.
[93] A. Airapetian, et al., Measurement of Parton Distributions of Strange Quarks in the Nucleon from
Charged-Kaon Production in Deep-Inelastic Scattering on the Deuteron, Phys. Lett. B 666 (2008)
446–450. arXiv:0803.2993,doi:10.1016/j.physletb.2008.07.090.
[94] R. S. Towell, et al., Improved measurement of the anti-d / anti-u asymmetry in the nucleon sea, Phys.
Rev. D 64 (2001) 052002. arXiv:hep-ex/0103030,doi:10.1103/PhysRevD.64.052002.
[95] W.-C. Chang, J.-C. Peng, Extraction of Various Five-Quark Components of the Nucleons, Phys. Lett.
B 704 (2011) 197–200. arXiv:1105.2381,doi:10.1016/j.physletb.2011.08.077.
[96] A. Airapetian, et al., Reevaluation of the parton distribution of strange quarks in the nucleon, Phys.
Rev. D 89 (9) (2014) 097101. arXiv:1312.7028,doi:10.1103/PhysRevD.89.097101.
[97] W.-C. Chang, J.-C. Peng, Extraction of the intrinsic light-quark sea in the proton, Phys. Rev. D 92 (5)
(2015) 054020. arXiv:1410.7027,doi:10.1103/PhysRevD.92.054020.
[98] J. Dove, et al., Publisher Correction: The asymmetry of antimatter in the proton [doi:
10.1038/s41586-021-03282-z], Nature 590 (7847) (2021) 561–565. arXiv:2103.04024,doi:10.1038/
s41586-022-04707-z.
[99] R. S. Towell, et al., Improved measurement of the dbar/ubar asymmetry in the nucleon sea, Phys.
Rev. D 64 (2001) 052002. doi:10.1103/PhysRevD.64.052002.
URL https://link.aps.org/doi/10.1103/PhysRevD.64.052002
[100] K. Ackerstaff, et al., The Flavor asymmetry of the light quark sea from semiinclusive deep inelastic scat-
tering, Phys. Rev. Lett. 81 (1998) 5519–5523. arXiv:hep-ex/9807013,doi:10.1103/PhysRevLett.
81.5519.
[101] H. M. H. Gao, A. Bruell, et al., Probing the light quark sea flavor asymmetry with semi-inclusive
charged pion production in Hall C (2006).
URL https://www.jlab.org/exp_prog/proposals/06/PR12-06-111.pdf
[102] T. Liu, R. S. Sufian, G. F. de T´eramond, H. G. Dosch, S. J. Brodsky, A. Deur, Unified description
of polarized and unpolarized quark distributions in the proton, Phys. Rev. Lett. 124 (2020) 082003.
doi:10.1103/PhysRevLett.124.082003.
URL https://link.aps.org/doi/10.1103/PhysRevLett.124.082003
113
[103] A. Deur, S. J. Brodsky, G. F. de Teramond, The QCD Running Coupling, Nucl. Phys. 90 (2016) 1.
arXiv:1604.08082,doi:10.1016/j.ppnp.2016.04.003.
[104] P. A. Zyla, et al., Review of Particle Physics, PTEP 2020 (8) (2020) 083C01. doi:10.1093/ptep/
ptaa104.
[105] D. d’Enterria, et al., The strong coupling constant: State of the art and the decade ahead (3 2022).
arXiv:2203.08271.
[106] J. D. Bjorken, Applications of the Chiral U(6) x (6) Algebra of Current Densities, Phys. Rev. 148
(1966) 1467–1478. doi:10.1103/PhysRev.148.1467.
[107] S. Kuhn, et al., The Longitudinal Spin Structure of the Nucleon Jlab experiment E12-06-109 ”. (2006).
[108] A. L. Kataev, The Ellis-Jaffe sum rule: The Estimates of the next to next-to-leading order QCD
corrections, Phys. Rev. D 50 (1994) R5469–R5472. arXiv:hep-ph/9408248,doi:10.1103/PhysRevD.
50.R5469.
[109] A. L. Kataev, private communication in S. Incerti, Ph. D dissertation “Mesure de la fonction de
structure polaris´ee gn
1du neutron par l’experience e154 au slac”. (Jan. 1998).
[110] A. Deur, Y. Prok, V. Burkert, D. Crabb, F. X. Girod, K. A. Griffioen, N. Guler, S. E. Kuhn, N. Kval-
tine, High precision determination of the Q2evolution of the Bjorken Sum, Phys. Rev. D 90 (1) (2014)
012009. arXiv:1405.7854,doi:10.1103/PhysRevD.90.012009.
[111] B. A. Kniehl, A. V. Kotikov, A. I. Onishchenko, O. L. Veretin, Strong-coupling constant with flavor
thresholds at five loops in the anti-MS scheme, Phys. Rev. Lett. 97 (2006) 042001. arXiv:hep-ph/
0607202,doi:10.1103/PhysRevLett.97.042001.
[112] A. Deur, V. Burkert, J. P. Chen, W. Korsch, Experimental determination of the QCD effective charge
αg1(Q), Particles 5 (2022) 171. arXiv:2205.01169,doi:10.3390/particles5020015.
[113] S. J. Brodsky, G. F. de Teramond, A. Deur, Nonperturbative QCD Coupling and its β-function from
Light-Front Holography, Phys. Rev. D 81 (2010) 096010. arXiv:1002.3948,doi:10.1103/PhysRevD.
81.096010.
[114] Z.-F. Cui, J.-L. Zhang, D. Binosi, F. de Soto, C. Mezrag, J. Papavassiliou, C. D. Roberts, J. Rodr´ıguez-
Quintero, J. Segovia, S. Zafeiropoulos, Effective charge from lattice QCD, Chin. Phys. C 44 (8) (2020)
083102. arXiv:1912.08232,doi:10.1088/1674-1137/44/8/083102.
[115] P. C. Barry, L. Gamberg, W. Melnitchouk, E. Moffat, D. Pitonyak, A. Prokudin, N. Sato, Tomography
of pions and protons via transverse momentum dependent distributions (2 2023). arXiv:2302.01192.
[116] N. Y. Cao, P. C. Barry, N. Sato, W. Melnitchouk, Towards the three-dimensional parton structure of
the pion: Integrating transverse momentum data into global QCD analysis, Phys. Rev. D 103 (11)
(2021) 114014. arXiv:2103.02159,doi:10.1103/PhysRevD.103.114014.
[117] C. E. Keppel, et al., C12-15-006 JLab experiment: Measurement of tagged deep inelastic scattering
(2015).
[118] K. Park, et al., C12-15-006A JLab run group: Measurement of kaon structure through tagged deep
inelastic scattering (2017).
[119] B. Betev, et al., Differential Cross-section of High Mass Muon Pairs Produced by a 194-GeV/cπ−
Beam on a Tungsten Target, Z. Phys. C 28 (1985) 9. doi:10.1007/BF01550243.
[120] J. S. Conway, et al., Experimental Study of Muon Pairs Produced by 252-GeV Pions on Tungsten,
Phys. Rev. D 39 (1989) 92–122. doi:10.1103/PhysRevD.39.92.
[121] F. D. Aaron, et al., Measurement of Leading Neutron Production in Deep-Inelastic Scattering at HERA,
Eur. Phys. J. C 68 (2010) 381–399. arXiv:1001.0532,doi:10.1140/epjc/s10052-010-1369-4.
114
[122] S. Chekanov, et al., Leading neutron production in e+ p collisions at HERA, Nucl. Phys. B 637 (2002)
3–56. arXiv:hep-ex/0205076,doi:10.1016/S0550-3213(02)00439-X.
[123] J. Arrington, et al., Revealing the Structure of Light Pseudoscalar Mesons at the Electron-Ion Collider,
J. Phys. G 48 (2021) 075106.
[124] A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P. J. Mulders, M. Schlegel, Semi-inclusive deep inelastic
scattering at small transverse momentum, JHEP 02 (2007) 093. arXiv:hep-ph/0611265,doi:10.
1088/1126-6708/2007/02/093.
[125] J. Gonzalez-Hernandez, T. Rogers, N. Sato, B. Wang, Challenges with Large Transverse Momentum in
Semi-Inclusive Deeply Inelastic Scattering, Phys. Rev. D 98 (11) (2018) 114005. arXiv:1808.04396,
doi:10.1103/PhysRevD.98.114005.
[126] B. Wang, J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato, Large Transverse Momentum in Semi-
Inclusive Deeply Inelastic Scattering Beyond Lowest Order, Phys. Rev. D 99 (9) (2019) 094029. arXiv:
1903.01529,doi:10.1103/PhysRevD.99.094029.
[127] M. Boglione, J. Collins, L. Gamberg, J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato, Kinematics of
Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering, Phys. Lett. B 766 (2017)
245–253. arXiv:1611.10329,doi:10.1016/j.physletb.2017.01.021.
[128] J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato, B. Wang, Relating Transverse Momentum
Dependent and Collinear Factorization Theorems in a Generalized Formalism, Phys. Rev. D 94 (3)
(2016) 034014. arXiv:1605.00671,doi:10.1103/PhysRevD.94.034014.
[129] M. Boglione, A. Dotson, L. Gamberg, S. Gordon, J. Gonzalez-Hernandez, A. Prokudin, T. Rogers,
N. Sato, Mapping the Kinematical Regimes of Semi-Inclusive Deep Inelastic Scattering, JHEP 10
(2019) 122. arXiv:1904.12882,doi:10.1007/JHEP10(2019)122.
[130] H. Avakian, et al., Measurement of Single and Double Spin Asymmetries in Deep Inelastic Pion
Electroproduction with a Longitudinally Polarized Target, Phys. Rev. Lett. 105 (2010) 262002. arXiv:
1003.4549,doi:10.1103/PhysRevLett.105.262002.
[131] S. Jawalkar, et al., Semi-Inclusive π0target and beam-target asymmetries from 6 GeV electron scat-
tering with CLAS, Phys. Lett. B 782 (2018) 662–667. arXiv:1709.10054,doi:10.1016/j.physletb.
2018.06.014.
[132] B. U. Musch, P. Hagler, J. W. Negele, A. Schafer, Exploring quark transverse momentum distributions
with lattice QCD, Phys. Rev. D 83 (2011) 094507. arXiv:1011.1213,doi:10.1103/PhysRevD.83.
094507.
[133] H. Avakian, Hadronization of quarks and correlated di-hadron production in hard scattering, PoS
DIS2019 (2019) 265. doi:10.22323/1.352.0265.
[134] C. J. Bebek, C. N. Brown, M. Herzlinger, S. D. Holmes, C. A. Lichtenstein, F. M. Pipkin, S. Raither,
L. K. Sisterson, Scaling Behavior of Inclusive Pion Electroproduction, Phys. Rev. Lett. 34 (1975) 759.
doi:10.1103/PhysRevLett.34.759.
[135] C. J. Bebek, A. Browman, C. N. Brown, K. M. Hanson, R. V. Kline, D. Larson, F. M. Pipkin, S. W.
Raither, A. Silverman, L. K. Sisterson, Charged Pion Electroproduction from Protons Up to Q**2 =
9.5-GeV**2, Phys. Rev. Lett. 37 (1976) 1525–1528. doi:10.1103/PhysRevLett.37.1525.
[136] C. J. Bebek, C. N. Brown, M. S. Herzlinger, S. D. Holmes, C. A. Lichtenstein, F. M. Pipkin, S. W.
Raither, L. K. Sisterson, Inclusive Charged Pion Electroproduction, Phys. Rev. D 15 (1977) 3085.
doi:10.1103/PhysRevD.15.3085.
[137] A. Bacchetta, D. Boer, M. Diehl, P. J. Mulders, Matches and mismatches in the descriptions of semi-
inclusive processes at low and high transverse momentum, JHEP 08 (2008) 023. arXiv:0803.0227,
doi:10.1088/1126-6708/2008/08/023.
115
[138] M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, The Role of Cahn
and sivers effects in deep inelastic scattering, Phys. Rev. D 71 (2005) 074006. arXiv:hep-ph/0501196,
doi:10.1103/PhysRevD.71.074006.
[139] A. Bacchetta, V. Bertone, C. Bissolotti, G. Bozzi, M. Cerutti, F. Piacenza, M. Radici, A. Signori,
Unpolarized transverse momentum distributions from a global fit of Drell-Yan and semi-inclusive deep-
inelastic scattering data, JHEP 10 (2022) 127. arXiv:2206.07598,doi:10.1007/JHEP10(2022)127.
[140] C. Adolph, et al., Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic
scattering off unpolarised nucleons, Nucl. Phys. B 886 (2014) 1046–1077. arXiv:1401.6284,doi:
10.1016/j.nuclphysb.2014.07.019.
[141] A. Moretti, TMD observables in unpolarised Semi-Inclusive DIS at COMPASS, SciPost Phys. Proc. 8
(2022) 144. arXiv:2107.10740,doi:10.21468/SciPostPhysProc.8.144.
[142] A. Airapetian, et al., Azimuthal distributions of charged hadrons, pions, and kaons produced in deep-
inelastic scattering off unpolarized protons and deuterons, Phys. Rev. D 87 (1) (2013) 012010. arXiv:
1204.4161,doi:10.1103/PhysRevD.87.012010.
[143] M. Osipenko, et al., Measurement of unpolarized semi-inclusive pi+ electroproduction off the proton,
Phys. Rev. D 80 (2009) 032004. arXiv:0809.1153,doi:10.1103/PhysRevD.80.032004.
[144] S. Diehl, et al., First multidimensional, high precision measurements of semi-inclusive π+beam single
spin asymmetries from the proton over a wide range of kinematics (1 2021). arXiv:2101.03544.
[145] J. C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distri-
butions, Nucl. Phys. B 396 (1993) 161–182. arXiv:hep-ph/9208213,doi:10.1016/0550- 3213(93)
90262-N.
[146] A. Kerbizi, X. Artru, Z. Belghobsi, F. Bradamante, A. Martin, Recursive model for the fragmentation
of polarized quarks, Phys. Rev. D 97 (7) (2018) 074010. arXiv:1802.00962,doi:10.1103/PhysRevD.
97.074010.
[147] H. H. Matevosyan, A. Kotzinian, A. W. Thomas, Monte Carlo Implementation of Polarized Hadroniza-
tion, Phys. Rev. D 95 (1) (2017) 014021. arXiv:1610.05624,doi:10.1103/PhysRevD.95.014021.
[148] A. Kerbizi, L. L¨onnblad, StringSpinner - adding spin to the PYTHIA string fragmentation, Comput.
Phys. Commun. 272 (2022) 108234. arXiv:2105.09730,doi:10.1016/j.cpc.2021.108234.
[149] T. Sj¨ostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O.
