Available via license: CC BY-NC-ND 4.0
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Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
arXiv:hep-ex/9506009v2 20 Jun 1995
Diffractive Hard Photoproduction at HERA
and Evidence for the Gluon Content of the
Pomeron
ZEUS Collaboration
Abstract
Inclusive jet cross sections for events with a large rapidity gap with respect to the
proton direction from the reaction ep →jet +Xwith quasi-real photons have been
measured with the ZEUS detector. The cross sections refer to jets with transverse energies
Ejet
T>8 GeV. The data show the characteristics of a diffractive process mediated by
pomeron exchange. Assuming that the events are due to the exchange of a pomeron
with partonic structure, the quark and gluon content of the pomeron is probed at a scale
∼(Ejet
T)2. A comparison of the measurements with model predictions based on QCD plus
Regge phenomenology requires a contribution of partons with a hard momentum density in
the pomeron. A combined analysis of the jet cross sections and recent ZEUS measurements
of the diffractive structure function in deep inelastic scattering gives the first experimental
evidence for the gluon content of the pomeron in diffractive hard scattering processes. The
data indicate that between 30% and 80% of the momentum of the pomeron carried by
partons is due to hard gluons.
The ZEUS Collaboration
M. Derrick, D. Krakauer, S. Magill, D. Mikunas, B. Musgrave, J. Repond, R. Stanek, R.L. Talaga, H. Zhang
Argonne National Laboratory, Argonne, IL, USA p
R. Ayad1, G. Bari, M. Basile, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni, P. Bruni, G. Cara Romeo,
G. Castellini2, M. Chiarini, L. Cifarelli3, F. Cindolo, A. Contin, M. Corradi, I. Gialas4, P. Giusti, G. Iacobucci,
G. Laurenti, G. Levi, A. Margotti, T. Massam, R. Nania, C. Nemoz,
F. Palmonari, A. Polini, G. Sartorelli, R. Timellini, Y. Zamora Garcia1, A. Zichichi
University and INFN Bologna, Bologna, Italy f
A. Bargende5, J. Crittenden, K. Desch, B. Diekmann6, T. Doeker, M. Eckert, L. Feld, A. Frey, M. Geerts,
M. Grothe, H. Hartmann, K. Heinloth, E. Hilger, H.-P. Jakob, U.F. Katz, S.M. Mari4, S. Mengel, J. Mollen,
E. Paul, M. Pfeiffer, Ch. Rembser, D. Schramm, J. Stamm, R. Wedemeyer
Physikalisches Institut der Universit¨at Bonn, Bonn, Federal Republic of Germany c
S. Campbell-Robson, A. Cassidy, N. Dyce, B. Foster, S. George, R. Gilmore, G.P. Heath, H.F. Heath, T.J. Llewellyn,
C.J.S. Morgado, D.J.P. Norman, J.A. O’Mara, R.J. Tapper, S.S. Wilson, R. Yoshida
H.H. Wills Physics Laboratory, University of Bristol, Bristol, U.K. o
R.R. Rau
Brookhaven National Laboratory, Upton, L.I., USA p
M. Arneodo7, M. Capua, A. Garfagnini, L. Iannotti, M. Schioppa, G. Susinno
Calabria University, Physics Dept.and INFN, Cosenza, Italy f
A. Bernstein, A. Caldwell, N. Cartiglia, J.A. Parsons, S. Ritz8, F. Sciulli, P.B. Straub, L. Wai, S. Yang, Q. Zhu
Columbia University, Nevis Labs., Irvington on Hudson, N.Y., USA q
P. Borzemski, J. Chwastowski, A. Eskreys, K. Piotrzkowski, M. Zachara, L. Zawiejski
Inst. of Nuclear Physics, Cracow, Poland j
L. Adamczyk, B. Bednarek, K. Jele´n, D. Kisielewska, T. Kowalski, E. Rulikowska-Zar¸ebska,
L. Suszycki, J. Zaj¸ac
Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland j
A. Kota´nski, M. Przybycie´n
Jagellonian Univ., Dept. of Physics, Cracow, Poland k
L.A.T. Bauerdick, U. Behrens, H. Beier9, J.K. Bienlein, C. Coldewey, O. Deppe, K. Desler, G. Drews,
M. Flasi´nski10, D.J. Gilkinson, C. Glasman, P. G¨ottlicher, J. Große-Knetter, B. Gutjahr11, T. Haas, W. Hain,
D. Hasell, H. Heßling, Y. Iga, K. Johnson12, P. Joos, M. Kasemann, R. Klanner, W. Koch, L. K¨opke13, U. K¨otz,
H. Kowalski, J. Labs, A. Ladage, B. L¨ohr, M. L¨owe, D. L¨uke, J. Mainusch, O. Ma´nczak, T. Monteiro14,
J.S.T. Ng, S. Nickel15, D. Notz, K. Ohrenberg, M. Roco, M. Rohde, J. Rold´an, U. Schneekloth, W. Schulz,
F. Selonke, E. Stiliaris16, B. Surrow, T. Voß, D. Westphal, G. Wolf, C. Youngman, W. Zeuner, J.F. Zhou17
Deutsches Elektronen-Synchrotron DESY, Hamburg, Federal Republic of Germany
H.J. Grabosch, A. Kharchilava, A. Leich, M.C.K. Mattingly, A. Meyer, S. Schlenstedt, N. Wulff
DESY-Zeuthen, Inst. f¨ur Hochenergiephysik, Zeuthen, Federal Republic of Germany
G. Barbagli, P. Pelfer
University and INFN, Florence, Italy f
G. Anzivino, G. Maccarrone, S. De Pasquale, L. Votano
INFN, Laboratori Nazionali di Frascati, Frascati, Italy f
A. Bamberger, S. Eisenhardt, A. Freidhof, S. S¨oldner-Rembold18 , J. Schroeder19, T. Trefzger
Fakult¨at f¨ur Physik der Universit¨at Freiburg i.Br., Freiburg i.Br., Federal Republic of Germany c
I
N.H. Brook, P.J. Bussey, A.T. Doyle20, J.I. Fleck4, D.H. Saxon, M.L. Utley, A.S. Wilson
Dept. of Physics and Astronomy, University of Glasgow, Glasgow, U.K. o
A. Dannemann, U. Holm, D. Horstmann, T. Neumann, R. Sinkus, K. Wick
Hamburg University, I. Institute of Exp. Physics, Hamburg, Federal Republic of Germany c
E. Badura21, B.D. Burow22 , L. Hagge, E. Lohrmann, J. Milewski, M. Nakahata23, N. Pavel, G. Poelz, W. Schott,
F. Zetsche
Hamburg University, II. Institute of Exp. Physics, Hamburg, Federal Republic of Germany c
T.C. Bacon, N. Bruemmer, I. Butterworth, E. Gallo, V.L. Harris, B.Y.H. Hung, K.R. Long, D.B. Miller,
P.P.O. Morawitz, A. Prinias, J.K. Sedgbeer, A.F. Whitfield
Imperial College London, High Energy Nuclear Physics Group, London, U.K. o
U. Mallik, E. McCliment, M.Z. Wang, S.M. Wang, J.T. Wu
University of Iowa, Physics and Astronomy Dept., Iowa City, USA p
P. Cloth, D. Filges
Forschungszentrum J¨ulich, Institut f¨ur Kernphysik, J¨ulich, Federal Republic of Germany
