Eur. Phys. J. C 52, 515–530 (2007) THE EUROPEANPHYSICAL JOURNAL C

DOI 10.1140/epjc/s10052-007-0418-0

Regular Article – Experimental Physics

Forward-jet production in deep inelastic ep scattering at HERAThe ZEUS Collaboration

S. Chekanov1,a, M. Derrick1, S. Magill1, B. Musgrave1, D. Nicholass1,54, J. Repond1, R. Yoshida1,M.C.K. Mattingly2, M. Jechow3, N. Pavel3,†, A.G. Yagues Molina3, S. Antonelli4, P. Antonioli4, G. Bari4,M. Basile4, L. Bellagamba4, M. Bindi4, D. Boscherini4, A. Bruni4, G. Bruni4, L. Cifarelli4, F. Cindolo4, A. Contin4,M. Corradi4, S. De Pasquale4, G. Iacobucci4, A. Margotti4, R. Nania4, A. Polini4, G. Sartorelli4, A. Zichichi4,D. Bartsch5, I. Brock5, H. Hartmann5, E. Hilger5, H.-P. Jakob5, M. Jungst5, O.M. Kind5,55, A.E. Nuncio-Quiroz5,E. Paul5,b, R. Renner5,c, U. Samson5, V. Schonberg5, R. Shehzadi5, M. Wlasenko5, N.H. Brook6, G.P. Heath6,J.D. Morris6, M. Capua7, S. Fazio7, A. Mastroberardino7, M. Schioppa7, G. Susinno7, E. Tassi7, J.Y. Kim8,d,K.J. Ma8,e, Z.A. Ibrahim9, B. Kamaluddin9, W.A.T. Wan Abdullah9, Y. Ning10, Z. Ren10, F. Sciulli10,J. Chwastowski11, A. Eskreys11, J. Figiel11, A. Galas11, M. Gil11, K. Olkiewicz11, P. Stopa11, L. Zawiejski11,L. Adamczyk12, T. Bo�ld12, I. Grabowska-Bo�ld12, D. Kisielewska12, J. �Lukasik12, M. Przybycien12, L. Suszycki12,A. Kotanski13,f, W. S�lominski13,g, V. Adler14,56, U. Behrens14, I. Bloch14, C. Blohm14, A. Bonato14, K. Borras14,R. Ciesielski14, N. Coppola14, A. Dossanov14, V. Drugakov14, J. Fourletova14, A. Geiser14, D. Gladkov14,P. Gottlicher14,57, J. Grebenyuk14, I. Gregor14, T. Haas14, W. Hain14, C. Horn14,58, A. Huttmann14, B. Kahle14,I.I. Katkov14, U. Klein14,59, U. Kotz14, H. Kowalski14, E. Lobodzinska14, B. Lohr14, R. Mankel14,I.-A. Melzer-Pellmann14, S. Miglioranzi14, A. Montanari14, T. Namsoo14, D. Notz14, L. Rinaldi14, P. Roloff14,I. Rubinsky14, R. Santamarta14, U. Schneekloth14, A. Spiridonov14,60, H. Stadie14, D. Szuba14,61, J. Szuba14,62,T. Theedt14, G. Wolf14, K. Wrona14, C. Youngman14, W. Zeuner14, W. Lohmann15, S. Schlenstedt15, G. Barbagli16,E. Gallo16,h, P.G. Pelfer16, A. Bamberger17, D. Dobur17, F. Karstens17, N.N. Vlasov17,i, P.J. Bussey18,A.T. Doyle18, W. Dunne18, M. Forrest18, D.H. Saxon18, I.O. Skillicorn18, I. Gialas19,63, K. Papageorgiu19,T. Gosau20, U. Holm20, R. Klanner20, E. Lohrmann20, H. Salehi20, P. Schleper20, T. Schorner-Sadenius20,J. Sztuk20, K. Wichmann20, K. Wick20, C. Foudas21, C. Fry21, K.R. Long21, A.D. Tapper21, M. Kataoka22,64,T. Matsumoto22, K. Nagano22, K. Tokushuku22,65, S. Yamada22, Y. Yamazaki22,66, A.N. Barakbaev23, E.G. Boos23,N.S. Pokrovskiy23, B.O. Zhautykov23, V. Aushev24,a, M. Borodin24, A. Kozulia24, M. Lisovyi24, D. Son25,J. de Favereau26, K. Piotrzkowski26, F. Barreiro27, C. Glasman27,j, M. Jimenez27, L. Labarga27, J. del Peso27,E. Ron27, M. Soares27, J. Terron27, M. Zambrana27, F. Corriveau28, C. Liu28, R. Walsh28, C. Zhou28, T. Tsurugai29,A. Antonov30, B.A. Dolgoshein30, V. Sosnovtsev30, A. Stifutkin30, S. Suchkov30, R.K. Dementiev31, P.F. Ermolov31,L.K. Gladilin31, L.A. Khein31, I.A. Korzhavina31, V.A. Kuzmin31, B.B. Levchenko31,k, O.Yu. Lukina31,A.S. Proskuryakov31, L.M. Shcheglova31, D.S. Zotkin31, S.A. Zotkin31, I. Abt32, C. Buttner32, A. Caldwell32,D. Kollar32, W.B. Schmidke32, J. Sutiak32, G. Grigorescu33, A. Keramidas33, E. Koffeman33, P. Kooijman33,A. Pellegrino33, H. Tiecke33, M. Vazquez33,64, L. Wiggers33, N. Brummer34, B. Bylsma34, L.S. Durkin34, A. Lee34,T.Y. Ling34, P.D. Allfrey35, M.A. Bell35, A.M. Cooper-Sarkar35, R.C.E. Devenish35, J. Ferrando35, B. Foster35,K. Korcsak-Gorzo35, K. Oliver35, S. Patel35, V. Roberfroid35,l, A. Robertson35, P.B. Straub35, C. Uribe-Estrada35,R. Walczak35, P. Bellan36, A. Bertolin36, R. Brugnera36, R. Carlin36, F. Dal Corso36, S. Dusini36, A. Garfagnini36,S. Limentani36, A. Longhin36, L. Stanco36, M. Turcato36, B.Y. Oh37, A. Raval37, J. Ukleja37,m, J.J. Whitmore37,n,Y. Iga38, G. D’Agostini39, G. Marini39, A. Nigro39, J.E. Cole40, J.C. Hart40, H. Abramowicz41,67, A. Gabareen41,R. Ingbir41, S. Kananov41, A. Levy41, M. Kuze42, J. Maeda42, R. Hori43, S. Kagawa43,68, N. Okazaki43,S. Shimizu43, T. Tawara43, R. Hamatsu44, H. Kaji44,69, S. Kitamura44,o, O. Ota44, Y.D. Ri44, M.I. Ferrero45,V. Monaco45, R. Sacchi45, A. Solano45, M. Arneodo46, M. Ruspa46, S. Fourletov47, J.F. Martin47, S.K. Boutle48,63,J.M. Butterworth48, C. Gwenlan48,p, T.W. Jones48, J.H. Loizides48, M.R. Sutton48,p, M. Wing48, B. Brzozowska49,J. Ciborowski49,70, G. Grzelak49, P. Kulinski49, P. �Luzniak49,71, J. Malka49,71, R.J. Nowak49, J.M. Pawlak49,T. Tymieniecka49, A. Ukleja49, A.F. Zarnecki49, M. Adamus50, P. Plucinski50,q, Y. Eisenberg51, I. Giller51,D. Hochman51, U. Karshon51, M. Rosin51, E. Brownson52, T. Danielson52, A. Everett52, D. Kcira52,D.D. Reeder52,b, P. Ryan52, A.A. Savin52, W.H. Smith52, H. Wolfe52, S. Bhadra53, C.D. Catterall53, Y. Cui53,G. Hartner53, S. Menary53, U. Noor53, J. Standage53, J. Whyte53