Rasmussen, P. Z. Skands, An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015)
159–177. arXiv:1410.3012,doi:10.1016/j.cpc.2015.01.024.
[150] T. B. Hayward, et al., Observation of Beam Spin Asymmetries in the Process ep →e′π+π−Xwith
CLAS12, Phys. Rev. Lett. 126 (2021) 152501. arXiv:2101.04842,doi:10.1103/PhysRevLett.126.
152501.
[151] A. Kerbizi, X. Artru, A. Martin, Production of vector mesons in the String+3P0model of po-
larized quark fragmentation, Phys. Rev. D 104 (11) (2021) 114038. arXiv:2109.06124,doi:
10.1103/PhysRevD.104.114038.
[152] A. Bacchetta, P. J. Mulders, Deep inelastic leptoproduction of spin-one hadrons, Phys. Rev. D 62
(2000) 114004. arXiv:hep-ph/0007120,doi:10.1103/PhysRevD.62.114004.
[153] T. C. Collaboration, Collins and Sivers transverse-spin asymmetries in inclusive muoproduction of ρ0
mesons, CERN-EP-2022-234 (10 2022). arXiv:2211.00093.
[154] C. Adolph, et al., Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely
polarised protons, Phys. Lett. B 744 (2015) 250–259. arXiv:1408.4405,doi:10.1016/j.physletb.
2015.03.056.
116
[155] L. Trentadue, G. Veneziano, Fracture functions: An Improved description of inclusive hard processes
in QCD, Phys. Lett. B 323 (1994) 201–211. doi:10.1016/0370-2693(94)90292-5.
[156] M. Anselmino, V. Barone, A. Kotzinian, SIDIS in the target fragmentation region: Polarized and
transverse momentum dependent fracture functions, Phys. Lett. B 699 (2011) 108–118. arXiv:1102.
4214,doi:10.1016/j.physletb.2011.03.067.
[157] H. Avakian, et al., Observation of Correlations between Spin and Transverse Momenta in Back-to-
Back Dihadron Production at CLAS12, Phys. Rev. Lett. 130 (2) (2023) 022501. arXiv:2208.05086,
doi:10.1103/PhysRevLett.130.022501.
[158] P. Schweitzer, M. Strikman, C. Weiss, Intrinsic transverse momentum and parton correlations
from dynamical chiral symmetry breaking, JHEP 01 (2013) 163. arXiv:1210.1267,doi:10.1007/
JHEP01(2013)163.
[159] M. Sargsian, M. Strikman, Model independent method for determination of the DIS structure of free
neutron, Phys. Lett. B 639 (2006) 223–231. arXiv:hep-ph/0511054,doi:10.1016/j.physletb.2006.
05.091.
[160] W. Cosyn, C. Weiss, Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tag-
ging, Phys. Rev. C 102 (2020) 065204. arXiv:2006.03033,doi:10.1103/PhysRevC.102.065204.
[161] S. Bueltmann, M. Christy, H. Fenker, K. Griffioen, C. Keppel, S. Kuhn, W. Melnitchouk, V. s. Tvaskis,
The Structure of the Free Neutron at Large x-Bjorken; http://www.jlab.org/exp_prog/12GEV_EXP/
E1206113.htmlJLab Experiment E1206113 (2006).
URL http://www.jlab.org/exp_prog/12GEV_EXP/E1206113.html
[162] W. Armstrong, et al., Partonic Structure of Light Nuclei (2017). arXiv:1708.00888.
[163] J. T. Londergan, A. Pang, A. W. Thomas, Probing charge symmetry violating quark distributions in
semiinclusive leptoproduction of hadrons, Phys. Rev. D 54 (1996) 3154–3161. arXiv:hep-ph/9604446,
doi:10.1103/PhysRevD.54.3154.
[164] A. D. Martin, R. G. Roberts, W. J. Stirling, R. S. Thorne, Uncertainties of predictions from parton
distributions. 2. Theoretical errors, Eur. Phys. J. C 35 (2004) 325–348. arXiv:hep-ph/0308087,
doi:10.1140/epjc/s2004-01825-2.
[165] D. de Florian, R. Sassot, M. Stratmann, Global analysis of fragmentation functions for pions and
kaons and their uncertainties, Phys. Rev. D 75 (2007) 114010. arXiv:hep- ph/0703242,doi:10.
1103/PhysRevD.75.114010.
[166] I. Scimemi, A. Vladimirov, Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan
scattering at small transverse momentum, JHEP 06 (2020) 137. arXiv:1912.06532,doi:10.1007/
JHEP06(2020)137.
[167] M. Bury, F. Hautmann, S. Leal-Gomez, I. Scimemi, A. Vladimirov, P. Zurita, PDF bias and fla-
vor dependence in TMD distributions, JHEP 10 (2022) 118. arXiv:2201.07114,doi:10.1007/
JHEP10(2022)118.
[168] A. Bermudez Martinez, A. Vladimirov, Determination of the Collins-Soper kernel from cross-sections
ratios, Phys. Rev. D 106 (9) (2022) L091501. arXiv:2206.01105,doi:10.1103/PhysRevD.106.
L091501.
[169] M. Boglione, J. O. Gonzalez Hernandez, S. Melis, A. Prokudin, A study on the interplay between
perturbative QCD and CSS/TMD formalism in SIDIS processes, JHEP 02 (2015) 095. arXiv:1412.
1383,doi:10.1007/JHEP02(2015)095.
[170] B. Yoon, M. Engelhardt, R. Gupta, T. Bhattacharya, J. R. Green, B. U. Musch, J. W. Negele, A. V.
Pochinsky, A. Sch¨afer, S. N. Syritsyn, Nucleon Transverse Momentum-dependent Parton Distributions
in Lattice QCD: Renormalization Patterns and Discretization Effects, Phys. Rev. D 96 (9) (2017)
094508. arXiv:1706.03406,doi:10.1103/PhysRevD.96.094508.
117
[171] X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110 (2013) 262002. arXiv:1305.1539,
doi:10.1103/PhysRevLett.110.262002.
[172] X. Ji, Y.-S. Liu, Y. Liu, J.-H. Zhang, Y. Zhao, Large-momentum effective theory, Rev. Mod. Phys.
93 (3) (2021) 035005. arXiv:2004.03543,doi:10.1103/RevModPhys.93.035005.
[173] M. A. Ebert, I. W. Stewart, Y. Zhao, Determining the Nonperturbative Collins-Soper Kernel From
Lattice QCD, Phys. Rev. D 99 (3) (2019) 034505. arXiv:1811.00026,doi:10.1103/PhysRevD.99.
034505.
[174] X. Ji, Y. Liu, Y.-S. Liu, Transverse-momentum-dependent parton distribution functions from large-
momentum effective theory, Phys. Lett. B 811 (2020) 135946. arXiv:1911.03840,doi:10.1016/j.
physletb.2020.135946.
[175] P. Shanahan, M. Wagman, Y. Zhao, Collins-Soper kernel for TMD evolution from lattice QCD, Phys.
Rev. D 102 (1) (2020) 014511. arXiv:2003.06063,doi:10.1103/PhysRevD.102.014511.
[176] Q.-A. Zhang, et al., Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum
Effective Theory, Phys. Rev. Lett. 125 (19) (2020) 192001. arXiv:2005.14572,doi:10.22323/1.
396.0477.
[177] M. Schlemmer, A. Vladimirov, C. Zimmermann, M. Engelhardt, A. Sch¨afer, Determination of the
Collins-Soper Kernel from Lattice QCD, JHEP 08 (2021) 004. arXiv:2103.16991,doi:10.1007/
JHEP08(2021)004.
[178] M.-H. Chu, et al., Nonperturbative determination of the Collins-Soper kernel from quasitransverse-
momentum-dependent wave functions, Phys. Rev. D 106 (3) (2022) 034509. arXiv:2204.00200,doi:
10.1103/PhysRevD.106.034509.
[179] H.-T. Shu, M. Schlemmer, T. Sizmann, A. Vladimirov, L. Walter, M. Engelhardt, A. Sch¨afer, Y.-B.
Yang, Universality of the Collins-Soper kernel in lattice calculations (2 2023). arXiv:2302.06502.
[180] J.-C. He, M.-H. Chu, J. Hua, X. Ji, A. Sch¨afer, Y. Su, W. Wang, Y. Yang, J.-H. Zhang, Q.-A. Zhang,
Unpolarized Transverse-Momentum-Dependent Parton Distributions of the Nucleon from Lattice QCD
(11 2022). arXiv:2211.02340.
[181] Y. Zhou, N. Sato, W. Melnitchouk, How well do we know the gluon polarization in the proton?, Phys.
Rev. D 105 (7) (2022) 074022. arXiv:2201.02075,doi:10.1103/PhysRevD.105.074022.
[182] M. Alberg, G. A. Miller, Chiral Light Front Perturbation Theory and the Flavor Dependence of the
Light-Quark Nucleon Sea, Phys. Rev. C 100 (3) (2019) 035205. arXiv:1712.05814,doi:10.1103/
PhysRevC.100.035205.
[183] P. Amaudruz, et al., The Gottfried sum from the ratio F2(n) / F2(p), Phys. Rev. Lett. 66 (1991)
2712–2715. doi:10.1103/PhysRevLett.66.2712.
[184] K. Nagai, Measurement of Antiquark Flavor Asymmetry in the Proton by the Drell–Yan Experiment
SeaQuest at Fermilab, JPS Conf. Proc. 13 (2017) 020051. doi:10.7566/JPSCP.13.020051.
[185] C. A. Aidala, S. D. Bass, D. Hasch, G. K. Mallot, The Spin Structure of the Nucleon, Rev. Mod. Phys.
85 (2013) 655–691. arXiv:1209.2803,doi:10.1103/RevModPhys.85.655.
[186] L. Adamczyk, et al., Precision Measurement of the Longitudinal Double-spin Asymmetry for Inclusive
Jet Production in Polarized Proton Collisions at √s= 200 GeV, Phys. Rev. Lett. 115 (9) (2015)
092002. arXiv:1405.5134,doi:10.1103/PhysRevLett.115.092002.
[187] J. Adam, et al., Longitudinal double-spin asymmetry for inclusive jet and dijet production in pp
collisions at √s= 510 GeV, Phys. Rev. D 100 (5) (2019) 052005. arXiv:1906.02740,doi:10.1103/
PhysRevD.100.052005.
118
[188] M. S. Abdallah, et al., Longitudinal double-spin asymmetry for inclusive jet and dijet production in
polarized proton collisions at √s= 200 GeV, Phys. Rev. D 103 (9) (2021) L091103. arXiv:2103.05571,
doi:10.1103/PhysRevD.103.L091103.
[189] M. S. Abdallah, et al., Longitudinal double-spin asymmetry for inclusive jet and dijet production in
polarized proton collisions at √s= 510 GeV, Phys. Rev. D 105 (9) (2022) 092011. arXiv:2110.11020,
doi:10.1103/PhysRevD.105.092011.
[190] A. Adare, et al., Event Structure and Double Helicity Asymmetry in Jet Production from Polarized
p+pCollisions at √s= 200˜GeV, Phys. Rev. D 84 (2011) 012006. arXiv:1009.4921,doi:10.1103/
PhysRevD.84.012006.
[191] S. D. Bass, A. W. Thomas, The Nucleon’s octet axial-charge g(A)**(8) with chiral corrections, Phys.
Lett. B 684 (2010) 216–220. arXiv:0912.1765,doi:10.1016/j.physletb.2010.01.008.
[192] J. J. Ethier, N. Sato, W. Melnitchouk, First simultaneous extraction of spin-dependent parton distri-
butions and fragmentation functions from a global QCD analysis, Phys. Rev. Lett. 119 (13) (2017)
132001. arXiv:1705.05889,doi:10.1103/PhysRevLett.119.132001.
[193] A. Candido, S. Forte, F. Hekhorn, Can MS parton distributions be negative?, JHEP 11 (2020) 129.
arXiv:2006.07377,doi:10.1007/JHEP11(2020)129.
[194] J. Collins, T. C. Rogers, N. Sato, Positivity and renormalization of parton densities, Phys. Rev. D
105 (7) (2022) 076010. arXiv:2111.01170,doi:10.1103/PhysRevD.105.076010.
[195] B. Jager, M. Stratmann, S. Kretzer, W. Vogelsang, QCD hard scattering and the sign of the spin
asymmetry A**pi(LL), Phys. Rev. Lett. 92 (2004) 121803. arXiv:hep-ph/0310197,doi:10.1103/
PhysRevLett.92.121803.
[196] A. Adare, et al., Inclusive cross section and double-helicity asymmetry for π0production at midrapidity
in p+pcollisions at √s= 510 GeV, Phys. Rev. D 93 (1) (2016) 011501. arXiv:1510.02317,doi:
10.1103/PhysRevD.93.011501.
[197] A. Adare, et al., Charged-pion cross sections and double-helicity asymmetries in polarized p+p colli-
sions at √s=200 GeV, Phys. Rev. D 91 (3) (2015) 032001. arXiv:1409.1907,doi:10.1103/PhysRevD.
91.032001.
[198] U. A. Acharya, et al., Measurement of charged pion double spin asymmetries at midrapidity in
longitudinally polarized p+pcollisions at √s= 510 GeV, Phys. Rev. D 102 (3) (2020) 032001.
arXiv:2004.02681,doi:10.1103/PhysRevD.102.032001.
[199] R. M. Whitehill, Y. Zhou, N. Sato, W. Melnitchouk, Accessing gluon polarization with high-PT hadrons
in SIDIS, Phys. Rev. D 107 (3) (2023) 034033. arXiv:2210.12295,doi:10.1103/PhysRevD.107.
034033.
[200] M. V. Polyakov, P. Schweitzer, Forces inside hadrons: pressure, surface tension, mechanical radius,
and all that, Int. J. Mod. Phys. A 33 (26) (2018) 1830025. arXiv:1805.06596,doi:10.1142/
S0217751X18300259.
[201] C. Lorc´e, H. Moutarde, A. P. Trawi´nski, Revisiting the mechanical properties of the nucleon, Eur.
Phys. J. C 79 (1) (2019) 89. arXiv:1810.09837,doi:10.1140/epjc/s10052-019-6572-3.
[202] C. Lorc´e, On the hadron mass decomposition, Eur. Phys. J. C 78 (2) (2018) 120. arXiv:1706.05853,
doi:10.1140/epjc/s10052-018-5561-2.
[203] Y. Hatta, A. Rajan, K. Tanaka, Quark and gluon contributions to the QCD trace anomaly, JHEP 12
(2018) 008. arXiv:1810.05116,doi:10.1007/JHEP12(2018)008.
