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arXiv:hep-ex/9810046v1 28 Oct 1998
DESY–98–162
Measurement of Three-jet Distributions in
Photoproduction at HERA
ZEUS Collaboration
Abstract
The cross section for the photoproduction of events containing three jets with a
three-jet invariant mass of M3J >50 GeV has been measured with the ZEUS detec-
tor at HERA. The three-jet angular distributions are inconsistent with a uniform
population of the available phase space but are well described by parton shower
models and O(αα2
s) pQCD calculations. Comparisons with the parton shower model
indicate a strong contribution from initial state radiation as well as a sensitivity to
the effects of colour coherence.
The ZEUS Collaboration
J. Breitweg, S. Chekanov, M. Derrick, D. Krakauer, S. Magill, B. Musgrave, J. Repond,
R. Stanek, R. Yoshida
Argonne National Laboratory, Argonne, IL, USA p
M.C.K. Mattingly
Andrews University, Berrien Springs, MI, USA
G. Abbiendi, F. Anselmo, P. Antonioli, G. Bari, M. Basile, L. Bellagamba, D. Boscherini,
A. Bruni, G. Bruni, G. Cara Romeo, G. Castellini1, L. Cifarelli2, F. Cindolo, A. Contin,
N. Coppola, M. Corradi, S. De Pasquale, P. Giusti, G. Iacobucci, G. Laurenti, G. Levi,
A. Margotti, T. Massam, R. Nania, F. Palmonari, A. Pesci, A. Polini, G. Sartorelli,
Y. Zamora Garcia3, A. Zichichi
University and INFN Bologna, Bologna, Italy f
C. Amelung, A. Bornheim, I. Brock, K. Cob¨oken, J. Crittenden, R. Deffner, M. Eckert,
M. Grothe4, H. Hartmann, K. Heinloth, L. Heinz, E. Hilger, H.-P. Jakob, A. Kappes,
U.F. Katz, R. Kerger, E. Paul, M. Pfeiffer, H. Schnurbusch, A. Weber, H. Wieber
Physikalisches Institut der Universit¨at Bonn, Bonn, Germany c
D.S. Bailey, O. Barret, W.N. Cottingham, B. Foster, R. Hall-Wilton, G.P. Heath,
H.F. Heath, J.D. McFall, D. Piccioni, J. Scott, R.J. Tapper
H.H. Wills Physics Laboratory, University of Bristol, Bristol, U.K. o
M. Capua, A. Mastroberardino, M. Schioppa, G. Susinno
Calabria University, Physics Dept.and INFN, Cosenza, Italy f
H.Y. Jeoung, J.Y. Kim, J.H. Lee, I.T. Lim, K.J. Ma, M.Y. Pac5
Chonnam National University, Kwangju, Korea h
A. Caldwell6, N. Cartiglia, Z. Jing, W. Liu, B. Mellado, J.A. Parsons, S. Ritz7, R. Sacchi,
S. Sampson, F. Sciulli, Q. Zhu
Columbia University, Nevis Labs., Irvington on Hudson, N.Y., USA q
P. Borzemski, J. Chwastowski, A. Eskreys, J. Figiel, K. Klimek, M.B. Przybycie´n, L. Za-
wiejski
Inst. of Nuclear Physics, Cracow, Poland j
L. Adamczyk8, B. Bednarek, K. Jele´n, D. Kisielewska, A.M. Kowal, T. Kowalski,
M. Przybycie´n,
E. Rulikowska-Zar¸ebska, L. Suszycki, J. Zaj¸ac
Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow,
Poland j
Z. Duli´nski, A. Kota´nski
Jagellonian Univ., Dept. of Physics, Cracow, Poland k
L.A.T. Bauerdick, U. Behrens, H. Beier9, J.K. Bienlein, C. Burgard, K. Desler, G. Drews,
U. Fricke, F. Goebel, P. G¨ottlicher, R. Graciani, T. Haas, W. Hain, G.F. Hartner,
D. Hasell10, K. Hebbel, K.F. Johnson11, M. Kasemann12, W. Koch, U. K¨otz, H. Kowal-
ski, L. Lindemann, B. L¨ohr, M. Mart´ınez, J. Milewski13, M. Milite, T. Monteiro14,
D. Notz, A. Pellegrino, F. Pelucchi, K. Piotrzkowski, M. Rohde, J. Rold´an15, J.J. Ryan16,
P.R.B. Saull, A.A. Savin, U. Schneekloth, O. Schwarzer, F. Selonke, M. Sievers, S. Ston-
jek, B. Surrow14, E. Tassi, D. Westphal17, G. Wolf, U. Wollmer, C. Youngman, W. Zeuner
Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
I
B.D. Burow18, C. Coldewey, H.J. Grabosch, A. Lopez-Duran Viani, A. Meyer, K. M¨onig,
S. Schlenstedt, P.B. Straub
DESY-IfH Zeuthen, Zeuthen, Germany
G. Barbagli, E. Gallo, P. Pelfer
University and INFN, Florence, Italy f
G. Maccarrone, L. Votano
INFN, Laboratori Nazionali di Frascati, Frascati, Italy f
A. Bamberger, S. Eisenhardt, P. Markun, H. Raach, S. W¨olfle
Fakult¨at f¨ur Physik der Universit¨at Freiburg i.Br., Freiburg i.Br., Germany c
N.H. Brook, P.J. Bussey, A.T. Doyle19, S.W. Lee, N. Macdonald, G.J. McCance, D.H. Saxon,
L.E. Sinclair, I.O. Skillicorn, E. Strickland, R. Waugh
Dept. of Physics and Astronomy, University of Glasgow, Glasgow, U.K. o
