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DESY�02�142September 2002Leading proton produ tionin e+p ollisions at HERA

ZEUS CollaborationAbstra tEvents with a �nal-state proton arrying a large fra tion of the proton beam mo-mentum, xL > 0.6, and the square of the transverse momentum p2

T < 0.5 GeV2,have been studied in e+p ollisions with the ZEUS dete tor at HERA. Data withdi�erent photon virtualities were used: Q2 < 0.02 GeV2, 0.1 < Q2 < 0.74 GeV2and 3 < Q2 < 254 GeV2, orresponding to integrated luminosities of 0.9, 1.85and 3.38 pb−1. The ross se tions are given as a fun tion of xL, p2T , Q2 andthe Bjorken s aling variable, x. The ratio of the ross se tion for leading protonprodu tion to the in lusive e+p ross se tion shows only a mild dependen e on

Q2 and on x. In the region 0.6 < xL < 0.97, the relative yield of protons is onlya weak fun tion of xL.

The ZEUS CollaborationS. Chekanov, D. Krakauer, J.H. Loizides1, S. Magill, B. Musgrave, J. Repond, R. YoshidaArgonne National Laboratory, Argonne, Illinois 60439-4815 nM.C.K. MattinglyAndrews University, Berrien Springs, Mi higan 49104-0380P. Antonioli, G. Anzivino2, G. Bari, M. Basile, L. Bellagamba, D. Bos herini, A. Bruni,G. Bruni, G. Cara Romeo, M. Chiarini, L. Cifarelli, F. Cindolo, A. Contin, M. Corradi,S. De Pasquale, P. Giusti, G. Ia obu i, G. Levi, A. Margotti, T. Massam, R. Nania, C.Nemoz3, F. Palmonari, A. Pes i, G. Sartorelli, Y. Zamora Gar ia4, A. Zi hi hiUniversity and INFN Bologna, Bologna, Italy eG. Aghuzumtsyan, D. Barts h, I. Bro k, J. Crittenden5, S. Goers, H. Hartmann, E. Hilger,P. Irrgang, H.-P. Jakob, A. Kappes, U.F. Katz6, O. Kind, E. Paul, J. Rautenberg7,R. Renner, H. S hnurbus h, A. Stifutkin, J. Tandler, K.C. Voss, M. Wang, A. WeberPhysikalis hes Institut der Universität Bonn, Bonn, Germany bD.S. Bailey8, N.H. Brook8, J.E. Cole, B. Foster, G.P. Heath, H.F. Heath, T. Namsoo,S. Robins, E. Rodrigues9, M. WingH.H. Wills Physi s Laboratory, University of Bristol, Bristol, United Kingdom mR. Ayad10, M. Capua, L. Iannotti11, A. Mastroberardino, M. S hioppa, G. SusinnoCalabria University, Physi s Department and INFN, Cosenza, Italy eJ.Y. Kim, Y.K. Kim, J.H. Lee, I.T. Lim, M.Y. Pa 12Chonnam National University, Kwangju, Korea gA. Caldwell13, M. Helbi h, X. Liu, B. Mellado, Y. Ning, S. Paganis, Z. Ren, W.B. S hmidke,F. S iulliNevis Laboratories, Columbia University, Irvington on Hudson, New York 10027 oJ. Chwastowski, A. Eskreys, J. Figiel, K. Olkiewi z, P. Stopa, L. ZawiejskiInstitute of Nu lear Physi s, Cra ow, Poland iL. Adam zyk, T. Boªd, I. Grabowska-Boªd, D. Kisielewska, A.M. Kowal, M. Kowal,T. Kowalski, M. Przyby ie«, L. Suszy ki, D. Szuba, J. Szuba14Fa ulty of Physi s and Nu lear Te hniques, University of Mining and Metallurgy, Cra ow,Poland pA. Kota«ski15, W. Sªomi«ski16Department of Physi s, Jagellonian University, Cra ow, PolandI

L.A.T. Bauerdi k17, U. Behrens, I. Blo h, K. Borras, V. Chio hia, D. Dannheim, M. Derri k18,G. Drews, J. Fourletova, A. Fox-Murphy19, U. Fri ke, A. Geiser, F. Goebel13, P. Göttli her20,O. Guts he, T. Haas, W. Hain, G.F. Hartner, S. Hillert, U. Kötz, H. Kowalski21, G. Kram-berger, H. Labes, D. Lelas, B. Löhr, R. Mankel, I.-A. Melzer-Pellmann, M. Moritz22,D. Notz, M.C. Petru i23, A. Polini, A. Raval, U. S hneekloth, F. Selonke24, H. Wes-sole k, R. Wi hmann25, G. Wolf, C. Youngman, W. ZeunerDeuts hes Elektronen-Syn hrotron DESY, Hamburg, GermanyA. Lopez-Duran Viani26, A. Meyer, S. S hlenstedtDESY Zeuthen, Zeuthen, GermanyG. Barbagli, E. Gallo, C. Genta, P. G. PelferUniversity and INFN, Floren e, Italy eA. Bamberger, A. Benen, N. Coppola, H. Raa hFakultät für Physik der Universität Freiburg i.Br., Freiburg i.Br., Germany bM. Bell, P.J. Bussey, A.T. Doyle, C. Glasman, J. Hamilton, S. Hanlon, A. Lupi27,D.H. Saxon, I.O. Skilli ornDepartment of Physi s and Astronomy, University of Glasgow, Glasgow, United King-dom mI. GialasDepartment of Engineering in Management and Finan e, Univ. of Aegean, Gree eB. Bodmann, T. Carli, U. Holm, K. Klimek, N. Krumna k, E. Lohrmann, M. Milite,H. Salehi, S. Stonjek28, K. Wi k, A. Ziegler, Ar. ZieglerHamburg University, Institute of Exp. Physi s, Hamburg, Germany bC. Collins-Tooth, C. Foudas, R. Gonçalo9, K.R. Long, F. Metli a, D.B. Miller, A.D. Tap-per, R. WalkerImperial College London, High Energy Nu lear Physi s Group, London, United Kingdom mP. Cloth, D. FilgesFors hungszentrum Jüli h, Institut für Kernphysik, Jüli h, GermanyM. Kuze, K. Nagano, K. Tokushuku29, S. Yamada, Y. YamazakiInstitute of Parti le and Nu lear Studies, KEK, Tsukuba, Japan fA.N. Barakbaev, E.G. Boos, N.S. Pokrovskiy, B.O. ZhautykovInstitute of Physi s and Te hnology of Ministry of Edu ation and S ien e of Kazakhstan,Almaty,KazakhstanH. Lim, D. SonKyungpook National University, Taegu, Korea gII

F. Barreiro, O. González, L. Labarga, J. del Peso, I. Redondo30, J. Terrón, M. VázquezDepartamento de Físi a Teóri a, Universidad Autónoma Madrid,Madrid, Spain lM. Barbi, A. Bertolin, F. Corriveau, S. Gliga, S. Lainesse, S. Padhi, D.G. StairsDepartment of Physi s, M Gill University, Montréal, Québe , Canada H3A 2T8 aT. TsurugaiMeiji Gakuin University, Fa ulty of General Edu ation, Yokohama, JapanA. Antonov, P. Danilov, B.A. Dolgoshein, D. Gladkov, V. Sosnovtsev, S. Su hkovMos ow Engineering Physi s Institute, Mos ow, Russia jR.K. Dementiev, P.F. Ermolov, Yu.A. Golubkov, I.I. Katkov, L.A. Khein, I.A. Korzhav-ina, V.A. Kuzmin, B.B. Lev henko, O.Yu. Lukina, A.S. Proskuryakov, L.M. Sh heglova,N.N. Vlasov, S.A. ZotkinMos ow State University, Institute of Nu lear Physi s, Mos ow, Russia kC. Bokel, J. Engelen, S. Grijpink, E. Ko�eman, P. Kooijman, E. Maddox, A. Pellegrino,S. S hagen, E. Tassi, H. Tie ke, N. Tuning, J.J. Velthuis, L. Wiggers, E. de WolfNIKHEF and University of Amsterdam, Amsterdam, Netherlands hN. Brümmer, B. Bylsma, L.S. Durkin, J. Gilmore, C.M. Ginsburg, C.L. Kim, T.Y. LingPhysi s Department, Ohio State University, Columbus, Ohio 43210 nS. Boogert, A.M. Cooper-Sarkar, R.C.E. Devenish, J. Ferrando, G. Grzelak, S. Patel,M. Rigby, M.R. Sutton, R. Wal zakDepartment of Physi s, University of Oxford, Oxford United Kingdom mR. Brugnera, R. Carlin, F. Dal Corso, S. Dusini, A. Garfagnini, S. Limentani, A. Longhin,A. Parenti, M. Poso o, L. Stan o, M. Tur atoDipartimento di Fisi a dell' Università and INFN, Padova, Italy eE.A. Heaphy, B.Y. Oh, P.R.B. Saull31, J.J. Whitmore32Department of Physi s, Pennsylvania State University, University Park, Pennsylvania16802 oY. IgaPolyte hni University, Sagamihara, Japan fG. D'Agostini, G. Marini, A. NigroDipartimento di Fisi a, Università 'La Sapienza' and INFN, Rome, Italy eC. Corma k33, J.C. HartRutherford Appleton Laboratory, Chilton, Did ot, Oxon, United Kingdom m

III

E. Barberis34, C. Heus h, W. Lo kman, J.T. Rahn, H.F.-W. Sadrozinski, A. Seiden,D.C. WilliamsUniversity of California, Santa Cruz, California 95064 nI.H. ParkDepartment of Physi s, Ewha Womans University, Seoul, KoreaN. PavelFa hberei h Physik der Universität-Gesamtho hs hule Siegen, GermanyH. Abramowi z, A. Gabareen, S. Kananov, A. Kreisel, A. LevyRaymond and Beverly Sa kler Fa ulty of Exa t S ien es, S hool of Physi s, Tel-AvivUniversity, Tel-Aviv, Israel dT. Abe, T. Fusayasu, S. Kagawa, T. Kohno, T. Tawara, T. YamashitaDepartment of Physi s, University of Tokyo, Tokyo, Japan fR. Hamatsu, T. Hirose24, M. Inuzuka, H. Kaji, S. Kitamura35, K. Matsuzawa, T. NishimuraS. PatelTokyo Metropolitan University, Deptartment of Physi s, Tokyo, Japan fM. Arneodo36, N. Cartiglia, R. Cirio, M. Costa, M.I. Ferrero, L. Lamberti37, S. Maselli,V. Mona o, C. Peroni, M. Ruspa, R. Sa hi, A. Solano, A. StaianoUniversità di Torino, Dipartimento di Fisi a Sperimentale and INFN, Torino, Italy eR. Galea, T. Koop, G.M. Levman, J.F. Martin, A. Mirea, A. SabetfakhriDepartment of Physi s, University of Toronto, Toronto, Ontario, Canada M5S 1A7 aJ.M. Butterworth, C. Gwenlan, R. Hall-Wilton, T.W. Jones, M.S. LightwoodPhysi s and Astronomy Department, University College London, London, United King-dom mJ. Ciborowski38, R. Ciesielski39, R.J. Nowak, J.M. Pawlak, B. Smalska40, J. Sztuk41,T. Tymienie ka42, A. Ukleja42, J. Ukleja, A.F. �arne kiWarsaw University, Institute of Experimental Physi s, Warsaw, Poland qM. Adamus, P. Plu inskiInstitute for Nu lear Studies, Warsaw, Poland qY. Eisenberg, L.K. Gladilin43, D. Ho hman, U. KarshonDepartment of Parti le Physi s, Weizmann Institute, Rehovot, Israel cD. Kçira, S. Lammers, L. Li, D.D. Reeder, A.A. Savin, W.H. SmithDepartment of Physi s, University of Wis onsin, Madison, Wis onsin 53706 nA. Deshpande, S. Dhawan, V.W. Hughes, P.B. StraubDepartment of Physi s, Yale University, New Haven, Conne ti ut 06520-8121 n

IV

S. Bhadra, C.D. Catterall, S. Fourletov, S. Menary, M. Soares, J. StandageDepartment of Physi s, York University, Ontario, Canada M3J 1P3 a

V

1 also a�liated with University College London, UK2 now at Università di Perugia, Dipartimento di Fisi a, Perugia, Italy3 now at E.S.R.F., Grenoble, Fran e4 now at Inter Ameri an Development Bank, Washington DC, USA5 now at Cornell University, Itha a, NY, USA6 on leave of absen e at University of Erlangen-Nürnberg, Germany7 supported by the GIF, ontra t I-523-13.7/978 PPARC Advan ed fellow9 supported by the Portuguese Foundation for S ien e and Te hnology (FCT)

10 now at Temple University, Philadelphia, PA, USA11 now at Consoft Sistemi, Torino, Italy12 now at Dongshin University, Naju, Korea13 now at Max-Plan k-Institut für Physik, Mün hen, Germany14 partly supported by the Israel S ien e Foundation and the Israel Ministry of S ien e15 supported by the Polish State Committee for S ienti� Resear h, grant no. 2 P03B0932216 member of Dept. of Computer S ien e17 now at Fermilab, Batavia, IL, USA18 on leave from Argonne National Laboratory, USA19 now at R.E. Austin Ltd., Col hester, UK20 now at DESY group FEB21 on leave of absen e at Columbia Univ., Nevis Labs.,NY, USA22 now at CERN23 now at INFN Perugia, Perugia, Italy24 retired25 now at Mobil om AG, Rendsburg-Büdelsdorf, Germany26 now at Deuts he Börse Systems AG, Frankfurt/Main, Germany27 now at University of Pisa, Italy28 now at Univ. of Oxford, Oxford, UK29 also at University of Tokyo30 now at LPNHE E ole Polyte hnique, Paris, Fran e31 now at National Resear h Coun il, Ottawa, Canada32 on leave of absen e at The National S ien e Foundation, Arlington, VA, USA33 now at Univ. of London, Queen Mary College, London, UK34 now at Northeastern University, Dana Resear h Center, Boston, MA, USA35 present address: Tokyo Metropolitan University of Health S ien es, Tokyo 116-8551,Japan36 also at Università del Piemonte Orientale, Novara, Italy37 now at Università di Torino, Dipartimento di Medi ina Interna, Torino, ItalyVI

