踏花游湖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
