DESY 13-183 DO-TH13/26 LPN 13-068 SFB/CPP-13-71 October2013 3 1 The ABM parton distributions tuned to LHC data 0 2 t c O S. Alekhina,b,1, J. Blümleina,2, and S. Mocha,c,3 1 1 ] h aDeutschesElektronensynchrotronDESY p - Platanenallee6, D–15738Zeuthen,Germany p e bInstituteforHighEnergyPhysics h [ 142281Protvino,Moscowregion,Russia 1 c II. InstitutfürTheoretischePhysik, UniversitätHamburg v 9 Luruper Chaussee149, D–22761Hamburg,Germany 5 0 3 . 0 1 Abstract 3 1 We present a global fit of parton distributions at next-to-next-to-leading order (NNLO) in QCD. : v The fit is based on the world data for deep-inelastic scattering, fixed-target data for the Drell-Yan i X process and includes, for the first time, data from the Large Hadron Collider (LHC) for the Drell- r Yan process and the hadro-production of top-quark pairs. The analysis applies the fixed-flavor a number scheme for n = 3,4,5, uses the MS scheme for the strong coupling α and the heavy- f s quark masses and keeps full account of the correlations among all non-perturbative parameters. At NNLO this returns the values of α (M ) = 0.1132 0.0011 and m (pole) = 171.2 2.4 GeV s Z t ± ± for the top-quark pole mass. The fit results are used to compute benchmark cross sections for Higgs production at the LHC to NNLO accuracy. We compare our results to those obtained by other groups and show that differences can be linked to different theoretical descriptions of the underlyingphysicalprocesses. 1e-mail:[email protected] 2e-mail:[email protected] 3e-mail:[email protected] 1 Introduction Our knowledge of the proton structure builds on the accumulated world data from the deep- inelasticscattering(DIS)experiments,whichcoverabroadkinematicrangeintermsofthescaling variable x and the momentum Q2 transferred to the proton [1]. These data have been gathered in a variety of different scattering experiments, either on fixed targets or through colliding beams, and in thepasttwo decades, especiallytheHERA electron-protoncolliderhas contributedsignifi- cantlywithveryaccuratemeasurementsspanningawiderangein xand Q2. Thus,DISworlddata form the backbone for the determination of the parton distribution functions (PDFs) in the QCD improvedparton model. Modern PDFs, however, are expected to provide an accurate description of the parton content of the proton not only in a kinematic region for x and Q2 as wide as possible, but to deliver also information on the flavor composition of the proton as well as on other non-perturbative parametersassociatedtotheobservablesunderconsideration,suchasthestrongcouplingconstant α or the masses of the heavy quarks charm, bottom and top. In the theoretical predictions the s valuesforthesequantitiesareoftencorrelatedwiththePDFsand,therefore,havetobedetermined simultaneouslyinafit. A comprehensive picture of a composite object such as the proton does not emerge without the need for additional assumptions by relying, e.g., on DIS data from the HERA collider alone. Therefore, global PDF fits have to include larger sets of precision data for different processes, which have to be compatible, though. The release of the new data for so-called standard candle processes, i.e., precisely measured and theoretically well-understood Standard Model (SM) scat- teringreactions,initiatesthreestepsin theanalysis: i) check ofcompatibilityofthenewdatasetwiththeavailableworld data ii) studyofpotentialconstraintsdueto theadditionofthenew datasetto thefit iii) perform a high precision determination of the non-perturbative parameters: PDFs, α (M ) s Z andheavy-quark masses. Ofcourse,at everystepQCD precisionanalyseshavetoprovideadetailed accountofthesystem- aticerrorsandhavetoincorporateallknowntheoreticalcorrections. AttheLargeHadronCollider (LHC) PDFs are an indispensableingredient in almost every experimental analysis and the publi- cation of data for W - or Z-boson, top-quark pair or jet-production from the runs at √s =7 