1 Argonne National Laboratory, Argonne, Illinois 60439-4815, USAr2 Andrews University, Berrien Springs, Michigan 49104-0380, USA3 Institut fur Physik der Humboldt-Universitat zu Berlin, Berlin, Germany4 University and INFN Bologna, Bologna, Italys

5 Physikalisches Institut der Universitat Bonn, Bonn, Germanyt6 H.H. Wills Physics Laboratory, University of Bristol, Bristol, UKu

516 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

7 Calabria University, Physics Department and INFN, Cosenza, Italys8 Chonnam National University, Kwangju, South Koreav9 Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysiaw10 Nevis Laboratories, Columbia University, Irvington on Hudson, New York 10027, USAx11 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Polandy12 Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Cracow, Polandz13 Department of Physics, Jagellonian University, Cracow, Poland14 Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany15 Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany16 University and INFN Florence, Florence, Italys

17 Fakultat fur Physik der Universitat Freiburg i.Br., Freiburg i.Br., Germanyt18 Department of Physics and Astronomy, University of Glasgow, Glasgow, UKu19 Department of Engineering in Management and Finance, Univ. of Aegean, Mytilene, Greece20 Hamburg University, Institute of Exp. Physics, Hamburg, Germanyt21 Imperial College London, High Energy Nuclear Physics Group, London, UKu22 Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japanaa23 Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan24 Institute for Nuclear Research, National Academy of Sciences, Kiev and Kiev National University, Kiev, Ukraine25 Kyungpook National University, Center for High Energy Physics, Daegu, South Koreav

26 Institut de Physique Nucleaire, Universite Catholique de Louvain, Louvain-la-Neuve, Belgiumab27 Departamento de Fısica Teorica, Universidad Autonoma de Madrid, Madrid, Spainac

28 Department of Physics, McGill University, Montreal, Quebec, H3A 2T8 Canadaad29 Meiji Gakuin University, Faculty of General Education, Yokohama, Japanaa30 Moscow Engineering Physics Institute, Moscow, Russiaae

31 Moscow State University, Institute of Nuclear Physics, Moscow, Russiaaf32 Max-Planck-Institut fur Physik, Munchen, Germany33 NIKHEF and University of Amsterdam, Amsterdam, The Netherlandsag34 Physics Department, Ohio State University, Columbus, Ohio 43210, USAr35 Department of Physics, University of Oxford, Oxford, UKu36 Dipartimento di Fisica dell’ Universita and INFN, Padova, Italys37 Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USAx38 Polytechnic University, Sagamihara, Japanaa39 Dipartimento di Fisica, Universita ’La Sapienza’ and INFN, Rome, Italys40 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UKu

41 Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel-Aviv University, Tel-Aviv, Israelah42 Department of Physics, Tokyo Institute of Technology, Tokyo, Japanaa43 Department of Physics, University of Tokyo, Tokyo, Japanaa44 Tokyo Metropolitan University, Department of Physics, Tokyo, Japanaa45 Universita di Torino and INFN, Torino, Italys46 Universita del Piemonte Orientale, Novara, and INFN, Torino, Italys

47 Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canadaad48 Physics and Astronomy Department, University College London, London, UKu49 Warsaw University, Institute of Experimental Physics, Warsaw, Poland50 Institute for Nuclear Studies, Warsaw, Poland51 Department of Particle Physics, Weizmann Institute, Rehovot, Israelai52 Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USAr

53 Department of Physics, York University, Ontario, M3J 1P3 Canadaad54 also affiliated with University College London, UK55 now at Humboldt University, Berlin, Germany56 now at Univ. Libre de Bruxelles, Belgium57 now at DESY group FEB, Hamburg, Germany58 now at Stanford Linear Accelerator Center, Stanford, USA59 now at University of Liverpool, UK60 also at Institut of Theoretical and Experimental Physics, Moscow, Russia61 also at INP, Cracow, Poland62 on leave of absence from FPACS, AGH-UST, Cracow, Poland63 also affiliated with DESY64 now at CERN, Geneva, Switzerland65 also at University of Tokyo, Japan66 now at Kobe University, Japan67 also at Max Planck Institute, Munich, Germany, Alexander von Humboldt Research Award68 now at KEK, Tsukuba, Japan

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 517

69 now at Nagoya University, Japan70 also at �Lodz University, Poland71 �Lodz University, Poland† deceased

Received: 26 July 2007 /Published online: 3 October 2007 − © Springer-Verlag / Societa Italiana di Fisica 2007

Abstract. Forward jet cross sections have been measured in neutral current deep inelastic scattering at lowBjorken-x with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb−1. Measurements arepresented for inclusive forward jets as well as for forward jets accompanied by a dijet system. The exploredphase space, with jet pseudorapidity up to 4.3 is expected to be particularly sensitive to the dynamics ofQCD parton evolution at low x. The measurements are compared to fixed-order QCD calculations and toleading-order parton-shower Monte Carlo models.

a supported by DESY, Germanyb retiredc self-employedd supported by Chonnam National University in 2005e supported by a scholarship of the World Laboratory BjornWiik Research Projectf supported by the research grant no. 1 P03B 04529 (2005–2008)g This work was supported in part by the Marie Curie ActionsTransfer of Knowledge project COCOS (contract MTKD-CT-2004-517186)h e-mail: gallo@mail.desy.dei partly supported by Moscow State University, Russiaj Ramon y Cajal Fellowk partly supported by Russian Foundation for Basic Researchgrant no. 05-02-39028-NSFC-al EU Marie Curie Fellowm partially supported by Warsaw University, Polandn This material was based on work supported by the NationalScience Foundation, while working at the Foundationo Department of Radiological Sciencep PPARC Advanced fellowq supported by the Polish Ministry for Education and Sciencegrant no. 1 P03B 14129r supported by the US Department of Energys supported by the Italian National Institute for NuclearPhysics (INFN)t supported by the German Federal Ministry for Educationand Research (BMBF), under contract numbers HZ1GUA 2,HZ1GUB 0, HZ1PDA 5, HZ1VFA 5u supported by the Particle Physics and Astronomy ResearchCouncil, UKv supported by the Korean Ministry of Education and KoreaScience and Engineering Foundationw supported by theMalaysian Ministry of Science, Technologyand Innovation/Akademi Sains Malaysia grant SAGA 66-02-03-0048x supported by the US National Science Foundation. Anyopinion, findings and conclusions or recommendations ex-pressed in this material are those of the authors and do notnecessarily reflect the views of the National Science Foundationy supported by the Polish State Committee for Scientific Re-search, grant no. 620/E-77/SPB/DESY/P-03/DZ 117/2003-2005 and grant no. 1P03B07427/2004-2006z supported by the Polish Ministry of Science and Higher Ed-ucationas a scientific project (2006-2008)

