Eur. Phys. J. C (2009) 61: 223–235DOI 10.1140/epjc/s10052-009-1015-1

Regular Article - Experimental Physics

Measurement of charged current deep inelastic scattering crosssections with a longitudinally polarised electron beam at HERA

The ZEUS Collaboration

S. Chekanov1, M. Derrick1, S. Magill1, B. Musgrave1, D. Nicholass1,c, J. Repond1, R. Yoshida1, M.C.K. Mattingly2,P. Antonioli3, G. Bari3, L. Bellagamba3, D. Boscherini3, A. Bruni3, G. Bruni3, F. Cindolo3, M. Corradi3,G. Iacobucci3, A. Margotti3, R. Nania3, A. Polini3, S. Antonelli4, M. Basile4, M. Bindi4, L. Cifarelli4, A. Contin4,S. De Pasquale4,d, G. Sartorelli4, A. Zichichi4, D. Bartsch5, I. Brock5, H. Hartmann5, E. Hilger5, H.-P. Jakob5,M. Jüngst5, A.E. Nuncio-Quiroz5, E. Paul5, U. Samson5, V. Schönberg5, R. Shehzadi5, M. Wlasenko5, N.H. Brook6,G.P. Heath6, J.D. Morris6, M. Kaur7, P. Kaur7,e, I. Singh7,e, M. Capua8, S. Fazio8, A. Mastroberardino8,M. Schioppa8, G. Susinno8, E. Tassi8, J.Y. Kim9, Z.A. Ibrahim10, F. Mohamad Idris10, B. Kamaluddin10,W.A.T. Wan Abdullah10, Y. Ning11, Z. Ren11, F. Sciulli11, J. Chwastowski12, A. Eskreys12, J. Figiel12, A. Galas12,K. Olkiewicz12, B. Pawlik12, P. Stopa12, L. Zawiejski12, L. Adamczyk13, T. Bołd13, I. Grabowska-Bołd13,D. Kisielewska13, J. Łukasik13,f, M. Przybycien13, L. Suszycki13, A. Kotanski14,g, W. Słominski14,h, O. Behnke15,U. Behrens15, C. Blohm15, A. Bonato15, K. Borras15, D. Bot15, R. Ciesielski15, N. Coppola15, S. Fang15,J. Fourletova15,i, A. Geiser15, P. Göttlicher15,j, J. Grebenyuk15, I. Gregor15, T. Haas15,a, W. Hain15, A. Hüttmann15,F. Januschek15, B. Kahle15, I.I. Katkov15,k, U. Klein15,l, U. Kötz15, H. Kowalski15, M. Lisovyi15, E. Lobodzinska15,B. Löhr15, R. Mankel15,m, I.-A. Melzer-Pellmann15, S. Miglioranzi15,n, A. Montanari15, T. Namsoo15, D. Notz15,m,A. Parenti15, L. Rinaldi15,o, P. Roloff15, I. Rubinsky15, U. Schneekloth15, A. Spiridonov15,p, D. Szuba15,q, J. Szuba15,r,T. Theedt15, J. Ukleja15,s, G. Wolf15, K. Wrona15, A.G. Yagües Molina15, C. Youngman15, W. Zeuner15,m,V. Drugakov16, W. Lohmann16, S. Schlenstedt16, G. Barbagli17, E. Gallo17, P.G. Pelfer18, A. Bamberger19,D. Dobur19, F. Karstens19, N.N. Vlasov19,t, P.J. Bussey20,u, A.T. Doyle20, W. Dunne20, M. Forrest20, M. Rosin20,D.H. Saxon20, I.O. Skillicorn20, I. Gialas21,v, K. Papageorgiu21, U. Holm22, R. Klanner22, E. Lohrmann22,H. Perrey22, P. Schleper22, T. Schörner-Sadenius22, J. Sztuk22, H. Stadie22, M. Turcato22, C. Foudas23, C. Fry23,K.R. Long23, A.D. Tapper23, T. Matsumoto24, K. Nagano24, K. Tokushuku24,w, S. Yamada24, Y. Yamazaki24,x,A.N. Barakbaev25, E.G. Boos25, N.S. Pokrovskiy25, B.O. Zhautykov 25, V. Aushevy26, O. Bachynska26, M. Borodin26,I. Kadenko26, A. Kozulia26, V. Libov26, D. Lontkovskyi26, I. Makarenko26, Iu. Sorokin26, A. Verbytskyi26,O. Volynets26, D. Son27, J. de Favereau28, K. Piotrzkowski28, F. Barreiro29, C. Glasman29, M. Jimenez29,L. Labarga29, J. del Peso29, E. Ron29, M. Soares29, J. Terrón29, C. Uribe-Estrada29, M. Zambrana29, F. Corriveau30,C. Liu30, J. Schwartz30, R. Walsh30, C. Zhou30, T. Tsurugai31, A. Antonov32, B.A. Dolgoshein32, D. Gladkov32,V. Sosnovtsev32, A. Stifutkin32, S. Suchkov32, R.K. Dementiev33, P.F. Ermolov33,b, L.K. Gladilin33,Yu.A. Golubkov33, L.A. Khein33, I.A. Korzhavina33, V.A. Kuzmin33, B.B. Levchenko33,z, O.Yu. Lukina33,A.S. Proskuryakov33, L.M. Shcheglova33, D.S. Zotkin33, I. Abt34, A. Caldwell34, D. Kollar34, B. Reisert34,W.B. Schmidke34, G. Grigorescu35, A. Keramidas35, E. Koffeman35, P. Kooijman35, A. Pellegrino35, H. Tiecke35,M. Vázquez35,n, L. Wiggers35, N. Brümmer36, B. Bylsma36, L.S. Durkin36, A. Lee36, T.Y. Ling36, P.D. Allfrey37,M.A. Bell37, A.M. Cooper-Sarkar37, R.C.E. Devenish37, J. Ferrando37, B. Foster37, C. Gwenlan37,aa, K. Horton37,ab,K. Oliver37, A. Robertson37, R. Walczak37, A. Bertolin38, F. Dal Corso38, S. Dusini38, A. Longhin38, L. Stanco38,P. Bellan39, R. Brugnera39, R. Carlin39, A. Garfagnini39, S. Limentani39, B.Y. Oh40, A. Raval40, J.J. Whitmore40,ac,Y. Iga41, G. D’Agostini42, G. Marini42, A. Nigro42, J.E. Cole43,ad, J.C. Hart43, H. Abramowicz44,ae, R. Ingbir44,S. Kananov44, A. Levy44, A. Stern44, M. Kuze45, J. Maeda45, R. Hori46, S. Kagawa46,af, N. Okazaki46, S. Shimizu46,T. Tawara46, R. Hamatsu47, H. Kaji47,ag, S. Kitamura47,ah, O. Ota47,ai, Y.D. Ri47, M. Costa48, M.I. Ferrero48,V. Monaco48, R. Sacchi48, V. Sola48, A. Solano48, M. Arneodo49, M. Ruspa49, S. Fourletov50,i, J.F. Martin50,T.P. Stewart50, S.K. Boutle51,v, J.M. Butterworth51, T.W. Jones51, J.H. Loizides51, M. Wing51,aj, B. Brzozowska52,J. Ciborowski52,ak, G. Grzelak52, P. Kulinski52, P. Łuzniak52,al, J. Malka52,al, R.J. Nowak52, J.M. Pawlak52,W. Perlanski52,al, T. Tymieniecka52,am, A.F. Zarnecki52, M. Adamus53, P. Plucinski53,an, A. Ukleja53, Y. Eisenberg54,D. Hochman54, U. Karshon54, E. Brownson55, D.D. Reeder55, A.A. Savin55, W.H. Smith55, H. Wolfe55, S. Bhadra56,C.D. Catterall56, Y. Cui56, G. Hartner56, S. Menary56, U. Noor56, J. Standage56, J. Whyte56

