踏花游湖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