S.H. An, S.M. Hong, S.W. Nam, S.K. Park, M.H. Suh, S.H. Yon
Korea University, Seoul, Korea h
R. Imlay, S. Kartik, H.-J. Kim, R.R. McNeil, W. Metcalf, V.K. Nadendla
Louisiana State University, Dept. of Physics and Astronomy, Baton Rouge, LA, USA p
F. Barreiro24, G. Cases, J.P. Fernandez, R. Graciani, J.M. Hern´andez, L. Herv´as24, L. Labarga24 , M. Martinez,
J. del Peso, J. Puga, J. Terron, J.F. de Troc´oniz
Univer. Aut´onoma Madrid, Depto de F´ısica Te´or´ıca, Madrid, Spain n
G.R. Smith
University of Manitoba, Dept. of Physics, Winnipeg, Manitoba, Canada a
F. Corriveau, D.S. Hanna, J. Hartmann, L.W. Hung, J.N. Lim, C.G. Matthews, P.M. Patel,
L.E. Sinclair, D.G. Stairs, M. St.Laurent, R. Ullmann, G. Zacek
McGill University, Dept. of Physics, Montr´eal, Qu´ebec, Canada a, b
V. Bashkirov, B.A. Dolgoshein, A. Stifutkin
Moscow Engineering Physics Institute, Mosocw, Russia l
G.L. Bashindzhagyan, P.F. Ermolov, L.K. Gladilin, Yu.A. Golubkov, V.D. Kobrin, I.A. Korzhavina, V.A. Kuzmin,
O.Yu. Lukina, A.S. Proskuryakov, A.A. Savin, L.M. Shcheglova, A.N. Solomin,
N.P. Zotov
Moscow State University, Institute of Nuclear Physics, Moscow, Russia m
M. Botje, F. Chlebana, A. Dake, J. Engelen, M. de Kamps, P. Kooijman, A. Kruse, H. Tiecke, W. Verkerke,
M. Vreeswijk, L. Wiggers, E. de Wolf, R. van Woudenberg
NIKHEF and University of Amsterdam, Netherlands i
D. Acosta, B. Bylsma, L.S. Durkin, K. Honscheid, C. Li, T.Y. Ling, K.W. McLean25, W.N. Murray, I.H. Park,
T.A. Romanowski26, R. Seidlein27
Ohio State University, Physics Department, Columbus, Ohio, USA p
D.S. Bailey, A. Byrne28, R.J. Cashmore, A.M. Cooper-Sarkar, R.C.E. Devenish, N. Harnew,
M. Lancaster, L. Lindemann4, J.D. McFall, C. Nath, V.A. Noyes, A. Quadt, J.R. Tickner,
H. Uijterwaal, R. Walczak, D.S. Waters, F.F. Wilson, T. Yip
Department of Physics, University of Oxford, Oxford, U.K. o
G. Abbiendi, A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, M. De Giorgi, U. Dosselli,
S. Limentani, M. Morandin, M. Posocco, L. Stanco, R. Stroili, C. Voci
Dipartimento di Fisica dell’ Universita and INFN, Padova, Italy f
II
J. Bulmahn, J.M. Butterworth, R.G. Feild, B.Y. Oh, J.J. Whitmore29
Pennsylvania State University, Dept. of Physics, University Park, PA, USA q
G. D’Agostini, G. Marini, A. Nigro, E. Tassi
Dipartimento di Fisica, Univ. ’La Sapienza’ and INFN, Rome, Italy f
J.C. Hart, N.A. McCubbin, K. Prytz, T.P. Shah, T.L. Short
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. o
E. Barberis, T. Dubbs, C. Heusch, M. Van Hook, W. Lockman, J.T. Rahn, H.F.-W. Sadrozinski, A. Seiden,
D.C. Williams
University of California, Santa Cruz, CA, USA p
J. Biltzinger, R.J. Seifert, O. Schwarzer, A.H. Walenta, G. Zech
Fachbereich Physik der Universit¨at-Gesamthochschule Siegen, Federal Republic of Germany c
H. Abramowicz, G. Briskin, S. Dagan30, A. Levy31
School of Physics,Tel-Aviv University, Tel Aviv, Israel e
T. Hasegawa, M. Hazumi, T. Ishii, M. Kuze, S. Mine, Y. Nagasawa, M. Nakao, I. Suzuki, K. Tokushuku, S. Ya-
mada, Y. Yamazaki
Institute for Nuclear Study, University of Tokyo, Tokyo, Japan g
M. Chiba, R. Hamatsu, T. Hirose, K. Homma, S. Kitamura, Y. Nakamitsu, K. Yamauchi
Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan g
R. Cirio, M. Costa, M.I. Ferrero, L. Lamberti, S. Maselli, C. Peroni, R. Sacchi, A. Solano, A. Staiano
Universita di Torino, Dipartimento di Fisica Sperimentale and INFN, Torino, Italy f
M. Dardo
II Faculty of Sciences, Torino University and INFN - Alessandria, Italy f
D.C. Bailey, D. Bandyopadhyay, F. Benard, M. Brkic, M.B. Crombie, D.M. Gingrich32, G.F. Hartner, K.K. Joo,
G.M. Levman, J.F. Martin, R.S. Orr, S. Polenz, C.R. Sampson, R.J. Teuscher
University of Toronto, Dept. of Physics, Toronto, Ont., Canada a
C.D. Catterall, T.W. Jones, P.B. Kaziewicz, J.B. Lane, R.L. Saunders, J. Shulman
University College London, Physics and Astronomy Dept., London, U.K. o
K. Blankenship, B. Lu, L.W. Mo
Virginia Polytechnic Inst. and State University, Physics Dept., Blacksburg, VA, USA q
W. Bogusz, K. Charchu la, J. Ciborowski, J. Gajewski, G. Grzelak, M. Kasprzak, M. Krzy ˙zanowski,
K. Muchorowski, R.J. Nowak, J.M. Pawlak, T. Tymieniecka, A.K. Wr´oblewski, J.A. Zakrzewski, A.F. ˙
Zarnecki
Warsaw University, Institute of Experimental Physics, Warsaw, Poland j
M. Adamus
Institute for Nuclear Studies, Warsaw, Poland j
Y. Eisenberg30, U. Karshon30 , D. Revel30, D. Zer-Zion
Weizmann Institute, Nuclear Physics Dept., Rehovot, Israel d
I. Ali, W.F. Badgett, B. Behrens, S. Dasu, C. Fordham, C. Foudas, A. Goussiou, R.J. Loveless, D.D. Reeder,
S. Silverstein, W.H. Smith, A. Vaiciulis, M. Wodarczyk
University of Wisconsin, Dept. of Physics, Madison, WI, USA p
T. Tsurugai
Meiji Gakuin University, Faculty of General Education, Yokohama, Japan
S. Bhadra, M.L. Cardy, C.-P. Fagerstroem, W.R. Frisken, K.M. Furutani, M. Khakzad, W.B. Schmidke
York University, Dept. of Physics, North York, Ont., Canada a
III
1supported by Worldlab, Lausanne, Switzerland
2also at IROE Florence, Italy
3now at Univ. of Salerno and INFN Napoli, Italy
4supported by EU HCM contract ERB-CHRX-CT93-0376
5now at M¨obelhaus Kramm, Essen
6now a self-employed consultant
7now also at University of Torino
8Alfred P. Sloan Foundation Fellow
9presently at Columbia Univ., supported by DAAD/HSPII-AUFE
10 now at Inst. of Computer Science, Jagellonian Univ., Cracow
11 now at Comma-Soft, Bonn
12 visitor from Florida State University
13 now at Univ. of Mainz
14 supported by DAAD and European Community Program PRAXIS XXI
15 now at Dr. Seidel Informationssysteme, Frankfurt/M.