1 Introduction

Deep inelastic lepton scattering (DIS) off protons providesa rich field for exploring the parton dynamics in QCD.HERA has extended the phase-space region in the Bjorkenscaling variable, xBj, down to a few 10

−5. At such lowxBj, several steps in the QCD cascade initiated by a par-ton from the proton can occur before the final interac-tion with the virtual photon takes place. The result ofthis cascade may be observed in the final state and pro-vides an opportunity to study the QCD parton evolution indetail.Within perturbative QCD (pQCD), fixed-order cal-

culations for the parton evolution are so far availableonly at next-to-leading order (NLO). A number of dif-ferent approximations to the QCD evolution have beendeveloped, based on summing of particular subsets of di-agrams in accordance with their importance in the phasespace considered.

aa supported by the Japanese Ministry of Education, Culture,Sports, Science and Technology (MEXT) and its grants for Sci-entific Researchab supported by FNRS and its associated funds (IISN andFRIA) and by an Inter-University Attraction Poles Programmesubsidised by the Belgian Federal Science Policy Officeac supported by the Spanish Ministry of Education and Sci-ence through funds provided by CICYTad supported by the Natural Sciences and Engineering Re-search Council of Canada (NSERC)ae partially supported by the German Federal Ministry for Ed-ucation and Research (BMBF)af supported by RF Presidential grant N 8122.2006.2 for theleading scientific schools and by the Russian Ministry of Edu-cation and Science through its grant Research on High EnergyPhysicsag supported by the Netherlands Foundation for Research onMatter (FOM)ah supported by the German-Israeli Foundation and the IsraelScience Foundationai supported in part by the MINERVA Gesellschaft furForschung GmbH, the Israel Science Foundation (grant no.293/02-11.2) and the U.S.-Israel Binational Science Foundation

518 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

The conventional DGLAP [1–3] approach sums up theleading logarithms in the virtuality of the exchanged bo-son,Q2, and is expected to be valid at not too small xBj andQ2. At small xBj, a better approximation is expected tobe provided by the BFKL formalism [4] which resums theleading logarithm terms in 1/x, where x is the fractionallongitudinal momentum of a parton. The CCFM [5, 6] ap-proach interpolates between the two types of evolution,DGLAP and BFKL.The DGLAP evolution equations have been success-

fully tested at HERA in inclusive measurements at lowxBj and no indication of BFKL dynamics was observed.The dynamics at low xBj can be further probed by meas-urements of the partonic final state that highlight the dif-ferences between predictions of the BFKL and DGLAPformalisms. BFKL evolution results in a larger fractionof small xBj events with forward jets

1 than the DGLAPevolution. A forward jet is characterised by a high frac-tional longitudinal momentum, xjet = pjetZ /p, where p isthe proton momentum and pjetZ is the longitudinal jetmomentum [7].A comparison of data on forward jets with the DGLAP

leading-order parton-shower Monte Carlo programmesperformed previously in DIS at HERA [8–10] has revealeda clear deficit of forward jets in the Monte Carlo. How-ever, the addition of a parton cascade evolved accordingto DGLAP on the photon side has significantly improvedthe description [11]. The simulation based on the colordipole model (CDM) [12–14], which includes parton emis-sions not ordered in transverse momentum, also succeededin describing the data. Fixed-order NLO QCD calcula-tions [15, 16] were also compared to the forward jets meas-urements in more recent publications and failed to describethe data. These studies were performed up to pseudora-pidities 3 [17] and 2.7 [18].In this paper, measurements of inclusive forward-jet

cross sections for pseudorapidities of up to 4.3 are pre-sented, based on a data sample which corresponds toa twofold increase in luminosity with respect to the pre-vious ZEUS analysis [17]. Furthermore, a comparisonof the measured cross sections with the Cascade MonteCarlo [19], based on the CCFM evolution, is presented.In addition, measurements of “forward jet + dijet” crosssections, as investigated by the H1 Collaboration [18],are reported. These measurements explore parton evolu-tion in a more exclusive way and are more sensitive to itsdetails.

2 Theoretical frameworkand phase-space definitions

The DGLAP evolution equations, based on collinear fac-torisation, assume that the dominant contribution to par-

1 The ZEUS coordinate system is a right-handed Cartesiansystem, with the Z axis pointing in the proton beam direction,referred to as the “forward direction”, and the X axis pointingtowards the centre of HERA. The coordinate origin is at thenominal interaction point.

ton evolution comes from subsequent parton emissionsthat are strongly ordered in transverse momenta, kT,where the parton with the largest kT interacts with thephoton. In this formalism, only the leading terms in lnQ2

in the QCD perturbative expansion are summed up. Sincethis approximation does not resum leading ln 1/x terms, itmay not be adequate at low xBj.Contrary to the DGLAP approach, the BFKL evolu-

tion equation resums the leading ln 1/x and the evolutionproceeds over x at fixed Q2. The BFKL approach imposesno ordering in kT but strong ordering in x, with the low-xparton interacting with the photon. At small xBj, the dif-ference between these approaches to the QCD parton evo-lution is expected to be most prominent for hard partonscreated at the beginning of the cascade, i.e. at pseudora-pidities close to the proton (forward region).The CCFM approach is based on the idea of coherent

gluon radiation, which leads to angular ordering of gluonemissions in the gluon ladder. It interpolates between theabove two types of evolution, so it should be applicableover a larger phase-space region.A phenomenological approach to parton evolution is

provided by CDM [12–14]. In this model, gluons are emit-ted by color dipoles successively spanned between partonsin the cascade. Due to independent radiation of the dipoles,the emitted gluons are not ordered in kT and thus CDMmimics the BFKL-type evolution.To investigate the relevance of different approaches,

events with a jet in the forward region were analysed in thelow-xBj region. Events were required to have at least onejet satisfying the following criteria:

–(pjetT

)2∼Q2;

– xjet� xBj,

where pjetT is the transverse momentum of the jet. The firstcondition suppresses strong ordering in the transverse mo-menta and decreases the probability of having a DGLAP-type evolution. The second condition enhances the phasespace for the BFKL evolution.A further event sample called “forward jet+dijet”,

which contains at least two hard jets in addition to theforward jet (fjet), was selected. The jets were ordered inpseudorapidity such that ηjet1 < ηjet2 < ηfjet. For this sam-ple, the pseudorapidity separation of dijets, ∆η1 = η

jet2 −ηjet1 , and the pseudorapidity difference between the for-ward and the second jet of the dijet, ∆η2 = η

fjet− ηjet2 ,were studied.The cross section as a function of ∆η2 was investi-

gated for two intervals of ∆η1, ∆η1 < 1 and ∆η1 > 1. Withsuch a choice of ∆η1, different dynamics of the partons inthe cascade are expected to be highlighted. For ∆η1 < 1,small invariantmasses of the dijet system are favoured and,therefore, partons with small values of xg are produced,where xg is the longitudinal momentum fraction carried bythe gluon coupled to the hard dijet system (Fig. 1). Con-sequently, a large space is left for BFKL-type evolution inx from the forward jet to the dijet system. When ∆η1 islarge, BFKL-like evolution can occur between the partonsproducing the dijet system.