and ± 8 TeV center-of-mass (c.m.s.) energy motivates the investigation of potential constraints on SM parameters anew. Precision data, of course, has to be confronted to high precision theory descriptions. In a hadroncolliderenvironment,thereduction ofthetheoreticaluncertaintybelow (10%)cannotbe O achieved without recourse to predictions at next-to-next-to-leading order (NNLO) in QCD [2,3] which has thus become the standard paradigm of QCD precision analyses of the proton’s parton content [4]. The PDF fits ABKM09 [5] and, subsequently, ABM11 [6] on which the current analysis is building, have been performed precisely in this spirit. At the same time, the NNLO paradigm has motivated continuous improvements in the theory description of processes where onlynext-to-leadingorder(NLO)corrections areavailable,such asthehadro-productionofjets. In the current article, we are, for the first time, tuning the ABM PDFs to the available LHC data for a number of standard candle processes including W - and Z-boson production as well ± as tt¯-production. We are demonstrating overall very good consistency of the ABM11 PDFs with theavailableLHC data. Particularaspects of thesefindingshavebeen reported previously[7–11]. 1 Subsequently,weperformaglobalfittoobtainanewABM12PDFsetandwediscussindetailthe obtained results for the PDFs, α (M ) and the quark masses along with their correlations and the s Z goodnessoffit. Theoutlineofthearticleisasfollows. WerecallinSec. 2thefootingofourfitandpresentthe basic improvements in the theory description and the new data sets included. These encompass the charm-production and high-Q neutral-current HERA data discussed in Sections. 2.1 and 2.2, the W - and Z-boson production data from the LHC investigated in Section 2.3 and, likewise, in ± Sec.2.4dataforthetotalcrosssectionoftt¯-production. TheresultsforABM12PDFsarediscussed in Section 3 in a detailed comparison with the ABM11 fit in Sec. 3.1 and with emphasis on the strong coupling constant and the charm quark mass, cf. Section 3.2. Finally, in Section 3.3 we provide cross section predictions of the ABM12 PDFs for a number of standard candle processes andthedominantSMHiggsproductionchannel. AppendixAdescribesafastalgorithmfordealing withthoseiterated theoreticalcomputationsinthePDF fit,which arevery time-consuming. 2 New data included and the theory update The present analysis is an extension of the earlier ABM11 fit [6] based on the DIS and DY data andperformedintheNNLOaccuracy. Theimprovementsarerelatedtoaddingrecentlypublished datarelevantforthePDF determination: semi-inclusive charm DIS production data obtained by combination of the H1 and ZEUS • results[12]. Thisdatasetprovidesanimprovedconstraintonthelow-xgluonandsea-quark distributionandallowsamendedvalidationofthec-quarkproductionmechanismintheDIS. theneutral-currentDISinclusivedatawiththemomentumtransferQ2>1000GeV2obtained • by the HERA experiments [13]. These data allow to check the 3-flavor scheme used in our analysis up to very high momentum transfers and, besides, to improve somewhat the determinationofthequark distributionsat x 0.1. ∼ the DY data obtained by the LHC experiments [14–17] improve the determination of the • quark distribution at x 0.1, and in particular provide a constraint on the d-quark distribu- ∼ tion,which isnotsensitivetothecorrection onthenucleareffects indeuteron. the total top-quark pair-production cross section data from LHC [18–22] and the Tevatron • combination [23] provide the possibility for a consistent determination the top-quark mass withfullaccount ofthecorrelationswiththegluonPDF andthestrongcouplingα . s Thetheoreticalframework oftheanalysisis properlyimprovedas compared totheABM11fit in accordance with the new data included. In this Section we describe details of these improve- mentsrelatedtoeach oftheprocessesand thedatasetsinvolved,check agreementofthenewdata withtheABM11 fit, and discusstheirimpactand thegoodnessoffit. 