I. Bohnet, N. Gendner, U. Holm, A. Meyer-Larsen, H. Salehi, K. Wick
Hamburg University, I. Institute of Exp. Physics, Hamburg, Germany c
A. Garfagnini, I. Gialas20, L.K. Gladilin21, D. K¸cira22, R. Klanner, E. Lohrmann,
G. Poelz, F. Zetsche
Hamburg University, II. Institute of Exp. Physics, Hamburg, Germany c
T.C. Bacon, J.E. Cole, G. Howell, L. Lamberti23, K.R. Long, D.B. Miller, A. Prinias24,
J.K. Sedgbeer, D. Sideris, A.D. Tapper, R. Walker
Imperial College London, High Energy Nuclear Physics Group, London, U.K. o
U. Mallik, S.M. Wang
University of Iowa, Physics and Astronomy Dept., Iowa City, USA p
P. Cloth, D. Filges
Forschungszentrum J¨ulich, Institut f¨ur Kernphysik, J¨ulich, Germany
T. Ishii, M. Kuze, I. Suzuki25, K. Tokushuku26, S. Yamada, K. Yamauchi, Y. Yamazaki
Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan g
S.H. Ahn, S.H. An, S.J. Hong, S.B. Lee, S.W. Nam27 , S.K. Park
Korea University, Seoul, Korea h
H. Lim, I.H. Park, D. Son
Kyungpook National University, Taegu, Korea h
F. Barreiro, J.P. Fern´andez, G. Garc´ıa, C. Glasman28, J.M. Hern´andez29, L. Labarga,
J. del Peso, J. Puga, I. Redondo30, J. Terr´on
Univer. Aut´onoma Madrid, Depto de F´ısica Te´orica, Madrid, Spain n
F. Corriveau, D.S. Hanna, J. Hartmann31, W.N. Murray16, A. Ochs, S. Padhi, C. Pin-
ciuc, M. Riveline, D.G. Stairs, M. St-Laurent
McGill University, Dept. of Physics, Montr´eal, Qu´ebec, Canada a,b
T. Tsurugai
Meiji Gakuin University, Faculty of General Education, Yokohama, Japan
V. Bashkirov, B.A. Dolgoshein, A. Stifutkin
Moscow Engineering Physics Institute, Moscow, Russia l
G.L. Bashindzhagyan, P.F. Ermolov, Yu.A. Golubkov, L.A. Khein, N.A. Korotkova,
I.A. Korzhavina, V.A. Kuzmin, O.Yu. Lukina, A.S. Proskuryakov, L.M. Shcheglova32,
A.N. Solomin32, S.A. Zotkin
Moscow State University, Institute of Nuclear Physics, Moscow, Russia m
II
C. Bokel, M. Botje, N. Br¨ummer, J. Engelen, E. Koffeman, P. Kooijman, A. van Sighem,
H. Tiecke, N. Tuning, W. Verkerke, J. Vossebeld, L. Wiggers, E. de Wolf
NIKHEF and University of Amsterdam, Amsterdam, Netherlands i
D. Acosta33, B. Bylsma, L.S. Durkin, J. Gilmore, C.M. Ginsburg, C.L. Kim, T.Y. Ling,
P. Nylander
Ohio State University, Physics Department, Columbus, Ohio, USA p
H.E. Blaikley, R.J. Cashmore, A.M. Cooper-Sarkar, R.C.E. Devenish, J.K. Edmonds,
J. Große-Knetter34, N. Harnew, T. Matsushita, V.A. Noyes35, A. Quadt, O. Ruske,
M.R. Sutton, R. Walczak, D.S. Waters
Department of Physics, University of Oxford, Oxford, U.K. o
A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, U. Dosselli, S. Limentani, M. Morandin,
M. Posocco, L. Stanco, R. Stroili, C. Voci
Dipartimento di Fisica dell’ Universit`a and INFN, Padova, Italy f
L. Iannotti36, B.Y. Oh, J.R. Okrasi´nski, W.S. Toothacker, J.J. Whitmore
Pennsylvania State University, Dept. of Physics, University Park, PA, USA q
Y. Iga
Polytechnic University, Sagamihara, Japan g
G. D’Agostini, G. Marini, A. Nigro, M. Raso
Dipartimento di Fisica, Univ. ’La Sapienza’ and INFN, Rome, Italy f
C. Cormack, J.C. Hart, N.A. McCubbin, T.P. Shah
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. o
D. Epperson, C. Heusch, H.F.-W. Sadrozinski, A. Seiden, R. Wichmann, D.C. Williams
University of California, Santa Cruz, CA, USA p
N. Pavel
Fachbereich Physik der Universit¨at-Gesamthochschule Siegen, Germany c
H. Abramowicz37, G. Briskin38, S. Dagan39, S. Kananov39, A. Levy39
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel-Aviv
University,
Tel-Aviv, Israel e
T. Abe, T. Fusayasu, M. Inuzuka, K. Nagano, K. Umemori, T. Yamashita
Department of Physics, University of Tokyo, Tokyo, Japan g
R. Hamatsu, T. Hirose, K. Homma40, S. Kitamura41, T. Nishimura
Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan g
M. Arneodo, R. Cirio, M. Costa, M.I. Ferrero, S. Maselli, V. Monaco, C. Peroni,
M.C. Petrucci, M. Ruspa, A. Solano, A. Staiano
Universit`a 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, C.-P. Fagerstroem, R. Galea, T. Koop, G.M. Levman, J.F. Martin, R.S. Orr,