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 519

Fig. 1. A schematic diagram of an interaction in which a for-ward jet and two additional hard jets can be produced

3 Experimental set-up

The analysis was performed with the data taken withthe ZEUS detector from 1998 to 2000, when HERA col-lided electrons or positrons2 with energy of Ee = 27.5GeVwith protons of energy Ep = 920GeV, yielding a centre-of-mass energy of 318GeV. The results are based on thesum of the e−p and e+p samples, corresponding to inte-grated luminosities of 16.4±0.3 pb−1 and 65.3±1.5 pb−1,respectively.A detailed description of the ZEUS detector can be

found elsewhere [20]. A brief outline of the componentsthat are most relevant for this analysis is given below.Charged particles are tracked in the central tracking de-

tector (CTD) [21–23], which operates in a magnetic fieldof 1.43 T provided by a thin superconducting solenoid.The CTD consists of 72 cylindrical drift chamber layers,organised in nine superlayers covering the polar-angle re-gion 15◦ < θ < 164◦. The transverse-momentum resolutionfor full-length tracks is σ(pT)/pT = 0.0058pT⊕ 0.0065⊕0.0014/pT, with pT in GeV.The high-resolution uranium–scintillator calorimeter

(CAL) [24–27] CAL consists of three parts: the for-ward (FCAL), the barrel (BCAL) and the rear (RCAL)calorimeters. Each part is subdivided transversely intotowers and longitudinally into one electromagnetic section(EMC) and either one (in RCAL) or two (in BCAL andFCAL) hadronic sections (HAC). The smallest subdivi-sion of the calorimeter is called a cell. The CAL energyresolutions, as measured under test-beam conditions, areσ(E)/E = 0.18/

√E for electrons and σ(E)/E = 0.35/

√E

for hadrons, with E in GeV.The luminosity wasmeasured using the bremsstrahlung

process ep→ eγp with the luminosity monitor [28–30],a lead-scintillator calorimeter placed in the HERA tunnelat Z =−107m.For the 1998–2000 running period, the forward plug

calorimeter (FPC) [31] was installed in the 20× 20 cm2

beam hole of the FCAL, with a small hole of radius 3.15 cm

2 Hereafter, both e+ and e− are referred to as electrons, un-less explicitly stated otherwise.

in the center to accommodate the beam pipe. The FPCincreased the forward calorimetric coverage by about 1unit of pseudorapidity to η ≤ 5. The FPC consisted ofa lead–scintillator sandwich calorimeter divided longitudi-nally into electromagnetic and hadronic sections that wereread out separately by wavelength-shifting fibers and pho-tomultipliers. The energy resolution, as measured undertest-beam conditions, was σ(E)/E = 0.41/

√E⊕0.062 and

σ(E)/E = 0.65/√E⊕0.06 for electrons and pions, respec-

tively, with E in GeV.

4 Event selection and jet definition

A three-level trigger was used to select events online [20].The neutral current DIS events were selected offline usingcriteria similar to those reported previously [32]. The mainsteps are outlined below.The scattered electron was identified using an algo-

rithm based on a neural network [33, 34]. The kinematicvariables Q2, xBj and the inelasticity y were reconstructedusing the double-angle method (DA) [35, 36], where thehadronic final state was reconstructed using combinationsof CTD tracks and energy clusters measured in the CAL toform energy-flow objects (EFOs) [37].The following criteria were applied offline to select DIS

events:

– a scattered electron with energy E′e above 10GeV, toensure a well reconstructed electron and to suppressthe background from photoproduction events, in whichthe scattered electron escapes undetected in the rearbeampipe;– 40< δ < 65GeV,whereδ =

∑i(Ei−PZ,i),whereEi and

PZ,i are the energy and Z-component of the momen-tum of each EFO and the scattered electron. This cutremoved events with large initial-state radiation and re-duced the background fromphotoproduction events;

– ye < 0.95, where ye = 1−E′e2Ee(1− cosθ′e) and θ

′e is the

polar angle of the electron. Along with the previousrequirements, this reduces the photoproduction back-ground to a negligible level;– |X|> 24 cm or |Y |> 12 cm, whereX and Y are the im-pact positions of the positron on the CAL, to avoid thelow-acceptance region adjacent to the rear beampipe;– the Z coordinate of the vertex, Zvtx, determined fromCTD tracks, was required to be in the range |Zvtx| <50 cm along the beam axis. This cut removed back-ground events from non-ep interactions;– 0.04< yDA < 0.7;– 20<Q2DA < 100GeV

2;– 0.0004< xDA < 0.005.

After this selection, the jets were identified using the kTcluster algorithm [38] in the longitudinally invariant inclu-sive mode [39] applied in the Breit frame [40] on the CALand FPC cells, excluding those belonging to the scatteredelectron. The reconstructed jets were then boosted back tothe laboratory frame. Jet-energy corrections were appliedin order to account for the energy loss in the inactive ma-terial in front of the detector. The events were required to

520 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

have at least one jet satisfying the following criteria in thelaboratory frame:

– the transverse energy of each jet was required to beEjetT > 5 GeV;– the pseudorapidity of each jet was required to be in theinterval 2< ηjet < 4.3;– xjet > 0.036, which selects forward jets with large en-ergy;– 0.5 < (EjetT )

2/Q2 < 2, which suppresses the DGLAP-type evolution;– jets with 2.8< ηjet < 3.35 and with the azimuthal angleof the jet, φ expressed in radians, in the ranges 0 <φjet < 0.4, 1.0< φjet < 2.2, 2.7< φjet < 3.6, 4.2< φjet <5.3 or 5.7< φjet < 6.3 were rejected due to poor recon-struction caused by the large cell size in the FCAL;

Using the sample described above, the triple differentialcross sections, with the 0.5< (EjetT )

2/Q2 < 2 cut removed,were measured in two intervals of Q2, 20<Q2 < 40 GeV2

and 40<Q2 < 100GeV2 and for EjetT > 5 GeV.For the “forward jet+dijet” analysis, the events were

required to have one forward jet, satisfying the same selec-tion criteria as above, with the exception of the (EjetT )

2/Q2

cut, and at least two additional jets with EjetT > 5 GeV.The two additional jets, chosen with the highest transverseenergy were required to lie in the pseudorapidity region−1.5< ηjet < 4.3. The three selected jets were ordered inηjet as described in Sect. 2.