2.1 The HERA charm data The HERA data on the c-quark DIS production [12] are obtained by combination of the ear- lier H1 and ZEUS results. The combined data span the region of Q2 = 2.5 2000 GeV2 and ÷ x = 3 10 5 0.05. The dominating channel of the c-quark production at this kinematics is the − · ÷ 2 photon-gluon fusion. Therefore it provides an additional constraint on the small-x gluon dis- tribution. Our theoretical description of the HERA data on charm-production is based on the fixed-flavor-number (FFN) factorization scheme with 3 light quarks in the initial state and the heavy-quarks appearing in the final state. The 3–flavor Wilson coefficients for the heavy-quark electro-production are calculated in NLO [24,25] and approximate NNLO corrections have been also derived recently [26]. The latter are obtained as a combination of the threshold resummation calculation [27] and the high-energy asymptotics [28] with the available Mellin moments of the massive operator matrix elements (OMEs) [29–32], which provide matching of these two. Two optionsoftheNNLOWilsoncoefficient’sshape,AandB,giveninRef.[26]encodetheremaining uncertainty due to higher Mellin moments than given in [31]. In the present analysis, the NNLO corrections are modeled as a linear combination of the option A and B of Ref. [26] with the in- terpolation parameter d with the values of d =0,1 for the options A and B, respectively. The N N interpolationparameter is fitted to thedata simultaneouslywith otherfit parameters and theshape ofthemassiveNNLOcorrectionpreferredbythedataisfoundtobeclosetooptionAwiththebest fitvalueofd = 0.10 0.15. Thesameapproachwasalsousedinourearlierdeterminationofthe N − ± c-quark mass from the DIS data including the HERA charm-production ones [33] with a similar valueofd obtained. Inouranalysiswealsoemploytherunning-massdefinitionfortheDISstruc- N ture functions [34]. For comparison, the ABM11 fit is based on the massive NNLO corrections stemmingfromthethresholdresummationonly[27]andtheiruncertaintyisnot considered. ThedescriptionoftheHERAcharm datawithintheABM12frameworkisquitegoodwiththe value of χ2/NDP = 62/52, where NDP stands for the number of data points. The pulls for this data set also do not demonstrate any statistically significant trend with respect to either x or Q2, cf. Fig.2.1. Inparticular,thisgivesanargumentinfavorofusingthe3-flavorschemeoverthefull rangeofexistingDISdatakinematics. 2.2 The high-Q neutral-current HERA data The HERA data for Q2 > 1000 GeV2 newly added to our analysis are part of the combined in- clusive sample produced using the H1 and ZEUS statistics collected during Run-I of the HERA operation [13]. Due to kinematic constraints of DIS these data are localized at relatively large valuesof x, wheretheyhavelimitedstatisticalpotentialforthePDF constraintas comparedto the fixed-target DIS data used in our analysis. For this reason this piece was not used in the ABM11 fit. In the present analysis we fill this gap for the purpose of completeness. At large Q2 the DIS cross section gets non-negligible contributions due to the Z-exchange, in addition to the photon- exchange term sufficient for the accurate description of the data at Q2 M2, where M is the ≪ Z Z Z-boson mass. The Z-boson contribution is taken into account using the formalism [35,36] with account of the correction to the massless Wilson coefficients up to NNLO [37]. In accordance with [35] the contribution due to the photon-Z interference term dominates over the one for the pure Z-exchange at HERA kinematics 1. The values of χ2/NDP obtained in our analysis for the whole inclusive HERA data set and for its neutral-current subset are 694/608 and 629/540, re- spectively. The data demonstrate no statistically significant trend with respect to the fit up to the highest values of Q2 covered by the data. This is illustrated in Fig. 2.2 with the example of the neutral-currente+pHERAdatasample,whichcontainsthemostaccurateHERAmeasurementsat large Q2. Forthee p samplethepictureis similarandthetotalvalueofχ2/NDP obtainedfor the − newlyaddedneutral-currentdatawithQ2 >1000GeV2 is147/142. Forcomparison,withthecuts 1Theversion1.6oftheOPENQCDRADcodeusedinouranalysistocomputetheDISstructurefunctionsincluding thecontributionduetotheZ-exchangeispubliclyavailableonline[38]. 