S. Polenz, A. Sabetfakhri, D. Simmons
University of Toronto, Dept. of Physics, Toronto, Ont., Canada a
J.M. Butterworth, C.D. Catterall, M.E. Hayes, E.A. Heaphy, T.W. Jones, J.B. Lane,
M. Wing
University College London, Physics and Astronomy Dept., London, U.K. o
III
J. Ciborowski, G. Grzelak42, R.J. Nowak, J.M. Pawlak, R. Pawlak, B. Smalska, T. Tymie-
niecka,
A.K. Wr´oblewski, J.A. Zakrzewski, A.F. ˙
Zarnecki
Warsaw University, Institute of Experimental Physics, Warsaw, Poland j
M. Adamus, T. Gadaj
Institute for Nuclear Studies, Warsaw, Poland j
O. Deppe, Y. Eisenberg39 , D. Hochman, U. Karshon39
Weizmann Institute, Department of Particle Physics, Rehovot, Israel d
W.F. Badgett, D. Chapin, R. Cross, C. Foudas, S. Mattingly, D.D. Reeder, W.H. Smith,
A. Vaiciulis, T. Wildschek, M. Wodarczyk
University of Wisconsin, Dept. of Physics, Madison, WI, USA p
A. Deshpande, S. Dhawan, V.W. Hughes
Yale University, Department of Physics, New Haven, CT, USA p
S. Bhadra, W.R. Frisken, M. Khakzad, S. Menary, W.B. Schmidke
York University, Dept. of Physics, North York, Ont., Canada a
IV
1also at IROE Florence, Italy
2now at Univ. of Salerno and INFN Napoli, Italy
3supported by Worldlab, Lausanne, Switzerland
4now at University of California, Santa Cruz, USA
5now at Dongshin University, Naju, Korea
6also at DESY
7Alfred P. Sloan Foundation Fellow
8supported by the Polish State Committee for Scientific Research, grant No. 2P03B14912
9now at Innosoft, Munich, Germany
10 now at Massachusetts Institute of Technology, Cambridge, MA, USA
11 visitor from Florida State University
12 now at Fermilab, Batavia, IL, USA
13 now at ATM, Warsaw, Poland
14 now at CERN
15 now at IFIC, Valencia, Spain
16 now a self-employed consultant
17 now at Bayer A.G., Leverkusen, Germany
18 now an independent researcher in computing
19 also at DESY and Alexander von Humboldt Fellow at University of Hamburg
20 visitor of Univ. of Crete, Greece, partially supported by DAAD, Bonn - Kz. A/98/16764
21 on leave from MSU, supported by the GIF, contract I-0444-176.07/95
22 supported by DAAD, Bonn - Kz. A/98/12712
23 supported by an EC fellowship
24 PPARC Post-doctoral fellow
25 now at Osaka Univ., Osaka, Japan
26 also at University of Tokyo
27 now at Wayne State University, Detroit
28 supported by an EC fellowship number ERBFMBICT 972523
29 now at HERA-B/DESY supported by an EC fellowship No.ERBFMBICT 982981
30 supported by the Comunidad Autonoma de Madrid
31 now at debis Systemhaus, Bonn, Germany
32 partially supported by the Foundation for German-Russian Collaboration DFG-RFBR
(grant no. 436 RUS 113/248/3 and no. 436 RUS 113/248/2)
33 now at University of Florida, Gainesville, FL, USA
34 supported by the Feodor Lynen Program of the Alexander von Humboldt foundation
35 Glasstone Fellow
36 partly supported by Tel Aviv University
37 an Alexander von Humboldt Fellow at University of Hamburg
38 now at Brown University, Providence, RI, USA
39 supported by a MINERVA Fellowship
40 now at ICEPP, Univ. of Tokyo, Tokyo, Japan
41 present address: Tokyo Metropolitan University of Health Sciences, Tokyo 116-8551,
Japan
42 supported by the Polish State Committee for Scientific Research, grant No. 2P03B09308
V
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 Education and Science, Research and
Technology (BMBF), under contract numbers 057BN19P, 057FR19P, 057HH19P,
057HH29P, 057SI75I
dsupported by the MINERVA Gesellschaft f¨ur Forschung GmbH, the German Israeli
Foundation, and by the Israel Ministry of Science
esupported by the German-Israeli Foundation, the Israel Science Foundation, the
U.S.-Israel Binational Science Foundation, and by the Israel Ministry of Science
fsupported by the Italian National Institute for Nuclear Physics (INFN)
gsupported by the Japanese Ministry of Education, Science and Culture (the Mon-
busho) 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. 115/E-
343/SPUB/P03/002/97, 2P03B10512, 2P03B10612, 2P03B14212, 2P03B10412,
2P03B05315
ksupported by the Polish State Committee for Scientific Research (grant No.