38 also at �ód¹ University, Poland39 supported by the Polish State Committee for S ienti� Resear h, grant no. 2 P03B0722240 now at The Boston Consulting Group, Warsaw, Poland41 �ód¹ University, Poland42 supported by German Federal Ministry for Edu ation and Resear h (BMBF), POL01/04343 on leave fromMSU, partly supported by University of Wis onsin via the U.S.-Israel BSF

VII

a supported by the Natural S ien es and Engineering Resear h Coun il ofCanada (NSERC)b supported by the German Federal Ministry for Edu ation and Resear h(BMBF), under ontra t numbers HZ1GUA 2, HZ1GUB 0, HZ1PDA 5,HZ1VFA 5c supported by the MINERVA Gesells haft für Fors hung GmbH, the IsraelS ien e Foundation, the U.S.-Israel Binational S ien e Foundation and theBenozyio Center for High Energy Physi sd supported by the German-Israeli Foundation and the Israel S ien e Foundatione supported by the Italian National Institute for Nu lear Physi s (INFN)f supported by the Japanese Ministry of Edu ation, Culture, Sports, S ien eand Te hnology (MEXT) and its grants for S ienti� Resear hg supported by the Korean Ministry of Edu ation and Korea S ien e and Engi-neering Foundationh supported by the Netherlands Foundation for Resear h on Matter (FOM)i supported by the Polish State Committee for S ienti� Resear h, grant no.620/E-77/SPUB-M/DESY/P-03/DZ 247/2000-2002j partially supported by the German Federal Ministry for Edu ation and Re-sear h (BMBF)k supported by the Fund for Fundamental Resear h of Russian Ministry forS ien e and Edu ation and by the German Federal Ministry for Edu ationand Resear h (BMBF)l supported by the Spanish Ministry of Edu ation and S ien e through fundsprovided by CICYT

m supported by the Parti le Physi s and Astronomy Resear h Coun il, UKn supported by the US Department of Energyo supported by the US National S ien e Foundationp supported by the Polish State Committee for S ienti� Resear h, grant no.112/E-356/SPUB-M/DESY/P-03/DZ 301/2000-2002, 2 P03B 13922q supported by the Polish State Committee for S ienti� Resear h, grant no.115/E-343/SPUB-M/DESY/P-03/DZ 121/2001-2002, 2 P03B 07022

VIII

1 Introdu tionEvents with a �nal-state proton arrying a large fra tion of the available energy but asmall transverse momentum have been studied in detail in high-energy hadron-proton ollisions [1℄. The ross se tion for su h leading proton events shows a peak for values ofthe �nal-state proton momentum lose to the maximum kinemati ally allowed value, theso- alled di�ra tive peak. For lower momenta, the ross se tion is lower and the fra tionof events with a leading proton is approximately independent of the energy and type ofthe in oming parti le. This hara teristi behaviour has led to studies of the asso iatedevent in terms of the e�e tive energy available for hadronisation [2, 3℄. More re ently,events with neutrons or protons arrying a large fra tion of the proton-beam momentumhave also been measured in positron-proton (e+p) s attering at HERA [4�8℄.The study of semi-in lusive rates in hadron-nu leon ollisions indi ates that parti le pro-du tion from the target nu leon is independent of the type of the in ident hadron, a prop-erty known as vertex fa torisation [1℄. This has been studied for instan e by omparingsemi-in lusive rates, normalised to the respe tive total ross se tions, for the produ tionof parti les in the fragmentation region of the target nu leon. The hadroni data [9℄ alsoshow that, in the high-energy limit, the momentum distribution of the parti les from thefragmentation of the target hadron is independent of the energy of the in oming parti- le. These hara teristi s have not yet been extensively studied for baryon produ tion inele tron-proton ollisions.Ele troprodu tion of leading baryons is also interesting in other respe ts. The virtualphoton mediating the intera tion, in the referen e frame in whi h the proton is at rest,�u tuates into a ve tor-meson-like obje t (the ve tor dominan e model, VDM [10℄). Thetransverse size of this proje tile an be varied by hanging the virtuality, Q2, of thephoton. Real photons (Q2 = 0) have hadroni size, while, as Q2 in reases, the photonsize de reases. It is thus possible to experiment with a proje tile of varying size. Thismay lead, for instan e, to di�erent absorptive res attering of the produ ed baryon as Q2 hanges [11℄, and hen e to a breaking of vertex fa torisation.Several me hanisms have been suggested to explain the hadroprodu tion or ele tropro-du tion of leading protons. None of them are as yet amenable to al ulations based onperturbative quantum hromodynami s (pQCD). This is, in part, a onsequen e of thefa t that the small pT of the leading proton ne essitates a non-perturbative approa h.Some models [12�16℄ are based on the Regge formalism, with leading proton produ tiono urring through t- hannel ex hanges, both isos alar and isove tor, notably Pomerons,Reggeons and pions. These ex hanges mediate the intera tion between the proton andthe �u tuations of the virtual photon. The relative ontribution of the di�erent ex hangesvaries as a fun tion of the momentum and type of the s attered baryon: for leading pro-1

tons, Pomeron ex hange dominates in the di�ra tive-peak region with Reggeon and pionex hanges ontributing for lower outgoing-proton momenta. Other theoreti al models re-tain quarks and gluons as fundamental entities, but add non-perturbative elements, su has soft- olour intera tions [17℄. The on ept of fra ture fun tions also o�ers a generaltheoreti al framework for a QCD-based study of leading baryon physi s [18℄.This paper reports studies of leading proton produ tion in e+p ollisions, e+p → e+Xp,emphasizing the non-di�ra tive region. This omplements the re ent ZEUS study ofleading neutrons [8℄. High-energy protons with low transverse momentum arrying atleast 60% of the in oming-proton momentum were measured in the ZEUS leading protonspe trometer (LPS) [19℄. The fra tion of su h events with a large rapidity gap in theforward region is presented. The longitudinal- and transverse-momentum spe tra arestudied for di�erent photon virtualities, from quasi-real photoprodu tion (Q2∼<0.02 GeV2)to Q2 = 254 GeV2. The dependen e of the ross se tion for the produ tion of leadingprotons on the deep inelasti s attering (DIS) variables x and Q2 is also measured and ompared to that for the in lusive rea tion e+p → e+X. The results are dis ussed in the ontext of vertex fa torisation and parti le-ex hange models. Finally, the properties ofevents with a leading proton and two jets are presented.2 Experimental set-upThe measurements were performed at the DESY ep ollider HERA using the ZEUS dete -tor. In 1994 and 1995, HERA operated at a proton energy Ep = 820 GeV and a positronenergy Ee = 27.5 GeV.A detailed des ription of the ZEUS dete tor an be found elsewhere [20℄. A brief outlineof the omponents that are most relevant for this analysis is given below.Charged parti les are tra ked by the entral tra king dete tor (CTD), whi h operates in amagneti �eld of 1.43T provided by a thin super ondu ting oil. The CTD onsists of 72 ylindri al drift- hamber layers, organised in nine superlayers overing the polar-angle1region 15◦ < θ < 164◦. The relative transverse-momentum resolution for full-length tra ksis σ(pt)/pt = 0.0058pt ⊕ 0.0065 ⊕ 0.0014/pt, with pt in GeV [21℄.The high-resolution uranium-s intillator alorimeter (CAL) [22℄ onsists of three parts:the forward (FCAL), barrel (BCAL) and rear (RCAL) alorimeters. Ea h part is subdi-1 The ZEUS oordinate system is a right-handed Cartesian system, with the Z axis pointing in theproton beam dire tion, referred to as the �forward dire tion�, and the X axis pointing left towardsthe entre of HERA. The oordinate origin is at the nominal intera tion point. The pseudorapidityis de�ned as η = − ln(tan θ

2 ), where the polar angle, θ, is measured with respe t to the proton beamdire tion. 2

vided transversely into towers and longitudinally into one ele tromagneti se tion (EMC)and either one (in RCAL) or two (in FCAL and BCAL) hadroni se tions (HAC). The rela-tive CAL energy resolutions are σ(E)/E = 0.18/√

E for ele trons and σ(E)/E = 0.35/√

Efor hadrons (E in GeV).A lead-s intillator alorimeter (LUMI-e) at Z = −35 m [23℄, with a relative energy reso-lution of σ(E)/E = 0.18/√

E (E in GeV), was used to tag events with positrons s atteredthrough angles up to about 5 mrad, and to measure the s attered-positron energy, E ′

e, overthe range 7 < E′

e < 21 GeV. These events have Q2 < 0.02 GeV2 and are hereafter referredto as the �photoprodu tion� sample. This sample was olle ted in 1994 and orrespondsto an integrated luminosity of 0.898 ± 0.014 pb−1.Low-Q2 events (0.1 < Q2 < 0.74 GeV2) were tagged by requiring the identi� ation of thes attered positrons in the beam pipe alorimeter (BPC) [24�27℄, a tungsten-s intillatorsampling alorimeter, lo ated lose to the beam pipe, 3m downstream of the intera tionpoint in the positron beam dire tion. This low-Q2 sample, hereafter referred to as the�BPC sample�, has an integrated luminosity of 1.85±0.02 pb−1 and was olle ted in 1995.For higher-Q2 events (Q2 > 3 GeV2), the impa t position on the CAL surfa e of thes attered positron was determined with the small-angle rear tra king dete tor (SRTD) [28℄or the CAL. The SRTD is atta hed to the front fa e of the RCAL and onsists of two planesof s intillator strips, 1 m wide and 0.5 m thi k, arranged in orthogonal orientations.Events with Q2 > 3 GeV2 are referred to as the �DIS sample� in the following. Theintegrated luminosity of this sample, whi h was olle ted in 1995, is 3.38 ± 0.03 pb−1.The leading proton spe trometer (LPS) [19℄ dete ted harged parti les s attered at smallangles and arrying a substantial fra tion of the in oming-proton momentum; these par-ti les remain in the beam pipe and their traje tories were measured by a system of sili onmi ro-strip dete tors inserted very lose (typi ally a few mm) to the proton beam. Thedete tors were grouped in six stations, S1 to S6, pla ed along the beam-line in the di-re tion of the proton beam, between Z = 20 m and Z = 90 m. The tra k de�e tionsindu ed by the magnets in the proton beam-line allow a momentum analysis of the s at-tered proton. During data taking, the dete tor planes were inserted lose to the beamby means of re-entrant pots and were retra ted during beam dump and �ll operationsof the HERA ma hine. For the present measurements, only the stations S4, S5 and S6were used. The intrinsi resolution is better than 1% on the longitudinal momentum and5 MeV on the transverse momentum. The e�e tive transverse-momentum resolution is,however, dominated by the intrinsi transverse-momentum spread of the proton beam atthe intera tion point, whi h was ≈ 40 MeV in the horizontal plane and ≈ 100 MeV in theverti al plane. 3

3 Kinemati s and ross se tionsFigure 1 illustrates semi-in lusive leading proton produ tion in ep ollisions. Four kine-mati variables are needed to des ribe the intera tion e+p → e+Xp. They are de�ned interms of the four-momenta of the in oming and outgoing positron, K and K ′, and of thein oming and outgoing proton, P and P ′, respe tively.Two of the kinemati variables were hosen from among the Lorentz invariants used inin lusive studies, of whi h only two are independent: Q2 = −q2 = −(K − K ′)2, thevirtuality of the ex hanged photon; x = Q2/(2P · q) and y = q ·P/(K ·P ) ≃ Q2/(sx); andW 2 = (P +K−K ′)2 = m2

p +Q2(1−x)/x, the square of the photon-proton entre-of-massenergy. In these equations, mp is the mass of the proton and √s = 300 GeV is the e+p entre-of-mass energy.Two additional variables are required to des ribe the leading proton. They an be hosenas the momentum fra tion arried by the outgoing proton

xL =P ′ · KP · Kand its transverse momentum with respe t to the dire tion of the in oming proton, pT .In terms of these variables, the square of the four-momentum transfer from the targetproton is given by

t = (P − P ′)2 ≃ −p2T

xL

− (1 − xL)2

xL

m2p,where the se ond term is the minimum kinemati ally allowed value of |t| for a given xL.In a parti le-ex hange model, t is the square of the four-momentum of the ex hangedparti le. The p2

T range overed by the present data, 0 < p2T < 0.5 GeV2, thus translatesinto 0 < |t| < 0.5 GeV2 at xL = 1 and 0.2 ∼< |t| ∼< 1 GeV2 at xL = 0.6.The di�erential ross se tion for in lusive e+p → e+X s attering is written in terms ofthe proton stru ture fun tion, F2(x, Q2), as

d2σe+p→e+X

dxdQ2=

4πα2

xQ4

(

1 − y +y2

2

)

