QCD analysis of ATLAS W boson production data in association … · 2019-04-09 · 3 Theoretical...

ATL

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ATLAS PUB NoteATL-PHYS-PUB-2019-016

8th April 2019

QCD analysis of ATLAS W± boson production data

in association with jets

The ATLAS Collaboration

The present note describes the QCD analysis of the ATLAS measurement of W+ and W−

boson production measurements in association with jets, performed with data from 2012 ata centre-of-mass energy of 8 TeV. These data are fitted together with ATLAS inclusive W±

and Z boson production measurements at√

s = 7 TeV and HERA deep-inelastic scatteringdata. The parton distribution functions extracted from the resulting fit show an improveddetermination of the high-x sea-quark densities, while confirming the unsuppressed strange-quark density at lower x . 0.02 found by previous ATLAS analyses. This new set of partondistribution functions is presented.

© 2019 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

1 Introduction

Precise knowledge of the content of colliding protons, the parton density functions (PDFs), is a necessaryingredient for accurate predictions of both StandardModel (SM) and Beyond StandardModel (BSM) crosssections at the Large Hadron Collider (LHC). In order to determine the PDFs to the required precision,a wide coverage of negative 4-momentum transfer, Q2 , and Bjorken-x, the fraction of the proton’slongitudinal momentum carried by the initial parton participating in the interaction, is required. This isfacilitated by combining new inputs with old data from various experiments and measurement of differentprocesses to constrain different regions of phase space, which span the kinematic region: 10−5 . x . 1and 1 . Q2 . 106GeV2.

Precision measurements by HERA [1] of neutral (NC) and charged current (CC) cross sections in e±pscattering constrain PDFs in a number of ways. The low Q2 NC cross sections give precise informationabout the low-x sea quark and antiquarks, but are not able to distinguish quark flavour between thedown-type quarks: d and s. Information on valence quark PDFs in the high-x range is provided by thedifference between the NC e+p and e−p cross sections and CC scattering, both at high Q2. The gluon PDFis determined indirectly from the dependence of structure function on Q2 (scaling violation) in the data.HERA data provide strong constraints on the low-x gluon, but leave the high-x gluon poorly constrained.Global PDF analyses [2–5] use a range of data from other experiments together with the HERA data forfurther constraining power. For example, additional information on quarks and antiquarks from mid tohigh-x comes from fixed-target deep inelastic scattering (DIS) experiments, as well as W± and Z datafrom the Tevatron and LHC experiments. Further information on the gluon PDF is derived from data ofinclusive jet and top-quark production at both the Tevatron and LHC. A list of experimental data sets usedin global fits is given, for example, in Tables I and II of Ref. [2].

More information on high-x quarks would be advantageous since a large fraction of the fixed target DISdata is in a kinematic region where non-perturbative effects, such as those from higher twist, are importantand must be computed from phenomenological models. In many PDF analyses, tight cuts are applied tothese data to avoid those effects. Furthermore, the interpretation of DIS data using deuterons or heaviernuclei as targets is subject to uncertain nuclear corrections. The Tevatron W± asymmetry data are freefrom these uncertainties, but there are tensions between the CDF [6] and DØ [7] collaborations, discussedin further detail by the MSTW group in Ref. [8]. Data on the production of W -bosons in association withjets at the LHC, W + jets, provides a novel source of input to PDF fits that is sensitive to partons at higherx than can be accessed by W and Z data [9].

Precision measurements from the ATLAS detector at the LHC have been used previously in fits togetherwith data from the HERA experiments, resulting in the ATLASepWZ16 and ATLASepWZtop18 PDFsets [10, 11]. In the former, inclusive differential W and Z/γ∗ boson cross sections at

√s = 7 TeV allowed

the strange content of the sea to be fitted rather than assumed to be a fixed fraction of the light sea; it wasfound that these data were significantly better described by an unsuppressed strange sea at x . 0.05, incontradiction to previous assumptions based on neutrino dimuon data [12]. Furthermore, the accuracy ofthe valence quark distributions at x < 0.1 was improved. The ATLASepWZtop18 PDF set used additionaldata from top-quark pair-production at

√s = 8 TeV with the ATLAS detector to constrain further the gluon

PDF for x > 0.01.

The observation of an unsuppressed strangeness at low x is supported by the ATLAS measurement ofW -boson production in association with a charm quark, where charm production was tagged by theproduction of D or D∗ mesons or muons produced in charm semi-leptonic decay [13]. However, a recent

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analysis of CMS W + c 7 and 13 TeV data [14] has found a suppressed strange-quark density, which ispotentially in tension with this result.

The tree-level production modes of a W + jet event is either a quark–antiquark initial state with gluonradiation, or a quark–gluon initial state. In the first case, the production is similar to that of inclusiveW, Z events. The leading-order process is also already sensitive to the gluon density of the proton. Bothproduction modes require a higher x and Q2 in comparison to inclusive production [15], therefore makingit a complementary data set to the inclusive W, Z measurements.

This note presents a QCD analysis including W±+jets data based on the ATLAS measurement usingproton–proton collisions at a centre-of-mass energy of 8 TeV [15] in combination with the previousinclusive W, Z measurement at a centre-of-mass energy of 7 TeV [10]. The PDF fit is performed at next-to-next-to-leading order (NNLO) in perturbative QCD, made possible by recent theoretical developments,providing NNLO predictions for vector boson production in association with one jet [16, 17].

Additionally, this analysis considers the systematic correlations between data sets fully and presents theeffect on the resulting fit. The resulting PDF set is called ATLASepWZWjets19, and contains informationfrom the combination of inclusive combined HERA data [1], ATLAS

√s =7 TeV inclusive W, Z data [10]

and the ATLAS√

s =8 TeV W + jets data [15].