[204] A. Metz, B. Pasquini, S. Rodini, Revisiting the proton mass decomposition, Phys. Rev. D 102 (11)
(2021) 114042. arXiv:2006.11171,doi:10.1103/PhysRevD.102.114042.
119
[205] K. Goeke, M. V. Polyakov, M. Vanderhaeghen, Hard exclusive reactions and the structure of hadrons,
Prog. Part. Nucl. Phys. 47 (2001) 401–515. arXiv:hep-ph/0106012,doi:10.1016/S0146-6410(01)
00158-2.
[206] M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41–277. arXiv:hep-ph/0307382,
doi:10.1016/j.physrep.2003.08.002.
[207] A. V. Belitsky, A. V. Radyushkin, Unraveling hadron structure with generalized parton distributions,
Phys. Rept. 418 (2005) 1–387. arXiv:hep-ph/0504030,doi:10.1016/j.physrep.2005.06.002.
[208] D. S. Carman, R. W. Gothe, V. I. Mokeev, C. D. Roberts, Nucleon Resonance Electroexcitation
Amplitudes and Emergent Hadron Mass, Particles 6 (1) (2023) 416.
[209] D. Kharzeev, H. Satz, A. Syamtomov, G. Zinovjev, J/ψ photoproduction and the gluon structure of the
nucleon, Eur. Phys. J. C 9 (1999) 459–462. arXiv:hep-ph/9901375,doi:10.1007/s100529900047.
[210] O. Gryniuk, M. Vanderhaeghen, Accessing the real part of the forward J/ψ-p scattering amplitude
from J/ψ photoproduction on protons around threshold, Phys. Rev. D 94 (7) (2016) 074001. arXiv:
1608.08205,doi:10.1103/PhysRevD.94.074001.
[211] K. A. Mamo, I. Zahed, Diffractive photoproduction of J/ψ and Υ using holographic QCD: gravitational
form factors and GPD of gluons in the proton, Phys. Rev. D 101 (8) (2020) 086003. arXiv:1910.04707,
doi:10.1103/PhysRevD.101.086003.
[212] K. A. Mamo, I. Zahed, J/ψnear threshold in holographic QCD: A and D gravitational form factors,
Phys. Rev. D 106 (8) (2022) 086004. arXiv:2204.08857,doi:10.1103/PhysRevD.106.086004.
[213] Y. Guo, X. Ji, Y. Liu, QCD Analysis of Near-Threshold Photon-Proton Production of Heavy Quarko-
nium, Phys. Rev. D 103 (9) (2021) 096010. arXiv:2103.11506,doi:10.1103/PhysRevD.103.096010.
[214] B. Duran, et al., Determining the gluonic gravitational form factors of the proton, Nature 615 (7954)
(2023) 813–816. arXiv:2207.05212,doi:10.1038/s41586-023-05730-4.
[215] D. A. Pefkou, D. C. Hackett, P. E. Shanahan, Gluon gravitational structure of hadrons of different
spin, Phys. Rev. D 105 (5) (2022) 054509. arXiv:2107.10368,doi:10.1103/PhysRevD.105.054509.
[216] J. P. Chen, H. Gao, T. K. Hemmick, Z. E. Meziani, P. A. Souder, A White Paper on SoLID (Solenoidal
Large Intensity Device) (9 2014). arXiv:1409.7741.
[217] M. V. Polyakov, C. Weiss, Skewed and double distributions in pion and nucleon, Phys. Rev. D 60
(1999) 114017. arXiv:hep-ph/9902451,doi:10.1103/PhysRevD.60.114017.
[218] M. V. Polyakov, Generalized parton distributions and strong forces inside nucleons and nuclei, Phys.
Lett. B 555 (2003) 57–62. arXiv:hep-ph/0210165,doi:10.1016/S0370-2693(03)00036-4.
[219] V. D. Burkert, L. Elouadrhiri, F. X. Girod, The pressure distribution inside the proton, Nature
557 (7705) (2018) 396–399. doi:10.1038/s41586-018-0060-z.
[220] V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorc´e, P. Schweitzer, P. E. Shanahan, Colloquium:
Gravitational Form Factors of the Proton (3 2023). arXiv:2303.08347.
[221] K. Kumeriˇcki, Measurability of pressure inside the proton, Nature 570 (7759) (2019) E1–E2. doi:
10.1038/s41586-019-1211-6.
[222] H. Moutarde, P. Sznajder, J. Wagner, Unbiased determination of DVCS Compton Form Factors, Eur.
Phys. J. C 79 (7) (2019) 614. arXiv:1905.02089,doi:10.1140/epjc/s10052-019-7117-5.
[223] G. Christiaens, et al., First CLAS12 measurement of DVCS beam-spin asymmetries in the extended
valence region (11 2022). arXiv:2211.11274.
120
[224] X.-D. Ji, Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett. 78 (1997) 610–613. arXiv:
hep-ph/9603249,doi:10.1103/PhysRevLett.78.610.
[225] A. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56 (1997) 5524–5557. arXiv:hep-ph/
9704207,doi:10.1103/PhysRevD.56.5524.
[226] K. Kumericki, S. Liuti, H. Moutarde, GPD phenomenology and DVCS fitting: Entering the
high-precision era, Eur. Phys. J. A 52 (6) (2016) 157. arXiv:1602.02763,doi:10.1140/epja/
i2016-16157-3.
[227] D. E. Soper, The Parton Model and the Bethe-Salpeter Wave Function, Phys. Rev. D 15 (1977) 1141.
doi:10.1103/PhysRevD.15.1141.
[228] M. Burkardt, Impact parameter dependent parton distributions and off forward parton distributions
for zeta —>0, Phys. Rev. D 62 (2000) 071503, [Erratum: Phys.Rev.D 66, 119903 (2002)]. arXiv:
hep-ph/0005108,doi:10.1103/PhysRevD.62.071503.
[229] A. V. Belitsky, D. Mueller, A. Kirchner, Theory of deeply virtual Compton scattering on the nucleon,
Nucl. Phys. B 629 (2002) 323–392. arXiv:hep-ph/0112108,doi:10.1016/S0550-3213(02)00144-X.
[230] A. V. Belitsky, D. Mueller, Exclusive electroproduction revisited: treating kinematical effects, Phys.
Rev. D 82 (2010) 074010. arXiv:1005.5209,doi:10.1103/PhysRevD.82.074010.
[231] B. Kriesten, S. Liuti, A. Meyer, Novel Rosenbluth extraction framework for Compton form factors
from deeply virtual exclusive experiments, Phys. Lett. B 829 (2022) 137051. arXiv:2011.04484,
doi:10.1016/j.physletb.2022.137051.
[232] B. Kriesten, S. Liuti, Theory of deeply virtual Compton scattering off the unpolarized proton, Phys.
Rev. D 105 (1) (2022) 016015. arXiv:2004.08890,doi:10.1103/PhysRevD.105.016015.
[233] B. Kriesten, S. Liuti, L. Calero-Diaz, D. Keller, A. Meyer, G. R. Goldstein, J. Osvaldo Gonzalez-
Hernandez, Extraction of generalized parton distribution observables from deeply virtual electron
proton scattering experiments, Phys. Rev. D 101 (5) (2020) 054021. arXiv:1903.05742,doi:
10.1103/PhysRevD.101.054021.
[234] B. Kriesten, P. Velie, E. Yeats, F. Y. Lopez, S. Liuti, Parametrization of quark and gluon generalized
parton distributions in a dynamical framework, Phys. Rev. D 105 (5) (2022) 056022. arXiv:2101.
01826,doi:10.1103/PhysRevD.105.056022.
[235] K. Kumeriˇcki, Extraction of DVCS form factors with uncertainties, in: Probing Nucleons and Nuclei
in High Energy Collisions: Dedicated to the Physics of the Electron Ion Collider, 2020, pp. 25–29.
arXiv:1910.04806,doi:10.1142/9789811214950_0005.
[236] J. Grigsby, B. Kriesten, J. Hoskins, S. Liuti, P. Alonzi, M. Burkardt, Deep learning analysis of deeply
virtual exclusive photoproduction, Phys. Rev. D 104 (1) (2021) 016001. arXiv:2012.04801,doi:
10.1103/PhysRevD.104.016001.
[237] M. ˇ
Cui´c, K. Kumeriˇcki, A. Sch¨afer, Separation of Quark Flavors Using Deeply Virtual Comp-
ton Scattering Data, Phys. Rev. Lett. 125 (23) (2020) 232005. arXiv:2007.00029,doi:10.1103/
PhysRevLett.125.232005.
[238] M. Almaeen, J. Grigsby, J. Hoskins, B. Kriesten, Y. Li, H.-W. Lin, S. Liuti, Benchmarks for a Global
Extraction of Information from Deeply Virtual Exclusive Scattering (7 2022). arXiv:2207.10766.
[239] M. Guidal, M. Vanderhaeghen, Double deeply virtual Compton scattering off the nucleon, Phys. Rev.
Lett. 90 (2003) 012001. arXiv:hep-ph/0208275,doi:10.1103/PhysRevLett.90.012001.
[240] A. V. Belitsky, D. Mueller, Exclusive electroproduction of lepton pairs as a probe of nucleon structure,
Phys. Rev. Lett. 90 (2003) 022001. arXiv:hep-ph/0210313,doi:10.1103/PhysRevLett.90.022001.
121
[241] S. Zhao, A. Camsonne, D. Marchand, M. Mazouz, N. Sparveris, S. Stepanyan, E. Voutier, Z. W. Zhao,
Double deeply virtual Compton scattering with positron beams at SoLID, Eur. Phys. J. A 57 (7) (2021)
240. arXiv:2103.12773,doi:10.1140/epja/s10050-021-00551-3.
[242] D. Y. Ivanov, B. Pire, L. Szymanowski, O. V. Teryaev, Probing chiral odd GPD’s in diffractive
electroproduction of two vector mesons, Phys. Lett. B 550 (2002) 65–76. arXiv:hep-ph/0209300,
doi:10.1016/S0370-2693(02)02856-3.
[243] R. Boussarie, B. Pire, L. Szymanowski, S. Wallon, Exclusive photoproduction of a γ ρ pair with a large
invariant mass, JHEP 02 (2017) 054, [Erratum: JHEP 10, 029 (2018)]. arXiv:hep-ph/1609.03830,
doi:10.1007/JHEP02(2017)054.
[244] G. Duplanˇci´c, S. Nabeebaccus, K. Passek-Kumeriˇcki, B. Pire, L. Szymanowski, S. Wallon, Probing
chiral-even and chiral-odd leading twist quark generalised parton distributions through the exclusive
photoproduction of a γρ pair (2 2023). arXiv:2302.12026.
[245] A. Pedrak, B. Pire, L. Szymanowski, J. Wagner, Hard photoproduction of a diphoton with a large
invariant mass, Phys. Rev. D 96 (7) (2017) 074008, [Erratum: Phys.Rev.D 100, 039901 (2019)]. arXiv:
hep-ph/1708.01043,doi:10.1103/PhysRevD.96.074008.
[246] O. Grocholski, B. Pire, P. Sznajder, L. Szymanowski, J. Wagner, Phenomenology of diphoton pho-
toproduction at next-to-leading order, Phys. Rev. D 105 (9) (2022) 094025. arXiv:2204.00396,
doi:10.1103/PhysRevD.105.094025.
[247] O. Grocholski, B. Pire, P. Sznajder, L. Szymanowski, J. Wagner, Collinear factorization of diphoton
photoproduction at next to leading order, Phys. Rev. D 104 (11) (2021) 114006. arXiv:2110.00048,
doi:10.1103/PhysRevD.104.114006.
[248] J.-W. Qiu, Z. Yu, Single diffractive hard exclusive processes for the study of generalized parton distribu-
tions, Phys. Rev. D 107 (1) (2023) 014007. arXiv:2210.07995,doi:10.1103/PhysRevD.107.014007.
[249] S. V. Goloskokov, P. Kroll, The pion pole in hard exclusive vector-meson leptoproduction, The Euro-
pean Physical Journal A 50 (9) (sep 2014). doi:10.1140/epja/i2014-14146-2.
URL https://doi.org/10.1140%2Fepja%2Fi2014-14146-2
[250] C. Mezrag, H. Moutarde, F. Sabati´e, Test of two new parametrizations of the generalized parton
distribution H, Phys. Rev. D 88 (1) (2013) 014001. arXiv:1304.7645,doi:10.1103/PhysRevD.88.
014001.
[251] A. Pedrak, B. Pire, L. Szymanowski, J. Wagner, Electroproduction of a large invariant mass photon
pair, Phys. Rev. D 101 (11) (2020) 114027. arXiv:hep-ph/2003.03263,doi:10.1103/PhysRevD.101.
114027.
[252] B. Berthou, et al., PARTONS: PARtonic Tomography Of Nucleon Software: A computing framework
for the phenomenology of Generalized Parton Distributions, Eur. Phys. J. C 78 (6) (2018) 478. arXiv:
hep-ph/1512.06174,doi:10.1140/epjc/s10052-018-5948-0.
[253] E. C. Aschenauer, V. Batozskaya, S. Fazio, K. Gates, H. Moutarde, D. Sokhan, H. Spiesberger, P. Sz-
najder, K. Tezgin, EpIC: novel Monte Carlo generator for exclusive processes, Eur. Phys. J. C 82 (9)
(2022) 819. arXiv:2205.01762,doi:{10.1140/epjc/s10052-022-10651-z}.
[254] P. Kroll, K. Passek-Kumeriˇcki, Transition GPDs and exclusive electroproduction of π-∆(1232) final
states, Phys. Rev. D 107 (5) (2023) 054009. arXiv:2211.09474,doi:10.1103/PhysRevD.107.054009.
[255] P. A. M. Guichon, L. Moss´e, M. Vanderhaeghen, Pion production in deeply virtual Compton scattering,
Phys. Rev. D 68 (2003) 034018. arXiv:hep-ph/0305231,doi:10.1103/PhysRevD.68.034018.
[256] K. M. Semenov-Tian-Shansky, M. Vanderhaeghen, Deeply-Virtual Compton Process e−N→e−γπN
to Study Nucleon to Resonance Transitions - arXiv:2303.00119 [hep-ph] (2023). arXiv:2303.00119.
122
[257] H. F. Jones, M. D. Scadron, Multipole γ N –∆ form factors and resonant photoproduction and electro-
production, Annals Phys. 81 (1973) 1–14. doi:10.1016/0003-4916(73)90476-4.
[258] S. L. Adler, Photoproduction, electroproduction and weak single pion production in the (3,3) resonance
region, Annals Phys. 50 (1968) 189–311. doi:10.1016/0003-4916(68)90278-9.
