NLO QCD fits using the DGLAP formalism have been made to the high precision
ZEUS $e^+p$ reduced cross-section data and to fixed target structure function
data, in order to detrmine parton distribution functions and the value of
$\alpha_s(M^2_Z)$, taking full account of correlated systematic errors.
Preliminary results are reported.Comment: 6 pages,6 figures, accepted by Int. Europhysics Conf. on HEP 2001,
  Budapes

Cooper-Sarkar, A.

English

arXiv

NLO QCD fits using the DGLAP formalism have been made to the high precision ZEUS $e^+p$ reduced cross-section data and to fixed target structure function data, in order to detrmine parton distribution functions and the value of $\alpha_s(M^2_Z)$, taking full account of correlated systematic errors. Preliminary results are reported

Cooper-Sarkar, A

CERN Document Server

PrHEP hep2001International Europhysics Conference on HEPPROCEEDINGSZEUS NLOQCD fitsAmanda Cooper-SarkarAddress: NAPL,Keble Rd, OXFORD, UKE-mail: a.cooper-sarkar1@physics.ox.ac.ukAbstract: NLO QCD ts using the DGLAP formalism have been made to the high precision ZEUSe+p reduced cross-section data and to xed target structure function data, in order to determineparton distribution functions and the value of αs(M2Z), taking full account of correlated systematicerrors.The new high precision ZEUS data on the neutral current e+p reduced cross section [1] are t tothe predictions of NLO QCD using the DGLAP equations, in order to determine parton distributionfunctions and the value of αs(M2Z). The increased range (6.3  10−5 < x < 0.65, 2.7 < Q2 <30000GeV 2) and precision (systematic errors  3%, statistical errors < 1%, for 2 < Q2 < 800GeV 2) ofthe ZEUS data allow a much improved determination of the gluon and sea distributions compared toour previous work [2]. In recent years more emphasis has been placed on estimating errors on extractedparton distributions. We present parton distributions including full accounting for uncertainties fromexperimental correlated systematic errors. We are also able to measure the value of αs(M2Z) taking fullaccount of the correlations between the shape of the parton distribution functions and αS . Full detailsof the analysis are given in [3].This analysis is performed within the conventional paradigm of leading twist, NLO QCD, with therenormalisation and factorization scales chosen to be Q2. The heavy quark production scheme is thegeneral mass variable flavour number scheme of Roberts and Thorne [4]The kinematics of lepton hadron scattering is described in terms of the variables Q2, the invariant massof the exchanged vector boson, Bjorken x, the fraction of the momentum of the incoming nucleon takenby the struck quark (in the quark-parton model), and y which measures the energy transfer betweenthe lepton and hadron systems. The dierential cross-section for the process is given in terms of thestructure functions byd2σdxdQ2=2piα2Q4x[Y+ F2(x,Q2)− y2 FL(x,Q2)− Y− xF3(x,Q2)],where Y = 1  (1 − y)2. The structure functions F2 and xF3 are directly related to non-singletand singlet quark distributions, and their Q2 dependence, or scaling violation, is predicted by pQCD.At Q2 < 1000GeV2 F2 dominates the charged lepton-hadron cross-section and for x < 10−2 the gluoncontribution dominates the Q2 evolution of F2, such that ZEUS data provide crucial information onquark and gluon distributions. (Schematically, F2  xq, dF2/dlnQ2  αsPqgxg).∗Speaker.PrHEP hep2001International Europhysics Conference on HEP Amanda Cooper-SarkarWe have performed a global t of ZEUS and xed target DIS data. The xed target data sets usedare those with precision data for which full information on the correlated systematic errors is available(NMC, E665, BCDMS muon induced F2 data on proton and deuterium targets and CCFR ν, ν xF3data on an Fe target [5]). These data are used to gain information on the valence quark distributionsand the flavour composition of the sea, and to constrain the ts at high x. However, our focus is onthe additional information to be gained from the new precision ZEUS data, particularly on the gluonand quark densities at low x and on the