Section 2 contains the data used in this fit, with citations to further details of the analysis. In section3, the framework of the fit is described including the details of the theoretical predictions for each dataset. Furthermore, the parameterisation is described. Section 4 gives the results of the fit. Section 4.1shows the result of a fit including ATLAS W + jets data. Section 4.2 discusses the dependence of thesefits on parameterisation and model choice, and presents the extracted PDFs with additional model andparameterisation uncertainties. Sections 4.3 and 4.4 will discuss the resulting strange quark density andx(d − u) distributions, respectively, in comparison to other PDFs.

2 Input data sets

The final combined e±p cross section measurements at HERA [1] cover the kinematic range of Q2

from 0.045GeV2 to 50 000GeV2 and of Bjorken x from 0.65 down to 6 × 10−7, though data belowx = 10−5 are removed from this analysis by requiring Q2 > 10 GeV2. For the final HERA data set,there are 169 correlated sources of uncertainty. Total uncertainties are below 1.5% over the Q2 range of3 < Q2 < 500GeV2 and below 3% up to Q2

= 3 000GeV2.

The ATLAS W± differential cross sections are measured using data from both electron and muon decaychannels as functions of the W decay lepton (e, µ) pseudorapidity, η` , with an experimental precision of0.6%−1.0%. The Z/γ∗ boson rapidity, y`` , has been measured in three mass ranges: 46 < m`` < 66GeV;66 < m`` < 116GeV and 116 < m`` < 150GeV and in central and forward rapidity ranges, with anexperimental precision of up to 0.4% for central rapidity and 2.3% for forward rapidity. The absolutenormalisation of the W, Z cross sections is known to within 1.8%. There are a total of 131 sources ofcorrelated systematic uncertainty across theW , Z data sets [10]. This datawas used for theATLASepWZ16fit in a format in which the electron and muon channels were combined, whereas this analysis uses the databefore the combination of e and µ channels, hereafter referred to as “uncombined”, throughout, unless

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stated otherwise1. This choice was made as the uncombined data retain the physical origin of the sourcesof correlated uncertainties, thereby allowing to correlate data sets in a more straight-forward way. PDFsextracted from fits in this analysis using only HERA inclusive data and ATLAS inclusive W, Z data arelabelled ATLASepWZ19C and ATLASepWZ19U for use of combined and uncombined data, respectively;while containing the same data, these ATLASepWZ19 PDFs use precisely the same settings as the fitsincluding additional data to give a like-for-like comparison. The differences between these settings andthose used in the ATLASepWZ16 fit are the use of one further parameter, labelled Du, to describe thePDFs at the starting scale, and a tighter selection of NC HERA data of Q2 > 10GeV2, a change motivatedby the previously observed worse fit quality in the removed kinematic region compared to the rest ofthe HERA data [1]. More recently, this was explained by the need for resummation corrections at lowx [18], but these corrections are not included in this analysis. These changes were also used in theATLASepWZtop18 fit [11]. A more detailed discussion of the differences between ATLASepWZ16 andATLASepWZ19 PDFs is given in Appendix A.

TheATLASW± + jets differential cross sections are based on data recorded during proton-proton collisionswith centre-of-mass energy of 8 TeV, and a total luminosity of 20.2 fb−1, in the electron decay channelonly. Each event contains at least one jet with transverse momentum pT > 30GeV and rapidity |y | < 4.4.The data are split into W+ and W− cross sections, the correlations between which are large and fullyconsidered. Four differential spectra are available. These are functions of the transverse momentum of theW boson (pWT ), in the range 0 < pWT < 1500 GeV; the transverse momentum of the leading jet (pleadingT ),in the range 30 < pleadingT < 1500 GeV; the absolute rapidity of the leading jet (|yleading |), in the range0 < |yleading | < 4.4, and the scalar sum of transverse momenta of the electron, all jets with pT > 30 GeVand themissing transverse momentum (Emiss

T ) in the event, labelled HT, in the range 50 < HT < 2500GeV.Of these spectra, |yleading |and HT were not used as the first proved to have no sensitivity to PDFs in themeasured range for which NNLO corrections are available (0.0 < |yleading | < 2.5) and the second requiredlarge corrections from NLO to NNLO, implying large uncertainties. The statistical precision ranges from0.1 to 43.0% from low to high pT, respectively [15]. The uncertainty on the total luminosity of the dataset is 1.9%; this is treated as uncorrelated from the 7 TeV luminosity uncertainty. There are 50 sourcesof correlated systematic uncertainty common between the different spectra, as well as five sources ofuncorrelated uncertainties, including the data statistics. In particular the two-point systematic relatedto the difference between generators used in the unfolding of spectra is decorrelated between bins inthis analysis, as it was found to have a large statistical component; correlating this source of uncertaintybetween all W + jets bins increases the χ2 by 200 for 34 data points, despite insignificant changes to theresulting PDFs. This source of systematic uncertainty is counted in the five uncorrelated sources. Fullinformation on the statistical bin-to-bin correlations in data is available for each spectrum.

Systematic uncertainties related to jets and EmissT are assumed to be fully correlated between the 8 TeVW +

jets and the 7 TeV inclusive W, Z data sets. They are summed to six components including the EmissT scale,

the EmissT resolution, the jet combined energy scale (including those related to pileup-dependence), and the

jet energy resolution. The effect of including the correlation between data sets is shown in Appendix B.

1 Although the uncombined data is used for the purposes of this analysis to account for correlations between data sets, it isgenerally recommended that the combined data is used otherwise.