5 Monte Carlo simulations

Various MC samples were generated. Samples of LEPTOand ARIADNE generators were used to simulate the detec-tor response to jets of hadrons and to determine the hadro-nisation corrections needed for comparison with pertur-bative QCD calculations. The same samples were used tocompare the measurements to the LEPTO and ARIADNEmodels. In addition, the data were compared to expec-tations of the ARIADNE generator with its newly tunedproton-remnant treatment, “ARIADNE tuned”, and tothe CASCADE generator.The LEPTO [41] MC program is based on first-order

QCD matrix elements supplemented with parton showers(MEPS), which follow DGLAP evolution.The CDM approach is represented by the ARIADNE

4.08 [42] MC program and its tuned variant (“ARIADNEtuned”3) as described in a recent H1 publication [18].The CASCADE MC program [19, 43] is based on the

CCFM evolution and uses kT-factorisation of the cross sec-tion into an off-shell matrix element and an unintegratedparton (gluon) density function (uPDF). Predictions of

3 The following parameters have been changed from theirdefault values: the powers, defining the fraction of the pro-ton remnant participating in the emission, PARA(10) = 1.2(default = 1.0) and PARA(25) = 1.2 (default = 2.0); the squareroot of the mean value of the primordial p2⊥ in the proton rem-nant, PARA(27) = 0.9 (default = 0.6).

CASCADE were obtained with the J2003 set-1 and set-2uPDFs [44]. The J2003 set-2 includes non-singular termsin the splitting function and reduces the cross sections atlow xBj.In all MC models, the fragmentation of the final-state

partons has been performed using the LUND [45] stringmodel as implemented in JETSET 7.4 [46].Both LEPTO and ARIADNE were interfaced to HER-

ACLES 4.6.1 [47] via DJANGOH 1.1 [48]. The HERA-CLES program simulates first-order electroweak radiativecorrections. The CTEQ5L [49] proton parton distributionfunctions (PDF) were used in both cases.The events generated with LEPTO and ARIADNE

were passed through the GEANT 3.13-based [50] ZEUSdetector and trigger simulation programs [20]. They werereconstructed and analysed using the same program chainas the data.

6 Acceptance correctionand systematic studies

The correction factors to the data for detector-acceptanceeffects were obtained with the ARIADNE and LEPTOMCprograms. These correction factors were calculated bin bybin as

CAcc =NdetMCNhadMC

,

where NdetMC(NhadMC

)is the number of jets in bins of the

detector (hadron) level distribution. For this approach tobe valid, the distributions in the data must be well de-scribed by the MC simulation at the detector level, a condi-tion which was in general satisfied by both ARIADNE andLEPTO. The average between the correction factors ob-tained with ARIADNE and LEPTOwas taken. The valuesof CAcc were generally between 0.4 and 1.2 for the inclu-sive forward-jet sample, and 0.5 to 1.4 for the “forwardjet+dijet” sample.To ensure the correct MC reconstruction of the jets

near the boundary between FCAL and FPC, jet profiles inthe data and MC were compared and found to be in goodagreement.The major sources of systematic uncertainty were as

follows (the effects on the cross sections are shown inparentheses):

– the largest uncertainty resulted from the model depen-dence of the acceptance corrections. This uncertaintywas estimated using the deviations of LEPTO andARI-ADNE corrections from their average (≤ 10% for inclu-sive forward jet sample, < 25% for forward jet+dijetsample);– ±3% shift of jet energies due to the CAL energy-scaleuncertainty (< 10%);– ±10% shift of jet energies due to the FPC energy-scaleuncertainty (∼ 15% for the last ηjet bin, negligible else-where);

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 521

– the selection of inclusive DIS events (< 1%). The cutson the scattered-electron energy, the X and Y positionof the electron, δ and Zvtx were varied.

These systematic uncertainties, except for the energy-scaleuncertainty, were added in quadrature separately for thepositive and negative variations in each bin. The energyscale uncertainties, which are correlated between bins, areshown separately. The uncertainty in the luminosity of±2.2% is not included in the figures.

7 NLO QCD calculations

For inclusive forward jets, fixed-order calculations wereperformed with the Disent [15] code, at O(αα2s) in the MSrenormalisation and factorisation schemes. The number offlavours was set to five; the renormalisation (µR) and fac-torisation (µF) scales were both set to µR = µF =Q. TheCTEQ6M [51] parameterisation of the proton PDFs wasused. The theoretical uncertainty in the calculations wasestimated considering the following three sources:

– µR was varied up and down by a factor of two, whichcontributed up to 57% depending on the phase-spaceregion;– µF was also varied up and down by a factor of two andthe resulting uncertainty was less than 5% except in thelowest xBj bin and the most forward region;– the PDF uncertainty was estimated using the 40 differ-ent sets of CTEQ6 parton distribution functions [51].

For “forward jet+dijet” cross sections, the program Nlo-jet++ [16] was used. This program calculates three-jet pro-duction in DIS at NLO O(αα3s) and uses the MS scheme.The number of flavours, µR and µF were set as in Disent.In order to compare the data to NLO calculations,

corrections from the parton to the hadron level, CHAD,were determined in each bin. The hadronisation correc-tions CHAD were calculated as an average between thoseobtained from LEPTO and from ARIADNE and appliedto the NLO calculations. The uncertainty of the hadroni-sation correction CHAD was assumed to be the absolutedifference in the two values.

8 Results

Cross sections for inclusive forward jets and for eventscontaining a dijet system in addition to the forward jet,were measured in the kinematic region given by 20<Q2 <100GeV2, 0.04 < y < 0.7 and 0.0004< xBj < 0.005. Thedifferential jet cross sections are presented as functions ofthe variable ξ = Q2, xBj, E

jetT , η

jet. They were determinedas

dσ

dξ=N jetdataL∆ξ

CQED

CAcc,

where N jetdata is the number of jets in a bin of width ∆ξ, Lis the integrated luminosity, and CQED =NnoQEDMC /NQEDMC ,

whereNQEDMC (NnoQEDMC ) is the number of events selected atthe hadron level in a given ξ bin in the MC sample gener-ated with (without) QED radiation.The triple differential cross sections were obtained in

a similar manner,

d3σ

dQ2d(EjetT )2dη

=N jetdata

L∆Q2∆(EjetT )2∆η

CQED

CAcc.

8.1 Inclusive forward-jet measurements

The measured differential forward-jet cross sections asfunctions of Q2, xBj, E

jetT and η

jet are shown in Fig. 2 andTables 1–4, where they are compared to NLO calculations.The calculations predict lower cross sections than ob-

tained from the data by as much as a factor two; however,they have a large theoretical uncertainty. The strong de-pendence of the calculation on µR can be related to the factthat in this kinematic region higher-order terms becomerelevant. As a demonstration, the leading-order calculationis also shown in Fig. 2 for each differential cross section. Itis far below the measurement, indicating that the contribu-tion ofO(α2s ) terms is significant. A recent publication [18],which used a harder renormalisation scale (the averageE2T of the dijets coming from the hard scattering), reporteda smaller renormalisation-scale uncertainty.A comparison of the data with the ARIADNE and

LEPTO MC is shown in Fig. 3. The predictions of theCDM obtained with “ARIADNE default” are in fair agree-ment with the data with the exception of high EjetT andhigh ηjet, where ARIADNE overestimates the cross sec-tions. An investigation has shown that in ARIADNE theproton-remnant fragments are generated with high pT,therefore they show up at much lower η than in othergenerators. The newly tuned ARIADNE, also shown inFig. 3, yields lower cross sections, in particular at highEjetT and high η

jet, and provides a good description of thedata.The predictions of the LEPTO MC are found to be in

agreement with data in shape for all distributions, howeverthe absolute normalisation is below the measurements bya factor of two.The measurement of differential forward-jet cross sec-

tions is compared to the prediction of the CASCADE MCmodel in Fig. 4. Neither of the investigated uPDF sets givesa satisfactory agreement with the measurements in all dis-tributions, suggesting that a further adjustment of the in-put parameters of the CASCADE model is necessary.