224 Eur. Phys. J. C (2009) 61: 223–235

1Argonne National Laboratory, Argonne, IL 60439-4815, USAbb

2Andrews University, Berrien Springs, MI 49104-0380, USA3INFN Bologna, Bologna, Italyas

4University and INFN Bologna, Bologna, Italyas

5Physikalisches Institut der Universität Bonn, Bonn, Germanyap

6H.H. Wills Physics Laboratory, University of Bristol, Bristol, UKba

7Department of Physics, Panjab University, Chandigarh, India8Physics Department and INFN, Calabria University, Cosenza, Italyas

9Chonnam National University, Kwangju, South Korea10Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysiabf

11Nevis Laboratories, Columbia University, Irvington on Hudson, NY 10027, USAbc

12The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Polandaw

13Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Cracow, Polandbd

14Department of Physics, Jagellonian University, Cracow, Poland15Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany16Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany17INFN Florence, Florence, Italyas

18University and INFN Florence, Florence, Italyas

19Fakultät für Physik der Universität Freiburg i.Br., Freiburg i.Br., Germanyap

20Department of Physics and Astronomy, University of Glasgow, Glasgow, UKba

21Department of Engineering in Management and Finance, Univ. of Aegean, Aegean, Greece22Hamburg University, Institute of Exp. Physics, Hamburg, Germanyap

23High Energy Nuclear Physics Group, Imperial College London, London, UKba

24Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japanat

25Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan26Institute for Nuclear Research, National Academy of Sciences, Kiev and Kiev National University, Kiev, Ukraine27Center for High Energy Physics, Kyungpook National University, Daegu, South Koreaau

28Institut de Physique Nucléaire, Université Catholique de Louvain, Louvain-la-Neuve, Belgiumbe

29Departamento de Física Teórica, Universidad Autónoma de Madrid, Madrid, Spainaz

30Department of Physics, McGill University, Montréal, Québec, Canada H3A 2T8ao

31Meiji Gakuin University, Faculty of General Education, Yokohama, Japanat

32Moscow Engineering Physics Institute, Moscow, Russiaax

33Moscow State University, Institute of Nuclear Physics, Moscow, Russiaay

34Max-Planck-Institut für Physik, München, Germany35NIKHEF and University of Amsterdam, Amsterdam, Netherlandsav

36Physics Department, Ohio State University, Columbus, OH 43210, USAbb

37Department of Physics, University of Oxford, Oxford, UKba

38INFN Padova, Padova, Italyas

39Dipartimento di Fisica dell’ Università and INFN, Padova, Italyas

40Department of Physics, Pennsylvania State University, University Park, PA 16802, USAbc

41Polytechnic University, Sagamihara, Japanat

42Dipartimento di Fisica, Università ‘La Sapienza’ and INFN, Rome, Italyas

43Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UKba

44Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, Israelar

45Department of Physics, Tokyo Institute of Technology, Tokyo, Japanat

46Department of Physics, University of Tokyo, Tokyo, Japanat

47Tokyo Metropolitan University, Department of Physics, Tokyo, Japanat

48Università di Torino and INFN, Torino, Italyas

49Università del Piemonte Orientale, Novara, and INFN, Torino, Italyas

50Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7ao

51Physics and Astronomy Department, University College London, London, UKba

52Warsaw University, Institute of Experimental Physics, Warsaw, Poland53Institute for Nuclear Studies, Warsaw, Poland54Department of Particle Physics, Weizmann Institute, Rehovot, Israelaq

55Department of Physics, University of Wisconsin, Madison, WI 53706, USAbb

56Department of Physics, York University, Toronto, Ontario, Canada M3J 1P3ao

Received: 5 January 2009 / Published online: 8 April 2009© Springer-Verlag / Società Italiana di Fisica 2009

a e-mail: tobias.haas@desy.debDeceased.

cAlso affiliated with University College London, United Kingdom.dNow at University of Salerno, Italy.