F2(x, Q2)(1 + ∆), (1)where ∆ is a orre tion that takes a ount of photon radiation, Z0 ex hange, and thelongitudinal stru ture fun tion, FL. In analogy with this, the di�erential ross se tion forsemi-in lusive leading proton produ tion, e+p → e+Xp, is written asd4σe+p→e+Xp

dxdQ2dxLdp2T

=4πα2

xQ4

(

1 − y +y2

2

)

F LP(4)2 (x, Q2, xL, p2

T )(1 + ∆LP ), (2)where ∆LP is the analogue of ∆. 4

3.1 Re onstru tion of the kinemati variablesThree samples of data were used:• the photoprodu tion sample, with the s attered positron tagged in the LUMI-e alorime-ter;• the BPC sample, with the s attered positron measured in the BPC;• the DIS sample, with the s attered positron dete ted in the CAL.Di�erent methods were used for the re onstru tion of the kinemati variables, Q2 and W ,for the three data sets. Tagging of the s attered positron in the LUMI-e alorimeter forphotoprodu tion events does not allow the measurement of Q2 event by event; however,the angular a eptan e of the LUMI-e alorimeter limits the Q2 range to the region

Q2 < 0.02GeV2. For these events, W was measured fromW 2 = ys, with y = (Ee−E ′

e)/Ee,where E ′

e denotes the energy of the outgoing positron. For the BPC sample, Ee and thepositron s attering angle, ϑe, as measured in the BPC, were used (�ele tron method� [24℄)to determine Q2, W , x and y. For the DIS sample, these variables were re onstru tedusing the double angle method [29℄.For the re onstru tion of the hadroni �nal state, X, the energy deposits in the CALand the tra k momenta measured in the CTD for the harged parti les were lusteredinto energy-�ow obje ts (EFOs) whi h are assumed to orrespond to parti les and areassigned the pion mass [30,31℄. The EFOs were used to re onstru t the mass, MX , of thehadroni �nal state ontained in the entral dete tor. Using the EFOs, the y variable wasalso re onstru ted with the Ja quet-Blondel method [32℄, whi h uses information fromthe hadroni �nal state to re onstru t the event kinemati s, and was denoted by yJB.Furthermore, the variableδ =

∑

i

(Ei − pZ,i) + E ′

e(1 − cos ϑe)was evaluated, where ∑

i denotes a sum over all EFOs, ex luding those assigned to thes attered positron, and Ei and pZ,i are the energy and the longitudinal momentum ofea h EFO, respe tively. For perfe t resolution and fully ontained events, energy andmomentum onservation onstrain δ to be twi e the positron beam energy. The angle ofthe hadroni �nal state (as measured in the ZEUS entral dete tor) with respe t to thein oming-proton dire tion was evaluated fromcos γh =

(∑

i pT,i)2 − (

∑

i(Ei − pz,i))2

(∑

i pT,i)2 + (∑

i(Ei − pz,i))2,where the sums ∑

i run over all EFOs ex luding those assigned to the s attered positron.5

The modulus of the momentum of the s attered proton, p′, was measured in the LPS,along with its omponent perpendi ular to the mean proton beam dire tion, pT . Thevariable xL was evaluated as xL = p′/Ep. The mean dire tion of the in oming protonbeam was determined for ea h proton �ll of HERA using the rea tion ep → eρ0p atQ2 ≈ 0 [19℄.In the following, the term �leading proton� is used to indi ate a positively harged parti ledete ted in the LPS. In the present measurement, xL is restri ted to values larger than 0.6.Charged-parti le produ tion measured at the ISR [2, 33℄ shows that the pion-to-protonratio at xL = 0.6 is about 10% and falls rapidly for in reasing values of xL.4 Event sele tionPhotoprodu tion events were sele ted at the trigger level by requiring a oin iden e be-tween an energy deposit of at least 5 GeV in the LUMI-e and of at least 464 MeV inthe RCAL (ex luding the towers immediately adja ent to the beam-pipe) or at least1250 MeV (in luding those towers). This requirement helps to suppress the ba kgroundfrom bremsstrahlung events (ep → eγp) hara terised by having a s attered positron inthe LUMI-e and no a tivity in the rest of the dete tor. The BPC and DIS events weretriggered by requiring the presen e of a s attered positron in the BPC and the CAL,respe tively. No requirement was imposed on the �nal-state proton at the trigger level.Events were sele ted o�ine in three steps: �rst in lusive events with the s attered positronin the LUMI-e, the BPC or the CAL were sele ted; then, a tra k in the LPS was required;�nally a sear h for jets was arried out in the hadroni �nal state, X. The details of thesele tion pro edure are presented in the rest of this se tion. The following requirementswere imposed for all samples:• the Z oordinate of the re onstru ted vertex, if measured, in the range −50 < Z <

50 m;• the timing of the intera tion, as measured by the CAL, onsistent with the timing ofan e+p bun h rossing.For the BPC and DIS samples, the requirement 35 < δ < 65 GeV was also imposedin order to redu e the photoprodu tion ba kground and to minimise the e�e t of theradiative orre tions.The photoprodu tion sample [34℄ was sele ted by requiring that a positron be measuredin the LUMI-e with energy in the range 12 < E′

e < 18 GeV, orresponding to 176 <

W < 225 GeV. Overlay events, in whi h some a tivity in the RCAL a identally overlaps6

with the s attered positron of a bremsstrahlung event (ep → eγp) in the LUMI-e, weresubtra ted as dis ussed in an earlier study [35℄. The subtra tion was less than 3%.The BPC sample [24, 36℄ was sele ted by requiring a s attered positron measured in theBPC with E ′

e > 7 GeV and a photon virtuality in the range 0.1 < Q2 < 0.74 GeV2. Inaddition, the requirement 0.08 < y < 0.74 was imposed, whi h orresponds to 85 < W <

258 GeV. Finally, yJB > 0.05 was required, thus ensuring hadroni a tivity away from theforward dire tion and redu ing the migration of events from low y, where the resolutionof the ele tron method is poor.In the DIS analysis [34, 36℄, a s attered positron with energy E ′

e > 10 GeV was requiredin the CAL; the photon virtuality was restri ted to the interval 3 < Q2 < 254 GeV2 andW to the region 45 < W < 225 GeV. Finally, the ondition yJB > 0.03 was imposed.The total number of events thus sele ted was approximately 94 000 for the photoprodu -tion sample, 50 000 for the BPC sample and 386 000 for the DIS sample.Next, high-momentum protons in the LPS were sele ted by requiring:• one tra k in the LPS with p2

T < 0.5 GeV2 and 0.6 < xL < 1.02. For xL > 0.97, a lowerbound on p2T was also imposed: p2

T > 0.073 GeV2. For the 1994 data, the p2T rangewas restri ted to p2

T < 0.04 GeV2. The p2T uts and the lower limit on xL restri t thedata to a region of well understood a eptan e;

• no andidate tra k was a epted if, at any point, the minimum distan e of approa hto the beam pipe, ∆pipe, was less than 0.4 mm (0.5 mm for the 1994 data). This ut redu ed the sensitivity of the a eptan e to the un ertainty on the lo ation of thebeam-pipe apertures;• events in whi h the re onstru ted proton tra k passed loser than a distan e ∆plane =

0.2 mm to the edge of any LPS dete tor were reje ted. This ensured that the tra kwas well within the a tive region of the dete tors;• the total E + pZ of the event was required to be smaller than 1655 GeV. For fully ontained events, this quantity should be equal to 2Ep = 1640 GeV. This ut reje tsrandom overlays of a beam-halo proton and an event satisfying the trigger and sele tion uts applied to the non-LPS variables;• for xL > 0.97, MX > 2 GeV was required, where MX is the re onstru ted hadroni mass in the CAL. This reje ts ontributions from ex lusive produ tion of low-massve tor mesons, whi h have Q2 and t dependen es di�erent from those of the in lusiveevents [37℄.After this sele tion, the total number of events with a good LPS tra k was 1834 for thephotoprodu tion sample, 1697 for the BPC sample and 13335 for the DIS sample.7

Finally, a sear h was performed for jets in the hadroni �nal state [38℄. Be ause of thelimited statisti s of the photoprodu tion and BPC samples, the sear h was limited tothe DIS data. The jets were re onstru ted using the kT algorithm [39℄, requiring a jettransverse energy ET > 4 GeV in the γ∗p entre-of-mass system and a jet pseudorapidity,in the laboratory frame, in the range −2 < ηjet < 2.2. A sample of 225 events with exa tlytwo jets was sele ted.5 Monte Carlo simulationSeveral Monte Carlo (MC) generators were used to determine the a eptan e of the ap-paratus for events with a leading proton. The EPSOFT2.0 Monte Carlo [40�42℄ was usedfor the BPC data. This generator simulates di�ra tive pro esses with disso iation of thevirtual photon, as well as non-di�ra tive pro esses. Vertex fa torisation is assumed. TheHERACLES4.6 Monte Carlo [43℄, whi h simulates initial- and �nal-state QED radiation,is interfa ed to EPSOFT. Samples of DIS events were simulated with RAPGAP [44, 45℄version 2.06/06, whi h in orporates meson and Pomeron ex hange; it also assumes vertexfa torisation. QED radiation was also simulated using HERACLES. Weights were as-signed to the events generated with EPSOFT and RAPGAP su h that the re onstru tedproton xL and p2T spe tra agreed with the data. For the photoprodu tion data, and forsystemati studies, events that only ontain a proton with distributions in xL and p2

Ttuned to those of the data were generated. This simulation produ ed the same results forthe LPS a eptan e as EPSOFT and RAPGAP.All generated events were passed through the trigger-simulation pa kage and the stan-dard ZEUS dete tor simulation, based on the GEANT 3.13 program [46℄. The simulationin ludes the geometry of the beam-pipe apertures, the HERA magnets and their mag-neti �elds. The spread of the intera tion-vertex position was also simulated, as were theproton-beam angle with respe t to the nominal dire tion and its dispersion at the intera -tion point. The simulated events were then passed through the same re onstru tion andanalysis programs as the data.Figures 2a)- ) ompare the distributions of the re onstru ted variables E ′

e, ϑe, and yJBin events generated with EPSOFT with those for the BPC data. The agreement betweenthe data and the simulated distributions is good. A similarly good des ription of the DISdata by RAPGAP is shown in Figs. 2d)-f) for the variables E ′

e, ϑe and γh.The agreement between the data and the MC simulation of the leading-proton variablesis also good for all three samples. As an example, the distributions for the re onstru tedEPSOFT events as a fun tion of xL, p2T , ∆pipe and ∆plane are ompared with those of theBPC data in Fig. 3. 8

6 A eptan eFigure 4 shows the ranges of pX and pY a essed by the LPS for six values of xL, usingthe oin iden e of any two of the S4, S5 and S6 stations. Here, pX and pY are the X andY omponents of the s attered-proton momentum. The region overed is determined bythe beam-pipe apertures, the shape of the sensitive region of the LPS dete tors and themagnet strengths; it is limited to xL ∼> 0.5 and p2

T = p2X + p2

Y ∼< 0.7 GeV2. Integratedover the falling p2T distribution, the LPS geometri al a eptan e rea hes a maximum for

xL in the range 0.8 to 0.9.The a eptan e was omputed as the ratio of the number of re onstru ted events in abin of a given variable to the number of generated events in that bin. The a eptan ethus in ludes the e�e ts of the geometri al a eptan e of the apparatus, its e� ien y andresolution, as well as the event sele tion and re onstru tion e� ien ies. Values of thea eptan e are given in Se tion 8.7 Systemati un ertaintiesThe systemati un ertainties were obtained by modifying the requirements and the anal-ysis pro edures as listed below:• the sensitivity to the sele tion of the proton tra k was studied by the following pro e-dure [19℄:� the tra k-sele tion requirements were varied. In parti ular, the minimum-allowedvalues of ∆pipe were hanged from 0.2 to 0.6 mm and the minimum value of ∆planewas varied from 0.1 to 0.3 mm;� the positions of some of the elements of the proton beam-line were varied withintheir un ertainties. This is parti ularly relevant at low xL, where the protonmomentum is signi� antly lower than that of the xL ≈ 1 protons used in the LPSalignment pro edure;� the LPS dete tor positions varied slightly from �ll to �ll in the 94 sample. Thesmall deviations of the a eptan e implied by these movements were estimatedby dividing the data into a �low a eptan e� and a �high a eptan e� sample,depending on the positions of the LPS stations;• the sensitivity to the remaining sele tion uts was also investigated:� for the in lusive photoprodu tion sample, the sele tion uts were tightened: the E ′

erange was restri ted to 13 < E′

e < 16 GeV, orresponding to 195 < W < 215 GeV9

and the minimum energy deposition in the RCAL was raised to 2 GeV. In addition,the orre tion for the bremsstrahlung ba kground was removed [35℄;� for the BPC sample, the BPC energy s ale was varied by ±1% and the sizes of theparameters in the BPC energy alibration were hanged within their un ertain-ties [24℄. The sele tion limits on the positron- andidate shower width were alsovaried [24℄;� for the DIS sample, the positron-sele tion pro edure was varied. The ut on thes attered-positron energy was hanged to 8 GeV and 12 GeV and the size of the�du ial region for the impa t position of the s attered positron in the SRTD wasraised by ±0.5 m in both X and Y ;� for both the BPC and the DIS samples, the lower limit on δ was varied between32 and 38 GeV and the upper limit between 60 and 68 GeV; the ut on yJB wasvaried by ±0.01;� the allowed range of values for the Z oordinate of the vertex was restri ted to−40 < Z < 40 m. The e�e t of removing the vertex requirement was also studied;� in addition, for the jet studies, the minimum jet energy was varied between 3.8and 4.2 GeV, and the upper limit on ηjet was varied between 2 and 2.4.The total systemati un ertainty on the ross se tions, obtained by summing all the above ontributions in quadrature, totalled about ±20% at xL ≈ 0.65, de reasing to ±(10-15)% for xL ∼> 0.75. The dominant ontributions are those related to the tra k-sele tionrequirements in the LPS.8 The ratio methodIn the following, several results are presented in terms of the ratios, rLP(2) and rLP(3), ofthe ross se tion for produ tion of leading protons to the ross se tion for in lusive e+ps attering; these ratios are evaluated in bins of x and Q2 (rLP(2)), or in bins of x, Q2 and xL(rLP(3)). They are obtained from the measured fra tion of the events, in a given bin, thathave a leading proton, NLP/N . In this fra tion, the a eptan e orre tions related to thepositron sele tion pro edure an el, and so do the orresponding systemati un ertainties.The only remaining orre tion to apply is that for the LPS a eptan e, ǫLPS.The ratio rLP(2) was thus obtained as

rLP(2)(x, Q2) =NLP(x, Q2)