16 now at Inst. of Accelerating Systems Applications (IASA), Athens
17 now at Mercer Management Consulting, Munich
18 now with OPAL Collaboration, Faculty of Physics at Univ. of Freiburg
19 now at SAS-Institut GmbH, Heidelberg
20 also supported by DESY
21 now at GSI Darmstadt
22 also supported by NSERC
23 now at Institute for Cosmic Ray Research, University of Tokyo
24 partially supported by CAM
25 now at Carleton University, Ottawa, Canada
26 now at Department of Energy, Washington
27 now at HEP Div., Argonne National Lab., Argonne, IL, USA
28 now at Oxford Magnet Technology, Eynsham, Oxon
29 on leave and partially supported by DESY 1993-95
30 supported by a MINERVA Fellowship
31 partially supported by DESY
32 now at Centre for Subatomic Research, Univ.of Alberta, Canada and TRIUMF, Vancouver, Canada
asupported by the Natural Sciences and Engineering Research Council of Canada (NSERC)
bsupported by the FCAR of Qu´ebec, Canada
csupported by the German Federal Ministry for Research and Technology (BMFT)
dsupported by the MINERVA Gesellschaft f¨ur Forschung GmbH, and by the Israel Academy of
Science
esupported by the German Israeli Foundation, and by the Israel Academy of Science
fsupported by the Italian National Institute for Nuclear Physics (INFN)
gsupported by the Japanese Ministry of Education, Science and Culture (the Monbusho) and its
grants for Scientific Research
hsupported by the Korean Ministry of Education and Korea Science and Engineering Foundation
isupported by the Netherlands Foundation for Research on Matter (FOM)
jsupported by the Polish State Committee for Scientific Research (grant No. SPB/P3/202/93) and
the Foundation for Polish- German Collaboration (proj. No. 506/92)
ksupported by the Polish State Committee for Scientific Research (grant No. PB 861/2/91 and No.
2 2372 9102, grant No. PB 2 2376 9102 and No. PB 2 0092 9101)
lpartially supported by the German Federal Ministry for Research and Technology (BMFT)
msupported by the German Federal Ministry for Research and Technology (BMFT), the Volkswagen
Foundation, and the Deutsche Forschungsgemeinschaft
nsupported by the Spanish Ministry of Education and Science through funds provided by CICYT
osupported by the Particle Physics and Astronomy Research Council
psupported by the US Department of Energy
qsupported by the US National Science Foundation
IV
1 Introduction
Electron-proton collisions at HERA have shown evidence for hard processes in diffractive re-
actions. Both in deep inelastic scattering (DIS) (Q2>10 GeV2, where Q2is the virtuality of
the exchanged photon) [1, 2, 3] and in photoproduction (Q2∼0) [4, 5], events characterized
by a large rapidity gap towards the proton direction have been observed and interpreted as
resulting from diffractive scattering [1, 2, 4]. In the DIS regime, hard scattering for this class
of events has been revealed through the virtuality of the probing photon [1, 3] and through
the observation of jet structure in the final state [2]. In the photoproduction domain, the hard
scattering has been identified through jet production [4, 5].
Diffractive processes are generally considered to proceed through the exchange of a colour-
less object with the quantum numbers of the vacuum, generically called the pomeron (IP ).
Although the description of soft diffractive processes in terms of pomeron exchange has been
a phenomenological success, the description of the pomeron in terms of a parton structure at
first lacked experimental support. On the basis of pp data [6] from the CERN ISR, Ingelman
and Schlein [7] suggested that the pomeron may have a partonic structure. The observation of
jet production in p¯pcollisions with a tagged proton (or antiproton) made by the UA8 Collab-
oration [8] gave strong evidence for such a structure. Further evidence has been provided by
the observations made at HERA [1 −5], which in addition include the first measurements of
the diffractive structure function in DIS [9, 10].
The description of diffractive processes in terms of QCD has remained elusive, in part due
to the lack of a sufficiently large momentum transfer on which to base the perturbative expan-
sion. Cross sections for diffractive processes involving large transverse energy jets or leptons
in the final state are, however, amenable to perturbative QCD calculations [7,11 −17]. Their
measurement could answer several questions concerning the structure of the pomeron such as:
whether the parton picture is valid for the pomeron and universal parton densities can be de-
fined; what fraction of the pomeron momentum is carried by gluons and what by quarks; and
whether a momentum sum rule applies to the pomeron [18].
This paper presents the first measurement of inclusive jet cross sections in photoproduction
at centre-of-mass energies ∼200 GeV with a large rapidity gap. This process is sensitive to both
the gluon and quark content of the pomeron. In order to examine the partonic structure of the
pomeron, these jet cross sections are compared to predictions from models based on perturbative
QCD and Regge phenomenology. The jet cross sections measured in photoproduction, combined
with the results on the diffractive structure function in deep inelastic scattering [10], give the
first experimental evidence for the gluon content of the pomeron. The result does not depend
on the flux of pomerons from the proton nor on the assumption that a momentum sum rule can
be defined for the pomeron. The data sample used in this analysis corresponds to an integrated
luminosity of 0.55 pb−1and was collected during 1993 with the ZEUS detector at HERA.
2 Experimental setup
2.1 HERA operation
The experiment was performed at the electron-proton collider HERA using the ZEUS detector.
During 1993 HERA operated with electrons of energy Ee= 26.7 GeV colliding with protons of
energy Ep= 820 GeV. HERA is designed to run with 210 bunches separated by 96 ns in each of
the electron and proton rings. For the 1993 data-taking, 84 bunches were filled for each beam
5
and an additional 10 electron and 6 proton bunches were left unpaired for background studies.
The electron and proton beam currents were typically 10 mA, with instantaneous luminosities
of approximately 6 ·1029 cm−2s−1.
2.2 The ZEUS detector and trigger conditions
ZEUS is a multipurpose magnetic detector. The configuration for the 1993 running period
has been described elsewhere [2, 19]. A brief description concentrating on those parts of the
detector relevant to this analysis is presented here.
Charged particles are tracked by two concentric cylindrical drift chambers, the vertex de-
tector (VXD) and the central tracking detector (CTD), operating in a magnetic field of 1.43 T
provided by a thin superconducting coil. The coil is surrounded by a high-resolution uranium-
scintillator calorimeter (CAL) divided into three parts, forward1(FCAL) covering the pseudora-
pidity2region34.3≥ηd≥1.1, barrel (BCAL) covering the central region 1.1≥ηd≥ −0.75
and rear (RCAL) covering the backward region −0.75 ≥ηd≥ −3.8. The solid angle cover-
age is 99.7% of 4π. The CAL parts are subdivided into towers which in turn are subdivided
longitudinally into electromagnetic (EMC) and hadronic (HAC) sections. The sections are sub-
divided into cells, each viewed by two photomultiplier tubes. The CAL is compensating, with
equal response to hadrons and electrons. Measurements under test beam conditions show that
the energy resolution is σE/E = 0.18/√E(Ein GeV) for electrons and σE/E = 0.35/√Efor
hadrons [20]. In the analysis presented here, CAL cells with EMC (HAC) energy below 60 MeV
(110 MeV) are excluded to minimize the effect of calorimeter noise. This noise is dominated by
the uranium activity and has an r.m.s. value below 19 MeV for EMC cells and below 30 MeV
for HAC cells. For measuring the luminosity as well as for tagging very small Q2processes, two
lead-scintillator calorimeters [21], located at 107 m and 35 m downstream from the interaction
point in the electron direction, detect the bremsstrahlung photons and the scattered electrons
respectively.
Data were collected using a three-level trigger [19]. The first-level trigger (FLT) is built as
a deadtime-free pipeline. The FLT for the sample of events analysed in this paper required
a logical OR of different conditions on sums of energy in the CAL cells. The average FLT
acceptance for the events under study was approximately 90%. The second-level trigger used
information from a subset of detector components to differentiate physics events from back-
grounds consisting mostly of proton beam gas interactions. The third-level trigger (TLT) used
the full event information to apply specific physics selections. For this analysis, the following
conditions were required: a) the event has a vertex reconstructed by the tracking chambers
(VXD+CTD) with the Zvalue in the range |Z|<75 cm; b) E−pZ≥8 GeV, where Eis the
total energy as measured by the CAL
E=X
i
Ei,
pZis the Z-component of the vector
~p =X
i
Ei~ri,
1The ZEUS coordinate system is defined as right-handed with the Zaxis pointing in the proton beam
direction, hereafter referred to as forward, and the Xaxis horizontal, pointing towards the centre of HERA.