Eur. Phys. J. C (2009) 61: 223–235 225

Abstract Measurements of the cross sections for chargedcurrent deep inelastic scattering in e−p collisions withlongitudinally polarised electron beams are presented. Themeasurements are based on a data sample with an integratedluminosity of 175 pb−1 collected with the ZEUS detectorat HERA at a centre-of-mass energy of 318 GeV. The totalcross section is given for positively and negatively polarisedelectron beams. The differential cross-sections dσ/dQ2,dσ/dx and dσ/dy are presented for Q2 > 200 GeV2.The double-differential cross-section d2σ/dxdQ2 is pre-sented in the kinematic range 280 < Q2 < 30 000 GeV2 and

eAlso working at Max Planck Institute, Munich, Germany.fNow at Institute of Aviation, Warsaw, Poland.gSupported by the research grant no. 1 P03B 04529 (2005–2008).hThis work was supported in part by the Marie Curie Actions Transferof Knowledge project COCOS (contract MTKD-CT-2004-517186).iNow at University of Bonn, Germany.jNow at DESY group FEB, Hamburg, Germany.kAlso at Moscow State University, Russia.lNow at University of Liverpool, UK.mOn leave of absence at CERN, Geneva, Switzerland.nNow at CERN, Geneva, Switzerland.oNow at Bologna University, Bologna, Italy.pAlso at Institut of Theoretical and Experimental Physics, Moscow,Russia.qAlso at INP, Cracow, Poland.rAlso at FPACS, AGH-UST, Cracow, Poland.sPartially supported by Warsaw University, Poland.tPartly supported by Moscow State University, Russia.uRoyal Society of Edinburgh, Scottish Executive Support ResearchFellow.vAlso affiliated with DESY, Germany.wAlso at University of Tokyo, Japan.xNow at Kobe University, Japan.ySupported by DESY, Germany.zPartly supported by Russian Foundation for Basic Research grant no.05-02-39028-NSFC-a.aaSTFC Advanced Fellow.abNee Korcsak-Gorzo.acThis material was based on work supported by the National ScienceFoundation, while working at the Foundation.adNow at University of Kansas, Lawrence, USA.aeAlso at Max Planck Institute, Munich, Germany, Alexander vonHumboldt Research Award.afNow at KEK, Tsukuba, Japan.agNow at Nagoya University, Japan.ahMember of Department of Radiological Science, Tokyo MetropolitanUniversity, Japan.aiNow at SunMelx Co. Ltd., Tokyo, Japan.

0.015 < x < 0.65. The measured cross sections are com-pared with the predictions of the Standard Model.

1 Introduction

Deep inelastic scattering (DIS) of leptons off nucleons hasproved to be a key process in the understanding of thestructure of the proton and testing of the Standard Model

ajAlso at Hamburg University, Inst. of Exp. Physics, Alexander vonHumboldt Research Award and partially supported by DESY, Ham-burg, Germany.akAlso at Łódz University, Poland.alMember of Łódz University, Poland.amAlso at University of Podlasie, Siedlce, Poland.anNow at Lund Universtiy, Lund, Sweden.aoSupported by the Natural Sciences and Engineering Research Coun-cil of Canada (NSERC).apSupported by the German Federal Ministry for Education and Re-search (BMBF), under contract numbers 05 HZ6PDA, 05 HZ6GUA,05 HZ6VFA and 05 HZ4KHA.aqSupported in part by the MINERVA Gesellschaft für ForschungGmbH, the Israel Science Foundation (grant no. 293/02-11.2) and theU.S.-Israel Binational Science Foundation.arSupported by the Israel Science Foundation.asSupported by the Italian National Institute for Nuclear Physics(INFN).atSupported by the Japanese Ministry of Education, Culture, Sports,Science and Technology (MEXT) and its grants for Scientific Re-search.auSupported by the Korean Ministry of Education and Korea Scienceand Engineering Foundation.avSupported by the Netherlands Foundation for Research on Matter(FOM).awSupported by the Polish State Committee for Scientific Research,project no. DESY/256/2006-154/DES/2006/03.axPartially supported by the German Federal Ministry for Educationand Research (BMBF).aySupported by RF Presidential grant N 1456.2008.2 for the leadingscientific schools and by the Russian Ministry of Education and Sci-ence through its grant for Scientific Research on High Energy Physics.azSupported by the Spanish Ministry of Education and Science throughfunds provided by CICYT.baSupported by the Science and Technology Facilities Council, UK.bbSupported by the US Department of Energy.bcSupported by the US National Science Foundation. Any opinion,findings and conclusions or recommendations expressed in this ma-terial are those of the authors and do not necessarily reflect the viewsof the National Science Foundation.bdSupported by the Polish Ministry of Science and Higher Educationas a scientific project (2006–2008).beSupported by FNRS and its associated funds (IISN and FRIA) andby an Inter-University Attraction Poles Programme subsidised by theBelgian Federal Science Policy Office.bfSupported by an FRGS grant from the Malaysian government.

