踏花游湖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)
20