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3 Theoretical framework

The present QCD analysis uses the xFitter framework, v2.0.0 (Frozen Frog) [19–21]. This programinterfaces to theoretical calculations directly or uses fast interpolation grids to predict the consideredprocesses. The program MINUIT [22] is used for the minimisation of the PDF fit. Each step is cross-checked with an independent fit program [23].

For the DIS processes, coefficient functions with massless quarks are calculated at NNLO as implementedin QCDNUM v17-01-13 [24]. The contributions of heavy quarks are calculated in the general-massvariable-flavor-number scheme of Refs. [25–27]. The renormalisation and factorisation scales for the DIS

processes are taken as µr = µ f =

√Q2.

For the differential W and Z/γ∗ boson cross sections, the theoretical framework is the same as that usedin Ref. [10]. The xFitter package uses outputs from the APPLGRID code [28] interfaced to the MCFMprogram [29, 30] for fast calculation of the differential cross sections atNLO inQCDandLO in electroweak(EW) couplings. Corrections to higher orders are implemented using a K-factor technique, correctingon a bin-by-bin basis from NLO to NNLO in QCD and from LO to NLO for the EW contribution. TheNNLO QCD corrections are derived with the DYNNLO v1.5 [31, 32] and the FEWZ v3.1.b2 [33, 34]programs. The scales for the DY processes are taken to be the decay dilepton invariant mass appropriateto the centre of the mass bin in the Z/γ∗ case and the W -boson mass for W production. The obtainedK-factors are typically close to unity between 1% and 2%. In Ref. [10], the effect of variations ofscales to compute NNLO QCD predictions as well as the difference between DYNNLO and FEWZ werestudied and constituted a significant source of uncertainty. The effect of this theoretical uncertainty is notconsidered in this analysis.

Predictions for W + jets production are obtained at fixed order up to NNLO in QCD and to LO in EWusing the Njetti program [16]. Outputs from the APPLGRID code are used for fast calculation at NLOin QCD and LO in EW, and K-factors from the aforementioned Njetti prediction are used to correct thiscalculation to NNLO in QCD. The K-factor is derived as the ratio of the NNLO to the NLO calcuationfrom Njetti with the same kinematic selection as the W+jets data, except that |yleading | < 2.5 is required.No higher-order or non-perturbative EW corrections are applied. The renormalisation and factorisation

scales are set to µR/F =

√m2W + Σ(pj

T)2, where the second term in the square root is a sum over thetransverse momentum of each jet. Additionally, all non-perturbative corrections, such as for hadronisationeffects, are included in the K-factors2. More details on the prediction are given in the respective ATLASpublication [15]. The K-factors for W + jets production are typically within 11% of unity, but can beas high as 160% at pWT < 25 GeV. The impact of theoretical uncertainties in the W + jets data is notconsidered in this analysis.

The DGLAP evolution equations of QCD yield the proton PDFs at any value of Q2 given that they areparameterised as functions of x at an initial scale Q2

0. In this analysis, the initial scale is chosen to beQ2

0 = 1.9 GeV2 such that it is below the charm mass matching scale, µ2c, which is set equal to the charm

mass, µc = mc. The heavy quark masses are set to mc = 1.43 GeV and mb = 4.5 GeV, and the strongcoupling constant is fixed to αS (mZ ) = 0.118. All of these assumptions, along with the requirementon HERA NC data that Q2 > Q2

min (where Q2min = 10 GeV2), are varied in the evaluation of model

uncertainties.

2 The K-factor for the W− data in the pWT spectrum for 450 < pWT < 500 GeV was interpolated between neighbouring bins as itsuffered from a large statistical fluctuation.

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The quark distributions at the initial scale are assumed to behave according to the following parameterisa-tion:

xqi (x) = AixBi (1 − x)Ci Pi (x), (1)

where Pi (x) = (1 + Dix + Eix2)eFi x . The parameterised quark distributions, xqi, are chosen to be the

valence quark distributions (xuv, xdv) and the light antiquark distributions (xu, xd, xs). The gluondistribution is parameterised with the more flexible form:

xg(x) = AgxBg (1 − x)Cg Pg (x) − A′gxB′g (1 − x)C′g

where C ′g is set to a value of 25 to suppress negative contributions at high x, as in Ref. [1]. Theparameters Auv

and Advare fixed using the quark counting rule and Ag using the momentum sum rule.

The normalisation and slope parameters, A and B, of u and d are set equal such that xu = xd at x → 0.The strange PDF xs is parameterised as in Eq. (1), with Ps = 1 and Bs = Bd, leaving two free strangenessparameters, As and Cs. By default it is assumed that xs = xs.

The D, E and F terms in the expression Pi (x) are used only if required by the data, following the proceduredescribed in Ref. [20]. This leads to the usage of two additional parameters, Puv

(x) = 1 + Euvx2

and Pu = 1 + Dux. The form of the central parameterisation follows that of the ATLASepWZtop18analysis [11]; the differences between this and the ATLASepWZ16 fit are discussed in further detail inappendix A.

There are 16 free parameters used in total in the central fit, but alternative parameterisations are used inthe evaluation of a parameterisation uncertainty.The agreement of the data with the predictions from a PDF parameterisation is quantifiedwith the χ2/NDF.The definition of the χ2 is as follows:

χ2=∑ik

*.,Di − Ti (1 −

∑j

γi jbj )+/-

C−1stat,ik (Di, Dk ) *.