2The pseudorapidity is defined as −ln(tan θ
2), where the polar angle θis taken with respect to the proton
beam direction, and is denoted by ηd(η) when the polar angle is measured with respect to the nominal interaction
point (the reconstructed vertex of the interaction).
3The FCAL has the forward edge at ηedge = 4.3 with full acceptance for ηd<3.7.
6
the sums run over all CAL cells, Eiis the energy of the calorimeter cell iand ~riis a unit
vector along the line joining the reconstructed vertex and the geometric centre of the cell i; c)
pZ/E ≤0.94 to reject beam-gas interactions; and d) the total transverse energy as measured
by the CAL, excluding the cells whose polar angles are below 10◦, exceeds 12 GeV.
3 Diffractive hard photoproduction
Diffractive hard photoproduction processes in ep collisions are characterized by Q2≈0 and
by a final state consisting of a hadronic system Xcontaining one or more jets, the scattered
electron and the scattered proton
e+pi→e+X+pf→e+ (jet +Xr) + pf(1)
where pi(pf) denotes the initial (final) state proton and Xconsists of at least one jet plus the
remaining hadronic system (Xr).
The kinematics of this process are described in terms of four variables. Two of them describe
the electron-photon vertex and can be taken to be the virtuality of the exchanged photon (Q2)
and the inelasticity variable ydefined by
y= 1 −E′
e
Ee
1−cos θ′
e
2
where E′
edenotes the scattered electron energy and θ′
eis the electron scattering angle. The
other two variables describe the proton vertex: the fraction of the momentum of the initial
proton carried by the scattered proton (xf), and the square of the momentum transfer (t)
between the initial and final state proton. In terms of these variables and at low values of Q2
and t, the square of the mass of the hadronic system Xis given by
M2
X≈(1 −xf)y s (2)
where sis the square of the ep centre-of-mass energy.
Diffractive processes in which the photon dissociates give rise to a large rapidity gap between
the hadronic system Xand the scattered proton:
∆yGAP =ypf−yhad
max (3)
where ypfis the rapidity of the scattered proton and yhad
max is the rapidity of the most forward
going hadron belonging to the system X. The same signature is expected for double dissociation
where the scattered proton is replaced by a low mass baryonic system (N). In this paper, the
outgoing proton (or system N) was not observed, and instead of yhad
max the pseudorapidity (ηhad
max)
of the most forward-going hadron in the detector was used.
Two cross sections are presented in this paper. First, the cross section for inclusive jet
production is measured as a function of the pseudorapidity of the jet (ηjet) (for the definition of
the jet variables see section 4) in reaction (1) with the most-forward going hadron at ηhad
max <1.8.
This corresponds to a rapidity gap of at least 2.5 units measured from the edge of the CAL
(∆ηGAP =ηedge −ηhad
max). This cross section is denoted by
dσ
dηj et (ηhad
max <1.8) (4)
7
and is measured in the ηj et range between −1 and 1. Second, the integrated cross section for
inclusive jet production is determined as a function of η0
max
σ(ηhad
max < η0
max) = Z+1
−1dηj et dσ
dηj et (ηhad
max < η0
max) (5)
and is measured in the range of η0
max between 1 and 2.4. Both measurements include contribu-
tions from double dissociation where the large-rapidity-gap requirement is satisfied.
The jet cross sections refer to jets at the hadron level with a cone radius, R=√∆η2+ ∆φ2,
of one unit in pseudorapidity (η)−azimuth (φ) space and integrated over the transverse
energy of the jet Ejet
T>8 GeV. They are given in the kinematic region Q2<4 GeV2and
0.2< y < 0.85. This region corresponds to photoproduction interactions at centre-of-mass
energies in the range 130-270 GeV with a median Q2≈10−3GeV2.
3.1 Models
The description of diffractive hard processes in terms of QCD is still in an early stage. Two
main theoretical approaches have been considered. Both assume that a pomeron (IP ) is emitted
by the proton. The variable xIP ≡1−xfis then the fraction of the initial proton’s momen-
tum carried by the pomeron and M2
X≈xIP ys is the square of the γIP centre-of-mass energy.
The two approaches differ in the modelling of jet production in γIP collisions. One of them
[7,11 −13] assumes factorisation (factorisable models) while the other one does not [14,16]
(non-factorisable models). The latter are, however, not considered in what follows due to the
lack of a Monte Carlo generator with an appropriate description of the event jet structure.
Calculations based on factorisable models involve three basic ingredients: the flux of pomerons
from the proton as a function of xIP and t, the parton densities in the pomeron and the matrix
elements for jet production. The pomeron is assumed to be a source of partons which inter-
act either with the photon (direct component) or with a partonic constituent of the photon
(resolved component). As an example, the contribution of the direct component to the cross
section for reaction (1) is given by
σdir =Zdyfγ/e(y)Z Z dxIP dtfIP /p (xIP , t)X
iZdβ X
j,k Zdˆp2
T
dˆσi+γ→j+k
dˆp2
T
(ˆs, ˆp2
T, µ2)fi/IP (β, µ2)
(6)
where fγ/e is the flux of photons from the electron4and fIP /p is the flux of pomerons from
the proton. The sum in iruns over all possible types of partons present in the pomeron, and
fi/IP (β, µ2) is the density of partons of type icarrying a fraction βof the pomeron momentum at
a scale µ2and is assumed to be independent of t. The sum in jand kruns over all possible types
of final state partons and ˆσi+γ→j+kis the cross section for the two-body collision i+γ→j+k
and depends on the square of the centre-of-mass energy (ˆs), the transverse momentum of the
two outgoing partons (ˆpT) and the momentum scale (µ) at which the strong coupling constant
(αs(µ2)) is evaluated. One possible choice is µ2= ˆp2
T. In these models, the pomeron flux
factor is extracted from hadron-hadron collisions using Regge theory, and the matrix elements
are computed in perturbative QCD. However, the parton densities in the pomeron have to
be extracted from experiment. While the recent measurements of the diffractive structure
function in DIS at HERA [9, 10] give information on the quark densities in the pomeron, the
gluon content has so far not been determined.
4The Q2dependence has been integrated out using the Weizs¨acker-Williams approximation.
8
Two forms of the pomeron flux factor are commonly used. The Ingelman-Schlein form (IS)
[22] uses a parametrisation of UA4 data [23]:
fIP /p(xIP , t) = c0
xIP ·(3.19e8t+ 0.212e3t) (7)
where c0=1
2.3GeV−2and tis in GeV2. The Donnachie-Landshoff form (DL) [12] is calculated
in Regge theory, with parameters determined by fits to hadron-hadron data:
fIP /p(xIP , t) = 9b2
0
4π2F1(t)2x1−2α(t)
IP (8)
using the elastic form factor F1(t) of the proton, the pomeron-quark coupling b0≃1.8 GeV−1
and the pomeron trajectory α(t) = 1.085 + 0.25twith tin GeV2.
Various parametrisations of the parton densities in the pomeron have been suggested on
theoretical grounds [7,11 −13]. The following represent extreme possibilities for the shape of
the quark and gluon momentum densities:
•hard gluon density βfg /IP (β, µ2) = 6β(1 −β);
•soft gluon density βfg /IP (β, µ2) = 6(1 −β)5;
•hard quark density (for two flavours) βfq/IP (β, µ2) = 6
4β(1 −β).
The first two assume a pomeron made entirely of gluons and the last one a pomeron made of
u¯uand d¯
dpairs. In all cases a possible µ2dependence of the parton densities is neglected5and
the densities are normalised such that all of the pomeron’s momentum is carried by the partons
under consideration, ΣIP (µ2)≡R1
0dβ Piβfi/IP (β, µ2) = 1.
However, since the pomeron is not a particle, it is unclear whether or not the normalisations of
the pomeron flux factor and the momentum sum of the pomeron can be defined independently.
Nevertheless, for an assumed normalisation of the flux factor, the momentum sum ΣIP (µ2) can
be measured. The definition used for the DL form of the pomeron flux factor is the appropriate
one if the pomeron were an ordinary hadron and, hence, the one in which the momentum sum
rule might be fulfilled [24].