N(x, Q2)

1

ǫLPS

.Averaged over the region 0.6 < xL < 0.97 and p2T < 0.5 GeV2, ǫLPS is approximately 23%;over the region 0.6 < xL < 0.97 and p2

T < 0.04 GeV2, ǫLPS ≈ 51%.10

From Eqs. (1) and (2), it is apparent that the ross se tion ratio rLP(2) is also equal tothe ratio of the proton tagged and in lusive stru ture fun tions:rLP(2)(x, Q2) =

F̄LP(2)

2 (x, Q2)

F2(x, Q2), (3)where F̄

LP(2)2 is obtained from F

LP(4)2 by integration over the measured xL and p2

T ranges:F̄

LP(2)2 (x, Q2) =

p2T max∫

0

dp2T

0.97∫

0.6

dxL FLP(4)2 (x, Q2, xL, p2

T ).The radiative orre tions and the ontributions from FL are assumed to be the same forthe in lusive and the proton-tagged rea tions.The ratio rLP(3)(x, Q2, xL) is de�ned in analogy to rLP(2)(x, Q2):rLP(3)(x, Q2, xL) =

NLP(x, Q2, xL)

N(x, Q2)

1

ǫLPS(xL)∆xL

, (4)where ∆xL indi ates the size of the xL bins. In analogy with Eq. (3),rLP(3)(x, Q2, xL) =

F̄LP(3)2 (x, Q2, xL)

F2(x, Q2), (5)where F̄

LP(3)2 (x, Q2, xL) di�ers from F̄

LP(2)2 (x, Q2) in that no integration over xL is per-formed.The ratios rLP(2) and rLP(3) an also be interpreted in terms of the virtual photon-proton ross se tion for the pro ess γ∗p → Xp and the total virtual photon-proton ross se tion,

σtot. For example, the ratio rLP(3) an be written asrLP(3)(x, Q2, xL) =

1

σtot

p2T max∫

0

dp2T

d2σγ∗p→Xp

dxLdp2T

=1

σtot

dσγ∗p→Xp

dxL

,where the virtual photon-proton ross se tion, d2σγ∗p→Xp/dxLdp2T , is related to the positron-proton ross se tion, d4σe+p→e+Xp/dQ2dxdxLdp2

T , byd4σe+p→e+Xp

dQ2dxdxLdp2T

= Γd2σγ∗p→Xp

dxLdp2T

,where Γ = (α/xQ2π)[1 + (1 − y2)], is the photon �ux fa tor and α is the �ne-stru ture onstant. 11

9 ModelsThe data were tested against the hypothesis of vertex fa torisation, a very general featureof hadron-hadron intera tions [1℄ whi h relates rea tions with di�erent beam parti les totheir respe tive total ross se tions. In parti ular, in the rea tion γ∗p → Xp, the γ∗-Xand p-p verti es fa torise if the amplitude for the rea tion an be written as the produ tof two vertex fun tions, Gγ∗X(x, Q2) and Gpp(xL, p2T ). In this ase, the ross se tion as afun tion of the lepton variables x and Q2 should be independent of the baryon variables

xL and p2T , and vi e versa.The data were also ompared to the following spe i� models:

• the LUND string-fragmentation model as implemented in JETSET [47℄ and used inDJANGO [48℄, in whi h leading baryons originate from the hadronisation of the target;• the soft- olour-intera tion model (SCI) [17℄, as implemented in LEPTO 6.5 [49℄, whereleading protons are obtained from standard DIS events by means of a non-perturbativeredistribution of olour among the fragmenting partons;• the Regge model of Sz zurek et al. [16℄, whi h assumes a superposition of Pomeron,Reggeon and pion ex hanges;• the QCD-inspired model of Durães et al. [50℄, developed in the framework of theintera ting-gluon model [51℄, whi h assumes that high-energy hadron-hadron ollisionsare dominated by multiple in oherent gluon-gluon intera tions. The valen e quarksthat do not take part in the intera tion give rise to the leading baryons. The extensionto ep ollisions is made in the VDM framework.10 Results10.1 Leading proton events with a forward large rapidity gapSome indi ation of the produ tion me hanism of leading protons an be obtained fromthe rapidity distribution of the hadroni �nal-state parti les. In parti ular, events ofdi�ra tive origin, i.e. due to Pomeron ex hange, are hara terised by a gap in the rapiditydistribution in the forward dire tion.Figure 5a) shows the distribution of the DIS events in the (ηmax, xL) plane, where ηmaxis the pseudorapidity of the most-forward energy deposit of at least 400 MeV in theCAL. The a umulation of events at xL ≈ 1, whi h mostly have ηmax < 2.5, is dueto di�ra tive events [52℄, e+p → e+Xp, in whi h the �nal-state proton remains inta tand arries approximately the same momentum as the in oming proton. Events with12

ηmax < 2.5 and xL ∼< 0.97 are as ribed to double di�ra tive disso iation, e+p → e+XN ,where the proton disso iates into the state N , with mass MN . Although N is produ edat xL ≃ 1, the proton from the de ay of N has a lower value of xL. When both MN andMX are small, the systems X and N are separated by a large gap in pseudorapidity. IfMN < 4-5 GeV, only the proton from the system N is measured, while the other parti leses ape undete ted down the beam pipe. The topology of a doubly disso iative event isthus hara terised by a rapidity gap in the forward region in onjun tion with a low-xLproton.To sele t a sample of di�ra tive events, the requirement ηmax < 2.5 was imposed. Fig-ure 5b) shows the fra tion of BPC and DIS events with a leading proton that also haveηmax < 2.5 (see also Table 1). Events with a large rapidity gap dominate for xL ≈ 1.For 0.6 < xL < 0.97, the fra tion of leading proton events with a large rapidity gap isless than 10% in any given bin, and is only weakly dependent on Q2 and xL. This result,whi h indi ates that di�ra tion is not the main me hanism responsible for produ tionof leading protons in this region, is onsistent with the predi tions of the Regge-basedmodels [16, 53℄.10.2 Momentum spe tra of leading protons10.2.1 Longitudinal-momentum spe traThe normalised ross-se tion rLP(3) = (1/σtot)·dσγ∗p→Xp/dxL for the rea tion e+p → e+Xpwith a leading proton having xL > 0.6 and p2

T < 0.5 GeV2 is shown in Fig. 6 andgiven in Table 2 for the BPC sample, integrated over the range 0.1 < Q2 < 0.74 GeV2,85 < W < 258 GeV, 1.5 × 10−6 < x < 1.0 × 10−4, and for the DIS sample, integratedover the region 3 < Q2 < 254 GeV2, 45 < W < 225 GeV, 1.2 × 10−4 < x < 4 × 10−2.These results are ompared with those from the rea tion pp → pX at √s = 19.6 GeV [54℄,integrated over the same p2

T region and normalised to the orresponding inelasti rossse tion. For xL ∼< 0.9, the fra tion of events with a leading proton is onsistent for thepp and γ∗p data sets, in a ord with vertex fa torisation. A dependen e on the entre-of-mass energy is apparent for xL > 0.9, as expe ted from Regge parametrisations of thepp → pX data [55, 56℄.Figure 7 and Table 3 present the photoprodu tion, BPC and DIS data for the lower p2

Tregion, p2T < 0.04 GeV2 and 0.6 < xL < 0.95, where the upper ut on xL, whi h removesthe di�ra tive events, is set by the LPS a eptan e for this p2

T range. The fra tion ofevents with a leading proton is approximately the same in all three regimes. The ppdata [54℄ for p2T < 0.05 GeV2 again agree with the ep data for xL ∼< 0.9. The present13

photoprodu tion results, however, are signi� antly higher than those found by H1 [7℄ insimilar ranges of Q2, W and p2T .Figure 8 ompares the DIS data to the spe i� models of Se tion 9. The standard DISMonte Carlo generator DJANGO [48℄ predi ts a stronger de rease of the ross se tionwith xL than that observed and, in addition, has no di�ra tive peak. It also substantiallyunderestimates the rate of leading proton produ tion in the measured xL range. The SCImodel [17℄, as implemented in LEPTO6.5 [49℄, also falls below the data, even though itgenerates a larger number of leading protons than DJANGO and has a peak at xL = 1.These two models are ruled out by the data.The QCD-inspired model of Durães et al. [50, 57℄ is in better agreement with the data,but is too low in the di�ra tive peak region. Nevertheless, the similarity to the data isremarkable, given the small number of free parameters in the model.The Regge-based al ulation of Sz zurek et al. [16℄ agrees with the data, although it issomewhat too low at small values of xL. In this approa h, leading proton produ tionfor 0.6 < xL < 0.9 is dominated by isos alar Reggeon ex hange; di�ra tive pro esses,due to Pomeron ex hange, be ome in reasingly important as xL approa hes unity. The ontribution of pion ex hange, in luding the produ tion of ∆ baryons, is also evaluated.The normalisation of the Reggeon ontribution has a large theoreti al un ertainty [16,58℄and the present data suggest that this ontribution should be in reased with respe t tothe assumption made by Sz zurek et al. [16℄.10.2.2 Transverse-momentum spe traThe ross-se tions dσγ∗p→Xp/dp2

T are shown in Fig. 9 for the BPC sample integrated overthe range 0.1 < Q2 < 0.74 GeV2, 85 < W < 258 GeV, 1.5 × 10−6 < x < 1.0 × 10−4for di�erent xL sele tions. Similar distributions for the DIS sample are shown in Fig. 10,integrated over the region 3 < Q2 < 254 GeV2, 45 < W < 225 GeV, 1.2 × 10−4 < x <

4 × 10−2. In all regions, the form dσγ∗p→Xp/dp2T = Ae−bp2

T �ts satisfa torily the data.The values of the slope-parameters b obtained for ea h xL bin are, within un ertainties,independent of xL, as shown in Fig. 11 (see also Table 4).The BPC and DIS data together indi ate that b is independent of Q2 and xL. Themean value of b for the BPC data is 〈b〉 = 6.6 ± 0.6 (stat.) ± 0.8 (syst.) GeV−2 and〈b〉 = 6.9 ± 0.2 (stat.) ± 0.8 (syst.) GeV−2 for the DIS data for 0.6 < xL < 0.97. Alsoplotted in Fig. 11a) is the result obtained for di�ra tive photoprodu tion [59℄, whi his onsistent with the values found at higher Q2. In addition, the present results are ompatible with the pp → pX data [54℄, also shown in Fig. 11a). This, together withthe fa t that b is approximately Q2-independent, provides additional support for vertex14

fa torisation.The predi tions of Sz zurek et al. [16℄ are in a ord with the transverse-momentum data,as shown in Fig. 11b). In this model, no Q2 dependen e is expe ted for b [60℄. TheDJANGO program (not shown) has an e�e tive slope b ≈ 4 GeV−2. LEPTO6.5 (alsonot shown) has b ≈ 3.5 GeV−2. Both are independent of xL and signi� antly below thevalues measured. The model of Durães et al. [50℄ does not make expli it predi tions forthe transverse-momentum distribution.10.3 The proton-tagged stru ture-fun tion F̄ LP

2The a eptan e- orre ted fra tion of events with a leading proton is used to measure theproton-tagged stru ture-fun tion F̄ LP2 , as dis ussed in Se tion 8. To sele t a predominantlynon-di�ra tive sample, the ut xL < 0.97 was imposed.Figures 12 and 13 show rLP(3)(x, Q2, xL), determined using Eq. (4), for the BPC and DISsamples, respe tively, in several x and Q2 bins for p2

T < 0.5 GeV2. The data are also givenin Tables 5-7. Only a weak dependen e on x and Q2 is apparent, indi ating that F̄LP(3)2has approximately the same x and Q2 dependen e as F2(x, Q2). The data exhibit a weak

xL dependen e, as already seen in Fig. 6. Figure 14 shows rLP(2) for �xed Q2 values as afun tion of x; the results again have little x dependen e (see also Table 8).Figure 15a) and Table 9 present the BPC and DIS data for 0.6 < xL < 0.97 and p2T <

0.5 GeV2, averaged over x for di�erent Q2 ranges, 〈rLP(2)(Q2)〉. The leading protonyield in reases by approximately 20%, from 〈rLP(2)〉 ≈ 0.12 to 〈rLP(2)〉 ≈ 0.15, when Q2varies from ≈ 0.25 GeV2 (the average value of Q2 for the BPC sample) to 100 GeV2,indi ating a modest but de�nite breakdown of vertex fa torisation. Figure 15b) andTable 10 present the points of Fig.15a) normalised to 〈rLP(2)(Q2 = 0.25 GeV2)〉. Theresults for the restri ted p2T range, p2