,Dk − Tk (1 −

∑j

γk jbj )+/-

+∑j

b2j

+∑i

logδ2i,uncorT

2i + δ

2i,statDiTi

δ2i,uncorD

2i + δ

2i,statD

2i

(2)

where Di represent the measured data, Ti the corresponding theoretical prediction, δi,uncor and δi,stat arethe uncorrelated systematic and the statistical uncertainties on Di, and correlated systematics, describedby γi j , are accounted for using the nuisance parameters bj . Summations over i and k run over all datapoints and summation over j runs over all sources of correlated systematics. For each data set, the firstterm gives a partial χ2 and the second term gives a correlated χ2. The third term is a bias correctionterm, referred to as the log penalty, corresponding to a non-constant value of the covariance matrix, usedas standard in HERA and ATLAS PDF fits [35]. The statistical correlations considered in this analysisare the bin-to-bin correlation in W + jets data. There are no statistical correlations considered for the W ,Z inclusive and HERA data; in this case Cstat is a diagonal matrix and the χ2 definition simplifies to thefollowing:

χ2=∑i

[Di − Ti (1 −∑

j γi jbj )]2

δ2i,uncorT

2i + δ

2i,statDiTi

+∑j

b2j +∑i

logδ2i,uncorT

2i + δ

2i,statDiTi

δ2i,uncorD

2i + δ

2i,statD

2i

(3)

This is the same definition as was used for the HERAPDF2.0 [1] and ATLASepWZ16 [10] analyses.

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4 Results

4.1 Fits to W + jets

The QCD analysis is performed, fitting two W + jets spectra individually, together with the HERA andATLAS W , Z inclusive data. A combined fit of the W + jets spectra is not possible, as the spectraare highly correlated to each other, and information on the statistical correlation between them is notavailable. The statistical bin-to-bin correlations are available and used for both spectra; correlationsbetween neighbouring bins are as high as 0.5. The total χ2 per degree of freedom (NDF) for each fit tothe W + jets spectra, along with the partial χ2 for each data set, the correlated component of the χ2 andthe log penalty, is given in Table 1.

Fit ATLASepWZ19U ATLASepWZ19U + pWT ATLASepWZ19U + pleadingT

Total χ2/NDF 1310 / 1104 1354 / 1138 1365 / 1150HERA partial χ2/NDF 1123 / 1016 1132 / 1016 1141 / 1016HERA correlated χ2 48 49 50HERA log penalty χ2 -18 -22 -25ATLAS W, Z partial χ2/NDF 117 / 104 116 / 104 109 / 104ATLAS W + jets partial χ2/NDF - 18 / 34 43 / 46

ATLAS correlated χ2 40 62 47ATLAS log penalty χ2 -1 -1 0

Table 1: Total and partial χ2 for data sets entering the PDF fit, for each of the W+jets spectra separately, and theATLASepWZ19U fit for comparison.

For the pWT and pleadingT W + jet spectra, there is a good overall fit quality. The partial χ2 for the HERA dataand the ATLAS W , Z data are similar to those obtained in fits to the HERA+ATLAS W , Z data alone.This demonstrates that there is no tension between these data sets and the W + jets data.Fig. 1 displays a comparison of the W + jets data spectra compared to predictions computed at NLO andcorrected to NNLOwith the K-factors using the ATLASepWZ16 PDF set and the new fits with the plottedW + jets data included. For both spectra, the low pT bins are fitted equally well by the ATLASepWZ16 fitas by the new fit. At high pT the new fit significantly improves the description of the data, especially forthe W+ + jet data.As the fit to the pWT spectrum gives the lowest χ2/NDF and the smallest parameterisation uncertainty (seeSection 4.2), it is chosen as the main fit for the remainder of the note, while the fit to the pleadingT spectrumis presented for each result as a cross-check.

4.2 Parameterisation and model choice

A choice in the fitting framework that can affect the fit quality is the choice of the parameterisation. Thenumber of parameters can potentially limit the quality of the fit by not providing enough flexibility to fit thedata. In this case, including additional parameters in Eq. (1) can improve the χ2/NDF-values. Therefore,additional parameters were separately introduced that give flexibility to high-x regions of all distributions.In each PDF set, additional polynomial parameters (Di, Ei) were used along with an exponential termeFi x — in the nominal case, only Euv

and Du are non-zero. The additional gluon term affecting the low-x

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Figure 1: W+ + jets and W− + jets data as a function of pWT (a)-(b) and as a function of pleadingT (c)-(d). The dataare compared to the NLO cross section prediction from MCFM, corrected to NNLO with K-factors, using once theATLASepWZ16 PDF set and once the new fit with W + jets data included.

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shape was also removed by setting A′

g = 0. Furthermore, relaxations on previous constraints were tested,namely the low-x constraints that Au = Ad and Bu = Bd = Bs. The resulting χ2 with each variationin the parameterisation, in comparison to the nominal fit, is given in Table 2. There were no additionalparameters which gave a fit improving the χ2 by more than two units consistently across both the pWT andpleadingT spectra.Although these additional variations did not significantly improve the χ2, they provided fits of similarquality. Thus, the maximum difference between these variations and the central fit is used as a para-meterisation uncertainty at each x and Q2 value. This uncertainty is highly asymmetric, and is notsymmetrised in any subsequent plot.