Factorisable models presently account only for diffractive hard processes in which the proton
remains intact. Since the measurements are based on the requirement of a large rapidity gap in
the central detector, the contribution to the measured cross sections from double dissociation
has to be taken into account when comparing with model predictions.
4 Data selection and jet search
Events from quasi-real photon proton collisions were selected using the same criteria as reported
earlier [25]. The main steps are briefly discussed here.
Events satisfying the TLT selection described in section 2.2 are first selected. A cone algo-
rithm in η-φspace with a cone radius of 1 unit [26, 27] is then used to reconstruct jets, for both
data and simulated events (see next section) from the energy deposits in the CAL cells (cal
jets), and for simulated events also from the final state hadrons (had jets). The axis of the jet is
5The µ2dependence of the parton densities in the pomeron is expected to be smaller than the differences
between the various parton densities considered [7].
9
defined according to the Snowmass convention [27], ηjet (φj et) is the transverse energy weighted
mean pseudorapidity (azimuth) of all the objects (CAL cells or final state hadrons) belonging
to that jet. This procedure is explained in detail elsewhere [25]. The variables associated with
the cal jets are denoted by Ejet
T,cal,ηj et
cal , and φjet
cal, while the ones for the had jets by Ejet
T,ηjet,
and φjet.
A search for jet structure using the CAL cells is performed in the data. Events with at least
one jet fulfilling the conditions Ejet
T,cal >6 GeV and −1< ηj et
cal <2 are retained. Beam-gas
interactions, cosmic-ray showers, halo muons and DIS neutral current events are removed from
the sample as described previously [25]. The sample thus consists of events from ep interactions
with Q2<4 GeV2and a median Q2≈10−3GeV2. The γp centre-of-mass energy (W) is
calculated using the expression W=√ys. The event sample is restricted to the kinematic
range 0.2< y < 0.85 using the following procedure. The method of Jacquet-Blondel [28] is
used to estimate yfrom the energies measured in the CAL cells (see section 2.2)
yJB =E−pZ
2Ee
.
As can be verified using photoproduction events with an electron detected in the luminosity
monitor (tagged events), yJB systematically underestimates yby approximately 20%, which
is adequately reproduced in the Monte Carlo simulation of the detector. To allow for this
effect, the event selection required 0.16 < yJB <0.7. The sample thus obtained consists of
19,485 events containing 24,504 jets. The only significant background, which is from misiden-
tified DIS neutral current interactions with Q2>4 GeV2, is estimated to be below 2%. The
photoproduction origin of the sample is verified by the expected contribution (26%) of tagged
events.
5 Monte Carlo simulation
Events from diffractive hard photoproduction processes were simulated using the program
POMPYT [22]. These events were used to determine both the response of the detector to
the hadronic final state and the correction factors for the cross sections for jet production with
a large rapidity gap.
The POMPYT generator is a Monte Carlo implementation of the model proposed in [7].
The generator makes use of the program PYTHIA [29] to simulate electron-pomeron inter-
actions via resolved and direct photon processes. In PYTHIA, the lepton-photon vertex is
modelled according to the Weizs¨acker-Williams approximation and the effects of initial state
bremsstrahlung from the electron are simulated by using the next-to-leading order electron
structure function [30]. Radiative corrections in our kinematic region, where Wis larger than
100 GeV, are expected to be negligible [31]. For the resolved processes, the parton densities of
the photon were parametrised according to GS-HO [32] and evaluated at the momentum scale
set by the transverse momentum of the two outgoing partons, µ2= ˆp2
T. The parton densities
in the pomeron were parametrised according to the forms described in section 3.1 and were
taken to be independent of any scale. In PYTHIA, the partonic processes are simulated us-
ing leading order matrix elements, with the inclusion of initial and final state parton showers.
Fragmentation into hadrons was performed using the Lund string model [33] as implemented
in JETSET [34]. Samples of events were generated with different values of the minimum cutoff
for the transverse momentum of the two outgoing partons, starting at ˆpT min = 3 GeV.
10
The program PYTHIA was also used to simulate standard (non-diffractive) hard photo-
production events via resolved and direct photon processes. Events were generated using the
leading order predictions of GRV [35] for the photon parton densities and MRSD−[36] for the
proton parton densities.
All generated events were passed through the ZEUS detector and trigger simulation pro-
grams. They were reconstructed using the same standard ZEUS off-line programs as for the
data.
6 Event characteristics
The event variable ηmax , as in previous studies by ZEUS [1, 2, 4, 10], was used to select events
with a large rapidity gap. For the data, this variable is defined as the pseudorapidity (ηcal
max)
of the most forward condensate with an energy above 400 MeV. A condensate is a contiguous
energy deposit above 100 MeV for pure EMC and 200 MeV for HAC or mixed energy deposits
in CAL. In the samples of simulated events, the ηmax variable is defined at both the hadron
and CAL levels. At the hadron level, all particles with lifetimes larger than 10−13 s, energies
in excess of 400 MeV and pseudorapidities below 4.5 are considered as candidates for the most
forward final state particle, and ηhad
max defines the pseudorapidity of the most forward particle.
The CAL level uses the same definition as for the data.
The mass of the hadronic system (MX) of each event is reconstructed using the CAL cells,
Mcal
X=√E2−~p2[4]. The correlation between Mcal
Xand ηcal
max for the sample of events with
at least one cal jet fulfilling the conditions Ej et
T,cal >6 GeV and −1< ηj et
cal <1 is displayed in
Fig. 1a. As shown in our previous publication [4], there exists a distinct class of events with low
ηcal
max values. The large-rapidity-gap events (ηcal
max <1.8) are found to populate the region of low
Mcal
Xvalues, in contrast to the bulk of the data which have large Mcal
Xvalues. These features
of the data are reproduced by the Monte Carlo simulations: the events from a simulation of
standard hard photoproduction processes using PYTHIA populate the region of large ηcal
max and
large Mcal
Xvalues; the events from a simulation of diffractive hard processes using POMPYT
extend into the region of low ηcal
max and Mcal
Xvalues.
A study of the region of low Mcal
Xin the data sample reveals the following features. The
ηcal
max distribution for events with Mcal
X<30 GeV is shown in Fig. 1b along with the predictions
of PYTHIA and of POMPYT with a pomeron made of hard gluons (normalised to the number
of data events above and below ηcal
max = 2.5, respectively). The simulation of non-diffractive
processes by PYTHIA cannot reproduce the shape of the measured ηcal
max distribution. On the
other hand, the predictions of POMPYT describe well the shape of the data below ηcal
max ∼3.
The Mcal
Xdistribution for the sample of events with ηcal
max <1.8 is shown in Fig. 1c. This
sample consists of 49 events containing 68 jets. The data exhibit an enhancement at low masses,
15 GeV<
∼Mcal
X
<
∼30 GeV, which is reproduced by the simulation of POMPYT with a hard gluon
density (normalised to the number of data events). The Wof each event is reconstructed using
yJB,Wcal =√yJBs. The distribution of Wcal for events with ηcal
max <1.8 is shown in Fig. 1d
along with the expectations of POMPYT with a hard gluon density (normalised to the number
of data events). The Wcal dependence exhibited by the data sample is well reproduced by the
simulation of POMPYT. The expectations of POMPYT using a hard quark density (not shown)
also give a good description of the distributions of the data. Note that POMPYT assumes the
cross section to be independent of Was expected for diffractive processes mediated by pomeron
exchange. The good agreement with the data gives evidence for the diffractive nature of the
large-rapidity-gap events.