[259] S. L. Adler, Application of Current Algebra Techniques to Soft Pion Production by the Weak Neutral
Current: V,a Case, Phys. Rev. D 12 (1975) 2644. doi:10.1103/PhysRevD.12.2644.
[260] J.-Y. Kim, Parametrization of transition energy-momentum tensor form factors, Phys. Lett. B 834
(2022) 137442. arXiv:2206.10202,doi:10.1016/j.physletb.2022.137442.
[261] J.-Y. Kim, H.-Y. Won, J. L. Goity, C. Weiss, QCD angular momentum in N→∆ transitions (4 2023).
arXiv:2304.08575.
[262] V. Pascalutsa, M. Vanderhaeghen, New large-N(c) relations among the nucleon and nucleon-to-Delta
GPDs (11 2006). arXiv:hep-ph/0611050.
[263] P. Schweitzer, C. Weiss, Spin-flavor structure of chiral-odd generalized parton distributions in the large-
Nclimit, Phys. Rev. C 94 (4) (2016) 045202. arXiv:1606.08388,doi:10.1103/PhysRevC.94.045202.
[264] S. Diehl, et al., First measurement of hard exclusive π−∆++ electroproduction beam-spin asymmetries
off the proton (3 2023). arXiv:2303.11762.
[265] S. Diehl, et al., A multidimensional study of the structure function ratio σLT’/σ0 from hard exclusive
π+ electro-production off protons in the GPD regime, Phys. Lett. B 839 (2023) 137761. arXiv:
2210.14557,doi:10.1016/j.physletb.2023.137761.
[266] A. Kim, S. Diehl, K. J. et al. (CLAS Collaboration), to be submitted to Phys. Lett. B (2023).
[267] C. A. Gayoso, et al., Progress and opportunities in backward angle (u-channel) physics, Eur. Phys. J.
A 57 (12) (2021) 342. arXiv:2107.06748,doi:10.1140/epja/s10050-021-00625-2.
[268] L. L. Frankfurt, P. V. Pobylitsa, M. V. Polyakov, M. Strikman, Hard exclusive pseudoscalar meson
electroproduction and spin structure of a nucleon, Phys. Rev. D 60 (1999) 014010. arXiv:hep-ph/
9901429,doi:10.1103/PhysRevD.60.014010.
[269] B. Pire, L. Szymanowski, Hadron annihilation into two photons and backward VCS in the scaling
regime of QCD, Phys. Rev. D 71 (2005) 111501. arXiv:hep-ph/0411387,doi:10.1103/PhysRevD.
71.111501.
[270] B. Pire, K. Semenov-Tian-Shansky, L. Szymanowski, Transition distribution amplitudes and hard
exclusive reactions with baryon number transfer, Phys. Rept. 940 (2021) 1–121. arXiv:2103.01079,
doi:10.1016/j.physrep.2021.09.002.
[271] K. Park, et al., Hard exclusive pion electroproduction at backward angles with CLAS, Phys. Lett. B
780 (2018) 340–345. arXiv:1711.08486,doi:10.1016/j.physletb.2018.03.026.
[272] W. B. Li, et al., Unique Access to u-Channel Physics: Exclusive Backward-Angle Omega Meson
Electroproduction, Phys. Rev. Lett. 123 (18) (2019) 182501. arXiv:1910.00464,doi:10.1103/
PhysRevLett.123.182501.
[273] S. Diehl, et al., Extraction of Beam-Spin Asymmetries from the Hard Exclusive π+Channel off Protons
in a Wide Range of Kinematics, Phys. Rev. Lett. 125 (18) (2020) 182001. arXiv:2007.15677,doi:
10.1103/PhysRevLett.125.182001.
[274] W. B. Li, et al., Backward-angle Exclusive pi0 Production above the Resonance Region (8 2020).
arXiv:2008.10768.
123
[275] B. Pire, K. Semenov-Tian-Shansky, L. Szymanowski, πN transition distribution amplitudes: their
symmetries and constraints from chiral dynamics, Phys. Rev. D 84 (2011) 074014. doi:10.1103/
PhysRevD.84.074014.
[276] J. P. Lansberg, B. Pire, L. Szymanowski, Backward DVCS and Proton to Photon Transition Dis-
tribution Amplitudes, Nucl. Phys. A 782 (2007) 16–23. arXiv:hep-ph/0607130,doi:10.1016/j.
nuclphysa.2006.10.014.
[277] B. Pire, K. M. Semenov-Tian-Shansky, A. A. Shaikhutdinova, L. Szymanowski, Backward timelike
Compton scattering to decipher the photon content of the nucleon, Eur. Phys. J. C 82 (7) (2022) 656.
arXiv:2201.12853,doi:10.1140/epjc/s10052-022-10587-4.
[278] B. Pire, K. M. Semenov-Tian-Shansky, A. A. Shaikhutdinova, L. Szymanowski, Pion and photon beam
initiated backward charmonium or lepton pair production (12 2022). arXiv:2212.07688.
[279] S. Adhikari, et al., Measurement of the J/ψphotoproduction cross section over the full near-threshold
kinematic region (4 2023). arXiv:2304.03845.
[280] P. Jain, B. Pire, J. P. Ralston, The Status and Future of Color Transparency and Nuclear Filtering,
MDPI Physics 4 (2) (2022) 578–589. arXiv:2203.02579,doi:10.3390/physics4020038.
[281] G. M. Huber, W. B. Li, W. Cosyn, B. Pire, u-Channel Color Transparency Observables, MDPI Physics
4 (2) (2022) 451–461. arXiv:2202.04470,doi:10.3390/physics4020030.
[282] T. Horn, G. M. Huber, P. Markowitz, et al., Studies of the L/T Separated Kaon Electroproduction
Cross Sections from 5-11 GeV, jefferson Lab 12 GeV Experiment E12-09-011.
[283] G. M. Huber, D. Gaskell, T. Horn, et al., Measurement of the Charged Pion Form Factor to High Q2
and Scaling Study of the L/T-Separated Pion Electroproduction Cross Section at 11 GeV, jefferson
Lab 12 GeV Experiment E12-19-006 (2019).
URL https://www.jlab.org/exp_prog/proposals/19/E12-19-006.pdf
[284] M. K. Jones, et al., gE p/gM p ratio by polarization transfer in ep →ep, Phys. Rev. Lett. 84 (2000)
1398–1402. arXiv:nucl-ex/9910005,doi:10.1103/PhysRevLett.84.1398.
[285] O. Gayou, et al., Measurement of GEp/GM p in ep →ep to Q2= 5.6-GeV2, Phys. Rev. Lett. 88 (2002)
092301. arXiv:nucl-ex/0111010,doi:10.1103/PhysRevLett.88.092301.
[286] A. J. R. Puckett, et al., Recoil Polarization Measurements of the Proton Electromagnetic Form Factor
Ratio to Q2= 8.5 GeV2, Phys. Rev. Lett. 104 (2010) 242301. arXiv:1005.3419,doi:10.1103/
PhysRevLett.104.242301.
[287] American Physical Society 2017 Bonner Prize in Nuclear Physics Recipient Charles F. Perdrisat (Col-
lege of William and Mary), [Webpage].
[288] M. Y. Barabanov, et al., Diquark correlations in hadron physics: Origin, impact and evidence, Prog.
Part. Nucl. Phys. 116 (2021) 103835. arXiv:2008.07630,doi:10.1016/j.ppnp.2020.103835.
[289] F. Gross, et al., 50 Years of Quantum Chromodynamics (12 2022). arXiv:2212.11107.
[290] B. Schmookler, A. Pierre-Louis, A. Deshpande, D. Higinbotham, E. Long, A. J. R. Puckett, High Q2
electron-proton elastic scattering at the future Electron-Ion Collider (7 2022). arXiv:2207.04378.
[291] F. Englert, Nobel Lecture: The BEH Mechanism and its Scalar Boson, Rev. Mod. Phys. 86 (2014)
843.
[292] P. W. Higgs, Nobel Lecture: Evading the Goldstone theorem, Rev. Mod. Phys. 86 (2014) 851.
[293] D. Binosi, Emergent Hadron Mass in Strong Dynamics, Few Body Syst. 63 (2) (2022) 42.
[294] M. N. Ferreira, J. Papavassiliou, Gauge Sector Dynamics in QCD, Particles 6 (1) (2023) 312.
124
[295] M. Ding, C. D. Roberts, S. M. Schmidt, Emergence of Hadron Mass and Structure, Particles 6 (1)
(2023) 57.
[296] M. Y. Barabanov, et al., Diquark Correlations in Hadron Physics: Origin, Impact and Evidence,
Progress in Particle and Nuclear Physics 116 (2021) 103835.
[297] S. J. Brodsky, et al., Strong QCD from Hadron Structure Experiments: Newport News, VA, USA,
November 4-8, 2019, Int. J. Mod. Phys. E 29 (08) (2020) 2030006.
[298] V. D. Burkert, C. D. Roberts, Colloquium : Roper Resonance: Toward a Solution to the Fifty Year
Puzzle, Rev. Mod. Phys. 91 (1) (2019) 011003.
[299] V. V. Flambaum, et al., Sigma Terms of Light-Quark Hadrons, Few Body Syst. 38 (2006) 31.
[300] J. Ruiz de Elvira, M. Hoferichter, B. Kubis, U.-G. Meißner, Extracting the σ-Term from Low-Energy
Pion-Nucleon Scattering, J. Phys. G 45 (2) (2018) 024001.
[301] S. Aoki, et al., FLAG Review 2019, Eur. Phys. J. C 80 (2020) 113.
[302] A. C. Aguilar, et al., Pion and Kaon Structure at the Electron-Ion Collider, Eur. Phys. J. A 55 (2019)
190.
[303] D. P. Anderle, et al., Electron-Ion Collider in China, Front. Phys. (Beijing) 16 (6) (2021) 64701.
[304] J. S. Schwinger, Gauge Invariance and Mass. 2., Phys. Rev. 128 (1962) 2425.
[305] J. M. Cornwall, Dynamical Mass Generation in Continuum QCD, Phys. Rev. D 26 (1982) 1453.
[306] J. Mandula, M. Ogilvie, The Gluon Is Massive: A Lattice Calculation of the Gluon Propagator in the
Landau Gauge, Phys. Lett. B 185 (1987) 127.
[307] C. D. Roberts, D. G. Richards, T. Horn, L. Chang, Insights into the Emergence of Mass from Studies
of Pion and Kaon Structure, Prog. Part. Nucl. Phys. 120 (2021) 103883.
[308] N. Suzuki, B. Julia-Diaz, H. Kamano, T. S. H. Lee, A. Matsuyama, T. Sato, Disentangling the Dy-
namical Origin of P-11 Nucleon Resonances, Phys. Rev. Lett. 104 (2010) 042302.
[309] M. M. Giannini, E. Santopinto, The Hypercentral Constituent Quark Model and its Application to
Baryon Properties, Chin. J. Phys. 53 (2015) 020301.
[310] S.-X. Qin, C. D. Roberts, Impressions of the Continuum Bound State Problem in QCD, Chin. Phys.
Lett. 37 (12) (2020) 121201.
[311] F. Gao, L. Chang, Y.-X. Liu, C. D. Roberts, P. C. Tandy, Exposing Strangeness: Projections for Kaon
Electromagnetic Form Factors, Phys. Rev. D 96 (3) (2017) 034024.
[312] S.-S. Xu, Z.-F. Cui, L. Chang, J. Papavassiliou, C. D. Roberts, H.-S. Zong, New Perspective on Hybrid
Mesons, Eur. Phys. J. A (Lett.) 55 (2019) 113.
[313] Q.-W. Wang, S.-X. Qin, C. D. Roberts, S. M. Schmidt, Proton Tensor Charges from a Poincar´e-
Covariant Faddeev Equation, Phys. Rev. D 98 (2018) 054019.
[314] M. Chen, M. Ding, L. Chang, C. D. Roberts, Mass-Dependence of Pseudoscalar Meson Elastic Form
Factors, Phys. Rev. D 98 (2018) 091505(R).
[315] D. Binosi, L. Chang, M. Ding, F. Gao, J. Papavassiliou, C. D. Roberts, Distribution Amplitudes of
Heavy-Light Mesons, Phys. Lett. B 790 (2019) 257.
[316] C. Chen, G. I. Krein, C. D. Roberts, S. M. Schmidt, J. Segovia, Spectrum and Structure of Octet and
Decuplet Baryons and Their Positive-Parity Excitations, Phys. Rev. D 100 (2019) 054009.
125
[317] S.-X. Qin, C. D. Roberts, S. M. Schmidt, Spectrum of Light- and Heavy-Baryons, Few Body Syst. 60
(2019) 26.
[318] Y. Lu, C. Chen, Z.-F. Cui, C. D. Roberts, S. M. Schmidt, J. Segovia, H. S. Zong, Transition Form
Factors: γ∗+p→∆(1232), ∆(1600), Phys. Rev. D 100 (3) (2019) 034001.
[319] E. V. Souza, M. Narciso Ferreira, A. C. Aguilar, J. Papavassiliou, C. D. Roberts, S.-S. Xu, Pseudoscalar
Glueball Mass: A Window on Three-Gluon Interactions, Eur. Phys. J. A (Lett.) 56 (2020) 25.
[320] K. Raya, Z.-F. Cui, L. Chang, J.-M. Morgado, C. D. Roberts, J. Rodr´ıguez-Quintero, Revealing Pion
and Kaon Structure via Generalised Parton Distributions, Chin. Phys. C 46 (26) (2022) 013105.
[321] Z. F. Cui, M. Ding, J. M. Morgado, K. Raya, D. Binosi, L. Chang, J. Papavassiliou, C. D. Roberts,
J. Rodr´ıguez-Quintero, S. M. Schmidt, Concerning Pion Parton Distributions, Eur. Phys. J. A 58 (1)
(2022) 10.
[322] L. Liu, C. Chen, C. D. Roberts, Wave functions of (I, J P) = (1
2,3
2∓) baryons, Phys. Rev. D 107 (1)
(2023) 014002.
[323] F. Gao, S.-X. Qin, C. D. Roberts, J. Rodr´ıguez-Quintero, Locating the Gribov Horizon, Phys. Rev. D
97 (2018) 034010.
[324] O. Oliveira, P. J. Silva, J.-I. Skullerud, A. Sternbeck, Quark Propagator with Two Flavors of O(a)-
Improved Wilson Fermions, Phys. Rev. D 99 (9) (2019) 094506.
[325] D. Binosi, R.-A. Tripolt, Spectral Functions of Confined Particles, Phys. Lett. B 801 (2020) 135171.
[326] D. Boito, A. Cucchieri, C. Y. London, T. Mendes, Probing the Singularities of the Landau-Gauge
Gluon and Ghost Propagators with Rational Approximants, JHEP 02 (2023) 144.
