Measurement of D+- production and the charm contribution to

a r X i v :h e p -e x /9908012v 3 3 A p r 2000Measurement of D ?±production and the charm contribution to F 2in deep inelastic scattering at HERA

ZEUS Collaboration Abstract The production of D ?±(2010)mesons in deep inelastic scattering has been measured in the ZEUS detector at HERA using an integrated luminosity of 37pb ?1.The decay channels D ?+→D 0π+(+c.c.),with D 0→K ?π+or D 0→K ?π?π+π+,have been used to identify the D mesons.The e +p cross section for inclusive D ?±production with 1

rises from ?10%at Q 2?1.8GeV 2to ?30%at Q 2?130GeV 2for x values in the range 10?4to 10?3.Eur.Phys.J.C 12(2000)35-52

The ZEUS Collaboration

J.Breitweg,S.Chekanov,M.Derrick,D.Krakauer,S.Magill,B.Musgrave,A.Pellegrino, J.Repond,R.Stanek,R.Yoshida

Argonne National Laboratory,Argonne,IL,USA p

M.C.K.Mattingly

Andrews University,Berrien Springs,MI,USA

G.Abbiendi,F.Anselmo,P.Antonioli,G.Bari,M.Basile,L.Bellagamba,D.Boscherini1, A.Bruni,G.Bruni,G.Cara Romeo,G.Castellini2,L.Cifarelli3,F.Cindolo,A.Contin,N.Cop-pola,M.Corradi,S.De Pasquale,P.Giusti,G.Iacobucci4,5543a31d650e52ea55189803urenti,G.Levi,A.Margotti, T.Massam,R.Nania,F.Palmonari,A.Pesci,A.Polini,G.Sartorelli,Y.Zamora Garcia5, A.Zichichi

University and INFN Bologna,Bologna,Italy f

C.Amelung,A.Bornheim,I.Brock,K.Cob¨o ken,J.Crittenden,R.De?ner,M.Eckert6, H.Hartmann,K.Heinloth,E.Hilger,H.-P.Jakob,A.Kappes,U.F.Katz,R.Kerger,E.Paul, J.Rautenberg7,

H.Schnurbusch,A.Stifutkin,J.Tandler,A.Weber,H.Wieber

Physikalisches Institut der Universit¨a t Bonn,Bonn,Germany c

D.S.Bailey,O.Barret,W.N.Cottingham,B.Foster8,G.P.Heath,H.F.Heath,J.D.McFall, D.Piccioni,J.Scott,R.J.Tapper

H.H.Wills Physics Laboratory,University of Bristol,Bristol,U.K.o

M.Capua,A.Mastroberardino,M.Schioppa,G.Susinno

Calabria University,Physics Dept.and INFN,Cosenza,Italy f

H.Y.Jeoung,J.Y.Kim,J.H.Lee,I.T.Lim,K.J.Ma,M.Y.Pac9

Chonnam National University,Kwangju,Korea h

A.Caldwell,W.Liu,X.Liu,

B.Mellado,J.A.Parsons,S.Ritz10,R.Sacchi,S.Sampson, F.Sciulli

Columbia University,Nevis Labs.,Irvington on Hudson,N.Y.,USA q

J.Chwastowski,A.Eskreys,J.Figiel,K.Klimek,K.Olkiewicz,M.B.Przybycie′n,P.Stopa, L.Zawiejski

Inst.of Nuclear Physics,Cracow,Poland j

L.Adamczyk11,B.Bednarek,K.Jele′n,D.Kisielewska,A.M.Kowal,T.Kowalski,M.Przyby-cie′n,E.Rulikowska-Zar?e bska,L.Suszycki,J.Zaj?a c

Faculty of Physics and Nuclear Techniques,Academy of Mining and Metallurgy,Cracow,Poland j Z.Duli′n ski,A.Kota′n ski

Jagellonian Univ.,Dept.of Physics,Cracow,Poland k

1

L.A.T.Bauerdick,U.Behrens,J.K.Bienlein,C.Burgard,K.Desler,G.Drews,A.Fox-Murphy, U.Fricke,F.Goebel,P.G¨o ttlicher,R.Graciani,T.Haas,W.Hain,G.F.Hartner,D.Hasell12, K.Hebbel,K.F.Johnson13,M.Kasemann14,W.Koch,U.K¨o tz,H.Kowalski,L.Lindemann, B.L¨o hr,M.Mart′?nez,5543a31d650e52ea55189803ewski15,5543a31d650e52ea55189803ite,T.Monteiro16,M.Moritz,D.Notz,F.Peluc-chi,M.C.Petrucci,K.Piotrzkowski,M.Rohde,P.R.B.Saull,A.A.Savin,U.Schneekloth, O.Schwarzer17,F.Selonke,M.Sievers,S.Stonjek,E.Tassi,G.Wolf,U.Wollmer,C.Young-man,W.Zeuner

Deutsches Elektronen-Synchrotron DESY,Hamburg,Germany

B.D.Burow18,

C.Coldewey,H.J.Grabosch, A.Lopez-Duran Viani, A.Meyer,K.M¨o nig, S.Schlenstedt,P.B.Straub

DESY Zeuthen,Zeuthen,Germany

G.Barbagli,E.Gallo,P.Pelfer

University and INFN,Florence,Italy f

G.Maccarrone,L.Votano

INFN,Laboratori Nazionali di Frascati,Frascati,Italy f

A.Bamberger,S.Eisenhardt19,P.Markun,H.Raach,S.W¨o l?e

Fakult¨a t f¨u r Physik der Universit¨a t Freiburg i.Br.,Freiburg i.Br.,Germany c

N.H.Brook20,P.J.Bussey,A.T.Doyle,S.W.Lee,N.Macdonald,G.J.McCance,D.H.Saxon, L.E.Sinclair,I.O.Skillicorn,E.Strickland,R.Waugh

Dept.of Physics and Astronomy,University of Glasgow,Glasgow,U.K.o

I.Bohnet,N.Gendner,U.Holm,A.Meyer-Larsen,H.Salehi,K.Wick

Hamburg University,I.Institute of Exp.Physics,Hamburg,Germany c

A.Garfagnini,I.Gialas21,L.K.Gladilin22,D.K?c ira23,R.Klanner,E.Lohrmann,G.Poelz, F.Zetsche

Hamburg University,II.Institute of Exp.Physics,Hamburg,Germany c

T.C.Bacon,J.E.Cole,G.Howell,5543a31d650e52ea55189803mberti24,K.R.Long,5543a31d650e52ea55189803ler,A.Prinias25,J.K.Sedg-beer,D.Sideris,A.D.Tapper,R.Walker