T < 0.04 GeV2, are also shown. The breaking of vertexfa torisation is approximately the same for p2T < 0.5 GeV2 and for p2

T < 0.04 GeV2. Ane�e t of similar size was measured for leading neutron produ tion [8℄; the orrespondingdata, normalised to the value at Q2 = 0.25 GeV2, are also shown in Fig. 15b). Theneutron data are measured for s attering angles less than 0.8 mrad, orresponding top2

T < 0.43 · x2L GeV2.This Q2 dependen e of the proton yield an be qualitatively as ribed to absorptive e�e tsin the γ∗p system [11℄. The transverse size of the virtual photon de reases with in reasing

Q2, redu ing the likelihood that the produ ed baryon res atters on the hadroni ompo-nent of the virtual photon.The data of Fig. 14 are presented in Fig. 16 in terms of F̄LP(2)2 , obtained by multiplying

rLP(2) by F2. For the BPC region, a parameterisation of the ZEUS F2 results [25℄ was15

used. For the DIS region, the parameterisation of Botje [61℄ was used. Sin e rLP(2) isapproximately independent of Q2 and x, F̄LP(2)2 is approximately proportional to F2. Asindi ated in the �gure, the proportionality onstant between F̄

LP(2)2 and F2 is 〈rLP(2)〉 ≈

0.13.The H1 ollaboration has published [5℄ a study of leading proton produ tion for p2T <

0.04 GeV2, 0.7 < xL < 0.9, 2 < Q2 < 50 GeV2 and 6× 10−5 < x < 6× 10−3. The presentanalysis was repeated in the region of overlap with the H1 data set. A omparison of theH1 and ZEUS results is presented in Fig. 17. The agreement is good.10.4 Leading protons with asso iated dijet produ tionThe ratio rjetLP of the yield of leading proton DIS events with asso iated dijet produ tionto the in lusive yield of leading proton events is presented as a fun tion of xL and p2

Tin Fig. 18 and Tables 13-14. The LPS a eptan e, as well as the s attered positrona eptan e, an els in this ratio. The data are shown for the range 0.6 < xL < 0.97 andp2

T < 0.5 GeV2. No signi� ant deviation from a �at behaviour is seen as a fun tion of xL,although there is some p2T dependen e. The results of this exploratory study thus suggestthat the longitudinal- and transverse-momentum distributions of the leading proton arelargely insensitive to the presen e of a se ond hard s ale, given by the transverse energyof the jets.Figure 19 and Tables 15-17 present the fra tion of the dijet events with a leading proton,

rLPjet , plotted as a fun tion of ET , x and Q2. In this ase, all orre tions an el with theex eption of that due to the LPS a eptan e, whi h is, however, independent of ET , Q2and x. The ratio is approximately independent of these variables and its value is onsistentwith that of rLP(2). This suggests that the ET , Q2 and x dependen es of the dijet rossse tion are una�e ted by the requirement of a leading proton, and that the fra tion ofdijet events with a leading proton is the same as the fra tion of in lusive events with aleading proton.10.5 SummaryEvents of the type e+p → e+Xp with a �nal-state proton with xL > 0.6 have been studiedin e+p ollisions at HERA. The analyses used a photoprodu tion sample (Q2 < 0.02GeV2),a low-Q2 sample (0.1 < Q2 < 0.74 GeV2) and a DIS sample (3 < Q2 < 254 GeV2).For events with a leading proton in the range 0.6 < xL < 0.97 and p2

T < 0.5 GeV2, themain features of the data an be summarised as follows:16

• less than 10% of the leading proton events in any given xL bin exhibit a large rapiditygap (ηmax < 2.5), indi ating that di�ra tion is not the main me hanism responsiblefor the produ tion of leading protons in this region;• the proton xL spe trum is only a weak fun tion of xL for xL∼<0.97;• the p2

T dependen e of the ross se tion is well des ribed by an exponential fun tion,with a slope approximately independent of xL and Q2, b ≈ 7 GeV−2. The slope is also onsistent with the value measured for pp ollisions;• the x and Q2 dependen e of the semi-in lusive stru ture fun tion, F LP

2 , is similar tothat of F2, independently of xL. However, F LP2 grows with Q2 slightly faster than F2,resulting in a yield of leading protons about 20% larger at Q2 = 100 GeV2 than at

Q2 ≈ 0. A similar e�e t was observed for leading neutron produ tion;• the shapes of the xL and p2

T spe tra are largely una�e ted by requiring two jets withinthe hadroni �nal state X. The Q2, x and ET dependen es of the dijet ross se tionare also broadly onsistent for leading proton events and in lusive events.The main features of the data are reprodu ed by a Regge model assuming a superpositionof Pomeron, Reggeon and pion traje tories. The DJANGO and SCI models are ruled outby the data.For 0.6 < xL < 0.9, the proton spe trum for (virtual-) photon-proton ollisions is on-sistent with the results found in proton-proton rea tions at lower entre-of-mass energy.The fra tion of the events with a leading proton is approximately the same for the γ∗pand pp data, in agreement with vertex fa torisation.In the xL region explored, a modest violation of vertex fa torisation is observed. Never-theless, the results of this paper indi ate that the properties of the �nal-state proton arelargely independent of those of the virtual photon.A knowledgementsWe thank the DESY Dire torate for their en ouragement, and gratefully a knowledgethe support of the DESY omputing and network servi es. We are spe ially grateful tothe HERA ma hine group: ollaboration with them was ru ial to the su essful instal-lation and operation of the leading proton spe trometer. The design, onstru tion andinstallation of the ZEUS dete tor have been made possible by the ingenuity and e�ortof many people from DESY and home institutes who are not listed as authors. Finally,it is a pleasure to thank F.S. Navarra, N.N. Nikolaev and A. Sz zurek for many usefuldis ussions. 17

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[19℄ ZEUS Collab., M. Derri k et al., Z. Phys. C 73, 253 (1997).[20℄ ZEUS Collab., U. Holm (ed.), The ZEUS Dete tor, Status Report (unpublished)DESY, 1993, available onhttp://www-zeus.desy.de/bluebook/bluebook.html.[21℄ N. Harnew et al., Nu l. Instr. and Meth. A 279, 290 (1989);B. Foster et al., Nu l. Phys. Pro . Suppl. B 32, 181 (1993);B. Foster et al., Nu l. Instr. and Meth. A 338, 254 (1994).[22℄ M. Derri k et al., Nu l. Instr. and Meth. A 309, 77 (1991);A. Andresen et al., Nu l. Instr. and Meth. A 309, 101 (1991);A. Caldwell et al., Nu l. Instr. and Meth. A 321, 356 (1992);A. Bernstein et al., Nu l. Instr. and Meth. A 336, 23 (1993).[23℄ J. Andruszków et al., Report DESY-92-066, DESY, 1992;ZEUS Collab., M. Derri k et al., Z. Phys. C 63, 391 (1994);J. Andruszków et al., A ta Phys. Pol. B 32, 2025 (2001).[24℄ ZEUS Collab., J. Breitweg et al., Phys. Lett. B 407, 432 (1997).[25℄ ZEUS Collab., J. Breitweg et al., Phys. Lett. B 487, 53 (2000).[26℄ B. Surrow, Ph.D. thesis, University of Hamburg (1998), Report DESY-THESIS-1998-004.[27℄ T. Monteiro, Ph.D. thesis, University of Hamburg (1998), Report DESY-THESIS-1998-027.[28℄ A. Bamberger et al., Nu l. Instr. and Meth. A 401, 63 (1997).[29℄ S. Bentvelsen, J. Engelen and P. Kooijman, Pro eedings of the Workshop on Physi sat HERA, Volume 1, W. Bu hmüller and G. Ingelman (eds.), DESY (1991) p. 23;K. C. Hoeger, ibid., p. 43.[30℄ ZEUS Collab., J. Breitweg et al., Eur. Phys. J. C 6, 43 (1999).[31℄ G.M. Briskin, Ph.D. Thesis, University of Tel Aviv (1998), Report DESY-THESIS-1998-036.[32℄ F. Ja quet and A. Blondel, Pro eedings of the Study for an ep Fa ility for Europe,U. Amaldi (Ed.), p. 391, Hamburg, Germany (1979). Also Preprint DESY 79/48.[33℄ P. Capiluppi et al., Nu l. Phys. B 70, 1 (1974);P. Capiluppi et al., Nu l. Phys. B 79, 189 (1974);M.G. Albrow et al., Nu l. Phys. B 73, 40 (1974).[34℄ Y. Gar ia-Zamora, Ph.D. thesis, University of Geneva (1998) (unpublished).[35℄ ZEUS Collab., J. Breitweg et al., Eur. Phys. J. C 2, 247 (1998).19

[36℄ A. Garfagnini, Ph.D. thesis, University of Calabria (1998) (unpublished).[37℄ See e.g.:J.A. Crittenden, Ex lusive Produ tion of Neutral Ve tor Mesons at the Ele tron-Proton Collider HERA, Springer Tra ts in Modern Physi s, Vol. 140, Springer,Berlin, Germany (1997), and referen es therein;H. Abramowi z and A. Caldwell, Rev. Mod. Phys. 71, 1275 (1999), and referen estherein.[38℄ M.C. Petru i, Ph.D. thesis, University of Torino (1999), unpublished.[39℄ S. Catani et al., Phys. Lett. B 269, 432 (1991).[40℄ ZEUS Collab., J. Breitweg et al., Z. Phys. C 75, 421 (1997).[41℄ M. Kasprzak, Ph.D. thesis, University of Warsaw (1996), Internal Report DESY-F35D-96-16.[42℄ M. Inuzuka, Ph.D. thesis, University of Tokyo (1999), KEK Report 99-9.[43℄ K. Kwiatkowski, H. Spiesberger and H.-J. Möhring, Comp. Phys. Comm. 69, 155(1992).[44℄ H. Jung, Comp. Phys. Comm. 86, 147 (1995).[45℄ C.-P. Fagerstroem, Ph.D. Thesis, University of Toronto (1999), DESY Report DESY-THESIS-1999-039.[46℄ R. Brun et al., GEANT3 , Te hni al Report CERN DD/EE/84-1, CERN, 1987.[47℄ T. Sjöstrand, Comp. Phys. Comm. 82, 74 (1994).[48℄ G. A. S hüler and H. Spiesberger, Pro eedings of the Workshop on Physi s at HERA,Volume 3, W. Bu hmüller and G. Ingelman (eds.), DESY (1991), p. 1419;H. Spiesberger, DJANGOH, http://www.desy.de/~hspiesb/djangoh.html.[49℄ G. Ingelman, A. Edin and J. Rathsman, Comp. Phys. Comm. 101, 108 (1997).[50℄ F.O. Durães, F.S. Navarra and G. Wilk, Phys. Rev. D 58, 094034 (1998).[51℄ G.N. Fowler et al., Phys. Rev. C 40, 1219 (1989).[52℄ ZEUS Collab., M. Derri k et al., Z. Phys. C 68, 569 (1995).[53℄ H. Holtmann et al., Z. Phys. C 69, 297 (1996).[54℄ J. Whitmore et al., Phys. Rev. D 11, 3124 (1975).[55℄ S.N. Ganguli and D.P. Roy, Phys. Rep. 67, 201 (1980).[56℄ M. Batista and R.J.M. Covolan, Phys. Rev. D 59, 054006 (1999).[57℄ F.O. Durães, F.S. Navarra and G. Wilk, hep-ph/0209328 (2002).20

[58℄ N.N. Nikolaev, private ommuni ation.[59℄ ZEUS Collab., J. Breitweg et al., Eur. Phys. J. C 2, 237 (1998).[60℄ N.N. Nikolaev, A ta Phys. Pol. B 29, 2425 (1998).[61℄ M. Botje, Eur. Phys. J. C 14, 285 (2000).