8.2 Triple-differential forward-jet cross section

The triple-differential forward-jet cross sections as a func-tion of ηjet are presented in two intervals ofQ2 and three in-tervals of (EjetT )

2 in Fig. 5 and Table 5. Also shown in Fig. 5are the expectations of the NLO calculations from DIS-ENT. The calculations generally underestimate the crosssections. The largest discrepancy between the data and

522 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

Fig. 2. Measured differential cross sec-tions as a function of aQ2, b xBj, c E

jetT

and d ηjet for inclusive jet production(dots) compared with the NLO QCDcalculations (solid line). The hatchedarea shows the theoretical uncertaintiesand the shaded area shows the uncer-tainty after varying the CAL and FPCenergy scales. The inner error bars indi-cate the statistical uncertainties, whilethe outer ones correspond to statisti-cal and systematic uncertainties (exceptthe energy-scale uncertainty) added inquadrature

the theory is seen in the high-Q2 range and for (EjetT )2 <

100GeV2. This region is sensitive to multigluon emission,which is lacking in the NLO calculations.In Fig. 6, the data are compared with LEPTO and ARI-

ADNE. As was already observed in Fig. 3, the LEPTOMCis always below the measurements.The cross sections of “ARIADNE tuned” are below

those of the “ARIADNE default” in all the presented phasespace. The difference between the two versions is small-est in the lowest-(EjetT )

2 interval, where both are close tothe data. In the highest-(EjetT )

2 interval, the difference isbig and “ARIADNE tuned” gives a good description of thedata.A comparison of the data with the CASCADEMCwith

two sets of uPDFs is shown in Fig. 7.The expectations of CASCADE are close to the data in

the low-Q2 interval for set-1, while in the high-Q2 interval

the set-2 gives a better description of the data. None of thesets can accomodate all the features of the data.

8.3 Forward jet+dijet measurements

The measured cross sections for events with a dijet systemin addition to the forward jet are compared with fixed-order QCD calculations and LO parton-showerMCmodelsin Figs. 8–10. The cross sections are presented as a func-tion of ∆η1 and∆η2, and as a function of ∆η2 for two cases,namely, ∆η1 < 1 and ∆η1 > 1 (Tables 6–9).A comparison between data and the predictions of

NLOJET++ is shown in Fig. 8. As already observed by theH1 experiment [18], the NLOJET++ calculations agreewell with the data at large ∆η2, while they do not de-scribe the data at small ∆η2, especially for small ∆η1.

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 523

Fig. 3. Measured differential cross sections asa function of a Q2, b xBj, c E

jetT and d ηjet

for inclusive jet production (dots) comparedwith the ARIADNE (solid histogram), ARI-ADNE with new tuning (dashed histogram)and LEPTO (dotted histogram) predictions.The shaded area shows the uncertainty aftervarying the CAL and FPC energy scales. Theinner error bars indicate the statistical uncer-tainties, while the outer ones correspond tostatistical and systematic uncertainties (ex-cept the energy-scale uncertainty) added inquadrature

Fig. 4. Measured differential cross sections asa function of a Q2, b xBj, c E

jetT and d η

jet forinclusive jet production (dots) compared withthe CASCADE set-1 parametrisation (solidhistogram) and CASCADE set-2 (dashed his-togram) predictions. The shaded area shows theuncertainty after varying the CAL and FPCenergy scales. The inner error bars indicate thestatistical uncertainties, while the outer onescorrespond to statistical and systematic uncer-tainties (except the energy-scale uncertainty)added in quadrature

524 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

Fig. 5. Measured differential cross sections asa function of ηjet in different bins of Q2 and(EjetT )

2 for inclusive jet production (dots) com-pared with the NLO QCD calculations (solidline). The hatched area shows the theoreticaluncertainties and the shaded area shows theuncertainty after varying the CAL and FPCenergy scales. The inner error bars indicate thestatistical uncertainties, while the outer onescorrespond to statistical and systematic uncer-tainties (except the energy-scale uncertainty)added in quadrature

Fig. 6. Measured differential cross sectionsas a function of ηjet in different bins of Q2

and (EjetT )2 for inclusive jet production (dots)

compared with the ARIADNE (solid his-togram), ARIADNE with new tuning (dashedhistogram) and LEPTO (dotted histogram)predictions. The shaded area shows the un-certainty after varying the CAL and FPC en-ergy scales. The inner error bars indicate thestatistical uncertainties, while the outer onescorrespond to statistical and systematic uncer-tainties (except the energy-scale uncertainty)added in quadrature

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 525

Fig. 7. Measured differential cross sections asa function of ηjet in different bins of Q2 and(EjetT )

2 for inclusive jet production (dots) com-pared with the CASCADE set-1 parametri-sation (solid histogram) and CASCADE set-2 (dashed histogram) predictions. The shadedarea shows the uncertainty after varying theCAL and FPC energy scales. The inner errorbars indicate the statistical uncertainties, whilethe outer ones correspond to statistical andsystematic uncertainties (except the energy-scale uncertainty) added in quadrature

Fig. 8. Differential cross sections for forward+dijet sample as a function of a ∆η1, b ∆η2,c ∆η2 for ∆η1 < 1 and d ∆η2 for ∆η1 > 1.The data (dots) are compared with the NLOQCD calculations (solid line). The hatchedarea shows the theoretical uncertainties. Theshaded area shows the uncertainty after vary-ing the CAL and FPC energy scales. Theinner error bars indicate the statistical uncer-tainties, while the outer ones correspond tostatistical and systematic uncertainties (ex-cept the energy-scale uncertainty) added inquadrature

526 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

Fig. 9. The differential cross sections for for-ward+dijet sample as a function of a ∆η1, b∆η2, c ∆η2, for ∆η1 < 1 and d ∆η2 for ∆η1 >1. The data (dots) are compared with the ARI-ADNE (solid histogram), ARIADNE with newtuning (dashed histogram) and LEPTO (dot-ted histogram) predictions. The shaded areashows the uncertainty after varying the CALand FPC energy scales. The inner error barsindicate the statistical uncertainties, while theouter ones correspond to statistical and sys-tematic uncertainties (except the energy-scaleuncertainty) added in quadrature