Imperial College London,High Energy Nuclear Physics Group,London,U.K.o

U.Mallik,S.M.Wang

University of Iowa,Physics and Astronomy Dept.,Iowa City,USA p

P.Cloth,D.Filges

Forschungszentrum J¨u lich,Institut f¨u r Kernphysik,J¨u lich,Germany

T.Ishii,M.Kuze,I.Suzuki26,K.Tokushuku27,S.Yamada,K.Yamauchi,Y.Yamazaki Institute of Particle and Nuclear Studies,KEK,Tsukuba,Japan g

S.H.Ahn,S.H.An,S.J.Hong,S.B.Lee,S.W.Nam28,S.K.Park

Korea University,Seoul,Korea h

H.Lim,I.H.Park,D.Son

Kyungpook National University,Taegu,Korea h

2

F.Barreiro,J.P.Fern′a ndez,

G.Garc′?a,C.Glasman29,J.M.Hern′a ndez30,5543a31d650e52ea55189803barga,J.del Peso, J.Puga,I.Redondo31,J.Terr′o n

Univer.Aut′o noma Madrid,Depto de F′?sica Te′o rica,Madrid,Spain n

F.Corriveau,D.S.Hanna,J.Hartmann32,W.N.Murray33,A.Ochs,S.Padhi,M.Riveline, D.

G.Stairs,M.St-Laurent,M.Wing

McGill University,Dept.of Physics,Montr′e al,Qu′e bec,Canada a,b

T.Tsurugai

Meiji Gakuin University,Faculty of General Education,Yokohama,Japan

V.Bashkirov34,B.A.Dolgoshein

Moscow Engineering Physics Institute,Moscow,Russia l

G.L.Bashindzhagyan,P.F.Ermolov,Yu.A.Golubkov,L.A.Khein,N.A.Korotkova,I.A.Ko-rzhavina,V.A.Kuzmin,O.Yu.Lukina,A.S.Proskuryakov,L.M.Shcheglova35,A.N.Solomin35, S.A.Zotkin

Moscow State University,Institute of Nuclear Physics,Moscow,Russia m

C.Bokel,M.Botje,N.Br¨u mmer,J.Engelen,E.Ko?eman,P.Kooijman,A.van Sighem, H.Tiecke,N.Tuning,J.J.Velthuis,W.Verkerke,J.Vossebeld,L.Wiggers,E.de Wolf NIKHEF and University of Amsterdam,Amsterdam,Netherlands i

D.Acosta36,B.Bylsma,L.S.Durkin,J.Gilmore,C.M.Ginsburg,C.L.Kim,T.Y.Ling,P.Ny-lander

Ohio State University,Physics Department,Columbus,Ohio,USA p

H.E.Blaikley,S.Boogert,R.J.Cashmore16,A.M.Cooper-Sarkar,R.C.E.Devenish,J.K.Ed-monds,J.Gro?e-Knetter37,N.Harnew,T.Matsushita,V.A.Noyes38,A.Quadt16,O.Ruske, M.R.Sutton,R.Walczak,D.S.Waters

Department of Physics,University of Oxford,Oxford,U.K.o

A.Bertolin,R.Brugnera,R.Carlin,F.Dal Corso,S.Dondana,U.Dosselli,S.Dusini,S.Li-mentani,M.Morandin,M.Posocco,L.Stanco,R.Stroili,C.Voci

Dipartimento di Fisica dell’Universit`a and INFN,Padova,Italy f

L.Iannotti39,B.Y.Oh,J.R.Okrasi′n ski,W.S.Toothacker,J.J.Whitmore

Pennsylvania State University,Dept.of Physics,University Park,PA,USA q

Y.Iga

Polytechnic University,Sagamihara,Japan g

G.D’Agostini,G.Marini,A.Nigro,M.Raso

Dipartimento di Fisica,Univ.’La Sapienza’and INFN,Rome,Italy f

C.Cormack,J.C.Hart,N.A.McCubbin,T.P.Shah

Rutherford Appleton Laboratory,Chilton,Didcot,Oxon,U.K.o

D.Epperson,C.Heusch,H.F.-W.Sadrozinski,A.Seiden,R.Wichmann,D.C.Williams University of California,Santa Cruz,CA,USA p

N.Pavel

Fachbereich Physik der Universit¨a t-Gesamthochschule Siegen,Germany c

3

H.Abramowicz40,S.Dagan41,S.Kananov41,A.Kreisel,A.Levy41

Raymond and Beverly Sackler Faculty of Exact Sciences,School of Physics,Tel-Aviv University, Tel-Aviv,Israel e

T.Abe,T.Fusayasu,M.Inuzuka,K.Nagano,K.Umemori,T.Yamashita

Department of Physics,University of Tokyo,Tokyo,Japan g

R.Hamatsu,T.Hirose,K.Homma42,S.Kitamura43,T.Nishimura

Tokyo Metropolitan University,Dept.of Physics,Tokyo,Japan g

M.Arneodo44,N.Cartiglia,R.Cirio,M.Costa,M.I.Ferrero,S.Maselli,V.Monaco,C.Peroni, M.Ruspa,A.Solano,A.Staiano

Universit`a di Torino,Dipartimento di Fisica Sperimentale and INFN,Torino,Italy f

M.Dardo

II Faculty of Sciences,Torino University and INFN-Alessandria,Italy f

D.C.Bailey,C.-P.Fagerstroem,R.Galea,T.Koop,G.M.Levman,J.F.Martin,R.S.Orr, S.Polenz,A.Sabetfakhri,D.Simmons

University of Toronto,Dept.of Physics,Toronto,Ont.,Canada a

J.M.Butterworth,C.D.Catterall,M.E.Hayes,E.A.Heaphy,T.W.Jones,5543a31d650e52ea55189803ne,B.J.West University College London,Physics and Astronomy Dept.,London,U.K.o

J.Ciborowski,R.Ciesielski,G.Grzelak,R.J.Nowak,J.M.Pawlak,R.Pawlak,B.Smalska, T.Tymieniecka,A.K.Wr′o blewski,J.A.Zakrzewski,A.F.˙Zarnecki