21

Table 1: Fra tion of events with ηmax < 2.5. Statisti al un ertainties are given;systemati un ertainties mostly an el in the ratio.xL NLP(ηmax < 2.5)/NLPBPC0.63 0.054 ± 0.0300.66 0.116 ± 0.0330.69 0.075 ± 0.0180.72 0.070 ± 0.0200.75 0.083 ± 0.0210.78 0.099 ± 0.0200.81 0.077 ± 0.0180.84 0.044 ± 0.0140.87 0.066 ± 0.0170.90 0.042 ± 0.0140.93 0.011 ± 0.0080.96 0.040 ± 0.0160.99 0.355 ± 0.0641.00 0.812 ± 0.036DIS0.63 0.0674 ± 0.00930.66 0.0567 ± 0.00810.69 0.0728 ± 0.00720.72 0.0603 ± 0.00630.75 0.0543 ± 0.00570.78 0.0507 ± 0.00500.81 0.0597 ± 0.00470.84 0.0495 ± 0.00490.87 0.0364 ± 0.00400.90 0.0421 ± 0.00470.93 0.0304 ± 0.00530.96 0.0805 ± 0.01320.99 0.3445 ± 0.02311.00 0.7683 ± 0.0164

22

Table 2: The normalised ross-se tion (1/σtot) · dσγ∗p→Xp/dxL for the BPC andDIS data in the region p2T < 0.5 GeV2. The two rightmost values indi ate thestatisti al and systemati un ertainties, respe tively.

xL (1/σtot) · dσγ∗p→Xp/dxLBPC0.65 0.339 ± 0.022 ± 0.0500.75 0.399 ± 0.019 ± 0.0480.83 0.330 ± 0.014 ± 0.0490.93 0.331 ± 0.021 ± 0.0400.99 3.60 ± 0.37 ± 0.54DIS0.62 0.413 ± 0.019 ± 0.0910.65 0.431 ± 0.017 ± 0.0650.69 0.462 ± 0.016 ± 0.0560.71 0.445 ± 0.015 ± 0.0660.75 0.421 ± 0.012 ± 0.0880.77 0.433 ± 0.012 ± 0.0480.81 0.379 ± 0.010 ± 0.0460.83 0.359 ± 0.009 ± 0.0290.87 0.368 ± 0.010 ± 0.0370.89 0.333 ± 0.010 ± 0.0300.93 0.289 ± 0.012 ± 0.0260.95 0.46 ± 0.03 ± 0.110.99 2.48 ± 0.12 ± 0.37

23

Table 3: The normalised ross-se tion (1/σtot) · dσγ∗p→Xp/dxL for the photopro-du tion, BPC and DIS data for p2T < 0.04 GeV2. The two rightmost values indi atethe statisti al and systemati un ertainties, respe tively.

xL (1/σtot) · dσγ∗p→Xp/dxLPhotoprodu tion0.64 0.110 ± 0.017 ± 0.0220.70 0.081 ± 0.008 ± 0.0160.76 0.079 ± 0.006 ± 0.0120.82 0.090 ± 0.006 ± 0.0120.88 0.080 ± 0.006 ± 0.012BPC0.65 0.084 ± 0.007 ± 0.0130.75 0.099 ± 0.005 ± 0.0120.83 0.081 ± 0.005 ± 0.0120.93 0.0697 ± 0.0100 ± 0.0084DIS0.62 0.111 ± 0.008 ± 0.0240.65 0.105 ± 0.006 ± 0.0160.69 0.110 ± 0.005 ± 0.0130.71 0.103 ± 0.004 ± 0.0150.75 0.095 ± 0.003 ± 0.0200.77 0.102 ± 0.003 ± 0.0110.81 0.092 ± 0.003 ± 0.0110.83 0.0910 ± 0.0030 ± 0.00730.87 0.0910 ± 0.0040 ± 0.00910.89 0.0820 ± 0.0050 ± 0.0075

24

Table 4: The slopes, b, from �ts of the fun tional form e−bp2T to dσγ∗p→Xp/dp2

T forleading protons as a fun tion of xL for the BPC and DIS data samples. The tworightmost values indi ate the statisti al and systemati un ertainties, respe tively.xL b (GeV−2)BPC0.65 7.5 ± 1.2 +0.4

−1.90.75 7.6 ± 1.0 +1.2−1.10.83 6.2 ± 1.2 +1.2−0.70.93 4.5 ± 1.2 +1.5−0.8DIS0.62 7.4 ± 1.2 +1.0−1.30.65 7.7 ± 0.8 +2.0−1.20.69 7.3 ± 0.6 +0.8−0.80.71 6.8 ± 0.6 +0.3−0.60.75 6.1 ± 0.6 +1.2−1.20.77 6.8 ± 0.7 +0.4−0.40.81 7.9 ± 0.9 +0.8−0.90.83 7.3 ± 0.8 +0.6−0.90.87 7.2 ± 0.7 +1.1−1.80.89 6.6 ± 0.7 +0.6−0.50.93 5.9 ± 0.9 +1.2−1.00.95 4.4 ± 1.7 +1.5−0.40.99 7.0 ± 0.9 +1.9−1.1

25

Table 5: The ratio rLP(3) = F̄LP(3)2 /F2 as a fun tion of xL, x and Q2 (BPCsample), for protons with p2

T < 0.5 GeV2. The two rightmost values indi ate thestatisti al and systemati un ertainties, respe tively.Q2 (GeV2) x xL rLP(3)0.2 7.4E-06 0.67 0.310 ± 0.050 ± 0.0560.2 7.4E-06 0.79 0.408 ± 0.042 ± 0.0490.2 7.4E-06 0.91 0.367 ± 0.049 ± 0.0370.2 4.9E-06 0.67 0.308 ± 0.052 ± 0.0550.2 4.9E-06 0.79 0.331 ± 0.039 ± 0.0400.2 4.9E-06 0.91 0.361 ± 0.050 ± 0.0360.2 3.5E-06 0.67 0.281 ± 0.063 ± 0.0510.2 3.5E-06 0.79 0.333 ± 0.049 ± 0.0400.2 3.5E-06 0.91 0.377 ± 0.065 ± 0.0380.4 2.6E-05 0.67 0.357 ± 0.031 ± 0.0640.4 2.6E-05 0.79 0.356 ± 0.022 ± 0.0430.4 2.6E-05 0.91 0.317 ± 0.026 ± 0.0320.4 1.3E-05 0.67 0.356 ± 0.061 ± 0.0640.4 1.3E-05 0.79 0.405 ± 0.047 ± 0.0490.4 1.3E-05 0.91 0.265 ± 0.047 ± 0.0270.4 8.8E-06 0.67 0.357 ± 0.084 ± 0.0640.4 8.8E-06 0.79 0.317 ± 0.057 ± 0.0380.4 8.8E-06 0.91 0.298 ± 0.068 ± 0.0300.6 4.3E-05 0.67 0.438 ± 0.063 ± 0.0790.6 4.3E-05 0.79 0.386 ± 0.043 ± 0.0460.6 4.3E-05 0.91 0.354 ± 0.051 ± 0.035

26

Table 6: The ratio rLP(3) = F̄LP(3)2 /F2 as a fun tion of xL, x and Q2 (DIS sample,up to Q2 = 12 GeV2), for protons with p2

T < 0.5 GeV2. The two rightmost valuesindi ate the statisti al and systemati un ertainties, respe tively.Q2 (GeV2) x xL rLP(3)4.0 1.5E-04 0.67 0.344 ± 0.033 ± 0.0624.0 1.5E-04 0.79 0.345 ± 0.023 ± 0.0414.0 1.5E-04 0.91 0.326 ± 0.029 ± 0.0334.0 2.5E-04 0.67 0.327 ± 0.035 ± 0.0594.0 2.5E-04 0.79 0.353 ± 0.026 ± 0.0424.0 2.5E-04 0.91 0.313 ± 0.031 ±0.0314.0 4.4E-04 0.67 0.367 ± 0.035 ± 0.0664.0 4.4E-04 0.79 0.335 ± 0.024 ± 0.0404.0 4.4E-04 0.91 0.305 ± 0.029 ±0.0304.0 9.8E-04 0.67 0.443 ± 0.040 ± 0.0804.0 9.8E-04 0.79 0.354 ± 0.026 ± 0.0424.0 9.8E-04 0.91 0.303 ± 0.030 ± 0.0308.0 2.5E-04 0.67 0.398 ± 0.031 ± 0.0728.0 2.5E-04 0.79 0.359 ± 0.021 ± 0.0438.0 2.5E-04 0.91 0.382 ± 0.028 ± 0.0388.0 4.4E-04 0.67 0.387 ± 0.028 ± 0.0708.0 4.4E-04 0.79 0.409 ± 0.020 ± 0.0498.0 4.4E-04 0.91 0.335 ± 0.023 ± 0.0338.0 9.8E-04 0.67 0.451 ± 0.031 ± 0.0818.0 9.8E-04 0.79 0.420 ± 0.021 ± 0.0508.0 9.8E-04 0.91 0.375 ± 0.026 ± 0.0388.0 2.2E-03 0.67 0.515 ± 0.050 ± 0.0938.0 2.2E-03 0.79 0.380 ± 0.031 ± 0.0468.0 2.2E-03 0.91 0.421 ± 0.041 ± 0.04212.0 4.4E-04 0.67 0.355± 0.029 ± 0.06412.0 4.4E-04 0.79 0.379 ± 0.022 ± 0.04612.0 4.4E-04 0.91 0.396 ± 0.028 ± 0.04012.0 9.8E-04 0.67 0.416 ± 0.029 ± 0.07512.0 9.8E-04 0.79 0.387 ± 0.020 ± 0.04612.0 9.8E-04 0.91 0.369 ± 0.025 ± 0.03712.0 2.2E-03 0.67 0.437 ± 0.039 ± 0.07912.0 2.2E-03 0.79 0.407 ± 0.027 ± 0.04912.0 2.2E-03 0.91 0.445 ± 0.036 ± 0.04412.0 4.0E-03 0.67 0.462 ± 0.067 ± 0.08312.0 4.0E-03 0.79 0.427 ± 0.046 ± 0.05112.0 4.0E-03 0.91 0.349 ± 0.053 ± 0.035

27

Table 7: The ratio rLP(3) = F̄LP(3)2 /F2 as a fun tion of xL, x and Q2 (DIS sample,for Q2 > 12 GeV2), for protons with p2

T < 0.5 GeV2. The two rightmost valuesindi ate the statisti al and systemati un ertainties, respe tively.Q2 (GeV2) x xL rLP(3)21.0 9.8E-04 0.67 0.423 ± 0.027 ± 0.07621.0 9.8E-04 0.79 0.387 ± 0.019 ± 0.04621.0 9.8E-04 0.91 0.360 ± 0.023 ± 0.03621.0 2.2E-03 0.67 0.437 ± 0.034 ± 0.07921.0 2.2E-03 0.79 0.427 ± 0.024 ± 0.05121.0 2.2E-03 0.91 0.379 ± 0.029 ± 0.03821.0 4.0E-03 0.67 0.486 ± 0.049 ± 0.08721.0 4.0E-03 0.79 0.390 ± 0.031 ± 0.04721.0 4.0E-03 0.91 0.361 ± 0.038 ± 0.03621.0 5.9E-03 0.67 0.474 ± 0.066 ± 0.08521.0 5.9E-03 0.79 0.372 ± 0.042 ± 0.04521.0 5.9E-03 0.91 0.466 ± 0.059 ± 0.04746.0 2.2E-03 0.67 0.452 ± 0.043 ± 0.08146.0 2.2E-03 0.79 0.372 ± 0.028 ± 0.04546.0 2.2E-03 0.91 0.490 ± 0.040 ± 0.04946.0 4.0E-03 0.67 0.444 ± 0.055 ± 0.08046.0 4.0E-03 0.79 0.433 ± 0.039 ± 0.05246.0 4.0E-03 0.91 0.360 ± 0.045 ± 0.03646.0 5.9E-03 0.67 0.435 ± 0.064 ± 0.07846.0 5.9E-03 0.79 0.348 ± 0.041 ± 0.04246.0 5.9E-03 0.91 0.436 ± 0.059 ±0.04446.0 1.0E-02 0.67 0.453 ± 0.050 ± 0.08146.0 1.0E-02 0.79 0.412 ± 0.034 ± 0.04946.0 1.0E-02 0.91 0.409 ± 0.043 ± 0.041130.0 5.9E-03 0.67 0.441 ± 0.094 ± 0.079130.0 5.9E-03 0.79 0.327 ± 0.058 ± 0.039130.0 5.9E-03 0.91 0.528 ± 0.094 ± 0.053130.0 1.0E-02 0.67 0.408 ± 0.060 ± 0.073130.0 1.0E-02 0.79 0.505 ± 0.048 ± 0.061130.0 1.0E-02 0.91 0.358 ± 0.051 ± 0.036130.0 2.5E-02 0.67 0.421 ± 0.069 ± 0.076130.0 2.5E-02 0.79 0.430 ± 0.050 ± 0.052130.0 2.5E-02 0.91 0.403 ± 0.062 ± 0.040

28

Table 8: The ratio rLP(2) = F̄LP(2)2 /F2 as a fun tion of x for �xed Q2 values, forprotons with 0.6 < xL < 0.97 and p2

T < 0.5 GeV2. The statisti al un ertainty isgiven. A fully orrelated systemati un ertainty of ±13% is not in luded.Q2 (GeV2) x rLP(2)0.20 3.5E-06 0.118 ± 0.0120.20 4.9E-06 0.1177 ± 0.00930.20 7.4E-06 0.1309 ± 0.00950.36 8.8E-06 0.113 ± 0.0140.36 1.3E-05 0.124 ± 0.0100.36 2.6E-05 0.1211 ± 0.00920.60 4.3E-05 0.137 ± 0.0104.0 9.8E-04 0.1281 ± 0.00634.0 4.4E-04 0.1186 ± 0.00584.0 2.5E-04 0.1190 ± 0.00624.0 1.5E-04 0.1206 ± 0.00568.0 2.2E-03 0.1507 ± 0.00798.0 9.8E-04 0.1473 ± 0.00528.0 4.4E-04 0.1358 ± 0.00488.0 2.5E-04 0.1332 ± 0.005312.0 4.0E-03 0.147 ± 0.01112.0 2.2E-03 0.1511 ± 0.006712.0 9.8E-04 0.1382 ± 0.004912.0 4.4E-04 0.1345 ± 0.005321.0 5.9E-03 0.151 ± 0.01121.0 4.0E-03 0.1438 ± 0.007721.0 2.2E-03 0.1477 ± 0.005821.0 9.8E-04 0.1377 ± 0.004646.0 1.0E-02 0.1496 ± 0.008446.0 5.9E-03 0.140 ± 0.01146.0 4.0E-03 0.1472 ± 0.009246.0 2.2E-03 0.1512 ± 0.0072130.0 2.5E-02 0.149 ± 0.012130.0 1.0E-02 0.156 ± 0.011130.0 5.9E-03 0.147 ± 0.016

29

Table 9: The average ratio 〈rLP(2)〉 = F̄LP(2)2 /F2 as a fun tion of Q2 for 0.6 < xL <

0.97 and p2T < 0.5 GeV2. The statisti al un ertainty is given. A fully orrelatedsystemati un ertainty of 13% is not in luded.