226 Eur. Phys. J. C (2009) 61: 223–235

(SM). Neutral current (NC) DIS is mediated by photons andZ bosons and is sensitive to all quark flavours. However,at leading order only up-type quarks and down-type anti-quarks contribute to e−p charged current (CC) DIS. Thusthis process is a powerful probe of flavour-specific partondistribution functions (PDFs). Due to the chiral nature ofthe weak interaction, the SM predicts a linear dependenceof the CC cross section on the degree of longitudinal polari-sation of the electron beam. The cross section is expected tobe zero for a right-handed electron beam.

The HERA ep collider allowed the exploration of CCDIS [1–12] up to much higher Q2 than previously possi-ble in fixed-target experiments [13–16]. This paper presentsmeasurements of the cross sections for e−p CC DIS withlongitudinally polarised electron beams. The measured crosssections are compared to SM predictions and previousZEUS measurements of e+p CC DIS with longitudinallypolarised positron beams [17]. Similar results in e+p CCDIS have been published by the H1 Collaboration [18].

2 Kinematic variables and cross sections

Deep inelastic lepton-proton scattering can be described interms of the kinematic variables x, y and Q2. The variableQ2 is defined as Q2 = −q2 = −(k − k′)2 where k and k′ arethe four-momenta of the incoming and scattered lepton, re-spectively. Bjorken x is defined by x = Q2/2P · q where P

is the four-momentum of the incoming proton. The variabley is defined by y = P ·q/P ·k. The variables x, y and Q2 arerelated by Q2 = sxy, where s = 4EeEp is the square of thelepton-proton centre-of-mass energy (neglecting the massesof the incoming particles) and Ee and Ep are the energies ofthe incoming electron and proton, respectively.

The longitudinal polarisation of the electron beam, Pe , isdefined as

Pe = NR − NL

NR + NL

,

where NR and NL are the numbers of right- and left-handedelectrons in the beam. The electroweak Born-level cross sec-tion for the CC reaction, e−p → νeX, with longitudinallypolarised electron beams, can be expressed as [19]

d2σ CC(e−p)

dxdQ2= (1 − Pe)

G2F

4πx

(M2

W

M2W + Q2

)2

×[Y+F CC

2 (x,Q2) + Y−xF CC3 (x,Q2)

− y2FL(x,Q2)

],

where GF is the Fermi constant, MW is the mass of the W

boson and Y± = 1 ± (1 − y)2. The longitudinal structure

function gives a negligible contribution to the cross section,except at values of y close to 1. Within the framework of thequark-parton model, the structure functions F CC

2 and xF CC3

for e−p collisions can be written in terms of sums and dif-ferences of quark and anti-quark PDFs as follows:

F CC2 = x

[u(x,Q2) + c(x,Q2) + d(x,Q2) + s(x,Q2)

],

xF CC3 = x

[u(x,Q2) + c(x,Q2) − d(x,Q2) − s(x,Q2)

],

where, for example, the PDF u(x,Q2) gives the numberdensity of up quarks with momentum-fraction x at a givenQ2. Since the top-quark mass is large and the off-diagonalelements of the CKM matrix are small [20], the contributionfrom third-generation quarks may be ignored [21].

3 Experimental apparatus

A detailed description of the ZEUS detector can be foundelsewhere [22]. A brief outline of the components most rel-evant for this analysis is given below.

Charged particles were tracked in the central tracking de-tector (CTD) [23–25], which operated in a magnetic fieldof 1.43 T provided by a thin superconducting solenoid. TheCTD consisted of 72 cylindrical drift chamber layers, or-ganised in nine superlayers covering the polar-angle1 region15◦ < θ < 164◦. A silicon microvertex detector (MVD) [26]was installed between the beampipe and the inner radius ofthe CTD. The MVD was organised into a barrel with threecylindrical layers and a forward section with four planar lay-ers perpendicular to the HERA beam direction. Charged-particle tracks were reconstructed using information fromthe CTD and MVD.

The high-resolution uranium–scintillator calorimeter(CAL) [27–30] consisted of three parts: the forward (FCAL),the barrel (BCAL) and the rear (RCAL) calorimeter, cov-ering 99.7% of the solid angle around the nominal inter-action point. Each part was subdivided transversely intotowers and longitudinally into one electromagnetic sec-tion (EMC) and either one (in RCAL) or two (in BCALand FCAL) hadronic sections (HAC). The smallest sub-division of the calorimeter was called a cell. The CALrelative energy resolutions, as measured under test-beamconditions, were σ(E)/E = 0.18/

√E for electrons and

σ(E)/E = 0.35/√

E for hadrons, with E in GeV. The tim-ing resolution of the CAL was better than 1 ns for energydeposits exceeding 4.5 GeV.

1The ZEUS coordinate system is a right-handed Cartesian system, withthe Z axis pointing in the proton beam direction, referred to as the“forward direction”, and the X axis pointing left towards the centre ofHERA. The polar angle, θ , is measured with respect to the proton beamdirection. The coordinate origin is at the nominal interaction point.

Eur. Phys. J. C (2009) 61: 223–235 227

An iron structure that surrounded the CAL was instru-mented as a backing calorimeter (BAC) [31] to measureenergy leakage from the CAL. Muon chambers in the for-ward, barrel and rear [32] regions were used in this analysisto veto background events induced by cosmic-ray or beam-halo muons.

The luminosity was measured using the Bethe-Heitler re-action ep → eγp with the luminosity detector which con-sisted of two independent systems, a photon calorimeter anda magnetic spectrometer.