2P03B08614) and Foundation for Polish-German Collaboration
lpartially supported by the German Federal Ministry for Education and Science,
Research and Technology (BMBF)
msupported by the Fund for Fundamental Research of Russian Ministry for Science
and Education and by the German Federal Ministry for Education and Science,
Research and Technology (BMBF)
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
VI
1 Introduction
Calculations of photoproduction processes beyond leading order in perturbative QCD
(pQCD) predict a rich variety of phenoma. Some of these can be studied in final states
containing more than two jets. Also, the study of multijet production provides sensitive
tests of extensions to fixed order theories such as parton shower models. The properties
of multijet events in hadronic collisions have been the subject of earlier studies [1, 2, 3].
Dijet photoproduction accompanied by a third, low transverse energy cluster has been
studied by ZEUS [4]. In this paper, cross sections and angular distributions for three or
more moderately high transverse energy jets in photoproduction are presented for the
first time.
Apart from the azimuthal orientation, a system of two massless jets can be completely
specified in its centre-of-mass (CM) frame by the two-jet invariant mass, M2J and cos ϑ∗,
where ϑ∗is the angle between the jet axis and the beam-line. The distribution in cos ϑ∗
for photoproduction of dijets is forward-backward peaked with sensitivity to the spin of
the exchanged fermion or boson [5].
A set of observables describing events with an arbitrary number of jets has been proposed
which spans the multijet parameter space, facilitates the interpretation of the data within
pQCD and reduces to M2J and cos ϑ∗for the dijet case [6]. For three massless jets there
are five parameters which are defined in terms of the energies, Ei, and momentum
three-vectors, ~pi, of the jets in the three-jet CM frame and ~pB, the beam direction.1
The jets are numbered, 3, 4 and 5 in order of decreasing energy as illustrated in the
schematic drawing, Fig. 1. The parameters are: the three-jet invariant mass, M3J ; the
energy-sharing quantities X3and X4,
Xi≡2Ei
M3J
; (1)
the cosine of the scattering angle of the highest energy jet with respect to the beam,
cos ϑ3≡~pB·~p3
|~pB||~p3|; (2)
and ψ3, the angle between the plane containing the highest energy jet and the beam
and the plane containing the three jets. The latter is defined by
cos ψ3≡(~p3×~pB)·(~p4×~p5)
|~p3×~pB||~p4×~p5|.(3)
The definition of the angles ϑ3and ψ3is illustrated in Fig. 1. Since ϑ3involves only the
highest energy jet, the distribution of cos ϑ3in three-jet processes may be expected to
follow closely the distribution of cos ϑ∗in dijet events. The ψ3angle, on the other hand,
reflects the orientation of the lowest energy jet. In the case where this jet arises from
initial-state radiation, the coherence property of QCD will tend to orient the third jet
close to the incoming proton or photon direction. The two planes shown in Fig. 1 will
therefore tend to coincide leading to a ψ3distribution which peaks toward 0 and π.
1We take the nominal beam direction as ~pB= ˆz. In the ZEUS coordinate system the z-axis is
defined to be in the proton beam direction. Polar angles, ϑ, are measured with respect to the z-axis
and pseudorapidity is defined as η=−ln(tan ϑ
2).
1
This paper presents the three-jet inclusive cross section in photoproduction and the
distribution of the three-jet events with respect to M3J,X3,X4, cos ϑ3and ψ3. This
work was performed with the ZEUS detector using 16 pb−1of data delivered by HERA
in 1995 and 1996.