Warsaw University,Institute of Experimental Physics,Warsaw,Poland j

M.Adamus,T.Gadaj

Institute for Nuclear Studies,Warsaw,Poland j

O.Deppe,Y.Eisenberg41,D.Hochman,U.Karshon41

Weizmann Institute,Department of Particle Physics,Rehovot,Israel d

W.F.Badgett,D.Chapin,R.Cross,C.Foudas,S.Mattingly,D.D.Reeder,W.H.Smith, A.Vaiciulis45,T.Wildschek,M.Wodarczyk

University of Wisconsin,Dept.of Physics,Madison,WI,USA p

A.Deshpande,S.Dhawan,V.W.Hughes

Yale University,Department of Physics,New Haven,CT,USA p

S.Bhadra,W.R.Frisken,R.Hall-Wilton,M.Khakzad,S.Menary,W.B.Schmidke

York University,Dept.of Physics,Toronto,Ont.,Canada a

4

1now visiting scientist at DESY

2also at IROE Florence,Italy

3now at Univ.of Salerno and INFN Napoli,Italy

4also at DESY

5supported by Worldlab,Lausanne,Switzerland

6now at BSG Systemplanung AG,53757St.Augustin

7drafted to the German military service

8also at University of Hamburg,Alexander von Humboldt Research Award

9now at Dongshin University,Naju,Korea

10now at NASA Goddard Space Flight Center,Greenbelt,MD20771,USA

11supported by the Polish State Committee for Scienti?c Research,grant No.2P03B14912 12now at Massachusetts Institute of Technology,Cambridge,MA,USA

13visitor from Florida State University

14now at Fermilab,Batavia,IL,USA

15now at ATM,Warsaw,Poland

16now at CERN

17now at ESG,Munich

18now an independent researcher in computing

19now at University of Edinburgh,Edinburgh,U.K.

20PPARC Advanced fellow

21visitor of Univ.of Crete,Greece,partially supported by DAAD,Bonn-Kz.A/98/16764 22on leave from MSU,supported by the GIF,contract I-0444-176.07/95

23supported by DAAD,Bonn-Kz.A/98/12712

24supported by an EC fellowship

25PPARC Post-doctoral fellow

26now at Osaka Univ.,Osaka,Japan

27also at University of Tokyo

28now at Wayne State University,Detroit

29supported by an EC fellowship number ERBFMBICT972523

30now at HERA-B/DESY supported by an EC fellowship No.ERBFMBICT982981

31supported by the Comunidad Autonoma de Madrid

32now at debis Systemhaus,Bonn,Germany

33now a self-employed consultant

34now at Loma Linda University,Loma Linda,CA,USA

35partially supported by the Foundation for German-Russian Collaboration DFG-RFBR (grant no.436RUS113/248/3and no.436RUS113/248/2)

36now at University of Florida,Gainesville,FL,USA

37supported by the Feodor Lynen Program of the Alexander von Humboldt foundation

38now with Physics World,Dirac House,Bristol,U.K.

39partly supported by Tel Aviv University

40an Alexander von Humboldt Fellow at University of Hamburg

41supported by a MINERVA Fellowship

42now at ICEPP,Univ.of Tokyo,Tokyo,Japan

43present address:Tokyo Metropolitan University of Health Sciences,Tokyo116-8551,Japan 44now also at Universit`a del Piemonte Orientale,I-28100Novara,Italy,and Alexander von Humboldt fellow at the University of Hamburg

45now at University of Rochester,Rochester,NY,USA

5

a supported by the Natural Sciences and Engineering Research Council of

Canada(NSERC)

b supported by the FCAR of Qu′e bec,Canada

c supporte

d by th

e German Federal Ministry for Education and Science,

Research and Technology(BMBF),under contract numbers057BN19P, 057FR19P,057HH19P,057HH29P,057SI75I

d supported by th

e MINERVA Gesellschaft f¨u r Forschung GmbH,the German

Israeli Foundation,and by the Israel Ministry of Science

e supported by the German-Israeli Foundation,the Israel Science Foundation,

the U.S.-Israel Binational Science Foundation,and by the Israel Ministry of Science

f supported by the Italian National Institute for Nuclear Physics(INFN)

g supported by the Japanese Ministry of Education,Science and Culture(the

Monbusho)and its grants for Scienti?c Research

h supported by the Korean Ministry of Education and Korea Science and Engi-

neering Foundation

i supported by the Netherlands Foundation for Research on Matter(FOM)

j supported by the Polish State Committee for Scienti?c Research,grant No.115/E-343/SPUB/P03/154/98,2P03B03216,2P03B04616,2P03B10412, 2P03B03517,and by the German Federal Ministry of Education and Science, Research and Technology(BMBF)

k supported by the Polish State Committee for Scienti?c Research(grant No.

2P03B08614and2P03B06116)

l partially supported by the German Federal Ministry for Education and Science, Research and Technology(BMBF)

m supported by the Fund for Fundamental Research of Russian Ministry for Science and Education and by the German Federal Ministry for Education and Science,Research and Technology(BMBF)

n supported by the Spanish Ministry of Education and Science through funds provided by CICYT

o supported by the Particle Physics and Astronomy Research Council

p supported by the US Department of Energy

q supported by the US National Science Foundation

6

1Introduction

The?rst HERA measurements of the charm contribution,F cˉc2,to the proton structure function F2were reported by the H1and ZEUS collaborations from the analyses of their1994deep inelastic scattering(DIS)data sets[1,2].These early results,which were statistically limited, revealed a steep rise of F cˉc2as Bjorken-x decreases.At the lowest accessible x values,it was found that around25%of DIS events contained open charm,in contrast to the EMC?xed target measurements[3]in the high-x region where the charm contribution is small.Given the large charm content,the correct theoretical treatment of charm for F2analyses in the HERA regime has become essential.More detailed measurements of charm production will aid such analyses.

The early results[1,2]suggested that the production dynamics of charmed mesons in ep collisions are dominated by the boson-gluon-fusion(BGF)mechanism shown in Fig.1.In this case,the reactions e+p→e+D?±X are sensitive to the gluon distribution in the proton[4]. The measurement of charm production can also provide tests of perturbative QCD(pQCD), in particular,tests of the hard scattering factorization theorem,which states that the same, universal,gluon distribution should contribute to both F2and F cˉc2.In addition,the presence of two large scales,namely,the virtuality of the exchanged boson(Q2)and the square of the charm-quark mass(m2c),provides a testing ground for resummation techniques.