3 σcc (HERA RunI+II combined) 1 - y r Q2=2.5 GeV2 5 GeV2 7 GeV2 o e h t / a t a d 2 2 2 12 GeV 18 GeV 32 GeV 2 2 2 60 GeV 120 GeV 200 GeV 2 2 2 350 GeV 650 GeV 2000 GeV x x x Figure2.1: ThepullsversusBjorken xfortheHERAcombined dataonthecharmproduction [12]binned inmomentumtransfer Q2 withrespecttoourNNLOfit. ofQ2>100GeV2 andQ2>10GeV2 wegetforthesamesamplethevaluesofχ2/NDP=311/344 and486/469,respectively. InparticularthissaysthattheFFNschemeusedinouranalysisisquite sufficientforthedescriptionoftheexistingHERAdatainthewholekinematicalrange(cf.[39,40] formoredetails). 2.3 The LHC Drell-Yan data Data on the Drell-Yan (DY) process provide a valuable constraint on the PDFs extracted from a global PDF fit allowing to disentangle the sea and valence quark distributions. At the LHC these data are now available in the form of the rapidity distributions of charged leptons produced in the decays of the W-bosons and/or charged-lepton pairs from the Z-boson decays [14–17]. Due 4 1 - x=2.5E-05÷4.0E-05 x=4.0E-05÷6.3E-05 t i f / a at x=6.3E-05÷1.0E-04 x=1.0E-04÷1.6E-04 d x=1.6E-04÷2.5E-04 x=2.5E-04÷4.0E-04 x=4.0E-04÷6.3E-04 x=6.3E-04÷1.0E-03 x=1.0E-03÷1.6E-03 x=1.6E-03÷2.5E-03 x=2.5E-03÷4.0E-03 x=4.0E-03÷6.3E-03 x=0.006÷0.010 x=0.010÷0.016 x=0.016÷0.025 x=0.025÷0.040 x=0.040÷0.063 x=0.06÷0.10 x=0.10÷0.15 x=0.15÷0.21 x=0.21÷0.32 x=0.32÷0.51 x=0.51÷0.72 2 2 Q (GeV ) 2 2 Q (GeV ) Figure 2.2: The same as in Fig. 2.1 for the pulls of the HERA inclusive combined data [13] binned in Bjorken xversusmomentumtransfer Q2. to limited detector acceptance and the W/Z event selection criteria the LHC data are commonly obtained in a restricted phase space with a cut on the lepton transverse momentum Pl imposed. T Therefore, taking advantage of these data to constrain the PDFs requires fully exclusive calcu- lations of the Drell-Yan process. These are implemented up to NNLO in two publicly available codes, DYNNLO [41] and FEWZ [42]. Benchmarking these codes we found good mutual agreement for the LHC kinematics. We note that with the version 1.3 of DYNNLO the numerical convergence is achieved faster than for version 3.1 of FEWZ, although even in the former case a typical CPU timerequiredforcomputingrapiditydistributionwiththeaccuracybetterthan1%is200hoursfor the Intel model P9700/2.80 GHz. However, FEWZ (version 3.1) provides a convenient capability to estimate uncertainties in the cross sections due to the PDFs. Therefore we use in our analy- sis the benefits of both codes combining the central values of DYNNLO (version 1.3) and the PDF 5 ATLAS (7 TeV, 35 1/pb) 725 140 b) NNLO ABM11 b) b) p 525 p p η (l NNLO ABM12 η (l700 η (ll130 d 500 d d σd/ σd/ 675 σd/ 120 475 110 650 450 100 625 425 90 600 400 80 575 375 70 Z --> l+l- W- --> l-ν W+ --> l+ν 332550 PPTTνl>>2250 GGeeVV 552550 PPTTνl>>2250 GGeeVV 5600 PTl>20 GeV M >40 GeV M >40 GeV T T 300 500 40 0 1 2 0 1 2 0 2 η η η l l ll Figure2.3: TheATLASdata[14]ontherapiditydistribution ofchargedleptonsproduced inthedecaysof W -andW+-boson(leftandcentralpanel,respectively)andchargedleptonpairsfromthedecaysofZ-boson − (right panel) in comparison with the NNLO calculations based on the ABM11 PDFs (solid curves) taking intoaccount theuncertainties due toPDFs(greyarea). Thedashed curves display theABM12predictions. Thecutsonthelepton transverse momentum Pl andthetransverse mass M imposed toselectaparticular T T processsignalaregiveninthecorresponding panels. LHCb (7 TeV, 37 1/pb) 900 500 b) b) b) p NNLO ABM11 p p 70 η (µ 800 NNLO ABM12 η (µ 450 (µµ d d η σd/ 