[327] V. D. Burkert, Nucleon Resonances and Transition Form Factors – arXiv:2212.08980 [hep-ph] (2022).
[328] I. G. Aznauryan, V. D. Burkert, Electroexcitation of Nucleon Resonances, Prog. Part. Nucl. Phys. 67
(2012) 1–54.
[329] V. I. Mokeev, D. S. Carman, Photo- and Electrocouplings of Nucleon Resonances, Few Body Syst.
63 (3) (2022) 59.
[330] J. Segovia, B. El-Bennich, E. Rojas, I. C. Cloet, C. D. Roberts, S.-S. Xu, H.-S. Zong, Completing the
Picture of the Roper Resonance, Phys. Rev. Lett. 115 (17) (2015) 171801.
[331] D. J. Wilson, I. C. Cloet, L. Chang, C. D. Roberts, Nucleon and Roper Electromagnetic Elastic and
Transition Form Factors, Phys. Rev. C 85 (2012) 025205.
[332] Z.-F. Cui, C. Chen, D. Binosi, F. de Soto, C. D. Roberts, J. Rodr´ıguez-Quintero, S. M. Schmidt,
J. Segovia, Nucleon Elastic Form Factors at Accessible Large Spacelike Momenta, Phys. Rev. D 102
(2020) 014043.
[333] C. Chen, C. D. Roberts, Nucleon Axial Form Factor at Large Momentum Transfers, Eur. Phys. J. A
58 (10) (2022) 206.
[334] M. Ding, K. Raya, A. Bashir, D. Binosi, L. Chang, M. Chen, C. D. Roberts, γ∗γ→η , η′Transition
Form Factors, Phys. Rev. D 99 (2019) 014014.
[335] K. S. Egiyan, et al., Observation of nuclear scaling in the a(e, e′) reaction at xB>1, Phys. Rev. C 68
(2003) 014313. doi:10.1103/PhysRevC.68.014313.
[336] K. S. Egiyan, et al., Measurement of two- and three-nucleon short-range correlation probabilities in
nuclei, Phys. Rev. Lett. 96 (2006) 082501. doi:10.1103/PhysRevLett.96.082501.
126
[337] N. Fomin, et al., New Measurements of High-Momentum Nucleons and Short-Range Structures in
Nuclei, Phys. Rev. Lett. 108 (2012) 092502. doi:10.1103/PhysRevLett.108.092502.
[338] L. L. Frankfurt, M. I. Strikman, D. B. Day, M. Sargsian, Evidence for short range correlations from high
Q**2 (e, e-prime) reactions, Phys. Rev. C 48 (1993) 2451–2461. doi:10.1103/PhysRevC.48.2451.
[339] L. Frankfurt, M. Sargsian, M. Strikman, Recent observation of short range nucleon correlations in
nuclei and their implications for the structure of nuclei and neutron stars, Int. J. Mod. Phys. A 23 (20)
(2008) 2991–3055. doi:10.1142/s0217751x08041207.
[340] E. Piasetzky, M. Sargsian, L. Frankfurt, M. Strikman, J. W. Watson, Evidence for strong dominance of
proton-neutron correlations in nuclei, Phys. Rev. Lett. 97 (2006) 162504. doi:10.1103/PhysRevLett.
97.162504.
[341] R. Subedi, et al., Probing cold dense nuclear matter, Science 320 (5882) (2008) 1476–
1478. arXiv:https://science.sciencemag.org/content/320/5882/1476.full.pdf,doi:10.
1126/science.1156675.
[342] M. Duer, et al., Direct Observation of Proton-Neutron Short-Range Correlation Dominance in Heavy
Nuclei, Phys. Rev. Lett. 122 (2019) 172502. doi:10.1103/PhysRevLett.122.172502.
[343] M. Sargsian, T. Abrahamyan, M. Strikman, L. Frankfurt, Exclusive electrodisintegration of 3He at high
Q2. ii. decay function formalism, Phys. Rev. C 71 (4) (2005). doi:10.1103/physrevc.71.044615.
[344] R. Schiavilla, R. B. Wiringa, S. C. Pieper, J. Carlson, Tensor Forces and the Ground-State Structure
of Nuclei, Phys. Rev. Lett. 98 (2007) 132501. arXiv:nucl-th/0611037,doi:10.1103/PhysRevLett.
98.132501.
[345] M. M. Sargsian, New properties of the high-momentum distribution of nucleons in asymmetric nuclei,
Phys. Rev. C 89 (3) (2014) 034305. arXiv:1210.3280,doi:10.1103/PhysRevC.89.034305.
[346] O. Hen, et al., Momentum sharing in imbalanced fermi systems, Science 346 (6209) (2014) 614–
617. arXiv:https://science.sciencemag.org/content/346/6209/614.full.pdf,doi:10.1126/
science.1256785.
[347] M. Duer, et al., Probing the high-momentum protons and neutrons in neutron-rich nuclei, Nature 560
(2018) 617–621, https://doi.org/10.1038/s41586-018-0400-z.
[348] R. Jastrow, On the nucleon-nucleon interaction, Phys. Rev. 81 (1951) 165–170. doi:10.1103/PhysRev.
81.165.
[349] R. B. Wiringa, V. G. J. Stoks, R. Schiavilla, An Accurate nucleon-nucleon potential with charge inde-
pendence breaking, Phys. Rev. C 51 (1995) 38–51. arXiv:nucl- th/9408016,doi:10.1103/PhysRevC.
51.38.
[350] E. Epelbaum, H.-W. Hammer, U.-G. Meissner, Modern Theory of Nuclear Forces, Rev. Mod. Phys.
81 (2009) 1773–1825. arXiv:0811.1338,doi:10.1103/RevModPhys.81.1773.
[351] M. Harvey, Effective nuclear forces in the quark model with delta and hidden-color channel coupling,
Nucl. Phys. A 352 (3) (1981) 326–342. doi:https://doi.org/10.1016/0375-9474(81)90413-9.
[352] C. Ji, S. Brodsky, Quantum-chromodynamic evolution of six-quark states, Phys. Rev. D 34 (1986)
1460–1473. doi:10.1103/PhysRevD.34.1460.
[353] L. Frankfurt, M. Strikman, High-energy phenomena, short-range nuclear structure and QCD, Phys.
Rept. 76 (4) (1981) 215–347. doi:https://doi.org/10.1016/0370-1573(81)90129-0.
[354] G. Miller, Pionic and hidden-color, six-quark contributions to the deuteron b1structure function, Phys.
Rev. C 89 (2014) 045203. doi:10.1103/PhysRevC.89.045203.
127
[355] J. Rittenhouse West, Diquark induced short-range nucleon-nucleon correlations & the EMC effect,
Nucl. Phys. A 1029 (2023) 122563. arXiv:2009.06968,doi:10.1016/j.nuclphysa.2022.122563.
[356] J. Rittenhouse West, S. J. Brodsky, G. F. de Teramond, A. S. Goldhaber, I. Schmidt, QCD hidden-
color hexadiquark in the core of nuclei, Nucl. Phys. A 1007 (2021) 122134. arXiv:2004.14659,doi:
10.1016/j.nuclphysa.2020.122134.
[357] L. Frankfurt, M. Strikman, Hard nuclear processes and microscopic nuclear structure, Phys. Rept.
160 (5) (1988) 235–427. doi:10.1016/0370-1573(88)90179-2.
[358] M. M. Sargsian, Superfast quarks in the nuclear medium, Nucl. Phys. A 782 (2007) 199–206. doi:
10.1016/j.nuclphysa.2006.10.057.
[359] A. Freese, M. Sargsian, M. Strikman, Probing superfast quarks in nuclei through dijet production at
the LHC, Eur. Phys. J. C 75 (11) (nov 2015). doi:10.1140/epjc/s10052-015-3755-4.
[360] A. Freese, W. Cosyn, M. Sargsian, QCD evolution of superfast quarks, Phys. Rev. D 99 (2019) 114019.
doi:10.1103/PhysRevD.99.114019.
[361] N. Fomin, et al., Scaling of the F2structure function in nuclei and quark distributions at x > 1, Phys.
Rev. Lett. 105 (2010) 212502. doi:10.1103/PhysRevLett.105.212502.
[362] J. Arrington, D. Day, N. Fomin, P. Solvignon, E12-06-105: Inclusive Scattering from Nuclei at x > 1
in the quasielastic and deeply inelastic regimes (2006).
URL https://www.jlab.org/exp_prog/proposals/06/PR12-06-105.pdf
[363] C. Yero, et al., Probing the deuteron at very large internal momenta, Phys. Rev. Lett. 125 (2020)
262501. doi:10.1103/PhysRevLett.125.262501.
[364] M. Sargsian, D. Day, L. Frankfurt, M. Strikman, Searching for three-nucleon short-range correlations,
Phys. Rev. C 100 (4) (2019). doi:10.1103/physrevc.100.044320.
[365] D. Day, L. Frankfurt, M. Sargsian, M. Strikman, Toward observation of three-nucleon short-range
correlations in high-Q2a(e, e′)xreactions, Phys. Rev. C 107 (2023) 014319. doi:10.1103/PhysRevC.
107.014319.
[366] J. J. Aubert, et al., The ratio of the nucleon structure functions F2nfor iron and deuterium, Phys.
Lett. B 123 (1983) 275–278. doi:10.1016/0370-2693(83)90437-9.
[367] J. Seely, et al., New measurements of the EMC effect in very light nuclei, Phys. Rev. Lett. 103 (2009)
202301. arXiv:0904.4448,doi:10.1103/PhysRevLett.103.202301.
[368] L. B. Weinstein, E. Piasetzky, D. W. Higinbotham, J. Gomez, O. Hen, R. Shneor, Short Range
Correlations and the EMC Effect, Phys. Rev. Lett. 106 (2011) 052301. arXiv:1009.5666,doi:10.
1103/PhysRevLett.106.052301.
[369] B. Schmookler, et al., Modified structure of protons and neutrons in correlated pairs, Nature 566 (7744)
(2019) 354–358. arXiv:2004.12065,doi:10.1038/s41586-019-0925-9.
[370] S. J. Brodsky, G. F. de Teramond, H. G. Dosch, J. Erlich, Light-Front Holographic QCD and Emerging
Confinement, Phys. Rept. 584 (2015) 1–105. arXiv:1407.8131,doi:10.1016/j.physrep.2015.05.
001.
[371] D. N. Kim, G. A. Miller, Light-front holography model of the EMC effect, Phys. Rev. C 106 (5) (2022)
055202. arXiv:2209.13753,doi:10.1103/PhysRevC.106.055202.
[372] L. Frankfurt, V. Guzey, M. Strikman, Leading Twist Nuclear Shadowing Phenomena in Hard Processes
with Nuclei, Phys. Rept. 512 (2012) 255–393. arXiv:1106.2091,doi:10.1016/j.physrep.2011.12.
002.
128
[373] G. A. Miller, Revealing nuclear pions using electron scattering, Phys. Rev. C 64 (2001) 022201. arXiv:
nucl-th/0104025,doi:10.1103/PhysRevC.64.022201.
[374] D. M. Alde, et al., Nuclear dependence of dimuon production at 800-GeV. FNAL-772 experiment,
Phys. Rev. Lett. 64 (1990) 2479–2482. doi:10.1103/PhysRevLett.64.2479.
[375] M. Alvioli, M. Strikman, Hunting for an EMC-like effect for antiquarks (10 2022). arXiv:2210.12597.
[376] P. Kotko, K. Kutak, S. Sapeta, A. M. Stasto, M. Strikman, Estimating nonlinear effects in forward
dijet production in ultra-peripheral heavy ion collisions at the LHC, Eur. Phys. J. C 77 (5) (2017) 353.
arXiv:1702.03063,doi:10.1140/epjc/s10052-017-4906-6.
[377] L. L. Frankfurt, G. A. Miller, M. Strikman, The Geometrical color optics of coherent high-energy
processes, Ann. Rev. Nucl. Part. Sci. 44 (1994) 501–560. arXiv:hep-ph/9407274,doi:10.1146/
annurev.ns.44.120194.002441.
[378] E. M. Aitala, et al., Observation of color transparency in diffractive dissociation of pions, Phys. Rev.
Lett. 86 (2001) 4773–4777. arXiv:hep-ex/0010044,doi:10.1103/PhysRevLett.86.4773.
[379] B. Clasie, et al., Measurement of nuclear transparency for the A(e, e-prime’ pi+) reaction, Phys. Rev.
Lett. 99 (2007) 242502. arXiv:0707.1481,doi:10.1103/PhysRevLett.99.242502.
[380] L. El Fassi, et al., Evidence for the onset of color transparency in ρ0electroproduction off nuclei, Phys.
Lett. B 712 (2012) 326–330. arXiv:1201.2735,doi:10.1016/j.physletb.2012.05.019.
[381] L. El Fassi, Chasing QCD Signatures in Nuclei Using Color Coherence Phenomena, Physics 4 (3)
(2022) 970–980. doi:10.3390/physics4030064.
[382] D. Bhetuwal, et al., Ruling out Color Transparency in Quasielastic 12C(e,e’p) up to Q2of 14.2
(GeV/c)2, Phys. Rev. Lett. 126 (8) (2021) 082301. arXiv:2011.00703,doi:10.1103/PhysRevLett.
126.082301.
[383] O. Caplow-Munro, G. A. Miller, Color transparency and the proton form factor: Evidence for the Feyn-
man mechanism, Phys. Rev. C 104 (1) (2021) L012201. arXiv:2104.11168,doi:10.1103/PhysRevC.
104.L012201.
[384] K. Egiian, L. Frankfurt, W. R. Greenberg, G. A. Miller, M. Sargsian, M. Strikman, Searching for
color coherent effects at intermediate Q**2 via double scattering processes, Nucl. Phys. A 580 (1994)
365–382. arXiv:nucl-th/9401002,doi:10.1016/0375-9474(94)90903-2.
[385] L. L. Frankfurt, W. R. Greenberg, G. A. Miller, M. M. Sargsian, M. I. Strikman, Color transparency
effects in electron deuteron interactions at intermediate Q**2, Z. Phys. A 352 (1995) 97–113. arXiv:
nucl-th/9501009,doi:10.1007/BF01292764.
[386] L. L. Frankfurt, W. R. Greenberg, G. A. Miller, M. M. Sargsian, M. I. Strikman, Color transparency
and the vanishing deuterium shadow, Phys. Lett. B 369 (1996) 201–206. arXiv:nucl- th/9412033,
doi:10.1016/0370-2693(95)01558-2.
[387] D. J. Gross, F. Wilczek, Ultraviolet behavior of non-abelian gauge theories, Phys. Rev. Lett. 30 (1973)
1343–1346. doi:10.1103/PhysRevLett.30.1343.