This paper reports a measurement of D?±(2010)production using the1996and1997data sets collected with the ZEUS detector,corresponding to an integrated luminosity of37pb?1. During this period,HERA collided E e=27.5GeV positrons with E p=820GeV protons,

√

yielding a center-of-mass energy,

mass,variable-?avor-number scheme(ZM-VFNS).In this scheme,the resummation of large logarithms of Q2/m2c[9,10]results in a charm density which is added as a fourth?avor and which is then evolved in the same way as the light quark densities.At intermediate Q2values, the two schemes need to be merged.One way in which this is done is described by ACOT[9] and by Collins[11].An alternative matching method has been proposed by MRST[12].

A third method for modelling D?±production has recently been suggested by BKL[13]. This tree-level pQCD calculation,applicable for p T≥m c,considers the hadronization of the (cˉq)-state into a D?,in contrast to hadronizing an isolated c-quark.The D?is created from both color singlet and color octet con?gurations of the light and heavy quarks.Results from e+e?annihilation imply that the octet contribution is small.However,the singlet contribution alone underestimates[13]the ZEUS data on the photoproduction of charm[14].This calculation has been extended to DIS charm production and is compared to the D?±data reported here.

3Experimental setup

ZEUS is a multipurpose detector which has been described in detail elsewhere[15].The key component for this analysis is the central tracking detector(CTD)which operates in a magnetic ?eld of1.43T provided by a thin superconducting solenoid.The CTD[16]is a drift chamber consisting of72cylindrical layers,arranged in9superlayers covering the polar angle1region 15?<θ<164?.The transverse momentum resolution for full-length tracks isσ(p T)/p T= 0.0058p T 0.0065 0.0014/p T(p T in GeV).The CTD was also used to establish an interaction vertex for each event.

The uranium-scintillator sampling calorimeter(CAL)surrounds the solenoid.The CAL is hermetic and consists of5918cells,each read out by two photomultiplier tubes.The CAL contains three parts,the forward(FCAL),barrel(BCAL)and rear(RCAL),with longitudinal segmentation into electromagnetic and hadronic sections.The energy resolutions,as measured in test beams,areσ/E=0.18/ E(GeV)for electrons and hadrons,re-spectively[17].

The position of positrons scattered close to the positron beam direction is determined by a scintillator strip detector(SRTD)[18].The luminosity was measured from the rate of the bremsstrahlung process,e+p→e+γp,where the photon is measured by a lead/scintillator calorimeter[19]located at Z=?107m in the HERA tunnel.

4Kinematics and reconstruction of variables

The reaction e+(k)+p(P)→e+(k′)+X at?xed squared center-of-mass energy,s=(k+P)2, is described in terms of Q2=?q2=?(k?k′)2and Bjorken-x=Q2/(2P·q).The fractional energy transferred to the proton in its rest frame is y=Q2/(sx).The virtual photon(γ?)-proton center-of-mass energy W,given by W2=(q+P)2,is also used,see Fig.1.

In neutral current(NC)e+p DIS,both the?nal-state positron,with energy E′e and angle θ′e,and the hadronic system(with a characteristic angleγh,which,in the simple quark-parton model,is the polar angle of the struck quark)can be measured.The scattered positron was identi?ed using an algorithm based on a neural network[20].CAL cells were combined to form

clusters and combinations of these clusters and CTD tracks were used to reconstruct energy-

?ow objects(EFO’s)[21,22].For perfect detector resolution and acceptance,the quantity

δ≡Σi(E i?p z,i)is equal to2E e(55GeV).Here,E i and p z,i are the energy and longitudinal component of the momentum assigned to the i-th EFO.The sum runs over all EFO’s including

those assigned to the scattered positron.

In the K2πanalysis,Q2was reconstructed from the scattered positron(Q2e)with the electron

method[23]and y with the so-calledΣmethod[24]

δhad

yΣ=

,(2)

W

where p?(D?)is the D?±momentum in theγ?p center-of-mass frame.For the boost to theγ?p

system,the virtual-photon vector was reconstructed using the double-angle(DA)estimator[23] of the scattered positron energy,E′DA.In this method,only the anglesθ′e andγh are used[25]. E′DA is less sensitive to radiative e?ects at the leptonic vertex than the scattered e+energy determined using the electron method.

For the K4πanalysis,Q2,x and W were determined using the DA estimators(Q2DA,x DA

and W DA).

5Monte Carlo simulation

A GEANT3.13-based[26]Monte Carlo(MC)simulation program which incorporates the best

current knowledge of the ZEUS detector and trigger was used to correct the data for detector and acceptance e?ects.The event generator used for the simulation of the QED radiation from the leptonic vertex was RAPGAP[27]interfaced to HERACLES4.1[28].The charm quarks were produced in the BGF process calculated at leading order(LO).The charm mass was set to1.5GeV.The GRV94HO[29]parton distribution functions(pdf’s)were used for the proton.Fragmentation was carried out using the Lund model[30],as implemented in JETSET 7.4[31],with the full parton shower option.The fraction of the original c-quark momentum which is carried by the D?±is determined from the‘SLAC’fragmentation function,which is equivalent to the Peterson model[32],with the fragmentation parameter?set to0.035[33]. The HERWIG5.9[34]event generator was also used,with the same pdf’s and c-quark mass as used in RAPGAP,to investigate the e?ects of fragmentation.

Generated events with at least one D?+→D0π+s→(K?π+or K?π+π?π+)π+s(or c.c.) were selected.These events were then processed through the detector and trigger simulation and through the same reconstruction program as was used for the data.

6Event selection

9

6.1Trigger

Events were selected online with a three-level trigger[15].At the?rst level(FLT),inclusive DIS events are triggered by the presence of an isolated electromagnetic cluster in the RCAL or any energy deposition in excess of3GeV in any electromagnetic section of the CAL[35]. During high-luminosity periods,when the rate was high,a coincidence with an FLT track was also required.Tracks at the FLT are de?ned as a series of CTD hits pointing to the nominal interaction point.The e?ciency of this trigger,with respect to the calorimeter-only trigger, was greater than99.5%and in good agreement with the MC simulation.

At the second level,algorithms are applied to reduce the non-e+p background.The full event information is available at the third level trigger(TLT).At this level,events are accepted as DIS candidates if a high-energy scattered positron candidate is found within the CAL(‘in-clusive DIS trigger’).Because of the high rate of low-Q2events,this trigger was turned o?in the region around the RCAL beampipe during high-luminosity operation.For the K2πdecay channel,a D?-?nder(based on computing the Kππmass using tracking information and se-lecting loosely around the D?±mass)was available in the TLT.Events at low Q2were then kept by requiring a coincidence of an identi?ed scattered positron anywhere in the CAL and a tagged D?±candidate.This will be referred to as the‘D?trigger’.