11
In summary, the data exhibit a different behaviour in the region of low masses of the hadronic
system compared to that of high masses. At low masses, the shape of the ηcal
max distribution
in the data sample cannot be accounted for by the simulation of non-diffractive processes as
in PYTHIA. On the other hand, the features of the data are described by the predictions
of diffractive processes mediated by pomeron exchange as in POMPYT. These facts support
the interpretation of these large-rapidity-gap events as being produced by diffractive processes
via pomeron exchange. Therefore, the measurements of jet cross sections presented in the
next section are compared to the predictions of models based on pomeron exchange. However,
without a detected fast proton in the forward direction, the jet cross sections refer to events
with a large rapidity gap. These include events with a diffractively scattered proton as well as
those with a diffractively dissociated proton with mass less than approximately 4 GeV [10]. In
this way, the measurements are presented in a model independent form suitable for comparison
with calculations other than those presented here.
6.1 Energy and acceptance corrections
The method to correct the transverse energy of a jet as reconstructed using the CAL cells has
been discussed elsewhere [25]. For samples of simulated events, the transverse energy of a jet as
measured by the CAL (Ejet
T,cal) was compared to that reconstructed using the final state hadrons
(Ejet
T). The corrections to the jet transverse energy were constructed as multiplicative factors,
C(Ejet
T,cal, ηjet
cal ), which, when applied to the ETof the cal jets, give the corrected transverse
energies of the jets: Ej et
T=C(Ejet
T,cal, ηjet
cal )×Ejet
T,cal. The function Ccorrects for energy losses,
and for values Ejet
T,cal >10 GeV is approximately flat as a function of Ejet
T,cal and varies between
1.08 and 1.18 depending on ηj et
cal . For Ejet
T,cal near threshold, Ejet
T,cal ≈6 GeV, this correction
procedure can give values as large as 1.40. No correction is needed for ηjet (ηjet ≈ηj et
cal ). The
procedure was validated by comparing the momenta of the tracks in the cal jet in data and in
Monte Carlo simulations. From this comparison it was concluded that the energy scale of the
jets is corrected to within ±5% [25]. The correction procedure was applied to the data sample
of jets with Ejet
T,cal >6 GeV to select for further study those jets with corrected transverse
energies of Ejet
T>8 GeV and with the jet pseudorapidity in the range between −1 and 1.
The events generated by POMPYT were used to compute the acceptance correction for
the inclusive jet distributions. This correction function takes into account the efficiency of
the trigger, the selection criteria and the purity and efficiency of the jet and ηhad
max selection.
It also corrects for the migrations in the variable ηcal
max and yields cross sections for the true
rapidity gap defined by ηhad
max and η= 4.5. After applying the jet transverse energy corrections,
the purity was ∼40% and the efficiency was ∼50%. Cross sections were then obtained by
applying bin-by-bin corrections to the inclusive jet distributions of the data sample in the
variables ηjet and ηhad
max. The acceptance correction factors for the inclusive jet cross section
dσ/dηjet(ηhad
max <1.8) (σ(ηhad
max < η0
max)) were found to vary between 0.63 and 0.93 (0.59 and
0.84). The dependence of these correction factors on the choice of parametrisations of the
parton densities in the pomeron were found to be below ∼20%, and are taken into account in
the systematic uncertainty assigned to the measurements reported in the next section.
12
7 Results
In this section, first the measured jet cross sections are presented and the uncertanties of the
measurements discussed. These results are model-independent. Second, the expectations from
non-diffractive processes are found not to account for the measurements. Third, the predictions
from diffractive models are compared to the data and estimates of the momentum sum of the
pomeron and of the relative contribution of quarks and gluons in the pomeron are extracted
using solely the diffractive jet measurements. Fourth, the jet cross sections in photoproduction
are combined with the measurements of the DIS diffractive structure function to constrain
further the parton content of the pomeron.
7.1 Jet Cross Sections
The results for dσ/dηjet(ηhad
max <1.8) and σ(ηhad
max < η0
max) are presented in Figs. 2 and 3 and in
Tables 1 and 2. The differential cross section is flat as a function of ηjet. Since the measured
jet cross sections refer to events with a large rapidity gap they include a contribution from
double dissociation. The statistical errors of the measurements are indicated as the inner error
bars in Figs. 2 and 3. They are ∼30% for dσ/dηjet(ηhad
max <1.8) and constitute the dominant
source of uncertainty. For σ(ηhad
max < η0
max) the statistical error increases from 8% to 20% as
η0
max decreases. A detailed study of the systematic uncertainties of the measurements has been
carried out [25, 37]. The sources of uncertainty include the dependence on the choice of the
parton densities in the pomeron, the simulation of the trigger, the cuts used to select the data,
and the absolute energy scale of the cal jets [25].
The following systematic uncertainties related to the ηmax-cut were studied: the ηcal
max variable
in the data and the simulated events was recomputed after removing the CAL cells with η > 3.25
in order to check the dependence on the detailed simulation of the forward region of the detector,
resulting in changes up to 13% for σ(ηhad
max < η0
max) and up to 18% for dσ/dηjet(ηhad
max <1.8)
(except at the most forward data point, where the statistics are small and the change amounts
to 37%); the energy threshold in the computation of ηcal
max for data and simulated events was
decreased to 300 MeV, yielding changes up to 11% for dσ/dηj et(ηhad
max <1.8) and up to 14% for
σ(ηhad
max < η0
max) (except at the most backward data point, where the statistics are small and
the change amounts to 27%).
The dominant source of systematic error is the absolute energy scale of the cal jets, known
to within 5%, which results in a 20% error. The systematic uncertainties not associated with
the energy scale of the jets were added in quadrature to the statistical errors and are shown
as the total error bars. The additional uncertainty due to the energy scale of the jets is shown
as a shaded band. The systematic uncertainties have large bin to bin correlations. They are
to be understood as a conservative estimate of the error associated with each data point. An
additional overall normalisation uncertainty of 3.3% from the luminosity determination is not
included.
7.2 Comparison to non-diffractive model predictions
The contribution to the measured cross sections from non-diffractive processes was estimated
using PYTHIA including resolved and direct processes. H ad jets were selected in the generated6
events using the same jet algorithm as for the data and calculating ηhad
max as explained in section
6These generated events were analysed at the hadron level.
13
6. In PYTHIA the occurrence of a rapidity gap is exponentially suppressed and arises from a
fluctuation in the pseudorapidity distribution of the final state hadrons. The calculations using
MRSD−[36] for the proton and GRV-HO [35] for the photon parton densities are compared
to the measurements in Figs. 2 and 3. The non-diffractive contribution does not reproduce
the measurements. For the measured dσ/dηjet(ηhad
max <1.8) the non-diffractive contribution is
close to the data only at the most forward measured point. For the remaining ηjet range, the
data are a factor between 2 and 7 above the expectations from non-diffractive processes. In the
measured σ(ηhad
max < η0
max), the non-diffractive contribution as predicted by PYTHIA is smaller
than the data by factors between 3 and 9. These comparisons, together with the features of
the data shown in the previous section, demonstrate that the measured jet cross sections with
a large rapidity gap cannot be accounted for by non-diffractive processes. However, in the
discussion below, this non-diffractive contribution will be subtracted from the data.
7.3 Comparison to diffractive model predictions
The measured cross sections are compared to the predictions of the models for diffractive hard
scattering mediated by pomeron exchange, as implemented in the POMPYT generator. The
predictions have been obtained by selecting had jets in the generated events using the same jet
algorithm as for the data and calculating ηhad
max as explained in section 6.