value of αs(M2Z).In the standard t the following cuts are made on the ZEUS and the xed target data: (i) W 2 >20 GeV2 to reduce the sensitivity to target mass and higher twist contributions which become importantat high x and low Q2; (ii) Q2 > 2.5 GeV2 to remain in the kinematic region where perturbative QCDshould be applicable.The QCD predictions for the structure functions needed to construct the reduced cross-section areobtained by solving the DGLAP evolution equations at NLO in the MS scheme. These equationsyield the quark and gluon momentum distributions (and thus the structure functions) at all values ofQ2 provided they are input as functions of x at some input scale Q20. The parton distribution functions(PDFs) for u valence, d valence, total sea, gluon and the dierence between the d and u contributionsto the sea, are each parametrized by the formp1xp2(1− x)p3(1 + p5x)at Q20 = 7GeV2. Thus the flavour structure of the light quark sea allows for the violation of theGottfried sum rule. We also impose a suppression of the strange sea of a factor of 2 at Q20, consistentwith neutrino induced dimuon data from CCFR.The parameters p1− p5 are constrained to impose the momentum sum-rule and the number sum-ruleson the valence distributions. The gluon distribution has p5 = 0, because non zero values have minimaleect on the χ2 of the t, and because this choice constrains the high x gluon to be positive without theneed for penalty χ2 terms. There are 11 free parameters in the standard t when the strong couplingconstant is xed to αs(M2Z) = 0.118 [6], and 12 free parameters when αs(M2Z) is determined by the t.Full account has been taken of correlated experimental systematic errors as follows. The denition ofthe χ2 isχ2 =∑i[Fi(p, s)− Fi(meas))]2(σ2stat + σ2unc)+∑λs2λwhereFi(p, s) =Fi(NLOQCD)(p)[1 +∑λ sλsysiλ]The latter equation modies the NLOQCD prediction for the measured quantity F (structure functionor reduced cross-section), which is a function of the PDF parameters p, to include the eect of thecorrelated systematic errors. sysiλ is the fractional systematic error on data point i due to source λ andsλ are systematic error parameters. These systematic errors are assumed to represent a one standarddeviation error. The systematic error parameters are xed to zero for the t, but allowed to vary forerror analysis, such that both the error matricesMjk =12δ2χ2δpjδpk, Cjλ =12δ2χ2δpjδsλare evaluated, and the systematic covariance matrix is given by V ps = M−1CCTM−1, so that thetotal covariance matrix is given by V tot = V p + V ps, where V p = M−1. This method is equivalent{ 2 {PrHEP hep2001International Europhysics Conference on HEP Amanda Cooper-Sarkarto osetting each systematic parameter by 1, reminimizing and adding the resulting deviations, p,from the parameters determined in the standard t in quadrature [7]. Thus it produces a conservativeestimate of the eect of systematic errors. Normalization errors are included as correlated systematicerrors. In total 71 independent sources of systematic error are included.A good description of the structure function and reduced cross-section data over the whole range of Q2from 2.5 to 30000 GeV2 is obtained. The quality of the t to the new ZEUS NC reduced cross-sectionand F2 data is shown in [1]. The quality of the t to all the data sets may be judged from the χ2.Adding the statistical and systematic errors in quadrature gives a total χ2 per data point of 0.95 for1263 data points and 11 free parameters.The parton distributions extracted from the t are shown in Fig. 1.The ZEUS data are crucial in determining the gluonZEUS00.10.20.30.40.50.60.70.810 -3 10 -2 10 -1ZEUS NLO-QCD Fit(Prel.) 2001tot. errorstat.errorQ2=10 GeV2xuvxdvxg(x 0.05)xS(x 0.05)Xxq iFigure 1: The gluon, sea, u and d valence distri-butions extracted from the standard ZEUS t, atQ2 = 10GeV2, with the error bands resulting fromstatistical, uncorrelated and correlated systematicerrors.and the sea distributions so we consider these in moredetail. In Fig 2 we show the extracted gluon distribu-tion in several Q2 bins. The uncertainty in these dis-tributions is further