The lepton beam in HERA became naturally trans-versely polarised through the Sokolov-Ternov effect [33,34]. The characteristic build-up time for the HERA acceler-ator was approximately 40 minutes. Spin rotators on eitherside of the ZEUS detector changed the transverse polari-sation of the beam into longitudinal polarisation and backagain. The electron beam polarisation was measured usingtwo independent polarimeters, the transverse polarimeter(TPOL) [35] and the longitudinal polarimeter (LPOL) [36].Both devices exploited the spin-dependent cross section forCompton scattering of circularly polarised photons off elec-trons to measure the beam polarisation. The luminosity andpolarisation measurements were made over times that weremuch shorter than the polarisation build-up time.

The measurements are based on data samples collectedwith the ZEUS detector from 2004 to 2006 when HERAcollided protons of energy 920 GeV with electrons of energy

Fig. 1 The integrated luminosity collected as a function of the longi-tudinal polarisation of the electron beam

27.5 GeV, yielding collisions at a centre-of-mass energy of318 GeV. The integrated luminosities of the data sampleswere 104 pb−1 and 71 pb−1 at mean luminosity weightedpolarisations of −0.27 and +0.30, respectively. Figure 1shows the luminosity collected as a function of the longi-tudinal polarisation of the electron beam.

4 Monte Carlo simulation

Monte Carlo (MC) simulations were used to determine theefficiency for selecting events and the accuracy of kinematicreconstruction, to estimate the background rates from ep

processes other than CC DIS and to extract cross sections forthe full kinematic region. A sufficient number of events wasgenerated to ensure that the statistical uncertainties arisingfrom the MC simulation were negligible compared to thoseof the data. The MC samples were normalised to the totalintegrated luminosity of the data.

Charged current DIS events, including electroweak radia-tive effects, were simulated using the HERACLES 4.6.3 [37,38] program with the DJANGOH 1.3 [39] interface to the MCgenerators that provide the hadronisation. Initial-state radi-ation, vertex and propagator corrections and two-boson ex-change are included in HERACLES. The parameters of theSM were set to the PDG [20] values. The events were gen-erated using the CTEQ5D [40] PDFs. The colour-dipolemodel of ARIADNE 4.10 [41] was used to simulate O(αS)

plus leading-logarithmic corrections to the result of thequark-parton model. This program uses the Lund stringmodel of JETSET 7.4 [42–44] for the hadronisation. A setof NC DIS events generated with DJANGOH was used to es-timate the NC contamination in the CC sample. Photopro-duction background was estimated using events simulatedwith HERWIG 5.9 [45]. The background from W produc-tion was estimated using the EPVEC 1.0 [46] generator, andthe background from production of charged-lepton pairs wasgenerated with the GRAPE 1.1 [47] program.

The vertex distribution in data is a crucial input to the MCsimulation for the correct evaluation of the event-selectionefficiency. Therefore, the Z-vertex distribution used in theMC simulation was determined from a sample of NC DISevents in which the event-selection efficiency was indepen-dent of Z.

The ZEUS detector response was simulated with a pro-gram based on GEANT 3.21 [48]. The simulated events weresubjected to the same trigger requirements as the data, andprocessed by the same reconstruction programs.

5 Reconstruction of kinematic variables

The principal signature of CC DIS at HERA is large miss-ing transverse momentum, PT,miss, arising from the ener-getic final-state neutrino which escapes detection. PT,miss is

228 Eur. Phys. J. C (2009) 61: 223–235

related to the total hadronic momentum, PT , by P 2T ,miss =

(−−→P T )2, where

(−→P T )2 =

(∑i

Ei sin θi cosφi

)2

+(∑

i

Ei sin θi sinφi

)2

.

The sums run over all CAL energy deposits, Ei and θi and φi

are the polar and azimuthal angles. The calorimeter energydeposits are clustered cell energies corrected for energy lossin inactive material and reconstruction deficiencies [49]. Thepolar angle of the hadronic system, γh, is defined by

cosγh = ((−→P T )2 − δ2)/((

−→P T )2 + δ2),

where δ = ∑i Ei(1 − cos θi) = ∑

i (E − PZ)i . In the naivequark-parton model, γh is the angle of the scattered quark.Finally, the total transverse energy, ET , is given by ET =∑

i Ei sin θi .The ratio of the parallel, VP , and anti-parallel, VAP , com-

ponents of the hadronic transverse momentum can be usedto distinguish CC DIS from photoproduction events. Thesevariables are defined as

VP =∑

i

−→P T,i · −→n PT

for−→P T,i · −→n PT

> 0,

VAP = −∑

i

−→P T,i · −→n PT

for−→P T,i · −→n PT

< 0,

where the sums are performed over all calorimeter cells and−→n PT= −→

P T /PT .The kinematic variables were reconstructed using the

Jacquet-Blondel method [50]. The estimators of y, Q2 andx are: yJB = δ/(2Ee), Q2

JB = P 2T /(1 − yJB), and xJB =

Q2JB/(syJB).The resolution in Q2 is about 20%. The resolution in x

improves from about 20% at x = 0.01 to about 5% at x =0.5. The resolution in y ranges from about 14% at y = 0.05to about 8% at y = 0.83.

6 Event selection

Charged current DIS candidates were selected by requiringa large PT,miss. The main sources of background came fromNC DIS and high-ET photoproduction in which the finiteenergy resolution of the CAL or energy that escapes de-tection can lead to significant measured missing transversemomentum. Non-ep events such as beam-gas interactions,beam-halo muons or cosmic rays can also cause substantialimbalance in the measured transverse momentum and con-stitute additional sources of background. The selection cri-teria described below were imposed to separate CC eventsfrom all backgrounds.