Change in parameterisation pWT pleadingTNominal χ2/NDF 1354 / 1138 1365 / 1150

A′

g = 0 1409 / 1140 1428 / 1152Au , Ad 1352 / 1137 1363 / 1149Bu , Bd 1352 / 1137 1362 / 1149Bs , Bd 1353 / 1137 1363 / 1149Du = 0 1357 / 1139 1373 / 1151

Dd 1354 / 1137 1364 / 1149Ds 1353 / 1137 1359 / 1149Duv

1354 / 1137 1365 / 1149Ddv

1354 / 1137 1364 / 1149Dg 1353 / 1137 - / 1149Eu 1354 / 1137 1363 / 1149Ed 1354 / 1137 1365 / 1149Es 1354 / 1137 1362 / 1149Eg 1352 / 1137 1365 / 1149Fuv

1351 / 1137 1363 / 1149Fdv

1354 / 1137 1365 / 1149

Table 2: Total χ2/NDF for each parameterisation variation used, for each of the W + jets spectra. Where entries aremissing, the fit either did not converge, or a negative (unphysical) was strongly favoured, including the Ei and Fi

parameters not featured.

Furthermore, the theoretical model assumptions made on the masses of c and b quarks, Q20, Q2

min and αS,as discussed in Section 3, are varied and the impact on the fit result is investigated. These variations aregiven in Table 3, along with the resulting χ2 for a fit to eachW + jets spectrum; the αs and theQ2

0 variationshave the largest impact on the gluon and quark PDFs, respectively. The differences between the centralvalues of each PDF using these variations and the central fit are taken as a model uncertainty; the upwardand downward variations are treated separately, and the model uncertainties are summed in quadrature ateach x and Q2 to give a total model uncertainty, which can be highly asymmetric. The total uncertaintyis given by the sum in quadrature of the experimental, model and parameterisation uncertainties.

The PDFs extracted from fits to each of the W + jets spectra, together with the inclusive W, Z and HERAcombined data, are shown in comparison to each other and the ATLASepWZ19U fit in Fig. 2. Fits usingeach spectrum are consistent with each other for all distributions when model and parameterisation effectsare included in the uncertainty. The PDFs obtained from a fit with the pWT spectrum exhibit the smallest

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Change in model assumption pWT pleadingTNominal χ2/NDF 1354 / 1140 1365 / 1152

mb = 4.25GeV 1352 / 1140 1364 / 1152mb = 4.75GeV 1356 / 1140 1367 / 1152

Q2min = 7.5GeV2 1413 / 1180 1426 / 1192

Q2min = 12.5GeV2 1283 / 1091 1296 / 1103

Q20 = 1.6GeV2 and mc = 1.37GeV 1359 / 1140 1369 / 1152

Q20 = 2.0GeV2 and mc = 1.49GeV 1353 / 1140 1366 / 1152

αs (mZ ) = 0.116 1352 / 1140 1366 / 1152αs (mZ ) = 0.120 1357 / 1140 1366 / 1152

Table 3: Total χ2/NDF for each model and theoretical variation used, for each of the W + jets spectra separately.

total uncertainty for all parton flavours.

Note that the ATLASepWZ19U fit uses the electron and muon decay channels in the W and Z dataseparately, a different Q2 cutoff and a slightly different parameterisation compared to the original ATLASPDF fit with this data included: ATLASepWZ16. This leads to larger uncertainties in the strange anddown sea distributions where the largest improvement is now observed with respect to the W + jets data.For more details on the difference between ATLASepWZ19U and ATLASepWZ16 see Appendix A.

The PDFs extracted from the fit, using the pWT spectrum, with experimental, model and parameterisation un-certainties plotted as separate bands are given in Fig. 4. This PDF set is named “ATLASepWZWjet19”.

4.3 Strange-quark density

The QCD analysis of the inclusive W and Z measurements by ATLAS which formed the ATLASepWZ16PDF set led to the observation that strangeness is unsuppressed at low x (. 0.023) for Q2

= 1.9 GeV2.Before the first LHC precision W, Z data, it was widely assumed that the strange sea-quark density issuppressed for all x equally relative to the up and down sea by a factor of 2 at Q2

= 1.9 GeV2. It istherefore of particular interest to check the impact of the new W + jets data on the strange-quark density.

The fraction of the strange-quark density in the proton can be characterised by the quantity rs, defined bythe ratio:

rs =s + s2d

(4)

considering the d density as reference, or by the ratio Rs, defined as:

Rs =s + su + d

(5)

which uses the sum of u and d as reference for the strange-sea density.

The Rs distribution plotted as a function of x evaluated at Q2= 1.9 GeV2 is shown in Fig. 5. The effect of

theW + jets data is most significant in the kinematic region x > 0.02, where the uncertainty is significantlyreduced and the fit results in the Rs distribution falling from near-unity at x ∼ 0.01 to approximately 0.3at x = 0.1.

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Vxu

0

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WT


x3−10 2−10 1−10

Rat

io

0.5

1

1.5

(e)xg

0

2

4 ATLAS Preliminary2 = 1.9 GeV 2Qleading


WT


x3−10 2−10 1−10R

atio

0.5

1

1.5

(f)

Figure 2: PDFs obtained for the valence quarks (a)-(b), up and down sea quarks (c)-(d), strange sea quark (e) andgluon (f), when fitting W + jets, inclusive W, Z and HERA data. Inner error bands indicate the experimentaluncertainty, while outer error bands the total uncertainty, including parameterisation and model uncertainties. Thefit using W + jets pWT data is displayed with solid uncertainty bands, and the fit using W + jets pleadingT data withhashed uncertainty bands. The lower panel displays the ratio to the central value of the ATLASepWZ19U fit withthe W + jets pWT spectrum included.