2 Experimental Conditions
In this period HERA operated with protons of energy Ep= 820 GeV and positrons of
energy Ee= 27.5 GeV. The ZEUS detector is described in detail in [7, 8]. The main
components used in the present analysis are the central tracking system positioned
in a 1.43 T solenoidal magnetic field and the uranium-scintillator sampling calorimeter
(CAL). The tracking system was used to establish an interaction vertex. Energy deposits
in the CAL were used in the jet finding and to measure jet energies. The CAL is
hermetic and consists of 5918 cells each read out by two photomultiplier tubes. Under
test beam conditions the CAL has energy resolutions of 18%/pE(GeV) for electrons
and 35%/pE(GeV) for hadrons. Jet energies were corrected for the energy lost in
inactive material in front of the CAL which is typically about one radiation length
(see Section 3.4). The effects of uranium noise were minimized by discarding cells
in the electromagnetic or hadronic sections if they had energy deposits of less than
60 MeV or 110 MeV, respectively. The luminosity was measured from the rate of the
bremsstrahlung process e+p→e+pγ. A three-level trigger was used to select events
online [8, 9].
3 Analysis
3.1 Offline Cleaning Cuts
To reject residual beam-gas and cosmic ray backgrounds, tighter cuts using the final
z-vertex position, other tracking information and timing information are applied of-
fline. Neutral current deep inelastic scattering (DIS) events with an identified scattered
positron candidate in the CAL are removed from the sample as described in detail else-
where [5, 9]. Charged current DIS events are rejected by a cut on the missing transverse
momentum measured in the CAL. Finally, a restriction is made on the range of y, the
fraction of the positron’s energy carried by the incoming photon. The requirement,
0.15 < yJB <0.65 is made where yJB is an estimator of ywhich is determined from the
CAL energy deposits according to the Jacquet-Blondel method [10]. This requirement
corresponds to accepting events in the range 0.2< y < 0.8. These cuts restrict photon
virtualities to less than about 1 GeV2with a median of around 10−3GeV2.
3.2 Jet Finding
Jets are found using the KTCLUS [11] finder in the inclusive mode [12]. This is a
clustering algorithm which combines objects with small relative transverse energy into
jets. It is invariant under Lorentz boosts along the beam axis and is ideal for the study of
multijet processes since it suffers from no ambiguities due to overlapping jets. Once the
jets are determined, their transverse energy, pseudorapidity and azimuth are calculated
according to the Snowmass convention [13]; Ejet
T=PiETi,ηjet = (1/Ejet
T)PiETiηiand
2
ϕjet = (1/Ejet
T)PiETiϕi, where the sum runs over all objects assigned to the jet. The
energies and three-vectors of the jets are then determined from the Ejet
T,ηjet and ϕjet.
The objects input to the jet algorithm may be hadrons in a simulated hadronic final
state, the final state partons of a pQCD calculation, or energy deposits in the detector.
In the following, a jet quantity constructed from CAL cells with no energy correction
has the superscript “CAL” while a jet quantity constructed from CAL cells and then
subjected to a correction for energy loss in inactive material has the superscript “COR”.
There is no additional superscript for quantities referring to jets of final state partons
or hadrons.
3.3 Monte Carlo Event Simulation
The response of the detector to jets and the acceptance and smearing of the measured
distributions are determined using samples of events generated from Monte Carlo (MC)
simulations. We have used the programs PYTHIA 5.7 [14] and HERWIG 5.9 [15]
which implement the leading order matrix elements followed by parton showers. In these
simulations multijet events can originate through this parton shower mechanism. Colour
coherence in the parton shower is treated differently in the two models. In PYTHIA,
parton showers are evolved in the squared mass of the branching parton with colour
coherence effects implemented as a restriction on the opening angle of the radiation. In
contrast, in HERWIG a parton shower evolution variable is chosen which automatically
limits the branching to an angular ordered region. For both models, leading order direct
and resolved processes are generated separately and combined according to the ratio of
their generated cross sections. For the uncorrected distributions presented in this section
the minimum transverse momentum of the partonic hard scatter (ˆpmin
T) was set to 4 GeV.
In Section 4, corrected cross sections are presented and compared with the predictions
from HERWIG and PYTHIA with ˆpmin
T= 8 GeV (our conclusions are insensitive to this
parameter). The photon parton densities used were GRV LO [16] and the proton parton
densities were CTEQ4 LO [17]. In the HERWIG simulation of the resolved processes,
multiparton interactions have been included (these are not important in this kinematic
regime, as discussed in Section 4).