[388] Y. L. Dokshitzer, QCD phenomenology, 2003, pp. 1–33. arXiv:hep-ph/0306287.
[389] B. Andersson, G. Gustafson, C. Peterson, Quark Jet Fragmentation, Phys. Scripta 19 (1979) 184–190.
doi:10.1088/0031-8949/19/2/015.
[390] B. Andersson, G. Gustafson, G. Ingelman, T. Sjostrand, Parton Fragmentation and String Dynamics,
Phys. Rept. 97 (1983) 31–145. doi:10.1016/0370-1573(83)90080-7.
129
[391] L. S. Osborne, C. Bolon, R. L. Lanza, D. Luckey, D. G. Roth, J. F. Martin, G. J. Feldman, M. E. B.
Franklin, G. Hanson, M. L. Perl, Electroproduction of Hadrons From Nuclei, Phys. Rev. Lett. 40 (1978)
1624. doi:10.1103/PhysRevLett.40.1624.
[392] J. Ashman, et al., Comparison of forward hadrons produced in muon interactions on nuclear targets
and deuterium, Z. Phys. C 52 (1991) 1–12. doi:10.1007/BF01412322.
[393] A. Arvidson, et al., Hadron production in 200-GeV µ- copper and µ- carbon deep inelastic interactions,
Nucl. Phys. B 246 (1984) 381–407. doi:10.1016/0550-3213(84)90045-2.
[394] X. Artru, G. Mennessier, String model and multiproduction, Nucl. Phys. B 70 (1974) 93–115. doi:
10.1016/0550-3213(74)90360-5.
[395] E. V. Shuryak, Quark-Gluon Plasma and Hadronic Production of Leptons, Photons and Psions, Phys.
Lett. B 78 (1978) 150. doi:10.1016/0370-2693(78)90370-2.
[396] X.-N. Wang, Why the observed jet quenching at RHIC is due to parton energy loss, Phys. Lett. B 579
(2004) 299–308. doi:10.1016/j.physletb.2003.11.011.
[397] B. Z. Kopeliovich, J. Nemchik, E. Predazzi, A. Hayashigaki, Nuclear hadronization: Within or with-
out?, Nucl. Phys. A 740 (2004) 211–245. doi:10.1016/j.nuclphysa.2004.04.110.
[398] W. K. Brooks and J. A. L´opez, Estimating the color lifetime of energetic quarks, Phys. Lett. B 816
(2021) 136171. doi:10.1016/j.physletb.2021.136171.
[399] S. J. Brodsky, G. F. de Teramond, Spin Correlations, QCD Color Transparency and Heavy Quark
Thresholds in Proton Proton Scattering, Phys. Rev. Lett. 60 (1988) 1924. doi:10.1103/PhysRevLett.
60.1924.
[400] M. Sargsian, et al., Hadrons in the nuclear medium, J. Phys. G: Nucl. Part. Phys. 29 (3) (2003)
R1–R45. doi:10.1088/0954-3899/29/3/201.
[401] L. Frankfurt, G. A. Miller, M. Strikman, Precocious dominance of point - like configurations in hadronic
form-factors, Nucl. Phys. A 555 (1993) 752–764. doi:10.1016/0375-9474(93)90504-Q.
[402] J. Arrington, D. Higinbotham, G. Rosner, M. Sargsian, Hard probes of short-range nucleon–nucleon
correlations, Prog. Part. Nucl. Phys. 67 (4) (2012) 898–938. doi:https://doi.org/10.1016/j.ppnp.
2012.04.002.
[403] J. Arrington, N. Fomin, A. Schmidt, Progress in understanding short-range structure in nuclei: an
experimental perspective, Ann. Rev. Nucl. Part. Sci. (2022) 307arXiv:2203.02608.
[404] J. Arrington, Do ordinary nuclei contain exotic states of matter?, Acta Phys. Hung. A 21 (2004) 295.
arXiv:hep-ph/0304213,doi:10.1556/APH.21.2004.2-4.30.
[405] P. J. Mulders, A. W. Thomas, The ’Six Quark’ Component in the Deuteron From a Comparison
of Electron and Neutrino / Anti-neutrinos Structure Functions, Phys. Rev. Lett. 52 (1984) 1199.
doi:10.1103/PhysRevLett.52.1199.
[406] O. Hen, G. Miller, E. Piasetzky, L. Weinstein, Nucleon-Nucleon Correlations, Short-lived Excitations,
and the Quarks Within, Rev. Mod. Phys. 89 (4) (2017) 045002. doi:10.1103/RevModPhys.89.045002.
[407] I. Niculescu, et al., Experimental verification of quark hadron duality, Phys. Rev. Lett. 85 (2000)
1186–1189. doi:10.1103/PhysRevLett.85.1186.
[408] I. Niculescu, et al., Direct observation of quark-hadron duality in the free neutron F2structure function,
Phys. Rev. C 91 (5) (2015) 055206. arXiv:1501.02203,doi:10.1103/PhysRevC.91.055206.
[409] J. Arrington, R. Ent, C. E. Keppel, J. Mammei, I. Niculescu, Low Q scaling, duality, and the EMC
effect, Phys. Rev. C 73 (2006) 035205. arXiv:nucl-ex/0307012,doi:10.1103/PhysRevC.73.035205.
130
[410] W. Boeglin, M. Sargsian, Modern Studies of the Deuteron: from the Lab Frame to the Light Front,
Int. J. Mod. Phys. E 24 (03) (2015) 1530003. arXiv:1501.05377,doi:10.1142/S0218301315300039.
[411] W. U. Boeglin, et al., Probing the high momentum component of the deuteron at high Q2, Phys. Rev.
Lett. 107 (2011) 262501. doi:10.1103/PhysRevLett.107.262501.
[412] M. M. Sargsian, Large Q2electrodisintegration of the deuteron in the virtual nucleon approximation,
Phys. Rev. C 82 (2010) 014612. doi:10.1103/PhysRevC.82.014612.
[413] J. Laget, The electro-disintegration of few body systems revisited, Physics Letters B 609 (1) (2005)
49–56. doi:https://doi.org/10.1016/j.physletb.2005.01.046.
[414] W. P. Ford, S. Jeschonnek, J. W. Van Orden, Momentum distributions for 2H(e, e′p), Phys. Rev. C 90
(2014) 064006. doi:10.1103/PhysRevC.90.064006.
[415] F. Vera, Probing the structure of deuteron at very short distances (2021). doi:10.48550/ARXIV.2108.
11502.
URL https://arxiv.org/abs/2108.11502
[416] M. M. Sargsian, F. Vera, New Structure in the Deuteron, Phys. Rev. Lett. 130 (11) (2023) 112502.
arXiv:2208.00501,doi:10.1103/PhysRevLett.130.112502.
[417] C. Yero, Deuteron disintegration at large missing momenta (January 2023).
[418] C. Ciofi degli Atti, In-medium short-range dynamics of nucleons: Recent theoretical and experimental
advances, Phys. Rept. 590 (2015) 1–85. doi:10.1016/j.physrep.2015.06.002.
[419] H. Heiselberg, V. Pandharipande, Recent progress in neutron star theory, Ann. Rev. Nucl. Part. Sci.
50 (2000) 481–524. arXiv:astro-ph/0003276,doi:10.1146/annurev.nucl.50.1.481.
[420] M. Sargsian, T. Abrahamyan, M. Strikman, L. Frankfurt, Exclusive electrodisintegration of 3He at high
Q2. i. generalized eikonal approximation, Phys. Rev. C 71 (2005) 044614. doi:10.1103/PhysRevC.
71.044614.
[421] N. Fomin, D. Higinbotham, M. Sargsian, P. Solvignon, New results on short-range correlations in nuclei,
Ann. Rev. Nucl. Part. Sci. 67 (1) (2017) 129–159. doi:10.1146/annurev-nucl-102115-044939.
[422] D. Day, J. S. Mccarthy, I. Sick, R. G. Arnold, B. T. Chertok, S. Rock, Z. M. Szalata, F. Martin,
B. A. Mecking, G. Tamas, INCLUSIVE ELECTRON SCATTERING FROM HE-3, Phys. Rev. Lett.
43 (1979) 1143. doi:10.1103/PhysRevLett.43.1143.
[423] S. Rock, R. G. Arnold, B. T. Chertok, Z. M. Szalata, D. Day, J. S. McCarthy, F. Martin, B. A.
Mecking, I. Sick, G. Tamas, Inelastic Electron Scattering From 3He and 4He in the Threshold Region
at High Momentum Transfer, Phys. Rev. C 26 (1982) 1592. doi:10.1103/PhysRevC.26.1592.
[424] D. F. Geesaman, K. Saito, A. W. Thomas, The nuclear EMC effect, Ann. Rev. Nucl. Part. Sci. 45
(1995) 337–390. doi:10.1146/annurev.ns.45.120195.002005.
[425] P. R. Norton, The EMC effect, Rept. Prog. Phys. 66 (2003) 1253–1297. doi:10.1088/0034-4885/66/
8/201.
[426] S. Malace, D. Gaskell, D. W. Higinbotham, I. Cloet, The Challenge of the EMC Effect: existing
data and future directions, Int. J. Mod. Phys. E 23 (08) (2014) 1430013. arXiv:1405.1270,doi:
10.1142/S0218301314300136.
[427] N. Baillie, et al., Measurement of the neutron F2 structure function via spectator tagging with CLAS,
Phys. Rev. Lett. 108 (2012) 142001, [Erratum: Phys.Rev.Lett. 108, 199902 (2012)]. arXiv:1110.2770,
doi:10.1103/PhysRevLett.108.142001.
131
[428] S. Tkachenko, et al., Measurement of the structure function of the nearly free neutron using spectator
tagging in inelastic 2H(e, e’p)X scattering with CLAS, Phys. Rev. C 89 (2014) 045206, [Addendum:
Phys.Rev.C 90, 059901 (2014)]. arXiv:1402.2477,doi:10.1103/PhysRevC.89.045206.
[429] K. A. Griffioen, et al., Measurement of the EMC Effect in the Deuteron, Phys. Rev. C 92 (1) (2015)
015211. arXiv:1506.00871,doi:10.1103/PhysRevC.92.015211.
[430] A. V. Klimenko, et al., Electron scattering from high-momentum neutrons in deuterium, Phys. Rev.
C 73 (2006) 035212. arXiv:nucl-ex/0510032,doi:10.1103/PhysRevC.73.035212.
[431] A. Lovato, S. Gandolfi, J. Carlson, S. C. Pieper, R. Schiavilla, Electromagnetic response of 12 C: A
first-principles calculation, Phys. Rev. Lett. 117 (8) (2016) 082501. arXiv:1605.00248,doi:10.1103/
PhysRevLett.117.082501.
[432] I. C. Clo¨et, W. Bentz, A. W. Thomas, Relativistic and Nuclear Medium Effects on the Coulomb Sum
Rule, Phys. Rev. Lett. 116 (3) (2016) 032701. arXiv:1506.05875,doi:10.1103/PhysRevLett.116.
032701.
[433] M. M. Rvachev, et al., Quasielastic 3He(e, e′p)2H reaction at Q2= 1.5 gev2for recoil momenta up to
1 GeV/c, Phys. Rev. Lett. 94 (2005) 192302. doi:10.1103/PhysRevLett.94.192302.
[434] B. Hu, et al., Polarization transfer in the H-2(polarized-e, e-prime polarized-p) n reaction up to Q**2 =
1.61-(GeV/c)**2, Phys. Rev. C 73 (2006) 064004. arXiv:nucl-ex/0601025,doi:10.1103/PhysRevC.
73.064004.
[435] S. P. Malace, et al., A precise extraction of the induced polarization in the 4He(e,e’p)3H reaction,
Phys. Rev. Lett. 106 (2011) 052501. arXiv:1011.4483,doi:10.1103/PhysRevLett.106.052501.
[436] W. P. Ford, R. Schiavilla, J. W. Van Orden, The 3He(e, e′p)2H and 4He(e, e′p)3H reactions at high
momentum transfer, Phys. Rev. C 89 (3) (2014) 034004. arXiv:1401.4399,doi:10.1103/PhysRevC.
89.034004.
[437] R. Dupr´e, et al., Measurement of deeply virtual Compton scattering off 4He with the CEBAF Large
Acceptance Spectrometer at Jefferson Lab, Phys. Rev. C 104 (2) (2021) 025203. arXiv:2102.07419,
doi:10.1103/PhysRevC.104.025203.
[438] V. Guzey, A. W. Thomas, K. Tsushima, Medium modifications of the bound nucleon GPDs and
incoherent DVCS on nuclear targets, Phys. Lett. B 673 (2009) 9–14. arXiv:0806.3288,doi:10.
1016/j.physletb.2009.01.064.
[439] S. Liuti, S. K. Taneja, Nuclear medium modifications of hadrons from generalized parton distributions,
Phys. Rev. C 72 (2005) 034902. arXiv:hep-ph/0504027,doi:10.1103/PhysRevC.72.034902.
[440] M. Guidal, H. Moutarde, M. Vanderhaeghen, Generalized Parton Distributions in the valence region
from Deeply Virtual Compton Scattering, Rept. Prog. Phys. 76 (2013) 066202. arXiv:1303.6600,
doi:10.1088/0034-4885/76/6/066202.
[441] W. Armstrong, et al., Spectator-tagged deeply virtual compton scattering on light nuclei,
arXiv:1708.00835 (2017). doi:10.48550/ARXIV.1708.00835.
[442] S. Fucini, S. Scopetta, M. Viviani, Coherent deeply virtual compton scattering off 4He, Phys. Rev. C
98 (2018) 015203. doi:10.1103/PhysRevC.98.015203.
[443] P. Zurita, Medium modified Fragmentation Functions with open source xFitter (1 2021). arXiv:
2101.01088.
[444] K. Eskola, P. Paakkinen, H. Paukkunen, C. Salgado, EPPS21: a global QCD analysis of nuclear PDFs,
Eur. Phys. J. C 82 (5) (2022) 413. arXiv:2112.12462,doi:10.1140/epjc/s10052-022-10359-0.
132
[445] M. Walt, I. Helenius, W. Vogelsang, Open-source qcd analysis of nuclear parton distribution functions
at nlo and nnlo, Phys. Rev. D 100 (2019) 096015. doi:10.1103/PhysRevD.100.096015.
[446] W. Brooks, S. Kuhn, et al., The EMC Effect in Spin Structure Functions, CLAS12 E12-14-00 Experi-
ment (Run Group G) (2014).
[447] W. Brooks, S. Kuhn, et al., The EMC Effect in Spin Structure Functions, CLAS12 Run Group G
Jeopardy Update (2020).