illustrated in Fig 3 where the ra-tio of the error bands to the central value is shown. Inthese gures the innermost error bands show the sta-tistical and uncorrelated systematic error, the middleerror bands show the total experimental error includ-ing correlated systematic errors and the outer errorbands show the additional uncertainty coming fromvariation of the strong coupling constant αs(M2Z),which is taken into account with full correlations byallowing αs(M2Z) to be a parameter of the t.For Q2 > 5 GeV2, the gluon distribution rises steeplyat low x . It is well determined to within  10% forQ2 > 20 GeV2, 10−4 < x < 10−1, and its uncertaintydecreases as Q2 evolves upwards. Considerable uncer-tainty remains for x > 0.1, where one needs information from Tevatron jet studies or prompt photonZEUS01020 Q2=1 GeV2xg(x,Q2 )ZEUS NLO-QCD Fit(Prel.) 2001Q2=2.5 GeV2tot. error (αs-free  Fit)tot. error (αs-fixed Fit)stat.error (αs-fixed Fit)01020 Q2=7 GeV2 Q2=20 GeV20102010 -4 10 -3 10 -2 10 -1Q2=200 GeV210 -4 10 -3 10 -2 10 -1Q2=2000 GeV2XZEUS Preliminary-0.500.5∆ xg(x,Q2 ) / xg(x,Q2 ) Q2=1 GeV2 Q2=2.5 GeV2-0.500.5 Q2=7 GeV2 Q2=20 GeV2-0.500.510 -4 10 -3 10 -2 10 -1Q2=200 GeV2tot. error(αs-free  Fit)10 -4 10 -3 10 -2 10 -1XQ2=2000 GeV2tot. error(αs-fixed Fit)stat.error(αs-fixed Fit)Figure 2: The gluon distribution from the stan-dard ZEUS NLOQCD t.Figure 3: The uncertainties on the gluon distribu-tion from the standard ZEUS NLOQCD t, shownas the ratio of the error bands to the central value.{ 3 {PrHEP hep2001International Europhysics Conference on HEP Amanda Cooper-Sarkardata. At low Q2 the gluon shape is flatter at low x, and if the t is extrapolated back to Q2 = 1 GeV2the gluon shape becomes valence like, with low x values that are negative within errors. (This is alsotrue of the structure function FL which is closely related to the gluon.) The new precision ZEUS datacollected in 96/97 shows this tendency even more strongly than the previous 94/5 data [2].In Fig 4 we show the extracted sea distributions in several Q2 bins. The uncertainty in these distri-butions is is less than  5% for Q2 > 2.5 GeV2 and 10−4 < x < 10−1. It can be seen that even at thesmallest Q2  1 GeV2 the sea distribution is still rising slightly at small x. In the same Q2, x regionthe gluon distribution is falling and is consistent with zero. Thus the rise in the sea distribution cannotbe driven by the gluon g ! qq splitting in this region.We also make a t using only ZEUS data, includingZEUS01020 Q2=1 GeV2xS(x,Q2 )ZEUS NLO-QCD Fit(Prel.) 2001Q2=2.5 GeV2tot. error (αs-free  Fit)tot. error (αs-fixed Fit)stat.error (αs-fixed Fit)01020 Q2=7 GeV2 Q2=20 GeV20102010 -4 10 -3 10 -2 10 -1Q2=200 GeV210 -4 10 -3 10 -2 10 -1Q2=2000 GeV2XFigure 4: The sea distribution from the standardZEUS NLOQCD tthe charged current e+p reduced cross-section data [8]and the neutral and charged current e−p data [9], [10].This high Q2 data is very well described by the stan-dard t. However now we use this data to constrainthe valence distributions. The dv valence distributionfor this t is shown in Fig 5 where the dv distribu-tion for the standard t, including xed target data,is shown for comparison. Clearly the standard tgives a more precise determination, but the high Q2ZEUS reduced cross-section data is able to providesome constraint on the valence distributions. We cansee that ZEUS data prefer a larger d valence distri-bution at high x than the standard t.NLO DGLAP QCD ts give good descriptions of F2ZEUS10-310-210-11 Q2=1 GeV2xd V(x,Q2)Q2=2.5 GeV210-310-210-11 Q2=7 GeV2 Q2=20 GeV210-310-210-110 0.25 0.5 0.75 1Q2=200 GeV2ZEUS NLO-QCD Fit(Prel.) 2001tot. error0 0.25 0.5 0.75 1Q2=2000 GeV2XZEUS-ONLY Fittot. errorFigure 5: The xdv distribution from the NLOQCDt to ZEUS data alone.data down to Q2 values in the range 1− 2 GeV2 butsuch ts assume the validity of the NLO DGLAPQCD formalism even for low Q2 (where αS is becom-ing larger such that NNLO corrections are increas-ingly important) and very low x (where ln(1/x) re-summation terms could be important). The ts alsoignore high density and non-perturbative eects (seeRefs. [11] for