Using data selected from periods when both triggers were in use,the relative e?ciency of the D?trigger with respect to the inclusive DIS trigger is found to be about80%and independent of Q2,x,p T(D?)andη(D?)within the measured kinematic regions.The MC simulations reproduce this e?ciency to an accuracy better than the statistical accuracy of the data(≈2%).

6.2O?ine selection

The DIS event selection was similar to that described in an earlier publication[36];namely,the selection required:

?a positron,as identi?ed by a neural network algorithm,with a corrected energy above10 GeV;

?the impact point of the scattered positron on the RCAL was required to lie outside the region26×14cm2centered on the RCAL beamline;

?40<δ<65GeV;and

?a Z-vertex position|Z vtx|<50cm.

The DIS events were restricted to the kinematic region

?1

D?±candidates were reconstructed from CTD tracks which were assigned to the recon-structed event vertex.Only tracks with at least one hit in the third superlayer of the CTD were considered.This corresponds to an implicit requirement that p T>0.075GeV.Tracks were also required to have|η|<1.75,where the pseudorapidity is de?ned asη=?ln(tanθ

D0→K?π+π?π+(+c.c.).The branching ratio for D0to Kπ(K3π)is0.0385±0.0009(0.076±0.004)[37].The remaining selection criteria were di?erent for the two?nal states and are discussed separately.

6.3Selection for the K2π?nal state

Pairs of oppositely-charged tracks were?rst combined to form a D0candidate.Since no particle identi?cation was performed,the tracks were alternatively assigned the masses of a charged kaon and a charged pion.An additional slow track,with charge opposite to that of the kaon track and assigned the pion mass(πs),was combined with the D0candidate to form a D?±candidate.

The combinatorial background for the K2πdecay channel was further reduced by requiring ?that the transverse momenta of the K and theπwere greater than0.4GeV,and that of theπs was greater than0.12GeV.

In addition,the momentum ratio requirement

?p(D0)/p(πs)>8.0

was imposed.This requirement was used in the D?trigger to reduce the rate of candidate events with large?M≡(M Kππs?M Kπ),far from the signal region.

The D?±kinematic region of the present analysis was de?ned as

?1.5

Finally,the signal regions for the mass of the D0candidate,M(D0),and?M were ?1.80

?143

6.4Selection for the K4π?nal state

Permutations of two negatively-and two positively-charged tracks were?rst combined to form a D0candidate.As for the K2πchannel,the tracks were alternatively assigned the masses of a charged kaon and a charged pion.An additional track,with charge opposite to that of the kaon track and assigned the pion mass(πs),was combined with the D0candidate to form a D?±candidate.The combinatorial background for the K4πdecay channel was reduced by requiring

?that the transverse momentum of the K and eachπwas greater than0.5and0.2GeV, respectively,and that of theπs was greater than0.15GeV.

In addition,the momentum ratio requirement

?p(D0)/p(πs)>9.5

was imposed.

The D?±kinematic region was de?ned as

?2.5

The signal regions for M(D0)and?M≡(M Kππππs?M Kπππ)were

?1.81

?143

11

6.5Mass distributions

Figures2(a)and(c)show the distributions of M(D0)for candidates with?M in the signal region for the two?nal states,while Figs.2(b)and(d)show the distributions of?M for candidates with M(D0)in the signal region.Clear signals are observed around the expected mass values.

For the K2π?nal state,a?t to the M(D0)distribution of two Gaussians plus an exponen-tially falling background gives a peak at M(D0)=1863.2±0.8MeV and a width of23±2MeV. The second Gaussian around1.6GeV in Fig.2(a)originates primarily from D0decays to K?π+π0in which the neutral pion is not reconstructed.For the K4πchannel,the background level was determined by using the side-bands outside the?M signal region(see the dashed histogram in Fig.2(c))to make a M(D0)distribution.The?t to the M(D0)distribution,made by adding a Gaussian to the background distribution,yielded M(D0)=1862.7±1.5MeV and a width of20±2MeV.The deviations of the data from the?t,visible in the region just above the signal in Fig.2(c),are mostly due to the mass misassignments of the K andπcandidates with the same charge from D0decay.This was veri?ed by MC studies[38].The mass values found for the D0are consistent with the PDG[37]value of1864.6±0.5MeV.

The solid curve in Fig.2(b)shows a binned maximum-likelihood?t to the?M distri-bution from the K2πchannel using a Gaussian plus a background of the form A(?M?mπ)B exp[C(?M?mπ)],where A,B and C are free parameters and mπis the pion mass. The?t to the K2πplot gives a peak at?M=145.44±0.05MeV,in good agreement with the PDG value of145.397±0.030MeV,and a width of0.79±0.05MeV,in agreement with the experimental resolution.The multiplicative exponential term is needed to describe the background suppression at large?M,which comes from the requirement on the momentum ratio p(D0)/p(πs).

The solid curve in Fig.2(d)shows a?t of the?M distribution from the K4πchannel using a Gaussian plus a background distribution obtained from the side-bands outside the M(D0) signal region(see the dashed histogram in Fig.2(d)).The?t yields a peak at?M=145.61±0.05MeV and a width of0.78±0.07MeV.

For the K2πchannel,the number of D?±events obtained from a?t to the?M distribution in the restricted region of Q2,y,p T(D?)andη(D?)is2064±72.The number of events in the K4πchannel is determined from the?M distribution using the side band method[14],which properly accounts for the combinatorial background and the background arising from the mass misassignments.The side bands,1.74

7Data characteristics

The properties of the selected events are compared with those of the RAPGAP Monte Carlo simulation.All distributions shown are background-subtracted since they represent the number of signal events obtained by?tting the various mass distributions in a given bin.The data for the K2πchannel are shown in Figs.3and4as solid points and the RAPGAP simulation as shaded histograms.All MC plots are normalized to have the same area as the data distributions.

Figure3shows histograms of E′e,θ′e,γh andδand Fig.4(a-c)displays the distributions of Q2e,x eΣand W eΣ.In general,reasonable agreement is observed between data and the MC

12

simulation.Figure4(d-f)shows the transverse momentum,p T(D?),the pseudorapidity,η(D?), and the energy fraction carried by the D?±in theγ?p center-of-mass frame,x(D?).Although the p T(D?)spectrum of the data is well described,the MC pseudorapidity spectrum is shifted to lowerηcompared to the data and the x(D?)spectrum for the MC is shifted to slightly larger values.These discrepancies are examined in more detail below.