Q2 (GeV2) 〈rLP(2)〉0.29 0.1230 ± 0.00335.21 0.1312 ± 0.002016.60 0.1397 ± 0.002169.00 0.1471 ± 0.0036

Table 10: The average ratio 〈rLP(2)〉 as a fun tion of Q2 for two di�erent p2Tranges normalised to the value at Q2 = 0.25 GeV2. The statisti al un ertainty isgiven; systemati errors mostly an el in the ratio.

Q2 (GeV2) 〈rLP(2)(Q2)〉/〈rLP(2)(Q2 = 0.25 GeV2〉)p2

T < 0.04 GeV2 p2T < 0.5 GeV20.002 0.941 ± 0.0330.29 1.000 ± 0.000 1.000 ± 0.0005.21 1.062 ± 0.022 1.067 ± 0.03116.60 1.115 ± 0.023 1.136 ± 0.03169.00 1.152 ± 0.039 1.196 ± 0.037

30

Table 11: The stru ture-fun tion F̄LP(2)2 as a fun tion of x for 0.6 < xL <

0.97 and p2T < 0.5 GeV2. The statisti al un ertainty is given. A fully orrelatedsystemati un ertainty of ±13% is not in luded, nor is the un ertainty of the F2parametrisations used.

x Q2 (GeV2) F̄LP(2)23.5E-06 0.2 0.0286 ± 0.00294.9E-06 0.2 0.0277 ± 0.00227.4E-06 0.2 0.0296 ± 0.00218.8E-06 0.4 0.0391 ± 0.00481.3E-05 0.4 0.0412 ± 0.00352.6E-05 0.4 0.0378 ± 0.00294.3E-05 0.6 0.0559 ± 0.00421.5E-04 4.0 0.1126 ± 0.00522.5E-04 4.0 0.0991 ± 0.00524.4E-04 4.0 0.0872 ± 0.00439.8E-04 4.0 0.0793 ± 0.00392.5E-04 8.0 0.1518 ± 0.00604.4E-04 8.0 0.1347 ± 0.00489.8E-04 8.0 0.1201 ± 0.00422.2E-03 8.0 0.1014 ± 0.00534.4E-04 12.0 0.1563 ± 0.00629.8E-04 12.0 0.1303 ± 0.00462.2E-03 12.0 0.1157 ± 0.00514.0E-03 12.0 0.0969 ± 0.00739.8E-04 21.0 0.1552 ± 0.00522.2E-03 21.0 0.1325 ± 0.00524.0E-03 21.0 0.1093 ± 0.00595.9E-03 21.0 0.1029 ± 0.00742.2E-03 46.0 0.1659 ± 0.00794.0E-03 46.0 0.1339 ± 0.00845.9E-03 46.0 0.1127 ± 0.00861.0E-02 46.0 0.1026 ± 0.00585.9E-03 130.0 0.140 ± 0.0151.0E-02 130.0 0.1240 ± 0.00862.5E-02 130.0 0.0880 ± 0.0071

31

Table 12: The stru ture fun tion FLP(3)2 as a fun tion of xL in bins of x and

Q2 (DIS sample), for protons in a restri ted p2T range, p2

T < 0.04 GeV2. The tworightmost values indi ate the statisti al and systemati un ertainties, respe tively.Q2 (GeV2) x xL F̄

LP(3)24.4 3.3E-04 0.73 0.0675 ± 0.0080 ± 0.01574.4 3.3E-04 0.78 0.0724 ± 0.0078 ± 0.01164.4 3.3E-04 0.83 0.0756 ± 0.0082 ± 0.01064.4 3.3E-04 0.88 0.0585 ± 0.0082 ± 0.00984.4 1.0E-03 0.73 0.0489 ± 0.0077 ± 0.01254.4 1.0E-03 0.78 0.0552 ± 0.0077 ± 0.01014.4 1.0E-03 0.83 0.0605 ± 0.0083 ± 0.00994.4 1.0E-03 0.88 0.0460 ± 0.0083 ± 0.00937.5 3.3E-04 0.73 0.0962 ± 0.0079 ± 0.02097.5 3.3E-04 0.78 0.0955 ± 0.0074 ± 0.01367.5 3.3E-04 0.83 0.0822 ± 0.0070 ± 0.01017.5 3.3E-04 0.88 0.0855 ± 0.0083 ± 0.01157.5 1.0E-03 0.73 0.0899 ± 0.0085 ± 0.02007.5 1.0E-03 0.78 0.0737 ± 0.0072 ± 0.01147.5 1.0E-03 0.83 0.0682 ± 0.0071 ± 0.00947.5 1.0E-03 0.88 0.0715 ± 0.0084 ± 0.01077.5 3.3E-03 0.73 0.0587 ± 0.0081 ± 0.01437.5 3.3E-03 0.78 0.0563 ± 0.0075 ± 0.01007.5 3.3E-03 0.83 0.0505 ± 0.0072 ± 0.00857.5 3.3E-03 0.88 0.0619 ± 0.0093 ± 0.010913.3 1.0E-03 0.73 0.0957 ± 0.0078 ± 0.020813.3 1.0E-03 0.78 0.1023 ± 0.0076 ± 0.014413.3 1.0E-03 0.83 0.0886 ± 0.0072 ± 0.010713.3 1.0E-03 0.88 0.0729 ± 0.0074 ± 0.010113.3 3.3E-03 0.73 0.0666 ± 0.0061 ± 0.014713.3 3.3E-03 0.78 0.0698 ± 0.0059 ± 0.010213.3 3.3E-03 0.83 0.0677 ± 0.0059 ± 0.008413.3 3.3E-03 0.88 0.0658 ± 0.0067 ± 0.009128.6 1.0E-03 0.73 0.1249 ± 0.0125 ± 0.028128.6 1.0E-03 0.78 0.1290 ± 0.0119 ± 0.019528.6 1.0E-03 0.83 0.1007 ± 0.0107 ± 0.014028.6 1.0E-03 0.88 0.0956 ± 0.0121 ± 0.015028.6 3.3E-03 0.73 0.0906 ± 0.0089 ± 0.020328.6 3.3E-03 0.78 0.0934 ± 0.0085 ± 0.014028.6 3.3E-03 0.83 0.0701 ± 0.0075 ± 0.009728.6 3.3E-03 0.88 0.0758 ± 0.0089 ± 0.0114

32

Table 13: Fra tion of leading-proton DIS events with exa tly two jets with ET >4 GeV, rjet

LP, as a fun tion of xL for p2T < 0.5 GeV2. The two rightmost valuesindi ate the statisti al and systemati un ertainties, respe tively. The systemati un ertainties are highly orrelated.

xL rjetLP0.645 0.0209 ± 0.0031 ± 0.00530.735 0.0254 ± 0.0023 ± 0.00620.825 0.0242 ± 0.0019 ± 0.00600.920 0.0196 ± 0.0026 ± 0.0050

Table 14: Fra tion of leading-proton DIS events with exa tly two jets with ET >4 GeV, rjet

LP, as a fun tion of p2T for 0.6 < xL < 0.97. The two rightmost valuesindi ate the statisti al and systemati un ertainties, respe tively. The systemati un ertainties are highly orrelated.

p2T (GeV2) rjet

LP0.0105 0.0201 ± 0.0020 ± 0.00370.0355 0.0204 ± 0.0022 ± 0.00640.0900 0.0259 ± 0.0024 ± 0.00570.3150 0.0350 ± 0.0032 ± 0.0083

33

Table 15: Ratio of the yield of DIS events with exa tly two jets with ET > 4 GeVand an LPS proton to the yield of DIS events with exa tly two jets, also withET > 4 GeV, rLP

jet , as a fun tion of ET of the higher-energy jet. The statisti alun ertainty is given. A fully orrelated systemati un ertainty of ±13% is notin luded.ET (GeV) rLP

jet4.8 0.126 ± 0.0185.8 0.122 ± 0.0176.8 0.130 ± 0.0198.0 0.124 ± 0.01812.3 0.088 ± 0.014Table 16: Ratio of the yield of DIS events with exa tly two jets with ET > 4 GeVand an LPS proton to the yield of DIS events with exa tly two jets, also withET > 4 GeV, rLP

jet , as a fun tion of Q2. The statisti al un ertainty is given. A fully orrelated systemati un ertainty of ±13% is not in luded.Q2 (GeV2) rLP

jet6.6 0.123 ± 0.01319.4 0.097 ± 0.01736.0 0.111 ± 0.017106.8 0.121 ± 0.015Table 17: Ratio of the yield of DIS events with exa tly two jets with ET > 4 GeVand an LPS proton to the yield of DIS events with exa tly two jets, also withET > 4 GeV, rLP

jet , as a fun tion of x. The statisti al un ertainty is given. A fully orrelated systemati un ertainty of ±13% is not in luded.x rLP

jet0.00027 0.131 ± 0.0140.00093 0.109 ± 0.0150.0022 0.107 ± 0.0150.0079 0.109 ± 0.01734

++’

’

(∗)γ

pt

X

Qee

2

2W

K K

Pp P

Figure 1: S hemati diagram of the rea tion e+p → e+Xp.

35

ZEUS

0

100

200

300

0 10 20 30Ee

' (GeV)

even

ts 0.1 < Q2 < 0.74 GeV2

ZEUS 1995EPSOFT

a)

0

500

1000

1500

2000

0 10 20 30Ee

' (GeV)

even

ts 3 < Q2 < 254 GeV2

ZEUS 1995RAPGAP

d)

0

50

100

150

178 178.5 179ϑe (deg)

even

ts b)

0

500

1000

1500

2000

150 160 170 180ϑe (deg)

even

ts e)

0

50

100

150

0 0.2 0.4 0.6yJB

even

ts c)

0

250

500

750

1000

50 100 150γh (deg)

even

ts f)

Figure 2: Distributions of the variables a) E ′

e, b) ϑe and ) yJB for the re on-stru ted BPC data (squares) and the simulated events (EPSOFT), shown as theshaded histograms (normalised to the data); d) E ′

e, e) ϑe and f) γh for the re- onstru ted DIS data (dots) and the simulated events (RAPGAP), shown as thehat hed histograms (normalised to the data).36

ZEUS

0

25

50

75

100

0.6 0.8 1xL

even

ts 0.1 < Q2 < 0.74 GeV2

ZEUS 1995EPSOFT

a)

1

10

10 2

10 3

0 0.1 0.2 0.3 0.4 0.5pT

2 (GeV2)

even

ts b)

1

10

10 2

10 3

10-2

10-1

1∆pipe (cm)

even

ts c)

1

10

10 2

10-2

10-1

1∆plane (cm)

even

ts d)

Figure 3: Distributions of the variables a) xL, b) p2T , ) ∆pipe and d) ∆plane,for the re onstru ted BPC data (squares) and for the simulated events (EPSOFT)shown as the shaded histogram (normalised to the data). The arrows indi ate theminimum allowed values of ∆pipe and ∆plane (see text).

37

ZEUS

-0.5

0

0.5

p Y (

GeV

)

xL = 0.6 xL = 0.7

-0.5

0

0.5xL = 0.8 xL = 0.9

-0.5 0 0.5

-0.5

0

0.5xL = 0.95

-0.5 0 0.5

pX (GeV)

xL = 1

Figure 4: LPS geometri al a eptan e for di�erent xL values as a fun tion ofpX and pY . The shaded areas indi ate the regions of a eptan e. The dashed ir les indi ate the limits of the pT bins used in the analysis (the bin edges are0.124 GeV, 0.199 GeV, 0.280 GeV, 0.370 GeV, 0.470 GeV, 0.507 GeV, 0.707 GeV).38

ZEUS

η max

-2

0

2

4

6 a)

xL

NL

P(ηm

ax<2

.5)/N

LP

b)ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeV

ZEUS 1995, 0.1 < Q2 < 0.74 GeV2, 85 < W < 258 GeV} pT2 < 0.5 GeV2

0.6 0.7 0.8 0.9 1

10-2

10-1

Figure 5: a) Distribution of the DIS events in the (ηmax, xL) plane. The horizontaland verti al lines indi ate ηmax = 2.5 and xL = 0.97, respe tively. b) Fra tion ofevents with ηmax < 2.5 for both the BPC and the DIS samples. The BPC data areslightly shifted in xL for larity of presentation. The bars indi ate the statisti alun ertainties; systemati un ertainties mostly an el in the ratio.39

ZEUS

xL

1/σ to

t dσ γ *

p →

X p

/dx L 5

0.6 0.7 0.8 0.9 110

-1

1

ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeV

ZEUS 1995, 0.1 < Q2 < 0.74 GeV 2, 85 < W < 258 GeV} pT2 < 0.5 GeV2

Whitmore et al., pp → pX, √s = 19.6 GeV, pT2 < 0.5 GeV 2

Figure 6: The normalised ross-se tion (1/σtot) · dσγ∗p→Xp/dxL for the BPC andDIS data ompared to the pp data [54℄ in the region p2T < 0.5 GeV2. The innerbars indi ate the statisti al un ertainties and the outer bars are the statisti al andsystemati un ertainties summed in quadrature.