The quality of these simulations is illustrated in Fig. 2 which shows the transverse
energy flow around the jet axes. In this comparison the events have two jets with
Ejet CAL
T>5 GeV and a third jet with Ejet CAL
T>4 GeV and jet pseudorapidities
|ηjet CAL|<2.4. The additional requirements on the CM quantities, MCAL
3J >42 GeV,
|cos ϑ3|CAL <0.8 and XCAL
3<0.95, have also been applied. These conditions represent
those on the selected events (described in Section 3.5) to a good approximation. The
jets have a narrow core with little transverse energy in the pedestal, except for the
lowest Ejet CAL
Tjet where significant contribution to the “pedestal” from the other two
jets in the event would be expected. In the ∆ϕprofiles of the two highest Ejet CAL
T
jets, the peaks near ±πindicate that these are roughly back-to-back. The PYTHIA
and HERWIG event samples were passed through a detailed simulation of the ZEUS
detector and the same selection criteria as for the data were applied. The MC samples
provide a reasonable description of the energy flow in these three-jet events. HERWIG
generates somewhat too little transverse energy in regions far from the jet core in ϕfor
the lowest transverse energy jet, while PYTHIA slightly overestimates the transverse
energy in the core of this jet. These models are also able to reproduce satisfactorily the
3
yJB distribution for the three-jet events, the lab-frame Ejet CAL
Tand ηjet CAL distributions
as well as the transverse and longitudinal components of the boost from the lab-frame
to the CM-frame (not shown).
3.4 Jet Energy Corrections
Jets of hadrons lose about 15% of their transverse energy when passing through inactive
material before impinging on the CAL. This energy loss has been corrected using the
MC samples [9, 18]. The KTCLUS algorithm was applied to the hadronic final state
and from comparison of these hadron jets with the CAL jets obtained after the detector
simulation, correction factors were determined as a function of Ejet CAL
Tand ηjet CAL.
After applying these corrections the average shift in Ejet
Twithin the MC simulation is
less than 2% and the Ejet
Tresolution is 14%. This may be compared with the global
jet energy scale uncertainty of ±5% [9]. The correction also reduces the shift in the
reconstruction of M3J from 16% to less than 1%. After these corrections for jet energy
loss the average resolutions are 8% in M3J, 0.03 units in X3, 0.05 units in X4, 0.03 units
in cos ϑ3and 0.1 radians in ψ3and the distributions are well centred on their expected
values.
3.5 Event Selection
After the jet energy correction the events are required to have at least two jets with
Ejet COR
T>6 GeV, a third jet with Ejet COR
T>5 GeV and jet pseudorapidities in the
range |ηjet COR|<2.4. The requirement of high transverse energy for the jets ensures
that the process should be calculable within pQCD. However, it introduces a bias in the
angular distributions by excluding jets that are produced close to the beam-line. We
make the additional requirements MCOR
3J >50 GeV, |cos ϑ3|COR <0.8 and XCOR
3<0.95
to minimize such a bias. After these cuts the mean transverse energy of the highest,
second-highest and third-highest transverse energy jet is about 20 GeV, 15 GeV and
10 GeV. From 16 pb−1of data, 2821 events are selected. Around 15% of these have a
fourth jet with Ejet COR
T>5 GeV, in agreement with the prediction of the parton shower
models. Backgrounds from beam gas and cosmic ray events, determined from unpaired
bunch crossings, are negligible. The DIS contamination, determined using Monte Carlo
techniques, is around 1% and neglected.
3.6 Acceptance Correction
The MC samples have been used to correct the data for the inefficiencies of the trig-
ger and the offline selection cuts and for migrations caused by detector effects. The
correction factors are calculated as the ratio Ntrue/Nrec in each measured bin where
Ntrue is the number of events generated in the bin and Nrec is the number of events
reconstructed in the bin after detector smearing and all experimental cuts. The final
bin-by-bin correction factors lie between about 0.7 and 1.3, the dominant effect arising
from migrations across the M3J threshold. The cross sections were determined using the
corrections obtained with PYTHIA.
4
3.7 Systematic Uncertainties
A detailed study of the sources contributing to the systematic uncertainties of the mea-
surements was performed [19]. Only the significant sources are listed here.
•The acceptance correction was performed using HERWIG instead of PYTHIA.
The uncertainties associated with the model are typically around 20% and this
forms the dominant uncertainty on the area-normalized distributions.
•The absolute energy scale of the detector response to jets with Ejet
T>5 GeV is
known to ±5% [9]. This leads to an uncertainty of 15 to 20% on the cross section.
This is the dominant systematic uncertainty on the normalization of the cross
section but as this uncertainty is highly correlated between bins it has a negligible
affect on the area-normalized distributions.
•The results were recalculated allowing for fluctuations from outside the selected
kinematic region by relaxing each of the cut parameters by 1 σof the resolution.
This effect is typically 5%.
The systematic uncertainties have been added in quadrature to the statistical errors and
this is shown as the outer error bars in the figures, with the exception of the absolute
jet energy scale uncertainty which is shown as a shaded band for the cross sections. An
overall normalization uncertainty of 1.5% from the luminosity determination has not
been included.
4 Results and Discussion
The three-jet inclusive cross section is presented for events having at least two jets with
Ejet
T>6 GeV and a third jet with Ejet
T>5 GeV where the jets satisfy |ηjet|<2.4.