At low x (x < 0.023), the fit with the W + jets data maintains an unsuppressed strange-quark densitycompatible with the ATLASepWZ16 fit. Fitted values of rs and Rs, evaluated at x = 0.023 and Q2

=

1.9 GeV2, are given in Tables 4 and 5, respectively.

PDFs from both W + jets spectra give values of Rs and rs consistent with the previous ATLASepWZ16 fit,with the pWT spectrum providing the tightest constraints of the two. Summary plots of rs and Rs, evaluatedat x = 0.023 and Q2

= 1.9 GeV2, in comparison to the latest global PDF sets are given in Fig. 6. TheATLASepWZWjet19 fit favours lower values of Rs and rs than the ATLASepWZ16 fit, but is consistentto within a single standard deviation. Tension remains with the global analyses by more than one standarddeviation in all cases.

4.4 d and u sea quark distributions

An interesting quantity to look at for judging the performance of PDF sets is the difference between dand u PDFs. A measurement by the E866 collaboration of the ratio of Drell-Yan yields from an 800 GeV

11

Vxu

0

0.5

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ATLAS Preliminary2 = 1.9 GeV 2QATLASepWZ19U exp. unc. total unc.

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TATLASepWZ19U+p exp. unc. total unc.

x3−10 2−10 1−10

Rat

io

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xd

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W


x3−10 2−10 1−10R

atio

0.5

1

1.5

(f)

Figure 3: PDFs obtained for the valence quarks (a)-(b), up and down sea quarks (c)-(d), strange sea quark (e) andgluon (f), when fitting W + jets, inclusive W, Z and HERA data, compared to a similar fit without W + jets data.Inner error bands indicate the experimental uncertainty, while outer error bands the total uncertainty, includingparameterisation and model uncertainties. The fit using W + jets pWT data is displayed with hashed uncertaintybands, while the fit without is displayed using solid uncertainty bands.

Uncertainties

Fit rs Experimental Model Parameterisation

ATLASepWZ16 1.19 0.07 0.02 +0.02−0.10

ATLASepWZ19U 1.16 0.05 +0.04−0.19

+0.17−0.24

ATLASepWZ19U + pWT 0.99 0.04 +0.04−0.05

+0.02−0.11

ATLASepWZ19U + pleadingT 1.04 0.04 +0.05−0.07

+0.02−0.13

Table 4: Fitted rs values, evaluated at x = 0.023 and Q2= 1.9 GeV2, for each of the investigated fits compared to

the ATLASepWZ16 and ATLASepWZ19U results.

proton beam incident on liquid hydrogen and deuterium target found the proton x(d − u) distributionto be positive at high x, peaking at x(d − u) ∼ 0.04 at x ∼ 0.1 [12]. In contrast, the ATLASepWZ16PDF set gives a slightly negative central value for x(d − u), with its lowest value at x ∼ 0.1, though theuncertainties are large enough that it is compatible with zero within two standard deviations.

12

x

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ATLASepWZWjet19exp. unc.exp. + mod. unc.exp. + mod. + par. unc.

ATLAS Preliminary2 = 1.9 GeV 2Q

(a)

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x

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4.5ATLASepWZWjet19

exp. unc.exp. + mod. unc.exp. + mod. + par. unc.


(f)

Figure 4: PDFs obtained for the valence quarks (a)-(b), up and down sea quarks (c)-(d), strange sea quark (e)and gluon (f), when fitting W + jets, inclusive W, Z and HERA data. Experimental, model and parameterisationuncertainties are plotted as three separate bands.

13

x

3−10 2−10 1−10

)d +

u

)/(

s(s

+

0.5−

0

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1

1.5

2

2.5

3 ATLAS Preliminary2 = 1.9 GeV 2Q

leading


W


(a)

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)d +

u

)/(

s(s

+

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0

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ATLASepWZ19U exp. unc. total unc.

W


(b)

x

3−10 2−10 1−10

)d +

u

)/(

s(s

+

0

0.5

1

1.5

2 ATLASepWZWjet19exp. unc.exp. + mod. unc.exp. + mod. + par. unc.


(c)

Figure 5: The Rs distribution, evaluated at Q2= 1.9GeV2, determined from (a) fitting the W + jets data as a function

of pWT in comparison to pleadingT , (b) fitting the W + jets data as a function of pWT in comparison to the similar fitwithout W + jets data, and (c) the obtained ATLASepWZWjet19 fit corresponding to the fit with W + jets data inthe pWT spectrum. In (a) and (b), uncertainties in the PDFs are displayed as inner and outer bands for experimentaland total uncertainties, respectively. In (c), the uncertainty bands are displayed split in to the experimental, modeland parameterisation uncertainties.

14

Uncertainties

Fit Rs Experimental Model Parameterisation

ATLASepWZ16 1.13 0.05 0.02 +0.01−0.06

ATLASepWZ19U 1.12 0.04 +0.03−0.13

+0.13−0.18

ATLASepWZ19U + pWT 1.00 0.04 +0.04−0.05

+0.02−0.09


+0.02−0.11

Table 5: Fitted Rs values, evaluated at x = 0.023 and Q2= 1.9 GeV2, for each of the investigated fits compared to

the ATLASepWZ16 and ATLASepWZ19U results.

sr

0.2− 0 0.2 0.4 0.6 0.8 1 1.2 1.4

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty

exp.+mod. uncertainty

exp.+mod.+par. uncertainty

ATLAS Preliminary, x = 0.0232 = 1.9 GeV 2Q

(a)

sR

0.2− 0 0.2 0.4 0.6 0.8 1 1.2 1.4

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty




(b)

Figure 6: Summary plots of rs (a) and Rs (b) evaluated at x = 0.023 and Q2= 1.9GeV2, for the AT-

LASepWZWjet19 PDF set in comparison to global PDFs [2–5], and the ATLASepWZ16, ATLASepWZ19Uand ATLASepWZ19C sets. The experimental, model and parameterisation uncertainty bands are plotted separatelyfor the ATLASepWZWjet19 results. All uncertainty bands are at 68% confidence level. A similar plot at Q2

= M2Z

is given in Appendix C.