The HERWIG[34]Monte Carlo was used for systematic studies.This MC describes the D?±di?erential distributions better than RAPGAP,but does not give as good agreement with the DIS variables as RAPGAP since it does not contain QED radiative e?ects.

Photoproduction,where the?nal positron is scattered through very small angles and escapes undetected through the RCAL beamhole,is a possible background source.Hadronic activity in the RCAL can be wrongly identi?ed as the scattered positron,giving rise to fake DIS events. The e?ect was investigated using a large sample of photoproduced D?±events generated with the HERWIG MC.After the?nal selection cuts the photoproduction contamination is found to be less than1%,much smaller than the statistical error of the measurement,and so is neglected.

The overall contribution to D?±production from b quark decays in the measured kinematic region is estimated to be less than2%,using HVQDIS with m b=4.5GeV and a hadronization fraction of b→D?of0.173[39].A similar study using RAPGAP yields an estimate of～1% at low Q2and less than3%at high Q2.Hence the contribution from b quark decays has been neglected.

8Systematic uncertainties

The experimental systematic uncertainties in the cross section are grouped into several major categories:

?Systematic uncertainties related to the inclusive DIS selection of the events:variations were made in the y cut,the RCAL box cut,and the vertex position cut.In addition,for the K2π?nal state both Q2and y were determined using the DA method rather than using the eΣmethod.The combined variations resulted in a change of±1.5%to the nominal cross section.For the K4πchannel,the electron method was used rather than the DA method and the combined variations resulted in a change of±4.7%.?Systematic uncertainties in the D?±selection:for the K2π?nal state,the minimum transverse momentum of tracks used in the D?±reconstruction was raised and lowered by up to100MeV for the K andπand by25MeV for theπs and resulted in a±4.5% variation.The momentum ratio p(D0)/p(πs)was raised by+0.5and yielded a negligible change.For the K4πchannel,similar changes in the minimum transverse momenta and varying p(D0)/p(πs)by±0.5combine to give a±8.5%variation.?Systematic uncertainties related to the estimation of the number of events and back-ground uncertainty:for the K2πanalysis,aχ2?M-?t instead of a(binned)logarithmic-likelihood?t was performed.The M(D0)signal range,within which the?M distributions were?tted,was varied by±10MeV.These variations resulted in a change of±2.5%.For the K4πanalysis,the M(D0)signal range was also varied by±10MeV and the width of the side-bands used to estimate combinatorial background was varied.These variations resulted in a change of±5.8%.

?The systematic uncertainty related to the MC generator was estimated for the K2πanal-ysis by using the HERWIG MC generator to calculate the corrections for the cross section

13

determination.This variation yields a change of-1.3%.The larger overall systematic un-certainty for the K4πchannel means that this systematic uncertainty was negligible for this channel.

?Since approximately10%of the D?±events[40]are produced through a di?ractive mech-anism which was not included in the Monte Carlo generators used to correct the data, acceptance corrections have also been obtained using a sample of di?ractive events gen-erated with RAPGAP.The di?erence in the global correction factor for the di?ractive events was less than10%.This yielded a1.3%variation in the overall cross section and was neglected.

?The systematic uncertainty related to the trigger for the K2π?nal state was estimated to be±1%by an analysis using only the inclusive DIS triggers and was neglected.?The overall normalization uncertainties due to the luminosity measurement error of ±1.65%,and those due to the D?±and D0decay branching ratios[37]were not included in the systematic uncertainties.

The systematic uncertainties were added in quadrature.The total systematic uncertainty is less than the statistical error for most of the di?erential distributions and is of the same order as the statistical error for the integrated cross section.

9Cross sections

The cross sections for a given observable Y were determined from the equation:

dσ

(3)

A·L·B·?Y

where N is the number of D?±events in a bin of?Y,A is the acceptance(including migrations, e?ciencies and radiative e?ects)for that bin,L is the integrated luminosity and B is the product of the appropriate branching ratios for the D?±and D0.

The RAPGAP MC was used to estimate the acceptance.In the K2π(K4π)kinematic region the overall acceptance was25.4(18.0)%.The statistical error of the MC is negligible compared to that of the data.

The measured cross section in the region1

σ(e+p→e+D?±X)=8.31±0.31(stat.)+0.30

?0.50(syst.)nb,

and for2.5

σ(e+p→e+D?±X)=3.65±0.36(stat.)+0.20

?0.41(syst.)nb.

These results are in good agreement with the HVQDIS[6]calculations of8.44and4.13nb, respectively.The parton distribution functions resulting from a ZEUS NLO QCD?t[41]to the ZEUS,NMC and BCDMS data were used in these calculations.In this?t,only the gluon and three light quark?avors were assumed to be present.HVQDIS fragments the charm quark to a D?±using the Peterson fragmentation function.For the above calculation,m c was set to1.4GeV,the Peterson fragmentation parameter?=0.035,and the mass factorization and

14

renormalization scales were both set to

2Note that this procedure keeps the cross section in the overall phase space in p T(D?)andη(D?)equal to the HVQDIS result and is equivalent to applying the RAPGAP fragmentation to the HVQDIS charm quark prediction.

3Some double counting may occur between the NLO calculations and the parton shower,which contains resummed terms of all orders.This e?ect is estimated to be small from the calculations with the parton shower option in JETSET switched o?.

15

(cˉq)-state.The relative weight of these color con?gurations has been taken from comparisons of the BKL calculation to the published ZEUS D?cross sections in photoproduction[14].The calculation shows reasonable agreement with these DIS data.

Tables2and3give the resulting integrated cross sections binned in Q2and y for the K2πand K4π?nal states,respectively.The bin widths were chosen such that they contained of the order of100signal events.The resulting purity in each bin is better than70%.The resolutions in both Q2and y are better than10%in all bins.These bins were chosen to measure F cˉc2 as described in the next section.Tables2and3also show the HVQDIS predictions for the di?erent kinematic bins.The predictions are in good agreement with the data.

The quantitative agreement obtained between data and the HVQDIS calculation displayed in Fig.5and Tables2and3represents a con?rmation of the hard scattering factorization theorem, in that the same gluon and three light-quark-?avor parton distributions describe both the ZEUS F2data and the D?±di?erential cross sections reported here.In view of the agreement observed here,the HVQDIS program can be used to extrapolate outside the accessible kinematic region to obtain the total D?±cross section.