This cross section refers to jets in the hadronic final state. To minimize the effects of
these jet cuts on the distributions of physical interest, the requirements M3J >50 GeV,
|cos ϑ3|<0.8 and X3<0.95 have been imposed. The cross section is presented for
photon-proton CM energies Wγp in the range 134 GeV< Wγ p <269 GeV and the
negative square of the invariant mass of the incoming photon extending to 1 GeV2. The
cross section is σ= 162 ±4(stat.)+16
−6(sys.)+32
−25(energy scale) pb.
A study using the PYTHIA MC indicates that hadronization effects are small (∼5%),
and flat in the distributions presented here [19]. The measurements are directly con-
fronted with O(αα2
s) pQCD calculations from two groups of authors [20, 21, 22]. The
CTEQ4 LO [17] proton parton densities and the GRV LO [16] photon parton densities
have been used in these calculations. The renormalization and factorization scales, µ,
have been chosen to equal Emax
T, where Emax
Tis the largest of the Ejet
Tvalues of the
three jets. αswas calculated at one loop with Λ(5)
MS = 181 MeV. As the calculations are
leading order for three-jet production the normalization uncertainty due to the choice
of µis expected to be large. An uncertainty of a factor of two in the cross section for
variation of µbetween Emax
T/2 and 2Emax
Thas been quoted [22].
The three-jet invariant mass distribution is shown in Fig. 3. The cross section falls
approximately exponentially from the threshold value at 50 GeV to the highest measured
value, around 150 GeV. The data are compared with the two O(αα2
s) pQCD calculations.
5
These are in good agreement with the data, even though the calculations are leading
order for this process. The M3J distributions predicted by the parton shower models
PYTHIA and HERWIG are also in agreement with the data in shape although the
predicted cross sections are too low by 30-40%.
The distributions of the fraction of the available energy taken by the highest and second-
highest energy jets are shown in Figs. 4 (a) and (b), respectively. Here the prediction for
three jets uniformly distributed in the available phase space (i.e. with a constant matrix
element) is also shown as the dotted curve. The parton shower models give a reasonable
description of these energy sharing quantities. The pQCD calculations (overlapping)
are in excellent agreement with these distributions. However, the similarity between the
measured distributions and the three-body phase space prediction indicates that these
distributions have little sensitivity to the pQCD matrix elements.
In Figs. 4 (c) and (d) the cos ϑ3and ψ3distributions are shown. These angular dis-
tributions are dramatically different from the distributions obtained from phase space,
demonstrating that these quantities are sensitive to the pQCD matrix elements. The
cos ϑ3distribution has forward and backward peaks, as expected. The O(αα2
s) pQCD as
well as the parton shower calculations, which take into account the dependence of this
distribution on the spin of the exchanged quark or gluon, are in good agreement with the
data. The jet algorithm and minimum Ejet
Trequirements deplete the data near ψ3∼0
and πas indicated by the shape of the phase space curve in Fig. 4(d). With this taken
into account, the data indicate a strong tendency for the three-jet plane to lie near
the plane containing the beam and the highest energy jet. This effect is reproduced
in the O(αα2
s) matrix element calculations. It is interesting that the parton shower
Monte Carlo programs PYTHIA and HERWIG are also able to provide a reasonable
representation of the shape of the ψ3distribution.
Including a simulation of multiparton interactions in the parton shower programs has
been found to improve significantly the description of low Ejet
Tphotoproduction [9]. In
the present study the sensitivity to multiparton interactions has been investigated using
both PYTHIA and HERWIG [19]. In neither case do secondary parton interactions
cause a significant difference in the three-jet cross section in this kinematic regime, or in
the angular distributions generated. It appears therefore that the third jet arises here
from the parton shower and is not due to a second hard scatter.
Within the parton shower prescription, it is possible to separate the contributions of
initial and final state parton showers. In Fig. 5(a) the three-jet cross section as a function
of ψ3is shown and compared with the predictions of PYTHIA. The MC events have
been separated into three samples; initial-state radiation only, final-state radiation only,
and default PYTHIA which includes the interference of these two. The area-normalized
distributions of ψ3are compared with these models in Fig. 5(b). Both the normalization
and shape of these distributions indicate that the observed three-jet production occurs
predominantly through initial state radiation with the final state radiation making a
small contribution.