In a first step, the predictions of POMPYT, using the DL flux factor and the parametrisa-
tions of the pomeron parton densities suggested theoretically (see section 3.1), and assuming
ΣIP = 1, are compared to the measured cross sections in Figs. 2 and 3. For this initial com-
parison, the contributions from non-diffractive and double dissociation processes have not been
taken into account. As mentioned earlier (see section 3.1), the µ2dependence of the parton
densities has been neglected and, hence, the argument of ΣIP (µ2) is omitted. The scale rel-
evant for the measured jet cross sections is µ2∼(Ej et
T)2. We start by discussing the results
for dσ/dηjet(ηhad
max <1.8). The shape of the predictions of POMPYT using a hard parton
density compares well with the measured shape of the cross section. The shape predicted by
POMPYT using a soft gluon density does not describe the data. The calculations based on
a soft gluon density are smaller than the measurements by factors between 20 and 50. This
type of parametrisation was already disfavoured by previous studies [5]. The predictions using
a hard quark density are too small by factors between 3 and 10, but those using a hard gluon
density reproduce the measurements well. The predictions based on the IS flux factor lead to
similar conclusions. For the integrated cross section σ(ηhad
max < η0
max), the measured shape is in
each case described by the expectations from POMPYT, although the normalisation is incor-
rect by a factor depending on the model. A soft gluon (hard quark) density yields a prediction
which is too small by factors between 30 and 60 (5 and 10). A hard gluon density for the
pomeron gives a good description of the data. Based on the samples of events of POMPYT,
the measurements are sensitive to βvalues above approximately 0.3. Therefore, the data is not
sensitive to a possible additional contribution due to a soft parton component in the pomeron.
The data do not rule out a possible contribution from a super-hard parton component in the
pomeron [15 −17].
In principle, other processes could contribute to jet production with a large rapidity gap.
For example, the proton may emit a π+(instead of a pomeron), pi→nfπ+, and a partonic
constituent of the π+undergoes a hard interaction with the photon or its constituents. The
contribution from this reaction to the data is expected to be small due to the power law
decrease, ∼W−4, for pion exchange. Monte Carlo calculations using POMPYT confirm these
14
expectations.
In a second step, the data were compared to the predictions of POMPYT based on a pomeron
consisting of both quarks and gluons but without assuming ΣIP = 1. In addition, the con-
tribution from non-diffractive processes and from double dissociation to the measured cross
sections were taken into account. The non-diffractive contribution as predicted by PYTHIA7
was subtracted bin by bin from the data. The contribution from double dissociation for large-
rapidity-gap events was estimated to be (15 ±10)% [10]. This contribution was assumed to be
independent of ηjet and was also subtracted from the data. After the above subtractions, the
data were compared with the predictions of POMPYT using the DL flux factor and allowing for
a mixture of the hard gluon (6β(1−β)) and the hard quark ( 6
4β(1−β)) densities in the pomeron:
a fraction cgfor hard gluons and cq= 1 −cgfor hard quarks. The overall normalisation of
the POMPYT prediction was left as a free parameter: ΣIP . For this study, the contribution
to the cross sections and to ΣIP from possible soft gluon and soft quark components has been
neglected.
For each value of cg, a one-parameter (ΣIP )χ2-fit to the measured dσ/dηjet(ηmax
had <1.8) was
performed. The results are presented in Fig. 4. The thick solid line represents the value of ΣIP
for the minimum of the χ2-fit for each value of cgand the shaded band represents the 1 σrange
around those minima. For cg= 1 (gluons only) the fit yields ΣIP = 0.5±0.2 with χ2
min = 2.3
for three degrees of freedom, while for cg= 0 (quarks only) the fit yields ΣIP = 2.5±0.9 with
χ2
min = 2.8. The momentum sum rule (ΣIP = 1) is approximately satisfied for 0.2< cg<0.6
(statistical errors only). Note that for this estimate the DL form for the pomeron flux factor
was assumed.
This comparison of cross sections for jet production with a large rapidity gap between data
and model predictions is subject to the following uncertainties:
•The jet cross sections obtained from the Monte Carlo calculations presented here are
leading order calculations. In these calculations, αs(µ2) and the parton densities in the
proton and the photon are evaluated at µ2= ˆp2
T. These computations may be affected by
higher order QCD corrections, which are expected to change mainly the normalisation (K-
factor). The agreement between the PYTHIA calculations of the inclusive jet differential
cross sections and the measurements [25] indicate that in the case of the non-diffractive
contribution the K-factor is close to 1, within an uncertainty of ∼20%. The K-factor in
the case of POMPYT is expected to be similar (with a similar uncertainty), as the same
hard subprocesses are involved in the calculation of jet cross sections.
•The amount of the non-diffractive contribution to the measured cross section was modelled
using PYTHIA with some choices for the proton and photon parton densities. This
contribution is more sensitive to the choice of photon parton densities.
•The uncertainty in the estimation of the contribution from double dissociation.
•The POMPYT model for diffractive hard scattering assumes factorisation of the hard
process with respect to the soft diffractive reaction. The extent to which this assumption is
valid has to be determined experimentally through a detailed comparison of measurements
for different reactions (see next section).
7These calculations give a good description of the inclusive jet differential cross sections (without the large-
rapidity-gap requirement) in the range −1< ηjet <1 [25].
15
•The pomeron flux factors adopted in the various models are based on different assumptions
for the tand xIP dependences which are obtained from data on soft diffractive hadronic
processes. The uncertainty in the procedure used to extract the flux is about 30%.
The differences between the results obtained in each of the studies listed above and the
central values were combined in quadrature to yield the theoretical systematic uncertainties
(not shown in Fig. 4) of the fitted values of ΣIP . These uncertainties were then added in
quadrature with the statistical and systematic uncertainties of the measurements resulting in
the following ranges at the 1 σlevel: 1.4<ΣIP <3.8 for cg= 0 and 0.3<ΣIP <0.9 for cg= 1.
The range in ΣIP assumes the DL convention for the pomeron flux factor. This normalisation
has recently been discussed by Landshoff [38] who concludes that the normalisation is arbitrary
up to a multiplicative factor A. If the normalisation is changed by a factor A, the range of the
momentum sum is given by 1.4/A < ΣIP <3.8/A for cg= 0 and by 0.3/A < ΣIP <0.9/A for
cg= 1.
In summary, the comparison of model predictions with the jet cross section measurements
favours those models where the partonic content of the pomeron has a hard contribution. Given
the uncertainties mentioned above and the DL convention for the normalisation of the pomeron
flux factor, the data can be reproduced by a pomeron whose partonic content varies between a
pure hard quark density with momentum sum given by 1.4<ΣIP <3.8 and a pure hard gluon
density with 0.3<ΣIP <0.9.
7.4 The gluon content of the pomeron
The HERA experiments have recently presented the first measurements of the diffractive struc-
ture function in DIS [9, 10]. The results show that the quark densities in the pomeron have a
hard and a soft contribution. Assuming the DL form for the pomeron flux factor, the DIS data
do not favour a pomeron structure function which simultaneously fulfils the momentum sum
rule and consists exclusively of quarks.
If the pomeron parton densities are universal and describe both DIS and photoproduction
processes, the DIS results together with the photoproduction data further constrain the partonic
content of the pomeron. The measured diffractive structure function in DIS (FD(3)
2(β, Q2, xIP ))
[9, 10] can be used to extract the contribution of the quarks to the momentum sum (ΣIP q (Q2)).
The integral of FD(3)
2over xIP and βis proportional to ΣIP q (Q2):
ZxIP max
xIP min
dxIP Z1
0dβ F D(3)
2(β, Q2, xIP ) = kf·ΣIP q(Q2)·If lux (9)
where Iflux is the integral of the pomeron flux factor over tand over the same region in
xIP , and kfis a number which depends on the number of flavours assumed (5/18 for two
flavours and 2/9 for three flavours). For the left-hand side of Eq. (9), the parametrisation
of FD(3)
2(β, Q2, xIP ) obtained in [10] was used. The integral was performed over the range
6.3·10−4< xIP <10−2of the ZEUS DIS measurements. The DL form for the pomeron flux
factor was used to compute Iflux for the right hand side of Eq. (9). This procedure yields an
estimate of ΣIP q (Q2): 0.32 ±0.05 (0.40 ±0.07) for two (three) flavours. These estimates are
based on a parametrisation of FD(3)
2(β, Q2, xIP ) which was determined in the large βregion
(0.1< β < 0.8) and is assumed to be valid for the entire region 0 < β < 1. In the range of
Q2where the DIS measurements were done, 8 GeV2< Q2<100 GeV2, the pomeron structure
function is approximately independent of Q2and, thus, the estimated ΣIP q (Q2) does not depend
16
upon Q2. It should be noted that the scales at which the parton densities in the pomeron are
probed in DIS, Q2, and in photoproduction, µ2, are comparable. The estimate from DIS
imposes a constraint on the ΣIP −cgplane which, combined with the estimates obtained in the
preceding section, restricts the allowed ranges for ΣIP and the relative contributions of quarks
and gluons (cg). The DIS constraint, which can be written as ΣIP ·(1 −cg) = 0.32 (0.40) for
the two choices of the number of flavours, is included in Fig. 4 (the dark shaded area represents
the uncertainty in this constraint). Combining the estimates from photoproduction (thick solid
line) and DIS yields 0.5<ΣIP <1.1 and 0.35 < cg<0.7 (statistical errors only).