Fig. 10. The differential cross sections for for-ward+dijet sample as a function of a ∆η1,b ∆η2, c ∆η2, for ∆η1 < 1 and d ∆η2 for∆η1 > 1. The data (dots) are compared withthe CASCADE set-1 (solid histogram) andCASCADE set-2 (dashed histograms) predic-tions. The shaded area shows the uncertaintyafter varying the CAL and FPC energy scale.The inner error bars indicate the statistical un-certainties, while the outer ones correspondto statistical and systematic uncertainties (ex-cept the energy-scale uncertainty) added inquadrature

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 527

The large ∆η2 kinematics at low xBj favours dijets origi-nating from photon-gluon fusion, with an additional gluonresponsible for the forward jet. This case is well treated byNLOJET++. The small ∆η1 and ∆η2 region correspondsto the event configuration in which all the three jets tendto go forward, away from the hard interaction. This config-uration favours multigluon emission, which is not expectedto be described by NLOJET++.The comparison between data and the LEPTO and

ARIADNE MCs is shown in Fig. 9. As before, the LEPTO

Table 1. The differential cross section, dσ/dQ2, in bins of Q2 for inclusive forwardjets. The statistical (δstat), systematic (δsyst) and jet-energy-scale uncertainties forCAL and FPC (δCAL and δFPC) are shown separately. The multiplicative correc-tion applied to correct for QED radiative effects (CQED) and for hadronisation effects(CHAD) are shown in the last two columns

Q2 bin dσ/dQ2 δstat δsyst δCAL δFPC CQED CHAD(GeV2) (nb/GeV2)

20–30 23.21 ±0.43 +0.81−0.79

+1.39−1.95

+3.06−3.03 0.97 0.89

30–40 15.49 ±0.33 +0.48−0.54

+0.95−1.05

+1.73−1.61 0.96 0.89

40–50 9.76 ±0.26 +0.26−0.37

+0.54−0.77

+0.91−1.07 0.94 0.89

50–60 6.65 ±0.21 +0.27−0.22

+0.40−0.36

+0.55−0.51 0.97 0.91

60–80 3.21 ±0.10 +0.12−0.08

+0.20−0.18

+0.22−0.22 0.97 0.89

80–100 1.36 ±0.07 +0.07−0.03

+0.06−0.08

+0.08−0.09 0.94 0.91

Table 2. The differential cross section, dσ/dxBj, in bins of xBj for inclusive forwardjets. The statistical, systematic and jet-energy-scale uncertainties are shown sepa-rately (see the caption of Table 1)

xBj bin dσ/dxBj δstat δsyst δCAL δFPC CQED CHAD(pb)

0.0004–0.001 275 ±6 +19−19

+16−20

+34−35 0.97 0.86

0.001–0.002 200 ±4 +10−9

+14−14

+23−20 0.97 0.88

0.002–0.003 125 ±3 +2−3

+6−9

+11−12 0.96 0.90

0.003–0.004 89 ±2 +4−3

+5−6

+9−9 0.95 0.92

0.004–0.005 65 ±2 +1−1

+4−5

+6−6 0.94 0.95

Table 3. The differential cross section, dσ/dEjetT , in bins of EjetT for inclusive for-

ward jets. The statistical, systematic and jet-energy-scale uncertainties are shownseparately (see the caption of Table 1)

EjetT bin dσ/dEjetT δstat δsyst δCAL δFPC CQED CHAD(GeV) (nb/GeV)

5–6.5 245.1 ±3.2 +6.9−7.6

+15.0−18.7

+32.6−31.3 0.96 0.91

6.5–8 123.2 ±2.4 +4.5−4.5

+7.7−8.1

+10.0−10.2 0.97 0.92

8–9.5 42.04 ±1.40 +1.22−1.20

+1.9−2.35

+1.50−1.69 0.96 0.89

9.5–11 13.38 ±0.73 +1.17−0.99

+0.63−1.49

+0.62−1.35 0.96 0.87

11–14 2.21 ±0.21 +0.16−0.20

+0.05−0

+0.08−0.21 0.93 0.89

predictions are below the data for all differential cross sec-tions. The “ARIADNE default” overestimates the crosssections. This implies that energetic multiple jets areproduced too often in the “ARIADNE default”. Thetuning of the ARIADNE parameters brings this modelinto very good agreement with data for all differentialdistributions.The comparison of the CASCADE MC to the data is

presented in Fig. 10. As before, CASCADE does not satis-factorily reproduce the measurement.

528 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

Table 4. The differential cross section, dσ/dηjet, in bins of ηjet for inclusive forwardjets. The statistical, systematic and jet-energy-scale uncertainties are shown sepa-rately (see the caption of Table 1)

ηjet bin dσ/dηjet δstat δsyst δCAL δFPC CQED CHAD(nb)

2–2.3 118.0 ±5.1 +7.8−7.8

+8.4−6.8

+0−0.1 0.97 0.87

2.3–2.6 361.4 ±8.5 +20.0−21.0

+24.2−34.1

+0−1.3 0.95 0.90

2.6–2.9 438.2 ±9.6 +14.9−12.4

+40.9−48.7

+0.8−1.0 0.96 0.93

2.9–3.5 331.0 ±8.1 +19.2−20.2

+17.0−25.2

+15.5−15.4 0.95 0.92

3.5–4.3 211.6 ±4.2 +6.6−7.7

+4.8−5.1

+54.9−79.1 0.98 1.01

Table 5. The differential cross sections as a function of ηjet in different bins of Q2 and (EjetT )2 for inclusive forward jets. The

jet-energy-scale uncertainties are shown separately (see the caption of Table 1)

(EjetT )2 ηjet bin d3σ/dQ2d(E

jetT )

2dηjet± δstat± δsyst δCAL δFPC CQED CHAD(GeV2) (pb/GeV4)

20<Q2 < 40 (GeV2)

2.4–2.7 525±20+61−62+42−63 – 0.93 0.88

25–36 2.7–3.1 658±24+50−44+52−90

+1−2 0.94 0.91

3.1–3.7 463±20+20−31+22−10

+66−143 0.98 0.86

3.7–4.3 359±13+13−18+7−11

+111−197 0.96 0.93

2.0–2.4 133±4+10−10+10−12 – 0.96 0.95

2.4–2.7 200±6+13−13+15−18 – 0.98 0.89

36–100 2.7–3.1 170±6+6−6+17−14

+2−1 0.97 0.87

3.1–3.7 106±4+6−5+6−7

+12−15 0.97 0.89

3.7–4.3 73.2±2.6+2.6−2.7+1.7−1.2

+20.9−27.7 1.00 0.88

2.0–2.4 17.8±0.8+0.7−0.7+1.2−1.4 – 0.99 0.95

2.4–2.7 13.3±0.8+0.8−0.7+1.4−1.5 – 0.99 0.94

100–400 2.7–3.1 9.56±0.68+0.42−0.27+0.82−0.95 – 0.96 0.92

3.1–3.7 6.14±0.58+0.95−0.64+0.41−0.87

+0.86−1.55 0.97 0.98

3.7–4.3 2.66±0.25+0.18−0.16 – +0.83−1.48 0.98 0.93

40<Q2 < 100 (GeV2)