a discussion of these eects). To inves-tigate if there is a technical low Q2 limit to the NLOQCD t (in the sense that the t fails to convergeor gives a very bad χ2), we extrapolate our standardt into the region covered by the very low Q2 ZEUSBPT [12] data. In Fig 6 the main ZEUS data sampleand the ZEUS BPT data are shown in very low Q2bins compared to the t predictions.We see that NLO DGLAP t is unable to describe the very precise BPT data for Q2 < 0.65 GeV2,even when the full error bands on the t due to the correlated systematic errors are included. Thisremains true even if these data are included in the t: they produce very poor ts, with χ2 per datapoint of 3.9 or more. The predictions for FL for these low Q2 values are also signicantly negative forQ2 < 0.8 GeV2 indicating that the NLO DGLAP formlism cannot be valid in this region.{ 4 {PrHEP hep2001International Europhysics Conference on HEP Amanda Cooper-SarkarThe value of αs(M2Z) is measured by allowing it to be00.511.52 Q2=0.3 GeV2 Q2=0.4 GeV2 Q2=0.5 GeV200.511.52 Q2=0.585 GeV2F 2 em Q2=0.65 GeV2 Q2=0.8 GeV200.511.52 Q2=1.5 GeV2 Q2=2.7 GeV210 -5 10 -3 10 -11Q2=3.5 GeV200.511.5210 -5 10 -3 10 -11Q2=4.5 GeV210 -5 10 -3 10 -11Q2=6.5 GeV2XZEUS NLO-QCD Fit(Prel.) 2001tot. errorZEUS 96/7ZEUS BPT 97BCDMSE665NMCFigure 6: F2 data down to the very lowQ2 (includ-ing BPT data) compared to the standard NLOQCDt backward extrapolated.a parameter of the t. We obtain,αs(M2Z) = 0.11720.0008(stat+uncorr)0.0054(corr),where the rst error represents statistical and uncor-related systematic errors and the second error rep-resents the correlated systematic errors from all thecontributing experiments, including their normaliza-tion errors. The contribution of normalization errorsis as large as half the correlated systematic error.The renormalization and factorization scales used inthe t may be varied from Q2/2 ! 2Q2, as a wayof estimating the importance of NNLO and ln(1/x)terms. This produces variations in αs(M2Z) of 0.004.Within the paradigm of NLO DGLAP the contribu-tion of the correlated systematic errors is the mostsignicant source of uncertainty. Variation of analy-sis choices, such as the form of the parametrization atQ20, the value of Q20, the minimum Q2 of data enter-ing the t, do not produce a signicant model error.A more signicant choice is that of the heavy quarkproduction scheme. Repeating the standard t usingthe FFN scheme or the ZMVFN scheme produces avariation in αs(M2Z) of 0.001.The well known correlation of the value of αs(M2Z) to the gluon shape is accounted for by performinga simultaneous t for αs(M2Z) and the PDF parameters. The largest uncertainty in the gluon shape isnow at large x. Tevatron jet data suggests a larger gluon at high x than that found in our standard t,and if we use such data to constrain our t we obtain αs(M2Z)  0.121, a variation within the quotederror.Thus, when a full accounting of correlated systematic errors is included, there is no contradictionbetween the lower values of αs(M2Z) originally determined from xed target DIS data, e.g. αs(M2Z) =0.113 from BCDMS [13], and the higher values favoured by LEP data αs(M2Z)  0.120 [6].References[1] ZEUS Collaboration, S.Chekanov et al, DESY 01-064, hep-ex/0105090[2] J.Breitweg et al, Eur. Phys. J. C 7 (1999) 609[3] ZEUS Collaboration, paper 628, submitted to this conference[4] R.G. Roberts and R.S.Thorne, Phys. Rev. D 57 (1998) 6871[5] HEPDATA, http://durpdg.dur.ac.uk/hepdata/online/f2/structindex.html[6] Particle Data Group, D.E.Groom et al., Eur. Phys. J. C 15 (2000) 1[7] M. Botje, hep-th/0110123[8] J.Breitweg et al, Eur. Phys. J. C 12 (2000) 411{ 5 {PrHEP hep2001International Europhysics Conference on HEP Amanda Cooper-Sarkar[9] ZEUS Collaboration, paper 632, submitted to this conference[10] ZEUS Collaboration, paper 633, submitted to this conference[11] A.M. Cooper-Sarkar et al, Int. J. Mod. Phys. A 13 (1998) 3385, A.M.Cooper-Sarkar, hep-th/0102151.[12] J.Breitweg et al., Phys. Lett. B 487 (2000) 53[13] M. Virchaux & A. Milsztajn, Phys. Lett. B 274 (1992) 221{ 6 {

ZEUS NLO QCD fits

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