These results are subject to the uncertainties listed at the end of section 7.3. The allowed
range for ΣIP which results from the combination of the DIS and photoproduction measure-
ments was evaluated for each source of systematic uncertainty. Taking into account all the
uncertainties mentioned, the comparison between the DIS and photoproduction measurements
gives 0.4<ΣIP <1.6 for the momentum sum of the pomeron assuming the DL convention for
the flux. If the normalisation of the pomeron flux factor is changed by a multiplicative factor
A, the allowed range of the momentum sum is given by 0.4/A < ΣIP <1.6/A.
It should be noted that the evaluation of the cgrange allowed by the DIS and photoproduction
measurements is not affected by the normalisation of the pomeron flux factor or the uncertainty
on the double dissociation contribution since they cancel out in the comparison8. Taking into
account the remaining uncertainties the combination of the DIS and photoproduction data
gives 0.3< cg<0.8. This result does not depend on the validity of the momentum sum rule
for the pomeron.
8 Summary and conclusions
Measurements of ep cross sections for inclusive jet photoproduction with a large rapidity gap in
ep collisions at √s= 296 GeV using data collected by the ZEUS experiment in 1993 have been
presented. The measured jet cross sections are compared to perturbative QCD calculations of
diffractive hard processes and allow a model dependent determination of the parton content of
the pomeron. The measurements require a contribution from a hard momentum density of the
partons in the pomeron. This result is consistent with the observations of the UA8 Collaboration
made in p¯pcollisions. When the measured jet cross sections are combined with the results on the
diffractive structure function in deep inelastic scattering at HERA, first experimental evidence
for the gluon content of the pomeron is found. This evidence is independent of the normalisation
of the flux of pomerons from the proton and does not rely on assumptions on the momentum
sum of the pomeron. The data indicate that between 30% and 80% of the momentum of the
pomeron carried by partons is due to hard gluons.
Acknowledgements
We thank the DESY Directorate for their strong support and encouragement. The remark-
able achievements of the HERA machine group were essential for the successful completion of
this work and are greatly appreciated. We would like to thank J. Collins, G. Ingelman and G.
Kramer for valuable discussions.
8This cancellation occurs as long as the same pomeron flux factor is used in both DIS and photoproduction.
17
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19
ηjet dσ/dηjet(ηhad
max <1.8)±stat.±syst.±syst. Ejet
T-scale
range (in pb)
(-1,-0.5) 44 ±12 ±8+10
−8
(-0.5,0) 39 ±11 ±5+8
−5
(0,0.5) 37 ±10 ±10 +8
−6
(0.5,1) 16 ±6±7+3
−3
Table 1: Measured differential ep cross section dσ/dηjet(ηhad
max <1.8) for inclusive jet production
for Ejet
T>8 GeV and in the kinematic region Q2≤4 GeV2and 0.2< y < 0.85. The ηjet
ranges used for the measurements are shown. The cross sections are given at the centre of each
ηjet bin. The statistical and systematic errors are also indicated. The systematic uncertainties
associated with the energy scale of the jets are quoted separately. The overall normalisation
uncertainty of 3.3% is not included.
η0
max σ(ηmax < η0
max)±stat.±syst.±syst. Ejet
T-scale
(in pb)
1.0 27.3±5.5±9.9+5.9
−4.5
1.5 51.7±8.5±9.2+10.7
−9.1
1.8 67 ±10 ±12 +13
−11
2.0 98 ±12 ±14 +20
−17
2.2 145 ±15 ±29 +30
−23
2.4 208 ±18 ±43 +40
−34
Table 2: Measured integrated ep cross section σ(ηhad
max < η0
max) for inclusive jet production for
Ejet
T>8 GeV and −1< ηj et <1 in the kinematic region Q2≤4 GeV2and 0.2< y < 0.85. The
statistical and systematic errors are also indicated. The systematic uncertainties associated
with the energy scale of the jets are quoted separately. The overall normalisation uncertainty
of 3.3% is not included.
20
Figure 1: (a) The scatter plot of Mcal
Xversus ηcal
max for the sample of events with at least
one cal jet fulfilling the conditions Ejet
T,cal >6 GeV and −1< ηj et
cal <1; (b) the distribution
of ηcal
max for the events with Mcal
X<30 GeV along with the predictions of PYTHIA (shaded
area) and POMPYT with a hard gluon density in the pomeron (solid line). The predictions
are normalised to the number of data events above and below ηcal
max = 2.5, respectively; (c) the
distribution in Mcal
Xfor the events with ηcal
max <1.8 together with the prediction of POMPYT
with a hard gluon density in the pomeron (solid line) normalised to the number of data events;
(d) the distribution in Wcal for the events with ηcal
max <1.8 and the prediction of POMPYT as
in (c).
21
Figure 2: Measured differential ep cross section dσ/dηjet(ηhad
max <1.8) for inclusive jet produc-
tion for Ejet
T>8 GeV in the kinematic region Q2≤4 GeV2and 0.2< y < 0.85 (dots). The
measurements are not corrected for the contributions from non-diffractive processes and double
dissociation. The inner error bars represent the statistical errors of the data, and the total
error bars show the statistical and systematic errors −not associated with the energy scale of
the jets−added in quadrature. The shaded band displays the uncertainty due to the energy
scale of the jets. For comparison, POMPYT predictions for single diffractive jet production
(e+p→e+p+jet +Xr) using the DL flux factor for direct plus resolved processes for various
parametrisations of the pomeron parton densities (hard gluon, upper solid line; hard quark,
middle solid line; soft gluon, lower solid line) are also shown. The GS-HO photon parton densi-
ties have been used in POMPYT. The contribution from non-diffractive processes is exemplified
by the PYTHIA predictions using MRSD−(GRV-HO) for the proton (photon) parton densities
(dashed line). 22
Figure 3: Measured integrated ep cross section σ(ηhad
max < η0
max) for inclusive jet production for
−1< ηjet <1 and Ejet
T>8 GeV in the kinematic region Q2≤4 GeV2and 0.2< y < 0.85
(dots). The measurements are not corrected for the contributions from non-diffractive processes
and double dissociation. The inner error bars represent the statistical errors of the data, and
the total error bars show the statistical and systematic errors −not associated with the energy
scale of the jets−added in quadrature. The shaded band displays the uncertainty due to the
energy scale of the jets. For comparison, PYTHIA and POMPYT calculations (for the same
conditions as in Fig. 2) are included.
23
Figure 4: The plane of the variables ΣIP (momentum sum) and cg(relative contribution of
hard gluons in the pomeron). The thick solid line displays the minimum for each value of cg
obtained from the χ2fit (the shaded area represents the 1 σband around these minima) to
the measured dσ/dηjet (ηhad
max <1.8) using the predictions of POMPYT. The constraint imposed
in the ΣIP −cgplane by the measurement of the diffractive structure function in DIS (FD(3)
2)
[10] for two choices of the number of flavours (upper dot-dashed line for ΣIP q = 0.40 and lower
dot-dashed line for ΣIP q = 0.32) is also shown. The horizontal dashed line displays the relation
ΣIP = 1.
24