40

ZEUS

xL

1/σ to

t dσ γ *

p →

X p

/dx L

0.6 0.7 0.8 0.9 110

-2

10-1

1

ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeV

ZEUS 1995, 0.1 < Q2 < 0.74 GeV2, 85 < W < 258 GeV

ZEUS 1994, Q2 < 0.02 GeV2, 176 < W < 225 GeV} pT

2 < 0.04 GeV 2

Q2 < 0.01 GeV2, pT2 < 0.04 GeV2

H1 W = 91 GeV

H1 W = 187 GeV

H1 W = 231 GeV

Whitmore et al., pp → pX

√s = 19.6 GeV, pT2 < 0.05 GeV2

Figure 7: The normalised ross-se tion (1/σtot) · dσγ∗p→Xp/dxL for the pho-toprodu tion, BPC and DIS data ompared to the pp data [54℄ in the regionp2

T < 0.04 GeV2. The inner bars indi ate the statisti al un ertainties and theouter bars are the statisti al and systemati un ertainties summed in quadrature.The H1 results [7℄ are also shown.41

ZEUS

10-1

1

ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeV, pT2 < 0.5 GeV2

LEPTO SCIDJANGO

Dura∼es et al.

1/σ to

t dσ γ *

p →

X p

/dx L

a)

0.6 0.7 0.8 0.9 1

10-1

1

Szczurek et al.Pomeronπ ∆ π N

Reggeon

ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeV, pT2 < 0.5 GeV2

xL

b)

Figure 8: The normalised ross-se tion (1/σtot) · dσγ∗p→Xp/dxL for the DIS data(as shown in Fig. 6) ompared to a) the model of Durães et al. (solid urve),LEPTO6.5 (dashed urve) and DJANGO (dot-dashed urve), and b) to the modelof Sz zurek et al. (solid urve). For the latter, the individual ontributions ofPomeron, Reggeon and pion ex hanges are indi ated; for pion ex hange, the on-tribution of �nal states with isospin I = 1/2 and I = 3/2 are shown separately.42

ZEUS

10

10 2

dσγ

* p

→ X

p/d

p T2 (

nb/G

eV2 )

b = 7.5 ± 1.2 GeV-2 b = 7.6 ± 1.0 GeV-2

0 0.2 0.4pT

2 (GeV2)

10

10 2

b = 6.2 ± 1.2 GeV-2

0 0.2 0.4pT

2 (GeV2)

b = 4.5 ± 1.2 GeV-2

ZEUS 1995

0.1 < Q2 < 0.74 GeV2

85 < W < 258 GeV

Figure 9: The di�erential ross-se tion dσγ∗p→Xp/dp2T for several xL bins forthe BPC sample. The lines represent the results of �ts to the fun tional form

dσγ∗p→Xp/dp2T ∝ e−bp2

T . The �tted values of b and their statisti al un ertaintiesare also given. The inner bars indi ate the size of the statisti al un ertainties, theouter bars show the statisti al and systemati un ertainties summed in quadrature.43

ZEUS

10-1

1

10

dσγ *

p →

X p

/dp T2 (n

b/G

eV2 )

b = 7.4±1.2 GeV-2 b = 7.7±0.8 GeV-2 b = 7.3±0.6 GeV-2

10-1

1

10b = 6.8±0.6 GeV-2 b = 6.1±0.6 GeV-2 b = 6.8±0.7 GeV-2

10-1

1

10b = 7.9±0.9 GeV-2 b = 7.3±0.8 GeV-2 b = 7.2±0.7 GeV-2

10-1

1

10b = 6.6±0.7 GeV-2

0 0.2 0.4

pT2 (GeV2)

b = 5.9±0.9 GeV-2

0 0.2 0.4

pT2 (GeV2)

b = 4.4±1.7 GeV-2

0 0.2 0.410

-1

1

10

b = 7.0±0.9 GeV-2

pT2 (GeV2)

ZEUS 19953 < Q2 < 254 GeV2

45 < W < 225 GeVFigure 10: The di�erential ross-se tion dσγ∗p→Xp/dp2T for several xL bins forthe DIS sample. The lines represent the results of �ts to the fun tional form

dσγ∗p→Xp/dp2T ∝ e−bp2

T . The �tted values of b and their statisti al un ertaintiesare also given. The inner bars indi ate the size of the statisti al un ertainties, theouter bars show the statisti al and systemati un ertainties summed in quadrature.44

ZEUSa)

2

4

6

8

10

ZEUS 1995, 0.1 < Q2 < 0.74 GeV2, 85 < W < 258 GeV

b (G

eV-2

)

ZEUS 1995, 3 < Q2 < 254 GeV2, 45 < W < 225 GeVZEUS 1994, Q2 < 0.02 GeV2, 176 < W < 225 GeV

} pT2 < 0.5 GeV2

Whitmore et al., pp → pX, √s = 19.6 GeV, pT2 < 0.5 GeV 2

b)

0.6 0.7 0.8 0.9 1

2

4

6

8

10

xL

b (G

eV-2

)

Szczurek et al.

Figure 11: a) The slopes, b, of the p2T distributions for leading protons as afun tion of xL for the BPC and DIS data samples. For larity of presentation, theBPC points are plotted slightly shifted in xL. The inner bars indi ate the statisti alun ertainties and the outer are the statisti al and systemati un ertainties summedin quadrature. The photoprodu tion result at xL ≃ 1 is also shown, as are thedata from the rea tion pp → pX at √

s = 19.6 GeV. b) The slopes, b, of thep2

T distributions for leading protons as a fun tion of xL for the DIS data sample, ompared with the predi tion of Sz zurek et al. (dashed line).45

x

Q2 (GeV2)

ZEUS 1995, 0.1 < Q2 < 0.74 GeV2

85 < W < 258 GeVpT

2 < 0.5 GeV2

ZEUS

xL0.7 0.8 0.9

7.4 10-6

0.2

0.7 0.8 0.9

4.9 10-6

0.7 0.8 0.90.2

0.4

0.6

3.5 10-6

xL0.7 0.8 0.9

2.6 10-5

0.4

0.7 0.8 0.9

1.3 10-5

rLP

(3)

0.7 0.8 0.90.2

0.4

0.6

8.8 10-6

xL0.7 0.8 0.9

0.2

0.4

0.6

4.3 10-5

0.6

Figure 12: The ratio rLP(3) = F̄LP(3)2 /F2 as a fun tion of xL in bins of x and Q2(BPC sample), for protons with p2

T < 0.5 GeV2. The inner bars show the statisti alun ertainties and the outer bars the statisti al and systemati un ertainties addedin quadrature. The dashed line rLP(3) = 0.4 is overlaid to guide the eye.

46

x

Q2 (GeV2)

ZEUS 1995, 3 < Q2 < 254 GeV2

45 < W < 225 GeVpT

2 < 0.5 GeV2

ZEUS

0.7 0.8 0.90.2

0.4

0.6

1.5 10-4

0.7 0.8 0.9

2.5 10-4

0.7 0.8 0.9

4.4 10-4xL

0.7 0.8 0.9

9.8 10-4

4

0.2

0.4

0.6

xL0.7 0.8 0.9

2.2 10-3

8

0.2

0.4

0.6

xL0.7 0.8 0.9

4.0 10-3

12

rLP

(3)

0.2

0.4

0.6

xL0.7 0.8 0.9

5.9 10-3

21

0.2

0.4

0.6

xL0.7 0.8 0.9

1.0 10-2

46

0.2

0.4

0.6

xL0.7 0.8 0.9

2.5 10-2

130

Figure 13: The ratio rLP(3) = F̄LP(3)2 /F2 as a fun tion of xL in bins of x and Q2(DIS sample), for protons with p2

T < 0.5 GeV2. The inner bars show the statisti alun ertainties and the outer bars the statisti al and systemati un ertainties addedin quadrature. The dashed line rLP(3) = 0.4 is overlaid to guide the eye.47

ZEUS

x

rLP

(2)

10-6

10-4

10-2

0.1

0.2

Q2 = 0.20 GeV2

0.1

0.2

Q2 = 0.36 GeV2

0.1

0.2

Q2 = 0.60 GeV2

0.1

0.2

Q2 = 4 GeV2

0.1

0.2

Q2 = 8 GeV2

0.1

0.2

Q2 = 12 GeV2

0.1

0.2

Q2 = 21 GeV2

0.1

0.2

Q2 = 46 GeV2

0.1

0.2

Q2 = 130 GeV2

ZEUS 1995, 0.1 < Q2 < 0.74 GeV2

85 < W < 258 GeV

ZEUS 1995, 3 < Q2 < 254 GeV2

45 < W < 225 GeV

0.6 < xL < 0.97

pT2 < 0.5 GeV2

Figure 14: The ratio rLP(2) = F̄LP(2)2 /F2 as a fun tion of x for �xed Q2 values,for protons with 0.6 < xL < 0.97 and p2

T < 0.5 GeV2. The error bars show thestatisti al un ertainties. A fully orrelated systemati un ertainty of ±13% is notshown. The horizontal lines rLP(2) = 0.10 and rLP(2) = 0.15 are overlaid to guidethe eye.48

ZEUS<r

LP

(2) >

0.1

0.12

0.14

0.16ZEUS 1995, 0.6 < xL < 0.97, pT

2 < 0.5 GeV2 a)

0.8

1

1.2

10-3

10-2

10-1

1 10 102

Q2 (GeV2)

<rL

P(2

) > / <

rLP

(2) (Q

2 =0.2

5 G

eV2 )>

ZEUS 1995, 0.6 < xL < 0.97, pT2 < 0.5 GeV2

ZEUS 1995, 0.6 < xL < 0.97, pT2 < 0.04 GeV2

ZEUS 95-97, leading neutrons, 0.64 < xL < 0.82, θ < 0.8 mrad b)

Figure 15: The average ratio 〈rLP(2)〉 = F̄LP(2)2 /F2 as a fun tion of Q2. The errorbars show the statisti al un ertainties. A fully orrelated systemati un ertainty of13% is not shown. a) 〈rLP(2)〉 for the range 0.6 < xL < 0.97 and p2

T < 0.5 GeV2.b) 〈rLP(2)〉 as a fun tion of Q2 for two di�erent p2T ranges normalised to the valueat Q2 = 0.25 GeV2. The error bars show the statisti al un ertainties; systemati errors mostly an el in the ratio. The ZEUS data for leading neutron produ tion,also normalised to the value at Q2 = 0.25 GeV2, are also shown. The points for

p2T < 0.5 GeV2 are slightly shifted for larity of presentation.49

ZEUS

F––

2 LP(

2)

0.02

0.04

0.06

0.08 Q2 = 0.2 GeV2 Q2 = 0.36 GeV2 Q2 = 0.6 GeV2

0.6 < xL < 0.97 pT2 < 0.5 GeV2

ZEUS 199585 < W < 258 GeV

ZEUS REGGE (1997)scaled by 0.13

0.1

0.2

Q2 = 4 GeV2 Q2 = 8 GeV2 Q2 = 12 GeV2

10-5

10-4

10-3

10-2

0.1

0.2

Q2 = 21 GeV2

10-5

10-4

10-3

10-2

Q2 = 46 GeV2

10-5

10-4

10-3

10-2

x

Q2 = 130 GeV2

ZEUS 199545 < W < 225 GeV

F2p scaled by 0.13

Figure 16: The stru ture-fun tion F̄LP(2)2 as a fun tion of x for 0.6 < xL < 0.97and p2

T < 0.5 GeV2. The bands show the one-standard-deviation limits of theF2 parametrisations used, s aled by the average value of rLP(2) (〈rLP(2)〉 ≃ 0.13).The error bars show the statisti al un ertainties. A fully orrelated systemati un ertainty of ±13% is not shown.

50

x

Q2 (GeV2)

H1

ZEUS 1995

pT2 < 0.04 GeV2

ZEUS

0.75 0.8 0.85

0.1

0.2

3.3 10-4xL

0.75 0.8 0.85

1.0 10-3

4.4

0.1

0.2

xL

0.75 0.8 0.85

3.3 10-3

7.5

0.1

0.2

13.3

F––

2 L

P(3

)

0.1

0.2

28.6

Figure 17: The stru ture fun tion FLP(3)2 as a fun tion of xL in bins of x and

Q2 (DIS sample), for protons in a restri ted p2T range, p2

T < 0.04 GeV2. The innerbars show the statisti al un ertainties and the outer bars are the statisti al andsystemati un ertainties added in quadrature. The H1 results [5℄ are also shown.51

0

0.01

0.02

0.03

0.04

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

ZEUS

xL

r LPje

t

Njet = 2

pT2 < 0.5 GeV2 a)

ZEUS 1995

3 < Q2< 254 GeV2

pT2 (GeV2)

r LPje

t

Njet = 2

0.6<xL<0.97 b)

ZEUS 1995

3 < Q2< 254 GeV2

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5Figure 18: Fra tion of leading-proton DIS events with exa tly two jets withET > 4 GeV, rjet

LP, as a fun tion of a) xL for p2T < 0.5 GeV2 and b) p2

T for0.6 < xL < 0.97. The inner bars show the statisti al un ertainties and the outerbars show the statisti al and systemati un ertainties added in quadrature. Thesystemati un ertainties are highly orrelated.

52

0

0.03

0.06

0.09

0.12

0.15

0.18

100

0.03

0.06

0.09

0.12

0.15

0.18

10 102

ZEUS

ETjet (GeV)

r jetLP

4 6 8 206

a)

Q2 (GeV2)

r jetLP

b)

x

r jetLP

c)3 < Q2< 254 GeV2

0.6< xL < 0.97

pT2< 0.5 GeV2

45 < W< 225 GeV

Njet=2

ZEUS 1995

0

0.03

0.06

0.09

0.12

0.15

0.18

10-4

10-3

10-2Figure 19: Ratio of the yield of DIS events with exa tly two jets with ET > 4 GeVand an LPS proton to the yield of DIS events with exa tly two jets, also with

ET > 4 GeV, rLPjet , as a fun tion of a) ET of the higher-energy jet, b) Q2 and )

x. The error bars show the statisti al un ertainties. A fully orrelated systemati un ertainty of ±13% is not shown.53