The x(d − u) distribution as function of x at Q2= 1.9GeV2 for different variations of the aforementioned

ATLASepWZ19 fits are shown in Fig. 7 and the values at a fixed x = 0.1 are reported in Table 6.

The total uncertainty is significantly decreased by use of the W + jets data. The distributions when usingdifferent W + jets spectra are consistent with each other, with an overall positive x(d − u) distribution.The pWT spectrum gives the tightest constraints.In Fig. 8 the extracted values of x(d − u) at x = 0.1 and Q2

= 1.9GeV2 are shown in comparison to theresults of the latest global PDF sets, all of which use E866 data. While the central value of the new PDFset, ATLASepWZWjet19, is lower than that of global PDF analyses, it is consistent with these within alarger uncertainty.

15

x

3−10 2−10 1−10

)u -

d

x(

0.05−

0

0.05

0.1

0.15ATLAS Preliminary2 = 1.9 GeV 2Q

leading


W


(a)

x

3−10 2−10 1−10

)u -

d

x(0.05−

0

0.05

0.1



W


(b)

x

3−10 2−10 1−10

)u -

d

x(

0

0.01

0.02

0.03

0.04

0.05ATLASepWZWjet19

exp. unc.exp. + mod. unc.exp. + mod. + par. unc.


(c)

Figure 7: The x(d − u) distribution, evaluated at Q2= 1.9GeV2, determined from (a) fitting the W + jets data as a

function of pWT in comparison to pleadingT , (b) fitting the W + jets data as a function of pWT in comparison to the similarfit without W + jets data, and (c) the obtained ATLASepWZWjet19 fit corresponding to the fit with W + jets data inthe pWT spectrum. In (a) and (b), uncertainties in the PDFs are displayed as inner and outer bands for experimentaland total uncertainties, respectively. In (c), the uncertainty bands are displayed split in to the experimental, modeland parameterisation uncertainties.

16

Uncertainties

Fit x(d − u) Experimental Model Parameterisation

ATLASepWZ16 -0.026 0.007 +0.005−0.003

+0.011−0.001

ATLASepWZ19U -0.009 0.006 +0.055−0.008

+0.046−0.024

ATLASepWZ19U + pWT 0.029 0.006 +0.002−0.003

+0.008−0.004


+0.010−0.017

Table 6: Fitted x(d − u) values, evaluated at x = 0.1 and Q2= 1.9 GeV2, for each of the investigated fits compared

to the ATLASepWZ16 and ATLASepWZ19U results.

)u - dx(

0.1− 0

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty




Figure 8: Summary plot of x(d − u) evaluated at x = 0.1 and Q2= 1.9GeV2, for the ATLASepWZWjet19 PDF set

in comparison to global PDFs [2–5], and the ATLASepWZ16, ATLASepWZ19U and ATLASepWZ19C sets. Theexperimental, model and parameterisation uncertainty bands are plotted separately for the ATLASepWZWjet19results. All uncertainty bands are at 68% confidence level. A similar plot at Q2

= M2Z is given in Appendix C.

5 Conclusion

This note presented a QCD analysis using ATLAS data of W-boson production in association with atleast one jet. The W + jets data has been measured in pp-collisions at a centre-of-mass energy of 8 TeVand corresponds to 20.2 fb−1of integrated luminosity. The data was fitted together with the data setsused for the previous ATLASepWZ16 fit, i.e. the full combined inclusive data set from HERA andthe ATLAS inclusive W and Z production data recorded at a centre-of-mass energy of 7 TeV. For thepresented fit, all significant systematic correlations between data sets were considered. The resulting PDFset is similar to the ATLASepWZ16 set for the valence, up-quark sea and gluon. The down and strangesea-quark distributions are higher and lower, respectively, at the same range in x, with significantly smallerexperimental and parameterisation uncertainties. As a result, the rs distribution falls more steeply at highx, and the x(d − u) difference is positive, in better agreement with the global PDF analyses which useE866 Drell–Yan data. At low x . 0.023, the fit shows consistency with an unsuppressed strange PDF asobserved in the ATLASepWZ16 PDF set, while displaying a positive x(d − u) distribution at high x. Theresulting PDF set is called ATLASepWZWjet19.

17

Appendix

A Fits to inclusive W, Z data at√s =7 TeV and HERA data

The fits presented in this note are of W + jets data at√

s = 8 TeV in tandem with the inclusive W, Z dataat√

s = 7 TeV and the combined HERA data. They are compared in most cases to a fit to only W, Zdata at

√s = 7 TeV and the HERA data, showing the constraining power of the W + jets data. This fit

without W + jets data is similar to, but not the same as, the ATLASepWZ16 fit. This appendix details thedifferences between the ATLASepWZ16 fit and the corresponding fits, denoted as ATLASepWZ19U andATLASepWZ19C, used in this note as a comparison to the new PDF set ATLASepWZWjet19.

Firstly, for consistency with the ATLASepWZtop18 fit [11], a further parameter, Du has been introducedto the parameterisation of all fits presented in this note. This additional parameter was included in theparameterisation uncertainty of the ATLASepWZ16 fit, so despite different central values of some PDFsat x & 0.05, the fits remain consistent. Additionally, the requirement of Q2 > 10 GeV2 for neutral currentscattering, motivated by Ref. [18], has been implemented, similarly as for the ATLASepWZtop18 fit,whereas the corresponding constraint for the ATLASepWZ16 fit was Q2 > 7.5GeV2.