700 σd/ 400 σ/d 60 d 350 50 600 300 500 40 250 400 30 200 300 150 20 200 W+ --> µ+ν W- --> µ-ν Z --> µ+µ- 100 10 Pµ>20 GeV Pµ>20 GeV Pµ>20 GeV T 100 T 50 T 2<η <4.5 µ 0 0 0 2 3 4 2 3 4 2 3 4 η η η µ µ µµ Figure2.4: ThesameasinFig.2.3forthecharged muonsrapiditydistributions obtained byLHCb[15]. uncertaintiesofFEWZ (version3.1). The predictions obtained in such a way with the ABM11 PDFs [6] are compared to the LHC DY data [14–17] in Figs. 2.3, 2.4 and 2.5. The predictions systematically overshoot the ATLAS data [14]. However the offset is within the experimental uncertainty, which is dominated by the one of 3.5% due to the luminosity, cf. Fig 2.3. On the other hand, a good agreement is observed 6 LHCb (7 TeV, 940 1/pb) CMS (7 TeV, 840 1/pb) pb) 70 NNLO ABM11 etry0.26 ση/d (ee60 NNLO ABM12 asymm00..2224 NNLO ABM11 d ± 50 e NNLO ABM12 0.2 40 0.18 30 0.16 0.14 20 Z --> e+e- Pe>20 GeV 0.12 W± --> e±ν 10 2<Tη<4.5 PTe>35 GeV e 0.1 0 0.08 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 η η ee e Figure 2.5: The same as in Fig. 2.3 for the LHCb data [17] on the rapidity distribution of the e+e pairs − produced in the Z-boson decays (left panel) and the CMS data [16] on the charge asymmetry of electrons produced intheW -bosondecays(rightpanel). ± for the Z-boson data by LHCb [17] in the region overlapping with the ATLAS kinematics, cf. Fig2.5. Thissignalssomediscrepancybetweenthesetwosetsofdata,whichismostlikelyrelated to the general experimental normalization. In any case the normalization off-set cancels in the ratio and the ATLAS data on the charged-lepton asymmetry are in a good agreement with our predictions[14]. ThisisinsomecontrasttotheCMSresultswhereafewdatapointsgolowerthan theABM11 predictions,cf. Fig2.5. Agreement between the LHC data and the ABM11 predictions is quantified by the following χ2 functional χ2 = (y t(0))[C 1] (y t(0)), (2.1) i− i − ij j− j Xi,j (0) where y and t stand for the measurements and predictions, respectively, and C is the covari- i i ij ance matrix with the indices i, j running over the points in the data set. The covariance matrix is constructedas follows Nunc C =Cexp+ ∆t(k)∆t(k), (2.2) ij ij i j Xk=1 where the first term contains information about the experimental errors and their correlations and the second term comprises the PDF uncertainties in predictions. The later are quantified as shifts in the predictions due to the variation between the central PDF value and the ones encoding the PDF uncertainties. For ABM11 the latter appear primarily due to the variation of the fitted PDF parameters and, besides, due to the uncertainty in the nuclear correction applied to the deuteron DISdata. Therefore,thetotalnumberofPDFuncertaintymembersisN =N +1,whereN =27 unc p p is the number of eigenvectors in the space of fitted PDF parameters (cf. the Appendix for more details). 7 TheexperimentalcovariancematrixfortheATLASdata[14]is computedby 31 Cexp =δ σ2+ f(0)f(0) sksk, (2.3) ij ij i i j i j Xl=1 where σ are the statistical errors in the data combined in quadrature with the uncorrelated errors. i Here sl are the correlated systematic uncertainties representing 31 independent sources including i the normalization, and δ stands for the Kronecker symbol. In view of the small background for ij the W- and Z-production signal all systematic errors are considered as multiplicative. Therefore, (0) they are weighted with the theoretical predictions f . The experimental covariance matrices i for the CMS and LHCb data of Refs. [15–17] are employed directly as published in Eq. (2.2) afterre-weightingthembythetheoreticalpredictionssimilarlytoEq.