[448] S. J. Brodsky, I. Schmidt, J.-J. Yang, Nuclear antishadowing in neutrino deep inelastic scattering,
Phys. Rev. D 70 (2004) 116003. doi:10.1103/PhysRevD.70.116003.
[449] V. Guzey, M. Strikman, Nuclear effects in g1A(x, Q2) at small x in deep inelastic scattering on 7Li and
3He, Phys. Rev. C 61 (1999) 014002. doi:10.1103/PhysRevC.61.014002.
[450] L. Frankfurt, V. Guzey, M. Strikman, Dynamical model of antishadowing of the nuclear gluon distri-
bution, Phys. Rev. C 95 (2017) 055208. doi:10.1103/PhysRevC.95.055208.
[451] I. Clo¨et, W. Bentz, A. Thomas, EMC and polarized EMC effects in nuclei, Phy. Lett. B 642 (3) (2006)
210–217. doi:https://doi.org/10.1016/j.physletb.2006.08.076.
[452] J. Smith, G. Miller, Polarized quark distributions in nuclear matter, Phys. Rev. C 72 (2005) 022203.
doi:10.1103/PhysRevC.72.022203.
[453] H. Fanchiotti, C. A. Garc´ıa-Canal, T. Tarutina, V. Vento, Medium Effects in DIS from Polarized Nu-
clear Targets, Eur. Phys. J. A 50 (2014) 116. arXiv:1404.3047,doi:10.1140/epja/i2014-14116- 8.
[454] I. Clo¨et, W. Bentz, A. Thomas, Spin-dependent structure functions in nuclear matter and the polarized
emc effect, Phys. Rev. Lett. 95 (2005) 052302. doi:10.1103/PhysRevLett.95.052302.
[455] S. J. Brodsky, A. H. Mueller, Using Nuclei to Probe Hadronization in QCD, Phys. Lett. B 206 (1988)
685–690. doi:10.1016/0370-2693(88)90719-8.
[456] S. J. Brodsky, L. Frankfurt, J. F. Gunion, A. H. Mueller, M. Strikman, Diffractive leptoproduction of
vector mesons in QCD, Phys. Rev. D 50 (1994) 3134–3144. arXiv:hep- ph/9402283,doi:10.1103/
PhysRevD.50.3134.
[457] D. Dutta, K. Hafidi, M. Strikman, Color Transparency: past, present and future, Prog. Part. Nucl.
Phys. 69 (2013) 1–27. arXiv:1211.2826,doi:10.1016/j.ppnp.2012.11.001.
[458] S. J. Brodsky, G. F. de Teramond, Onset of Color Transparency in Holographic Light-Front QCD,
MDPI Physics 4 (2) (2022) 633–646. arXiv:2202.13283,doi:10.3390/physics4020042.
[459] B. Clasie, et al., Measurement of Nuclear Transparency for the A(e, e′π+) Reaction, Phys. Rev. Lett.
99 (2007) 242502. arXiv:0707.1481,doi:10.1103/PhysRevLett.99.242502.
[460] L. El Fassi, et al., Evidence for the onset of color transparency in ρ0electroproduction off nuclei, Phys.
Lett. B 712 (2012) 326–330. arXiv:1201.2735,doi:10.1016/j.physletb.2012.05.019.
[461] L. Frankfurt, G. A. Miller, M. Strikman, Color Transparency in Semi-Inclusive Electroproduction of
rho Mesons, Phys. Rev. C 78 (2008) 015208. arXiv:0803.4012,doi:10.1103/PhysRevC.78.015208.
[462] K. Gallmeister, M. Kaskulov, U. Mosel, Color transparency in hadronic attenuation of ρ0mesons,
Phys. Rev. C 83 (2011) 015201. arXiv:1007.1141,doi:10.1103/PhysRevC.83.015201.
[463] W. Cosyn, J. Ryckebusch, Nuclear ρmeson transparency in a relativistic Glauber model, Phys. Rev.
C 87 (6) (2013) 064608. arXiv:1301.1904,doi:10.1103/PhysRevC.87.064608.
[464] A. S. Carroll, et al., Nuclear Transparency to Large Angle pp Elastic Scattering, Phys. Rev. Lett. 61
(1988) 1698–1701. doi:10.1103/PhysRevLett.61.1698.
133
[465] I. Mardor, et al., Nuclear transparency in large momentum transfer quasielastic scattering, Phys. Rev.
Lett. 81 (1998) 5085–5088. doi:10.1103/PhysRevLett.81.5085.
[466] A. Leksanov, et al., Energy dependence of nuclear transparency in C(p, 2p) scattering, Phys. Rev. Lett.
87 (2001) 212301. arXiv:hep-ex/0104039,doi:10.1103/PhysRevLett.87.212301.
[467] J. Aclander, et al., Nuclear transparency in 90◦
c.m.quasielastic A(p, 2p) reactions, Phys. Rev. C 70
(2004) 015208. arXiv:nucl-ex/0405025,doi:10.1103/PhysRevC.70.015208.
[468] N. Makins, et al., Momentum transfer dependence of nuclear transparency from the quasielastic
12C(e,e’p) reaction, Phys. Rev. Lett. 72 (1994) 1986–1989. doi:10.1103/PhysRevLett.72.1986.
[469] T. G. O’Neill, et al., A-dependence of nuclear transparency in quasielastic A(e, e′p) at high Q2, Phys.
Lett. B 351 (1995) 87–92. arXiv:hep-ph/9408260,doi:10.1016/0370-2693(95)00362-O.
[470] D. Abbott, et al., Quasifree (e, e′p) reactions and proton propagation in nuclei, Phys. Rev. Lett. 80
(1998) 5072–5076. doi:10.1103/PhysRevLett.80.5072.
[471] K. Garrow, et al., Nuclear transparency from quasielastic A(e, e
′
p) reactions up to Q2= 8.1(GeV/c)2,
Phys. Rev. C 66 (2002) 044613. arXiv:hep-ex/0109027,doi:10.1103/PhysRevC.66.044613.
[472] D. Bhetuwal, J. Matter, H. Szumila-Vance, M. L. Kabir, D. Dutta, R. Ent, et al., Ruling out color
transparency in quasielastic 12C(e, e′p) up to Q2of 14.2 (GeV/c)2, Phys. Rev. Lett. 126 (2021) 082301.
doi:10.1103/PhysRevLett.126.082301.
[473] S. Li, C. Yero, J. R. West, C. Bennett, W. Cosyn, D. Higinbotham, M. Sargsian, H. Szumila-Vance,
Searching for an enhanced signal of the onset of color transparency in baryons with d(e,e’p)n scattering,
Physics 4 (4) (2022) 1426–1439. doi:10.3390/physics4040092.
[474] R. D. Field, R. P. Feynman, Quark Elastic Scattering as a Source of High Transverse Momentum
Mesons, Phys. Rev. D 15 (1977) 2590–2616. doi:10.1103/PhysRevD.15.2590.
[475] J.-J. Aubert, G. Bassompierre, K. Becks, C. Best, E. B¨ohm, X. de Bouard, F. Brasse, C. Broll,
S. Brown, J. Carr, et al., The ratio of the nucleon structure functions FN
2for iron and deuterium,
Physics Letters B 123 (3-4) (1983) 275–278.
[476] K. Adcox, S. Adler, S. Afanasiev, C. Aidala, N. Ajitanand, Y. Akiba, A. Al-Jamel, J. Alexander,
R. Amirikas, K. Aoki, et al., Formation of dense partonic matter in relativistic nucleus–nucleus colli-
sions at rhic: experimental evaluation by the phenix collaboration, Nuclear Physics A 757 (1-2) (2005)
184–283.
[477] J. Adams, et al., Experimental and theoretical challenges in the search for the quark gluon plasma:
The STAR Collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757
(2005) 102–183. arXiv:nucl-ex/0501009,doi:10.1016/j.nuclphysa.2005.03.085.
[478] A. Airapetian, et al., Transverse momentum broadening of hadrons produced in semi-inclusive deep-
inelastic scattering on nuclei, Phys. Lett. B 684 (2010) 114–118. doi:10.1016/j.physletb.2010.01.
020.
[479] A. Airapetian, et al., Multidimensional Study of Hadronization in Nuclei, Eur. Phys. J. A 47 (2011)
113. arXiv:1107.3496,doi:10.1140/epja/i2011-11113-5.
[480] A. Airapetian, et al., Hadronization in semi-inclusive deep-inelastic scattering on nuclei, Nucl. Phys.
B 780 (2007) 1–27. arXiv:0704.3270,doi:10.1016/j.nuclphysb.2007.06.004.
[481] A. Airapetian, et al., Double-hadron leptoproduction in the nuclear medium, Phys. Rev. Lett. 96
(2006) 162301. doi:10.1103/PhysRevLett.96.162301.
[482] S. J. Paul, S. Mor´an, M. Arratia, A. El Alaoui, H. Hakobyan, W. Brooks, et al., Observation of
azimuth-dependent suppression of hadron pairs in electron scattering off nuclei, Phys. Rev. Lett. 129
(2022) 182501. doi:10.1103/PhysRevLett.129.182501.
134
[483] A. Airapetian, et al., Hadron formation in deep inelastic positron scattering in a nuclear environment,
Eur. Phys. J. C 20 (2001) 479–486. doi:10.1007/s100520100697.
[484] S. Mor´an, R. Dupr´e, H. Hakobyan, M. Arratia, W. K. Brooks, A. B´orquez, A. El Alaoui, L. El Fassi,
K. Hafidi, R. Mendez, T. Mineeva, S. J. Paul, et al., Measurement of charged-pion production in
deep-inelastic scattering off nuclei with the CLAS detector, Phys. Rev. C 105 (2022) 015201. doi:
10.1103/PhysRevC.105.015201.
[485] A. Airapetian, et al., Quark fragmentation to π±,π0,K±,pand ¯pin the nuclear environment,
Phys. Lett. B 577 (2003) 37–46. doi:10.1016/j.physletb.2003.10.026.
[486] A. Airapetian, et al., Hadronization in semi-inclusive deep-inelastic scattering on nuclei, Nucl. Phys. B
780 (2007) 1–27. doi:10.1016/j.nuclphysb.2007.06.004.
[487] T. Chetry, L. El Fassi, et al., First measurement of Λ electroproduction off nuclei in the current and
target fragmentation regions, Phys. Rev. Lett. 130 (2023) 142301. doi:10.1103/PhysRevLett.130.
142301.
[488] A. Accardi, et al., Electron-Ion Collider: The next QCD frontier, The European Physical Journal A
52 (9) (2016) 268. doi:10.1140/epja/i2016-16268-9.
[489] V. Khachatryan, et al., Coherent J/ψ photoproduction in ultra-peripheral PbPb collisions at √sN N =
2.76 TeV with the CMS experiment, Physics Letters B 772 (2017) 489–511.
[490] B. Abelev, et al., Coherent J/ψ photoproduction in ultra-peripheral Pb–Pb collisions at √sNN =
2.76T eV , Physics Letters B 718 (4) (2013) 1273–1283. doi:https://doi.org/10.1016/j.physletb.
2012.11.059.
[491] S. Acharya, et al., First measurement of the |t|-dependence of coherent J/ψ photonuclear production,
Physics Letters B 817 (2021) 136280. doi:https://doi.org/10.1016/j.physletb.2021.136280.
[492] S. Acharya, et al., Coherent J/ψ and ψ′photoproduction at midrapidity in ultra-peripheral Pb–
Pb collisions at √sNN = 5.02 TeV, The European Physical Journal C 81 (8) (2021) 712. doi:
10.1140/epjc/s10052-021-09437-6.
[493] R. Aaij, et al., J/ψ photoproduction in Pb-Pb peripheral collisions at √sN N = 5 TeV, Phys. Rev. C
105 (2022) L032201. doi:10.1103/PhysRevC.105.L032201.
[494] M. S. Abdallah, et al., Probing the gluonic structure of the deuteron with J/ψ photoproduction in
d+ Au ultraperipheral collisions, Phys. Rev. Lett. 128 (2022) 122303. doi:10.1103/PhysRevLett.
128.122303.
[495] A. Ali, et al., First Measurement of Near-Threshold J/ψ Exclusive Photoproduction off the Proton,
Phys. Rev. Lett. 123 (2019) 072001. doi:10.1103/PhysRevLett.123.072001.
[496] T. Toll, T. Ullrich, Exclusive diffractive processes in electron-ion collisions, Phys. Rev. C 87 (2013)
024913. doi:10.1103/PhysRevC.87.024913.
[497] O. Hen, et al., Studying Short-Range Correlations with Real Photon Beams at GlueX (9 2020). arXiv:
2009.09617.
[498] U. Camerini, J. G. Learned, R. Prepost, C. M. Spencer, D. E. Wiser, W. W. Ash, R. L. Anderson,
D. M. Ritson, D. J. Sherden, C. K. Sinclair, Photoproduction of the ψParticles, Phys. Rev. Lett. 35
(1975) 483–486. doi:10.1103/PhysRevLett.35.483.
[499] R. B. Wiringa, R. Schiavilla, S. C. Pieper, J. Carlson, Nucleon and nucleon-pair momentum distribu-
tions in A≤12 nuclei, Phys. Rev. C 89 (2014) 024305. doi:10.1103/PhysRevC.89.024305.
[500] L. Gan, B. Kubis, E. Passemar, S. Tulin, Precision tests of fundamental physics with ηand η’ mesons,
Phys. Rept. 945 (2022) 1–105. arXiv:2007.00664,doi:10.1016/j.physrep.2021.11.001.
135
[501] S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426–2438. doi:
10.1103/PhysRev.177.2426.
[502] J. S. Bell, R. Jackiw, A PCAC puzzle: π0→γγ in the σmodel, Nuovo Cim. A 60 (1969) 47–61.
doi:10.1007/BF02823296.
[503] G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37 (1976) 8–11.
doi:10.1103/PhysRevLett.37.8.
[504] E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson, Nucl. Phys. B 156 (1979) 269–283.
doi:10.1016/0550-3213(79)90031-2.
[505] M. Gell-Mann, R. J. Oakes, B. Renner, Behavior of current divergences under SU(3) x SU(3), Phys.
Rev. 175 (1968) 2195–2199. doi:10.1103/PhysRev.175.2195.
[506] J. S. Bell, D. G. Sutherland, Current algebra and eta —>3 pi, Nucl. Phys. B 4 (1968) 315–325.
doi:10.1016/0550-3213(68)90316-7.
[507] D. G. Sutherland, Current algebra and the decay η→3π, Phys. Lett. 23 (1966) 384–385. doi:
10.1016/0031-9163(66)90477-X.