2.4–2.7 83.6±5.0+3.1−3.2+4.6−7.1

+0−0.2 0.89 0.90

25–36 2.7–3.1 105±5+6−4+8−11 – 0.94 0.90

3.1–3.7 78.3±4.7+4.2−4.2+2.0−4.5

+7.8−12.0 0.95 0.89

3.7–4.3 57.2±3.0+6.1−5.6+0.4−0.9

+15.7−26.3 0.94 0.85

2.0–2.4 24.2±10.0+1.9−1.9+1.5−1.4 – 0.94 0.92

2.4–2.7 35.8±1.4+2.1−2.2+3.1−2.3 – 0.98 0.93

36–100 2.7–3.1 26.5±1.2+1.5−1.3+2.2−2.2

+0.1−0.2 0.96 0.88

3.1–3.7 19.8±0.9+1.4−1.5+0.9−0.9

+1.4−1.5 0.96 0.89

3.7–4.3 13.7±0.6+0.4−0.4+0.2−0.2

+3.1−4.1 0.99 0.94

2.0–2.4 3.59±0.18+0.21−0.22+0.29−0.30 – 0.97 0.97

2.4–2.7 2.57±0.17+0.10−0.06+0.17−0.33 – 0.96 0.97

100–400 2.7–3.1 1.71±0.13+0.11−0.19+0.15−0.15 – 0.96 0.94

3.1–3.7 0.99±0.08+0.16−0.18 – +0.13−0.15 0.96 0.96

3.7–4.3 0.58±0.05+0.05−0.06 – +0.19−0.30 0.97 0.98

The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA 529

Table 6. The differential cross section, dσ/d∆η1, in bins of ∆η1 for “forwardjet+dijet” events. The statistical, systematic and jet-energy-scale uncertainties areshown separately (see the caption of Table 1)

∆η1 bin dσ/d∆η1 δstat δsyst δCAL δFPC CQED CHAD(nb)

0.0–0.7 82.88 ±3.77 +12.88−12.88

+8.24−10.9

+4.24−4.24 0.98 0.74

0.7–1.4 79.35 ±3.65 +11.18−11.01

+9.40−8.66

+5.18−4.13 0.99 0.76

1.4–2.1 50.68 ±2.62 +5.53−6.12

+4.79−6.91

+3.68−3.49 0.98 0.76

2.2–4 15.30 ±0.99 +2.35−1.67

+1.16−2.42

+1.36−2.10 0.96 0.75

Table 7. The differential cross section, dσ/d∆η2, in bins of ∆η2 for “forwardjet+dijet” events. The statistical, systematic and jet-energy-scale uncertainties areshown separately (see the caption of Table 1)

∆η2 bin dσ/d∆η1 δstat δsyst δCAL δFPC CQED CHAD(nb)

0.0–0.8 56.38 ±2.64 +5.26−4.72

+5.42−5.97

+1.35−1.42 0.98 0.78

0.8–1.6 76.23 ±3.33 +5.23−6.18

+7.44−9.52

+2.51−3.09 0.96 0.79

1.6–2.4 56.06 ±2.82 +9.33−8.69

+5.18−7.31

+4.44−4.79 1.01 0.75

2.4–3.2 19.44 ±1.27 +4.46−3.98

+2.12−2.70

+2.69−2.58 0.97 0.69

Table 8. The differential cross section, dσ/d∆η2, in bins of ∆η2 for “forwardjet+dijet” events in the case of ∆η1 < 1. The statistical, systematic and jet-energy-scale uncertainties are shown separately (see the caption of Table 1)

∆η2 bin dσ/d∆η1 δstat δsyst δCAL δFPC CQED CHAD(nb)

0.0–0.8 14.86 ±1.36 +1.17−1.71

+1.65−1.86

+0−0.24 1.00 0.82

0.8–1.6 30.04 ±2.17 +4.58−5.04

+3.21−3.04

+0.26−0.34 0.99 0.81

1.6–2.4 29.48 ±1.93 +4.13−3.78

+2.64−3.42

+1.12−0.79 1.02 0.78

2.4–3.4 12.33 ±0.94 +2.59−2.27

+1.44−1.78

+1.63−1.50 0.96 0.68

Table 9. The differential cross section, dσ/d∆η2, in bins of ∆η2 for “forwardjet+dijet” events in the case of ∆η1 > 1. The statistical, systematic and jet-energy-scale uncertainties are shown separately (see the caption of Table 1)

∆η2 bin dσ/d∆η1 δstat δsyst δCAL δFPC CQED CHAD(nb)

0.0–0.6 40.03 ±2.28 +5.32−4.81

+3.62−4.12

+1.19−1.14 0.97 0.75

0.6–1.2 46.58 ±2.59 +1.66−2.71

+3.87−5.97

+1.58−1.76 0.96 0.80

1.2–1.8 36.46 ±2.74 +7.01−5.80

+4.08−5.49

+4.38−5.49 0.98 0.76

1.8–2.8 10.27 ±1.03 +2.91−2.87

+0.80−1.44

+1.91−2.51 0.99 0.71

9 Summary

A new measurement of the inclusive jet cross sections hasbeen performed in an extended forward region, 2 < ηjet <4.3,with higher statistics and smaller systematic uncertain-

ties compared to previous studies. The measured differen-tial cross sections are presented as functions of Q2, xBj,EjetT and η

jet. The measurements were compared to the pre-dictions of next-to-leading-order QCD calculations, whichwere found to be below the data, in certain regions by as

530 The ZEUS Collaboration: Forward-jet production in deep inelastic ep scattering at HERA

much as a factor of two. The large contribution of next-to-leading-order corrections and the size of the theoreticaluncertainty indicate that in this phase space higher-ordercontributions are important. The best overall descriptionof the inclusive forward-jet cross sections was obtained bythe newly tuned ARIADNE MC model. The CASCADEMCwith J2003 set-1 and J2003 set-2 for unintegrated gluondensity failed to satisfactorily describe the data. Therefore,thesemeasurements canbeused for further adjusting the in-put parameters of the CASCADEmodel.The measurement of the cross sections of the events

containing a dijet system in addition to the forward jetis presented as functions of pseudorapidity separation be-tween jets composing the dijet, ∆η1, and pseudorapidityseparation between forward jet and dijet system, ∆η2, forall ∆η1 values and for ∆η1 < 1 and ∆η1 > 1. NLO calcu-lations describe the data at large ∆η2 but underestimatethe cross sections at small ∆η2, especially for small valuesof ∆η1, where, in the case of small xBj, the contribution ofmultiple gluon emission is expected to be large. The pre-dictions of LEPTO are significantly below the data. ARI-ADNE with default parameters significantly overestimatesthe cross sections whereas the new tuning provides a gooddescription of the data. The CASCADE MC, as in the in-clusive case, does not provide a satisfactory description ofmeasured cross sections.

Acknowledgements. We thank the DESY Directorate for the

strong support and encouragement. We are grateful for thesupport of the DESY computing and network services. Thediligent efforts of the HERA machine group are gratefully ac-

knowledged. The design, construction and installation of theZEUS detector have been made possible due to the ingenuityand efforts of many people from DESY and other institutes whoare not listed as authors. We also thank Hannes Jung and Her-

man Hessling for fruitful discussions.

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