(2.3)withthenormalization uncertaintytaken intoaccount in thesameway as fortheATLASdata. Experiment ATLAS[14] CMS[16] LHCb[15] LHCb[17] Finalstates W+ l+ν W+ e+ν W+ µ+ν Z e+e − → → → → W l ν W e ν W µ ν − − − − − − → → → Z l+l − → Luminosity(1/pb) 35 840 37 940 NDP 30 11 10 9 χ2 (ABM11) 35.7(7.7) 10.6(4.7) 13.1(4.5) 11.3(4.2) χ2 (ABM12) 35.6 9.3 14.4 13.4 Table 2.1: The value of χ2 obtained for different samples of the Drell-Yan LHC data with the NNLO ABM11 PDFsin comparison with the one obtained in the ABM12 fit. The figures in parenthesis give one standarddeviation ofχ2 equalto √2NDP. The values of χ2 computed according to Eq. (2.1) for each of the LHC DY data sets obtained with the ABM11 PDFs are given in Tab. 2.1. The description quality is somewhat worse for the ATLASandLHCbmuondata,however,ingeneraltheagreementbetweenthedataandpredictions is still good. The values of χ2/NDP are comparable to 1 within the statistical fluctuations in χ2. Therefore, the data can be easily accommodated in the ABM fit. Furthermore, in this case the PDFvariationisexpectedtobewithintheABM11PDFuncertainties. Thisallowstooptimizethe computation of the involved NNLO Drell-Yan corrections in the fit by extrapolation of the grid with the pre-calculated predictions for the ABM11 eigenvector basis (cf. App. A for the details on the implementation of this approach). The values of χ2 obtained for the LHC DY data sets in the ABM12 fit are quoted in Tab. 2.1. In this case the PDF uncertainties are irrelevant since the PDFs have been tuned to the data. Therefore, they are not included into the second term in the covariance matrix Eq. (2.2). Despite the difference in the definition, the ABM12 values of χ2 for the LHC DY data are in a good agreement with the ABM11 ones giving additional evidence for thecompatibilityofthesedatawiththeABM11PDFs. 2.4 The data for tt¯production in the ABM12 fit At the LHC tt¯-pair production proceeds predominantly through initial gluon-gluon scattering. Thus, the total tt¯cross section is sensitive to the gluon distribution at effective x values of x h i ≃ 8 450 σ p p → t -t [pb] at LHC8 450 σ p p → t -t [pb] at LHC8 400 400 NNLO NNLO 350 NLO 350 NLO LO LO 300 300 250 250 200 200 150 150 100 100 50 50 140 150 160 170 180 150 160 170 180 190 m(m)/GeV m(pole)/GeV t t t Figure 2.6: The LO, NLO and NNLO QCD predictions for the tt¯total cross section at the LHC (√s= 8TeV)asafunctionofthetop-quarkmassintheMS schemem(m)atthescaleµ=m(m)(left)andinthe t t t t on-shellschemem(pole)atthescaleµ=m(pole)(right)withtheABM12PDFs. t t 280 280 260 σ p p → t -t [pb] at LHC8 260 σ p p → t -t [pb] at LHC8 m(m) = 162 GeV m(pole) = 171 GeV 240 t t 240 t 220 220 200 200 180 180 160 160 140 140 120 120 100 100 1 1 µ/m(m) µ/m(pole) t t t Figure 2.7: The scale dependence of the LO, NLO and NNLO QCD predictions for the tt¯total cross section at the LHC (√s= 8 TeV) for a top-quark mass m(m)= 162 GeV in the MS scheme (left) and t t m(pole) = 171 GeV in the on-shell scheme (right) with the ABM12 PDFs and the choice µ = µ = µ . t r f The vertical bars indicate the size of the scale variation in the standard range µ/m(pole) [1/2,2] and t ∈ µ/m(m) [1/2,2],respectively. t t ∈ 2m /√s 0.04...0.05 for theruns at √s=7 and 8 TeV c.m.s. energy, aregion in x which is well t ≃ constrainedbydatafrom theHERA collider,though. The available data for the total tt¯cross section from ATLAS and CMS at √s=7 TeV [18,19] and at √s = 8 TeV [20–22] c.m.s. energy display good consistency, although, for the data sets at √s = 7 TeV only within the combined uncertainties. Generally, the systematic and luminos- ity uncertainties dominate over the small statistical uncertainty and the CMS data [19,21,22] as well as the result from the Tevatron combination [23] are accurate to (5%) while the ATLAS O measurements[18,20]havean error slightlylargerthan (10%). O The QCD corrections for inclusive tt¯-pair production are complete to NNLO [43–46], so that these data can be consistently added to the ABM11 PDF fit at NNLO. The theory predictions are available for the top-quark mass in the MSscheme with m (µ ) being the running mass [47] as t r well as for the pole mass m (pole) in the on-shell renormalization scheme [43–46]. The distinc- t 9