[508] V. A. Kuzmin, V. A. Rubakov, M. E. Shaposhnikov, On the Anomalous Electroweak Baryon Number
Nonconservation in the Early Universe, Phys. Lett. B 155 (1985) 36. doi:10.1016/0370-2693(85)
91028-7.
[509] T. Aoyama, et al., The anomalous magnetic moment of the muon in the Standard Model, Phys. Rept.
887 (2020) 1–166. arXiv:2006.04822,doi:10.1016/j.physrep.2020.07.006.
[510] M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, S. P. Schneider, Pion-pole contribution to hadronic
light-by-light scattering in the anomalous magnetic moment of the muon, Phys. Rev. Lett. 121 (11)
(2018) 112002. arXiv:1805.01471,doi:10.1103/PhysRevLett.121.112002.
[511] M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, S. P. Schneider, Dispersion relation for hadronic light-
by-light scattering: pion pole, JHEP 10 (2018) 141. arXiv:1808.04823,doi:10.1007/JHEP10(2018)
141.
[512] I. Larin, et al., Precision measurement of the neutral pion lifetime, Science 368 (6490) (2020) 506–509.
doi:10.1126/science.aay6641.
[513] A. G´erardin, H. B. Meyer, A. Nyffeler, Lattice calculation of the pion transition form factor with
Nf= 2 + 1 Wilson quarks, Phys. Rev. D 100 (3) (2019) 034520. arXiv:1903.09471,doi:10.1103/
PhysRevD.100.034520.
[514] J. L. Goity, A. M. Bernstein, B. R. Holstein, The Decay pi0 —>gamma gamma to next to leading
order in chiral perturbation theory, Phys. Rev. D 66 (2002) 076014. arXiv:hep-ph/0206007,doi:
10.1103/PhysRevD.66.076014.
[515] B. Ananthanarayan, B. Moussallam, Electromagnetic corrections in the anomaly sector, JHEP 05
(2002) 052. arXiv:hep-ph/0205232,doi:10.1088/1126-6708/2002/05/052.
[516] K. Kampf, B. Moussallam, Chiral expansions of the pi0 lifetime, Phys. Rev. D 79 (2009) 076005.
arXiv:0901.4688,doi:10.1103/PhysRevD.79.076005.
[517] S. A. Burri, et al., Pseudoscalar-pole contributions to the muon g−2 at the physical point, PoS
LATTICE2022 (2023) 306. arXiv:2212.10300,doi:10.22323/1.430.0306.
[518] A. G´erardin, J. N. Guenther, L. Varnhorst, W. E. A. Verplanke, Pseudoscalar transition form factors
and the hadronic light-by-light contribution to the muon g-2, PoS LATTICE2022 (2023) 332. arXiv:
2211.04159,doi:10.22323/1.430.0332.
136
[519] M. Hoferichter, B. Kubis, S. Leupold, F. Niecknig, S. P. Schneider, Dispersive analysis of the pion
transition form factor, Eur. Phys. J. C 74 (2014) 3180. arXiv:1410.4691,doi:10.1140/epjc/
s10052-014-3180-0.
[520] C. Hanhart, A. Kup´s´c, U.-G. Meißner, F. Stollenwerk, A. Wirzba, Dispersive analysis for η→γγ∗,
Eur. Phys. J. C 73 (12) (2013) 2668, [Erratum: Eur. Phys. J. C 75, 242 (2015)]. arXiv:1307.5654,
doi:10.1140/epjc/s10052-013-2668-3.
[521] B. Kubis, J. Plenter, Anomalous decay and scattering processes of the ηmeson, Eur. Phys. J. C 75 (6)
(2015) 283. arXiv:1504.02588,doi:10.1140/epjc/s10052-015-3495-5.
[522] S. Holz, J. Plenter, C.-W. Xiao, T. Dato, C. Hanhart, B. Kubis, U.-G. Meißner, A. Wirzba, Towards
an improved understanding of η→γ∗γ∗, Eur. Phys. J. C 81 (11) (2021) 1002. arXiv:1509.02194,
doi:10.1140/epjc/s10052-021-09661-0.
[523] S. Holz, C. Hanhart, M. Hoferichter, B. Kubis, A dispersive analysis of η′→π+π−γand η′→ℓ+ℓ−γ,
Eur. Phys. J. C 82 (5) (2022) 434, [Addendum: Eur. Phys. J. C 82, 1159 (2022)]. arXiv:2202.05846,
doi:10.1140/epjc/s10052-022-10247-7.
[524] P. Masjuan, P. S´anchez-Puertas, Pseudoscalar-pole contribution to the (gµ−2): a rational approach,
Phys. Rev. D 95 (5) (2017) 054026. arXiv:1701.05829,doi:10.1103/PhysRevD.95.054026.
[525] R. Escribano, S. Gonz`alez-Sol´ıs, P. Masjuan, P. S´anchez-Puertas, η’ transition form factor from space-
and timelike experimental data, Phys. Rev. D 94 (5) (2016) 054033. arXiv:1512.07520,doi:10.
1103/PhysRevD.94.054033.
[526] C. Alexandrou, et al., The η→γ∗γ∗transition form factor and the hadronic light-by-light η-pole
contribution to the muon g−2 from lattice QCD (12 2022). arXiv:2212.06704.
[527] A. Browman, J. DeWire, B. Gittelman, K. M. Hanson, E. Loh, R. Lewis, The Radiative Width of the
eta Meson, Phys. Rev. Lett. 32 (1974) 1067. doi:10.1103/PhysRevLett.32.1067.
[528] H. Primakoff, Photoproduction of neutral mesons in nuclear electric fields and the mean life of the
neutral meson, Phys. Rev. 81 (1951) 899. doi:10.1103/PhysRev.81.899.
[529] L. Gan, Test of fundamental symmetries via the Primakoff effect, EPJ Web Conf. 73 (2014) 07004.
doi:10.1051/epjconf/20147307004.
[530] A. M. Bernstein, B. R. Holstein, Neutral Pion Lifetime Measurements and the QCD Chiral Anomaly,
Rev. Mod. Phys. 85 (2013) 49. arXiv:1112.4809,doi:10.1103/RevModPhys.85.49.
[531] M. Tanabashi, et al., Review of Particle Physics, Phys. Rev. D 98 (3) (2018) 030001. doi:10.1103/
PhysRevD.98.030001.
[532] B. L. Ioffe, A. G. Oganesian, Axial anomaly and the precise value of the pi0 —>2 gamma decay width,
Phys. Lett. B 647 (2007) 389–393. arXiv:hep-ph/0701077,doi:10.1016/j.physletb.2007.02.021.
[533] A. Kastner, H. Neufeld, The K(l3) scalar form factors in the standard model, Eur. Phys. J. C 57 (2008)
541–556. arXiv:0805.2222,doi:10.1140/epjc/s10052-008-0703-6.
[534] D. Giusti, V. Lubicz, C. Tarantino, G. Martinelli, F. Sanfilippo, S. Simula, N. Tantalo, Leading isospin-
breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions, Phys. Rev.
D 95 (11) (2017) 114504. arXiv:1704.06561,doi:10.1103/PhysRevD.95.114504.
[535] A. Gasparian, L. Gan, et al., A precision measurement of the ηradiative decay width via the primakoff
effect, https://www.jlab.org/exp−prog/proposals/10/PR12-10-011.pdf.
[536] H. Leutwyler, Implications of eta eta-prime mixing for the decay eta —>3 pi, Phys. Lett. B 374 (1996)
181–185. arXiv:hep-ph/9601236,doi:10.1016/0370-2693(96)00167-0.
137
[537] R. Essig, et al., Working Group Report: New Light Weakly Coupled Particles, in: Community Summer
Study 2013: Snowmass on the Mississippi, 2013. arXiv:1311.0029.
[538] J. Alexander, et al., Dark Sectors 2016 Workshop: Community Report, 2016. arXiv:1608.08632.
[539] M. Battaglieri, et al., US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report, in:
U.S. Cosmic Visions: New Ideas in Dark Matter, 2017. arXiv:1707.04591.
[540] N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer, N. Weiner, A Theory of Dark Matter, Phys. Rev.
D 79 (2009) 015014. arXiv:0810.0713,doi:10.1103/PhysRevD.79.015014.
[541] M. Pospelov, A. Ritz, Astrophysical Signatures of Secluded Dark Matter, Phys. Lett. B 671 (2009)
391–397. arXiv:0810.1502,doi:10.1016/j.physletb.2008.12.012.
[542] Y.-S. Liu, I. C. Clo¨et, G. A. Miller, Eta Decay and Muonic Puzzles, Nucl. Phys. B (2019) 114638.
arXiv:1805.01028,doi:10.1016/j.nuclphysb.2019.114638.
[543] P. Fayet, U-boson production in e+ e- annihilations, psi and Upsilon decays, and Light Dark Matter,
Phys. Rev. D 75 (2007) 115017. arXiv:hep-ph/0702176,doi:10.1103/PhysRevD.75.115017.
[544] M. Pospelov, Secluded U(1) below the weak scale, Phys. Rev. D 80 (2009) 095002. arXiv:0811.1030,
doi:10.1103/PhysRevD.80.095002.
[545] A. J. Krasznahorkay, et al., Observation of Anomalous Internal Pair Creation in Be8 : A Possible
Indication of a Light, Neutral Boson, Phys. Rev. Lett. 116 (4) (2016) 042501. arXiv:1504.01527,
doi:10.1103/PhysRevLett.116.042501.
[546] J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, T. M. P. Tait, P. Tanedo, Protophobic Fifth-
Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions, Phys. Rev. Lett. 117 (7)
(2016) 071803. arXiv:1604.07411,doi:10.1103/PhysRevLett.117.071803.
[547] S. Tulin, H.-B. Yu, Dark Matter Self-interactions and Small Scale Structure, Phys. Rept. 730 (2018)
1–57. arXiv:1705.02358,doi:10.1016/j.physrep.2017.11.004.
[548] S. Tulin, H.-B. Yu, K. M. Zurek, Resonant Dark Forces and Small Scale Structure, Phys. Rev. Lett.
110 (11) (2013) 111301. arXiv:1210.0900,doi:10.1103/PhysRevLett.110.111301.
[549] S. Tulin, H.-B. Yu, K. M. Zurek, Beyond Collisionless Dark Matter: Particle Physics Dynamics for
Dark Matter Halo Structure, Phys. Rev. D 87 (11) (2013) 115007. arXiv:1302.3898,doi:10.1103/
PhysRevD.87.115007.
[550] D. Aloni, Y. Soreq, M. Williams, Coupling QCD-Scale Axionlike Particles to Gluons, Phys. Rev. Lett.
123 (3) (2019) 031803. arXiv:1811.03474,doi:10.1103/PhysRevLett.123.031803.
[551] D. Aloni, C. Fanelli, Y. Soreq, M. Williams, Photoproduction of Axionlike Particles, Phys. Rev. Lett.
123 (7) (2019) 071801. arXiv:1903.03586,doi:10.1103/PhysRevLett.123.071801.
[552] M. J. Dolan, T. Ferber, C. Hearty, F. Kahlhoefer, K. Schmidt-Hoberg, Revised constraints and Belle
II sensitivity for visible and invisible axion-like particles, JHEP 12 (2017) 094, [Erratum: JHEP 03,
190 (2021)]. arXiv:1709.00009,doi:10.1007/JHEP12(2017)094.
[553] J. D. Bjorken, S. Ecklund, W. R. Nelson, A. Abashian, C. Church, B. Lu, L. W. Mo, T. A. Nunamaker,
P. Rassmann, Search for Neutral Metastable Penetrating Particles Produced in the SLAC Beam Dump,
Phys. Rev. D 38 (1988) 3375. doi:10.1103/PhysRevD.38.3375.
[554] G. Abbiendi, et al., Multiphoton production in e+ e- collisions at s**(1/2) = 181-GeV to 209-GeV,
Eur. Phys. J. C 26 (2003) 331–344. arXiv:hep-ex/0210016,doi:10.1140/epjc/s2002-01074-5.
[555] S. Knapen, T. Lin, H. K. Lou, T. Melia, Searching for Axionlike Particles with Ultraperipheral
Heavy-Ion Collisions, Phys. Rev. Lett. 118 (17) (2017) 171801. arXiv:1607.06083,doi:10.1103/
PhysRevLett.118.171801.
138
[556] J. Blumlein, et al., Limits on the mass of light (pseudo)scalar particles from Bethe-Heitler e+ e- and
mu+ mu- pair production in a proton - iron beam dump experiment, Int. J. Mod. Phys. A 7 (1992)
3835–3850. doi:10.1142/S0217751X9200171X.
[557] P. A. Souder, P. E. Reimer, X. Zheng, Precision Measurement of Parity-violation in Deep Inelastic
Scattering Over a Broad Kinematic Range, Jefferson Lab Experiment E12-10-007, 2010 with 2022
update.
[558] D. Akimov, et al., Measurement of the Coherent Elastic Neutrino-Nucleus Scattering Cross Section
on CsI by COHERENT, Phys. Rev. Lett. 129 (8) (2022) 081801. arXiv:2110.07730,doi:10.1103/
PhysRevLett.129.081801.
[559] M. Battaglieri, et al., Dark Matter Search in a Beam-Dump eXperiment (BDX) at Jefferson Lab (7
2016). arXiv:1607.01390.
[560] L. Marsicano, M. Battaglieri, A. Celentano, R. De Vita, Y.-M. Zhong, Probing Leptophilic Dark
Sectors at Electron Beam-Dump Facilities, Phys. Rev. D 98 (11) (2018) 115022. arXiv:1812.03829,
doi:10.1103/PhysRevD.98.115022.
[561] M. Battaglieri, et al., Dark matter search with the BDX-MINI experiment, Phys. Rev. D 106 (7) (2022)
072011. arXiv:2208.01387,doi:10.1103/PhysRevD.106.072011.
[562] A. Bartnik, et al., CBETA: First Multipass Superconducting Linear Accelerator with Energy Recovery,
Phys. Rev. Lett. 125 (4) (2020) 044803. doi:10.1103/PhysRevLett.125.044803.
[563] S. Bogacz, et al., 20-24 GeV FFA CEBAF Energy Upgrade, Proc. IPAC’21, Campinas, Brazil, May
2021 (2023) 715–718doi:10.18429/JACoW-IPAC2021-MOPAB216.
[564] S. Brooks, S. Bogacz, Permanent Magnets forthe CEBAF 24GeV Upgrade, Proc. IPAC’22, Bangkok,
Thailand, Jun. 2022 (2022) 2792–2795doi:10.18429/JACoW-IPAC2022-THPOTK011.
[565] S. Brooks, et al., Open-Midplane Gradient Permanent Magnet with 1.53 T Peak Field, Proc. IPAC’23,
Venice, Italy, May 2023 (2023).
139