6.1 Trigger selection

ZEUS had a three-level trigger system [22, 51, 52]. At thefirst level, only coarse calorimeter and tracking informationwas available. Events were selected using criteria based onthe energy, transverse energy and missing transverse mo-mentum measured in the calorimeter. Generally, events weretriggered with low thresholds on these quantities if a coin-cidence with CTD tracks from the event vertex occurred,while higher thresholds were required for events with noCTD tracks.

At the second level, timing information from the calorime-ter was used to reject events inconsistent with the bunch-crossing time. In addition, the topology of the CAL energydeposits was used to reject background events. In particular,a tighter cut was made on missing transverse momentum,since the resolution in this variable was better at the secondlevel than at the first level.

At the third level, full track reconstruction and vertexfinding were performed and used to reject candidate eventswith a vertex inconsistent with an ep interaction. Cuts wereapplied to calorimeter quantities and reconstructed tracks tofurther reduce beam-gas contamination.

6.2 Offline selection

When γh is large, charged-particle tracks can be used toreconstruct the event vertex, strongly suppressing non-epbackgrounds. For CC events with small γh, the charged par-ticles of the hadronic final state are often outside the ac-ceptance of the tracking detectors. Such events populatethe high-x region of the kinematic plane. The events wereclassified according to γ0, the value of γh measured withrespect to the nominal interaction point. For events withlarge γ0 the kinematic quantities were recalculated usingthe Z-coordinate of the event vertex (Zvtx) determined fromcharged-particle tracks.

In events with γ0 > 0.4 rad a reconstructed vertex was re-quired. Additional requirements for event selection are givenbelow.

• selection of CC events:– |Zvtx| < 50 cm;– PT,miss > 12 GeV;

• rejection of beam-gas events:– P ′

T ,miss > 10 GeV and P ′′T ,miss > 8 GeV where P ′

T ,missis the missing transverse momentum calculated exclud-ing the ring of FCAL towers closest to the beam pipeand P ′′

T ,miss is the corresponding quantity calculatedexcluding the two rings of FCAL towers closest tothe beam pipe. These requirements strongly suppressbeam-gas events while maintaining high efficiency forCC events;

Eur. Phys. J. C (2009) 61: 223–235 229

Fig. 2 Comparison of the e−p

CC data sample with theexpectations of the MCsimulation as described inSect. 4 of the text. Thedistributions of (a) PT,miss,(b) Q2

JB, (c) xJB, (d) yJB,(e) VAP/VP and (f) Zvtx areshown

– tracks associated with the event vertex with transversemomentum in excess of 0.2 GeV and a polar angle inthe range 15◦ to 164◦ were defined as “good” tracks.In order to remove beam-gas background, at least onesuch track was required and a cut was also applied intwo dimensions on the number of good tracks versusthe total number of tracks. This cut was NGoodTrks >

0.3(NTrks − 20);• rejection of photoproduction:

– VAP /VP < 0.4 was required for events with PT,miss <

30 GeV. For events with PT,miss < 20 GeV this cutwas tightened to VAP /VP < 0.23. This selected eventswith a collimated energy flow, as expected from a sin-gle scattered quark;

– for charged current events, there is a correlation be-tween the direction of the PT,miss vector calculated us-

ing tracks and that obtained using the CAL. The dif-ference between these quantities was required to beless than 0.5 radians for PT,miss < 45 GeV. As lessbackground is expected for high PT,miss this require-ment was loosened to less than 1.0 radian for PT,miss ≥45 GeV;

• rejection of NC DIS: NC DIS events in which the energiesof the scattered electron or the jet are poorly measured canhave a considerable apparent missing transverse momen-tum. To identify such events, a search for candidate elec-trons was made using isolated electromagnetic clustersin the CAL [53, 54] for events with PT,miss < 30 GeV.Candidate electron clusters within the tracking accep-tance were required to have an energy above 4 GeV anda matching track. Clusters with θ > 164◦ were requiredto have a transverse momentum exceeding 2 GeV. Events

230 Eur. Phys. J. C (2009) 61: 223–235

with a candidate electron satisfying the above criteria andδ > 30 GeV were rejected, since for fully contained NCevents, δ peaks at 2Ee = 55 GeV;

• rejection of non-ep background: muon-finding algorithmsbased on CAL energy deposits or muon-chamber signalswere used to reject events produced by cosmic rays ormuons in the beam halo.

In events with γ0 < 0.4 rad some requirements weretightened to compensate for the relaxation of the track re-quirements. Additional requirements for event selection aregiven below.

• missing transverse momentum: events were required tosatisfy PT,miss > 14 GeV and P ′

T ,miss > 12 GeV;• rejection of non-ep background: A class of background

events arose from beam-halo muons that produced ashower inside the FCAL. To reduce this background, inaddition to the muon-rejection cuts described above, topo-logical cuts on the transverse and longitudinal showershape were imposed. These cuts rejected events in whichthe energy deposits were more collimated than for typicalhadronic jets.

The kinematic region was restricted to Q2JB > 200 GeV2

and yJB < 0.9 to ensure good resolution.A total of 7198 events satisfied these criteria. A back-

ground contamination from ep processes of 0.5%, domi-nated by the photoproduction component, is predicted. Fig-ure 2 compares the distributions of data events entering thefinal CC sample with the MC expectation for the sum of theCC signal and ep background events. The MC simulationsgive a reasonable description of the data.