The QCD phenomenon of colour coherence is implemented in the PYTHIA parton
shower model by prohibiting radiation into certain angular regions which are determined
by the colour flow of the primary scatter. It is possible within this model to switch
QCD colour coherence on and off. Figs. 5(c) and (d) again show the cross section and
the area-normalized distribution with respect to ψ3compared with the HERWIG and
PYTHIA predictions. The data lie above these predictions as previously mentioned,
6
however this discrepancy is not regarded as significant in view of the limited order
of the calculation. The predictions do reproduce reasonably well the shape of the ψ3
distribution. This is not the case if the simulation is done with colour coherence switched
off. The incoherent PYTHIA prediction is relatively flat in ψ3. Coherence reduces the
phase space available for large angle emissions as indicated by the drop in cross section
around ψ3∼π/2 for default PYTHIA. Colour coherence in the parton shower is needed
to describe the shape of this distribution. QCD colour coherence seems to be a stronger
effect in HERWIG than in PYTHIA however the present data are not precise enough
to discriminate between these two simulations.
5 Summary
The inclusive cross section for the photoproduction of three jets has been measured
by the ZEUS collaboration at HERA. O(αα2
s) pQCD calculations are able to describe
the cross section dσ/dM3J, while parton shower models underestimate the cross section
but are consistent in shape with the M3J distribution. The angular distributions of
the three jets are inconsistent with a uniform population of the available phase space
but are well described by both fixed-order pQCD calculations and parton shower Monte
Carlo models. Simulation of multiparton interactions does not help to describe the
data in this kinematic regime. Within the parton shower model the three-jet events
are found to occur predominantly due to initial state radiation, and the fundamental
QCD phenomenon of colour coherence is seen to have an important effect on the angular
distribution of the third jet.
Acknowledgements
The strong support and encouragement of the DESY Directorate have been invaluable,
and we are much indebted to the HERA machine group for their inventiveness and
diligent efforts. The design, construction and installation of the ZEUS detector have
been made possible by the ingenuity and dedicated efforts of many people from inside
DESY and from the home institutes who are not listed as authors. Their contributions
are acknowledged with great appreciation. We warmly thank B. Harris, M. Klasen and
J. Owens for providing their theoretical calculations.
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[15] G. Marchesini et al., Comp. Phys. Comm. 67 (1992) 465.
[16] M. Gl¨uck, E. Reya and A. Vogt, Phys. Rev. D46 (1992) 1973.
[17] CTEQ Collab., H. L. Lai et al., Phys. Rev. D55 (1997) 1280.
[18] ZEUS Collab., J. Breitweg et al., Eur. Phys. J. C4(1998) 591.
[19] E. Strickland, Ph.D. Thesis, University of Glasgow (1998).
[20] B.W. Harris and J.F. Owens, Phys. Rev. D56 (1997) 4007 and private communi-
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[22] M. Klasen, hep-ph/9808223.
8
.4 53
P
B
E > E > E
ϑ
THREE-BODY REST FRAME
1 + 2 3 + 4 + 5
3
3
3
5
4
ψ
Figure 1: Illustration of the angles ϑ3and ψ3for a particular three-jet configuration.
The beam direction is indicated by ~pB.
9
Figure 2: Uncorrected transverse energy flow with respect to the jet axis in the labora-
tory frame for three-jet events in order of Ejet CAL
T. On the left the uncorrected energy
flow with respect to ϕis shown for cells within one unit of ηof the jet axis while on the
right the profile with respect to ηis shown for cells within one radian of ϕof the jet
axis. The data are shown as black dots while the PYTHIA and HERWIG predictions
are shown by the solid and dashed histograms, respectively.
10
.
Figure 3: The measured three-jet cross section with respect to the three-jet invariant
mass, dσ/dM3J, is shown by the black dots where the inner error bar shows the statis-
tical error and the outer error bar is the sum in quadrature of the statistical error and
the systematic uncertainty. The jet energy-scale uncertainty, which is highly correlated
between bins, is shown separately as the shaded band. O(αα2
s) pQCD calculations by
Harris & Owens and Klasen are shown by the thick solid and dot-dashed lines, respec-
tively. The thin solid and dashed histograms show the predictions from two different
parton shower models, PYTHIA and HERWIG.
11
.
Figure 4: The distributions of the energy sharing quantities, X3and X4, are shown by
the black dots in (a) and (b), respectively, and the distributions of the cos ϑ3and ψ3are
shown in (c) and (d). Inner error bars show the statistical error and the outer error bars
show the quadratic sum of this with the systematic uncertainty. The fixed-order pQCD
predictions are shown by the thick solid and dot-dashed lines and the parton shower
model predictions are shown by the thin solid and dashed histograms. The phase space
distribution of three jets is indicated by the dotted line.
12
.
Figure 5: The measured cross section dσ/dψ3is shown in (a) and (c) and the area-
normalized distribution of ψ3is shown in (b) and (d). The error bars are as described
previously with the correlated systematic uncertainty due to the jet energy-scale shown
as the shaded band in (a) and (c). The solid histogram shows the default PYTHIA
prediction. In (a) and (b) the dashed and dot-dashed histograms show the predictions
from PYTHIA with final state radiation switched off and with initial state radiation
switched off. In (c) and (d) the dashed and dot-dashed histograms show the predictions
of HERWIG and of PYTHIA with colour coherence switched off.
13