10Extraction of F cˉc2

The charm contribution,F cˉc2,to the proton structure function F2can be related to the double di?erential cˉc cross section in x and Q2by

d2σcˉc(x,Q2)

xQ4{[1+(1?y)2]F cˉc2(x,Q2)?y2F cˉc L(x,Q2)}.(4) In this paper,the cˉc cross section is obtained by measuring the D?±production cross section and employing the hadronization fraction f(c→D?+)to derive the total charm cross section. Since only a limited kinematic region is accessible for the measurement of D?±,a prescription for extrapolating to the full kinematic phase space is needed.The contribution of F cˉc L(x,Q2)to the cross section in the measured Q2,y region is estimated from the NLO theoretical prediction[45] to be less than1%and is therefore neglected.Equation(4)de?nes F cˉc2as arising from events with one or more charm particles in the?nal state,but it is not a unique theoretical de?nition. It depends on the scheme and parton distributions[46].

In order to measure the contribution of charm to the inclusive F2,the integrated cross sections in the Q2and y kinematic bins of Tables2and3were extrapolated to the full p T(D?)andη(D?) phase space using HVQDIS with the RAPGAP-based fragmentation corrections discussed in the previous section.Typical extrapolation factors for the K2π(K4π)?nal state were between 4(10),at low Q2,and1.5(4),at high Q2.This procedure neglects the possibility of additional contributions outside the measured region due,for example,to intrinsic charm[47].

The extrapolated cross sections are converted into cˉc cross sections using the hadronization fraction of charm to D?+:f(c→D?+)=0.222±0.014±0.014[39].The use of this value from OPAL implicitly assumes that charm production in DIS and e+e?annihilation produces the same fractions of the various charm?nal-states.The production of charm bound states, such as e+p→e+J/ψX,is not accounted for when using the LEP c→D?+branching fraction. However,the inelastic J/ψcross section has been calculated[48]to be only2.5-4.5%of the total charm production cross section predicted by HVQDIS in the Q2,y range of this analysis. The elastic J/ψcross section has been measured in DIS[49]and is less than0.5%of the predicted total charm cross section in the range of that measurement.The9%uncertainty on

16

the c→D?+hadronization is larger than that arising from these J/ψcontributions,which have consequently been neglected.

The systematic uncertainty on the extrapolation of the measured D?±cross sections to the full p T(D?)andη(D?)phase space was investigated:varying the parameter m c by±0.15GeV gave a variation which was typically<5%;using the standard Peterson fragmentation parameter ?=0.035(instead of the RAPGAP fragmentation correction)yielded changes typically<15%; and using the GRV98HO pdf’s in the NLO calculation generally caused changes of<20%. If these uncertainties are added in quadrature,they are typically smaller than the statistical errors.However,the fact that the data are measured in a small part of the available phase space means that a realistic uncertainty on the extrapolation cannot be evaluated.Therefore these extrapolation uncertainties are not included in the systematic uncertainties discussed below.

Since the structure function varies only slowly,it is assumed to be constant within a given Q2and y bin,so that the measured F cˉc2in a bin i is given by

F cˉc2

meas (x i,Q2i)=

σi,meas(e+p→D?X)

4m2c+Q2)have been used as for the HVQDIS calculation of the di?erential cross sections.

10.1Combination of F cˉc2from both decays

Finally,the results from the two decay channels were combined in the eight common bins,tak-ing into account all systematic uncertainties.The combined value is a weighted average with weights according to the statistical precision of the inpidual measurements.The systematic uncertainties were assumed to be either uncorrelated or100%correlated between the analy-ses,as appropriate.All uncertainties concerning the DIS event selection were assumed to be correlated.Only the e?ect of the variation of the D0mass window and the changes in the p T requirements for the D0decay products were taken as uncorrelated.As in both analyses,the positive and negative errors were treated separately.The procedure leads to a gain in statistical precision of5-25%,compared to using only the K2πdecay channel.

10.2Results and discussion

Table4and Fig.7display the F cˉc2values in the various Q2bins as a function of x.The structure function F cˉc2shows a rise with decreasing x at constant values of Q2.The rise becomes steeper at higher Q2.

The curves in Fig.7represent the results of the NLO QCD calculation[45]with the ZEUS NLO QCD pdf’s.The central,solid curve corresponds to a charm quark mass of1.4GeV. Since good agreement was obtained between data and the HVQDIS calculation for the D?±di?erential cross sections and for the integrated cross sections shown in Tables2and3and since that calculation was used to extrapolate to the full kinematic range,the curves would be

17

expected to describe the resulting values of F cˉc2.The total uncertainty in the calculation of F cˉc2,shown as the band of dashed curves around the solid curve,corresponds to the uncertainty propagated from the ZEUS NLO QCD?t and is dominated by the uncertainty in the charm quark mass,which was varied from1.2to1.6GeV.

Figure8shows F cˉc2at constant x values as a function of Q2.Although the number of points is small,large scaling violations of the structure function are evident.The curves superimposed on the data are from the same calculation as shown in Fig.7.

Figure9shows the ratio of F cˉc2to F2,the inclusive proton structure function,as a function of x in?xed-Q2bins.The curves superimposed on the data are again from the calculation used for Fig.7.The values of F2used to determine the ratio were taken from the ZEUS NLO QCD ?t at the same Q2and x for which F cˉc2is quoted.The error on F2is negligible in comparison to F cˉc2.The charm contribution to F2rises steeply with decreasing x.In the measured x region,F cˉc2accounts for<10%of F2at low Q2and x?5·10?4and rises to?30%of F2for Q2>11GeV2at the lowest x measured.The strong rise of F cˉc2at low values of x is similar to that of the gluon density and thus supports the hypothesis that charm production is dominated by the boson-gluon-fusion mechanism.

11Summary

This paper presents an analysis of D?±production in DIS using the combined ZEUS1996and 1997data samples with an integrated luminosity of37pb?1,about ten times larger than in the previous ZEUS study.In addition,both the K2πand K4πdecay modes of the D?have been employed and their results combined.In the experimentally accessible region of1.5(2.5)

?0.50(sys)nb (3.65±0.36(stat)+0.20

?0.41(sys)nb).

QCD calculations of charm production based on the NLO boson-gluon-fusion process with three?avors of light quarks show excellent agreement with the overall cross section and with the Q2and y distributions.Theη(D?)and x(D?)distributions,however,cannot be reproduced with the standard Peterson fragmentation.Good agreement is obtained after a more appropriate c→D?+fragmentation,such as that in JETSET,is used.

The quantitative agreement between the NLO pQCD calculations and the ZEUS data pro-vides a con?rmation of the hard scattering factorization theorem,whereby the same gluon density in the proton describes both the inclusive F2and the DIS production of charm.