7 Cross-section determinationand systematic uncertainties

The measured cross section in a particular kinematic bin, forexample for d2σ/dxdQ2, was determined from

d2σ

dxdQ2= Ndata − Nbg

NMC· d2σ SM

Born

dxdQ2,

where Ndata is the number of data events, Nbg is the num-ber of background events estimated from the MC simula-tion and NMC is the number of signal MC events. The cross-

sectiond2σSM

BorndxdQ2 is the Standard Model prediction evaluated in

the on-shell scheme [55] using the PDG values for the elec-troweak parameters and the CTEQ5D PDFs [40]. A similarprocedure was used for dσ/dQ2, dσ/dx and dσ/dy. Con-sequently, the acceptance, as well as the bin-centring and ra-diative corrections were all taken from the MC simulation.The cross-sections dσ/dQ2 and dσ/dx were extrapolated

to the full y range using the SM predictions calculated withthe CTEQ5D PDFs.

The systematic uncertainties in the measured cross sec-tions were determined by changing the analysis procedurein turn and repeating the extraction of the cross sections.

• calorimeter energy scale: the relative uncertainty of thehadronic energy scale was 2%. Varying the energy scaleof the calorimeter by this amount in the detector simu-lation induces small shifts of the Jacquet-Blondel estima-tors of the kinematic variables. The variation of the energyscale for each of the calorimeters simultaneously up ordown by this amount gave the systematic uncertainty onthe total measured energy in the calorimeter. The result-ing systematic shifts in the measured cross sections weretypically within ±5%, but increased to ±(20–30)% in thehighest Q2 and x bins of the single-differential cross sec-tions and reached ±45% in the double-differential crosssection;

• reconstruction: an alternative analysis [56] was performedusing jets to reconstruct the kinematic quantities and re-ject background. The difference between the nominal andjet analyses was taken as an estimate of the systematic un-certainity on the reconstruction and background rejection.The difference was found to be typically within ±10%,but increased up to ±(20–25)% in the highest Q2 and x

bins of the cross sections;• background subtraction: the uncertainty in the small con-

tribution from photoproduction was estimated by varyingthe normalisation by ±60%, resulting [57, 58] in modifi-cations of the cross sections within ±2%;

• selection criteria: in order to estimate the bias introducedinto the measurements from an imperfect description ofthe data by the MC simulation, the efficiencies for each ofthe selection criteria were measured using the hadronic fi-nal state in NC DIS data. Using the measured efficienciesto extract the cross sections instead of the CC MC gavechanges in the cross sections that were typically within±2%, except for the two-dimensional tracking cut whichgave an effect of 10% at high Q2;

• the uncertainties associated with the trigger, choice ofPDFs in the MC and the measurement of the vertex po-sitions were negligible.

The individual uncertainties were added in quadrature sepa-rately for the positive and negative deviations from the nom-inal cross-section values to obtain the total systematic uncer-tainties. The O(α) electroweak corrections to CC DIS havebeen discussed by several authors [59, 60]. Various theoret-ical approximations and computer codes gave differences inthe CC cross sections of typically ±(1–2)% or less. How-ever, the differences can be as large as ±(3–8)% at high x

and high y. No uncertainty was included in the measuredcross sections from this source.

Eur. Phys. J. C (2009) 61: 223–235 231

The relative uncertainty in the measured polarisation was3.6% using the LPOL and 4.2% using the TPOL. The choiceof polarimeter measurement was made on a run-by-run ba-sis. The LPOL measurement was used when available, oth-erwise the TPOL measurement was used. The uncertainty of2.6% on the measured total luminosity was not included inthe differential cross-section figures or the tables.

8 Results

The total cross section, corrected to the Born level of theelectroweak interaction, for e−p CC DIS in the kinematicregion Q2 > 200 GeV2 was measured to be

σ CC(Pe = +0.30 ± 0.01) = 47.1 ± 1.1 (stat.)

± 2.2 (syst.) pb,

σ CC(Pe = −0.27 ± 0.01) = 83.1 ± 1.2 (stat.)

± 3.3 (syst.) pb.

The uncertainty in the measured luminosity is included inthe systematic uncertainty. The total cross section is shownas a function of the longitudinal polarisation of the lep-ton beam in Fig. 3, including previous ZEUS measure-

Fig. 3 The total cross sections for e−p and e+p CC DIS as a functionof the longitudinal polarisation of the lepton beam. The lines show thepredictions of the SM evaluated using the ZEUS-JETS, CTEQ6D andMRST04 PDFs. The shaded bands show the experimental uncertaintyfrom the ZEUS-JETS fit

ments from both e−p and e+p data [11, 12, 17]. Fig-ure 4 shows only the e−p data, with a finer binning to em-phasise the dependence on the lepton beam polarisation.2

The data are compared to the SM predictions evaluated atnext-to-leading-order in QCD using the ZEUS-JETS [61],CTEQ6D [62] and MRST04 [63] PDFs which describe thedata well.

The single-differential cross-sections dσ/dQ2, dσ/dx

and dσ/dy for CC DIS are shown in Figs. 5, 6 and 7.The measurements for positive and negative longitudinal po-larisation differ by a constant factor which is independentof the kinematic variables. The effects are well describedby the SM evaluated using the ZEUS-JETS, CTEQ6D andMRST04 PDFs. The precision of the data is comparable tothe uncertainties in the SM predictions, therefore these datahave the potential to further constrain the PDFs.

The reduced double-differential cross section, σ , is de-fined as

σ =[

G2F

2πx

(M2

W

M2W + Q2

)2]−1d2σ

dx dQ2.