The charm contribution,F cˉc2,to the proton structure function F2was obtained using the NLO QCD calculation to extrapolate outside the measured p T(D?)andη(D?)5543a31d650e52ea55189803pared to the previous ZEUS study,the kinematic range has been extended down to Q2=1.8GeV2and up to Q2=130GeV2,with reduced uncertainties.The structure function F cˉc2exhibits large scaling violations,as well as a steep rise with decreasing x at constant Q2.For Q2>11GeV2 and x?10?3,the ratio of F cˉc2to F2is about0.3.

12Acknowledgements

We thank the DESY Directorate for their strong support and encouragement.The remarkable achievements of the HERA machine group were essential for the successful completion of this work and are gratefully appreciated.We also acknowledge the many informative discussions

18

we have had with J.Amundson,A.Berezhnoy,J.Collins,S.Fleming,B.Harris,F.Olness,C. Schmidt,J.Smith,W.K.Tung and A.Vogt.

References

[1]H1Collab.,C.Adlo?et al.,Z.Phys.C72,593(1996)

[2]ZEUS Collab.,J.Breitweg et al.,Phys.Lett.B407,402(1997)

[3]EMC Collab.,J.J.Aubert et al.,Nucl.Phys.B213,31(1983)

[4]H1Collab.,C.Adlo?et al.,Nucl.Phys.B545,21(1999)

[5]S.Nussinov,Phys.Rev.Lett.35,1672(1975)

[6]B.W.Harris and J.Smith,Phys.Rev.D57,2806(1998)

[7]B.W.Harris and J.Smith,Nucl.Phys.B452,109(1995);Phys.Lett.B353,535(1995)

[8]5543a31d650e52ea55189803enen et al.,Nucl.Phys.B392,162(1993);ibid.,B392,229(1993)

[9]M.A.G.Aivazis et al.,Phys.Rev.D50,3102(1994)

[10]M.Buza et al.,Phys.Lett.B411,211(1997)

[11]J.C.Collins,Phys.Rev.D58,094002(1998)

[12]A.D.Martin et al.,Eur.Phys.J.C4,463(1998)

[13]A.V.Berezhnoy,V.V.Kiselev and A.K.Likhoded,hep-ph/9901333v2(1999)and hep-

ph/9905555(1999)

[14]ZEUS Collab.,J.Breitweg et al.,Eur.Phys.J.C6,67(1999)

[15]ZEUS Collab.,M.Derrick et al.,The ZEUS Detector,Status Report1993,DESY(1993)

[16]N.Harnew et al.,Nucl.Instr.and Meth.A279,290(1989);

B.Foster et al.,Nucl.Phys.B(Proc.Suppl.)32,181(1993);

B.Foster et al.,Nucl.Instr.and Meth.A338,254(1994)

[17]M.Derrick et al.,Nucl.Instr.and Meth.A309,77(1991);

A.Andresen et al.,ibid.,101(1991);

A.Caldwell et al.,ibid.A321,356(1992);

A.Bernstein et al.,ibid.A336,23(1993)

[18]A.Bamberger et al.,Nucl.Instr.and Meth.A401,63(1997)

[19]J.Andruszk′o w et al.,DESY92-066(1992)

[20]H.Abramowicz,A.Caldwell and R.Sinkus,Nucl.Instr.and Meth.A365,508(1995)

[21]ZEUS Collab.,M.Derrick et al.,Eur.Phys.J.C1,81(1998);ibid.C6,43(1999)

[22]G.Briskin,PhD Thesis,University of Tel Aviv,(1998)unpublished

19

[23]S.Bentvelsen,J.Engelen,and P.Kooijman,Proc.of the1991Workshop on Physics at

HERA,DESY,Hamburg,Vol.1(1992)p.23

[24]U.Bassler and G.Bernardi,Nucl.Instr.and Meth.A361,197(1995)

[25]ZEUS Collab.,M.Derrick et al.,Z.Phys.C67,93(1995)

[26]R.Brun et al.,CERN DD/EE/84-1(1987)

[27]H.Jung,5543a31d650e52ea55189803m.86,147(1995)

[28]A.Kwiatkowski,H.Spiesberger and H.-J.M¨o hring,Proc.of the1991Workshop on Physics

at HERA,DESY,Hamburg,Vol.3(1992),p.1294;Z.Phys.C50,165(1991)

[29]M.Gl¨u ck,E.Reya and A.Vogt,Z.Phys.C67,433(1995)

[30]B.Andersson et al.,Phys.Rep.97,31(1983)

[31]T.Sj¨o strand,5543a31d650e52ea55189803m.82,74(1994)

[32]C.Peterson et al.,Phys.Rev.D27,105(1983)

[33]OPAL Collab.,R.Akers et al.,Z.Phys.C67,27(1995)

[34]G.Marchesini et al.,5543a31d650e52ea55189803m.67,465(1992)

[35]W.H.Smith et al.,Nucl.Instr.and Meth.A355,278(1995)

[36]ZEUS Collab.,J.Breitweg et al.,Eur.Phys.J.C7609(1999)

[37]Particle Data Group,C.Caso et al.,Eur.Phys.J.C3,1(1998)

[38]R.Hall-Wilton,PhD Thesis,University of Bristol,(1999)unpublished

[39]OPAL Collab.,K.Ackersta?et al.,Eur.Phys.J.C1,439(1998)

[40]ZEUS Collab.,‘Open Charm Production in Deep Inelastic Di?ractive Scattering at HERA’,

Contribution No.785,ICHEP98,Vancouver,July23-29,1998

[41]The result of the ZEUS NLO QCD?t is described in[36].New?ts were made using various

charm masses

[42]M.Gl¨u ck,E.Reya and A.Vogt,Eur.Phys.J.C5,461(1998)

[43]S.Frixione et al.,Nucl.Phys.B412,225(1994)

[44]E.Norrbin and T.Sj¨o strand,hep-ph/9905493

[45]S.Riemersma,J.Smith and W.L.Van Neerven,Phys.Lett.B347,143(1995)

[46]CTEQ Collab.,5543a31d650e52ea55189803i et al.,hep-ph/9903282

[47]S.J.Brodsky et al.,Phys.Lett.93B,451(1980)

[48]S.Fleming and T.Mehen,Phys.Rev.D57,1846(1998)and private communication

[49]ZEUS Collab.,J.Breitweg et al.,Eur.Phys.J.C6,603(1999)

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