Fig. 4 The total cross sections for e−p CC DIS as a function of thelongitudinal polarisation of the electron beam. The lines show the pre-dictions of the SM evaluated using the ZEUS-JETS, CTEQ6D andMRST04 PDFs. The shaded band shows the experimental uncertaintyfrom the ZEUS-JETS fit

2All measured cross-section values are given in the DESY preprint.

232 Eur. Phys. J. C (2009) 61: 223–235

Fig. 5 (a) The e−p CC DIScross-section dσ/dQ2 for dataand the Standard Modelexpectation evaluated using theZEUS-JETS PDFs. The positive(negative) polarisation data areshown as the filled (open)points, the statisticaluncertainties are indicated bythe inner error bars (delimitedby horizontal lines) and the fullerror bars show the totaluncertainty obtained by addingthe statistical and systematiccontributions in quadrature.(b) The ratio of the measuredcross section, dσ/dQ2, to theStandard Model expectationevaluated using the ZEUS-JETSfit. The shaded band shows theexperimental uncertainty fromthe ZEUS-JETS fit

Fig. 6 (a) The e−p CC DIScross-section dσ/dx for dataand the Standard Modelexpectation evaluated using theZEUS-JETS PDFs. The positive(negative) polarisation data areshown as the filled (open)points, the statisticaluncertainties are indicated bythe inner error bars (delimitedby horizontal lines) and the fullerror bars show the totaluncertainty obtained by addingthe statistical and systematiccontributions in quadrature.(b) The ratio of the measuredcross section, dσ/dx, to theStandard Model expectationevaluated using the ZEUS-JETSfit. The shaded band shows theexperimental uncertainty fromthe ZEUS-JETS fit

Eur. Phys. J. C (2009) 61: 223–235 233

Fig. 7 (a) The e−p CC DIScross-section dσ/dy for dataand the Standard Modelexpectation evaluated using theZEUS-JETS PDFs. The positive(negative) polarisation data areshown as the filled (open)points, the statisticaluncertainties are indicated bythe inner error bars (delimitedby horizontal lines) and the fullerror bars show the totaluncertainty obtained by addingthe statistical and systematiccontributions in quadrature.(b) The ratio of the measuredcross section, dσ/dy, to theStandard Model expectationevaluated using the ZEUS-JETSfit. The shaded band shows theexperimental uncertainty fromthe ZEUS-JETS fit

Fig. 8 The e−p CC DISreduced cross section plotted asa function of x for fixed Q2.The circles represent the datapoints and the curves show thepredictions of the SM evaluatedusing the ZEUS-JETS,CTEQ6D and MRST04 PDFs.The dashed and dotted linesshow the contributions of thePDF combinations x(u + c) and(1 − y)2x(d + s), respectively

234 Eur. Phys. J. C (2009) 61: 223–235

Fig. 9 The e−p CC DISreduced cross section plotted asa function of (1 − y)2 forfixed x. The circles representthe data points and the curvesshow the predictions of the SMevaluated using theZEUS-JETS, CTEQ6D andMRST04 PDFs. The dashedlines show the contributions ofthe PDF combination x(u + c)

and the shaded band shows theexperimental uncertainty fromthe ZEUS-JETS fit

At leading order in QCD, σ (e−p → νeX) depends on thequark momentum distributions as follows:

σ (e−p → νeX) = x[u + c + (1 − y)2(d + s)

].

The reduced cross section was measured in the kinematicrange 280 < Q2 < 30 000 GeV2 and 0.015 < x < 0.65 andis shown as a function of x, at fixed values of Q2 in Fig. 8.The data points were corrected to Pe = 0 using the SMprediction. The predictions of the SM evaluated using theZEUS-JETS, CTEQ6D and MRST04 PDFs give a good de-scription of the data. The contributions from the PDF com-binations (u + c) and (d + s), obtained in the MS schemefrom the ZEUS-JETS fit, are shown separately.

The W boson couples only to left-handed fermions andright-handed anti-fermions. Therefore, the angular distribu-tion of the scattered quark in e−q CC DIS will be flat in theelectron-quark centre-of-mass scattering angle, θ∗, while itwill exhibit a (1 + cos θ∗)2 distribution in e−q scattering.Since (1 − y)2 ∝ (1 + cos θ∗)2, the helicity structure ofCC interactions can be illustrated by plotting the reduceddouble-differential cross section versus (1 − y)2 in bins ofx. This is shown in Fig. 9. In the region of approximate scal-ing, i.e. x ∼ 0.1, this yields a straight line. At leading order

in QCD, the intercept of this line gives the (u + c) contribu-tion, while the slope gives the (d + s) contribution.

9 Summary

The cross sections for charged current deep inelastic scatter-ing in e−p collisions with longitudinally polarised electronbeams have been measured. The measurements are basedon a data sample with an integrated luminosity of 175 pb−1

collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is givenfor positive and negative values of the longitudinal polarisa-tion of the electron beam. In addition, the differential cross-sections dσ/dQ2, dσ/dx and dσ/dy for Q2 > 200 GeV2

and d2σ/dxdQ2 are presented in the kinematic range 280 <

Q2 < 30 000 GeV2 and 0.015 < x < 0.65. Overall the mea-sured cross sections are well described by the predictions ofthe Standard Model.

Acknowledgements We appreciate the contributions to the con-struction and maintenance of the ZEUS detector of many people whoare not listed as authors. The HERA machine group and the DESY

Eur. Phys. J. C (2009) 61: 223–235 235

computing staff are especially acknowledged for their success in pro-viding excellent operation of the collider and the data-analysis environ-ment. We thank the DESY directorate for their strong support and en-couragement. It is also a pleasure to thank H. Spiesberger and W. Hol-lik for helpful discussions.

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