Furthermore, the analysis presented in this note uses awider range of parameterisation variations, discussedin Section 4.2, for the uncertainty than the original ATLASepWZ16 analysis. These additional variationswere used as inclusion of the additional W + jets data gives coverage up to a larger range in x, withdirect sensitivity up to x = 0.3, thereby requiring further cross-checks. For a direct comparison, theseadditional parameterisation variations are also considered in the total uncertainty of the ATLASepWZ19PDF sets.

The ATLASepWZ16 fit uses data with channels combined using the HERAverager program [36, 37]. Theresult of this combination is a smaller, simplified number of data sets, but with orthogonalised and rotatedsystematic uncertainties which no longer correspond to any physical origin of an uncertainty. When theuncertainties are in this format, it is not possible to correlate them to the same uncertainties in the W+ jets data, however the data sets are effectively equivalent. In contrast, the ATLASepWZ19U fit usesthe original recorded data, separated in to channels with electron final states (W → eν, Z/γ∗ → ee) andmuon final states (W → µν, Z/γ∗ → µµ). The effect of using uncombined data is directly investigated bycomparison to a further PDF set, ATLASepWZ19C, which uses the same settings as the ATLASepWZ19Uand ATLASepWZWjet19 fits but with combined inclusive W, Z data.

A comparison between the ATLASepWZ19U and ATLASepWZ19C PDF sets is shown in Figs. 9 and 10.The impact of using uncombined data is seen in the down and strange-sea PDFs, where the experimentaluncertainties are very similar but the use of uncombined data has lead to significantly larger total uncertain-ties. Both of the ATLASepWZ19C and ATLASepWZ19U PDF sets give the result of an unsuppressedstrange sea at low-x for all variations. Furthermore, both central x(d − u) distributions are negative,although some variations of the ATLASepWZ19U set are positive.

The ATLASepWZ19U set is shown in Figs. 11 and 12 with separate experimental, model and paramet-erisation uncertainties. The main contributions to the total uncertainty in the range 10−2 < x < 10−1 arethe model variation with a higher starting scale Q2

0 = 2.2GeV2 and higher charm mass mc = 1.49GeV;and the parameterisation not including the additional low-x gluon term parameterised by the A

′

, B′

and

18

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(d)

Figure 9: PDFs obtained for the valence quarks (a)-(b) and up and down sea quarks (c)-(d) when fitting to inclusiveW , Z data at

√s =7 TeV. Inner error bands indicate the experimental uncertainty, while outer error bands the total

uncertainty, including parameterisation and model uncertainties.

C′

parameters. At high x, there is a significant contribution to the upward parameterisation uncertainty inthe Rs and rs distributions from the Au and Bu variations.

B Systematic correlations between data sets

As discussed in previous sections, the correlations between the systematic uncertainties among the ATLASdata sets have been considered in this analysis. Systematics related to jet energy resolution and scale, andthe Emiss

T resolution and scale, were fully correlated between 7 TeV and 8 TeV data sets. This is the reasonfor using the uncombined 7 TeV data sets, as opposed to the version used in the ATLASepWZ16 PDF set,where the electron and muon channels of each measurement have been combined.

In Fig. 13, the new PDF set of this analysis, ATLASepWZWjet19, is displayed alongside a fit where thesystematic uncertainties common to the inclusive W, Z and the W + jets data have been left uncorrelated.

19

x

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(c)

x

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)u -

d

x(

0.05−

0

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0.1




(d)

Figure 10: PDFs obtained for the strange sea quark (a) and gluon (b), with the Rs (c) and x(d − u) (d) distributions,when fitting to inclusive W , Z data at

√s =7 TeV. Inner error bands indicate the experimental uncertainty, while

outer error bands the total uncertainty, including parameterisation and model uncertainties.

20

x

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Vxu

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(d)

Figure 11: PDFs obtained for the valence quarks (a)-(b) and up and down sea quarks (c)-(d) when fitting to inclusiveW , Z data at

√s =7 TeV. The experimental, model and parameterisation uncertainties are plotted separately.

Correlations between bins in a single data set, and betweenW+ + jets andW− + jets data, are still considered.The difference between these fits is non-zero, but typically smaller than experimental uncertainties.

C Comparisons to global PDFs at the Z-mass scale

Figure 14 shows summary plots of the rs and Rs values at x = 0.013, and x(d − u) at x = 0.1, all atQ2= m2

Z in comparison to other PDF sets, including CT14 [2], MMHT2014 [3], NNPDF3.1 [4], ABMP16(3-flavour) [5], ATLASepWZ16 [10] and ATLASepWZ19U. All PDF sets shown are the NNLO versions,and all uncertainties are at 68% confidence level.

21

x

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(a)

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)d +

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(c)

x

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)u -

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x(

0.05−

0

0.05

0.1

0.15 ATLASepWZ19Uexp. unc.exp. + mod. unc.exp. + mod. + par. unc.


(d)

Figure 12: PDFs obtained for the strange sea quark (a) and gluon (b), with the Rs (c) and x(d − u) (d) distributions,when fitting to inclusive W , Z data at

√s =7 TeV. The experimental, model and parameterisation uncertainties are

plotted separately.

22

Vxu

0

0.5

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ATLAS Preliminary2 = 1.9 GeV 2QATLASepWZWjet19 exp. unc.

ATLASepWZWjet19, Decorrelated exp. unc.

x3−10 2−10 1−10

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io

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(e)

xg

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x3−10 2−10 1−10

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Figure 13: PDFs obtained for the valence quarks (a)-(b), up and down sea quarks (c)-(d), strange sea quark (e) andgluon (f), when fitting W + jets, inclusive W, Z and HERA data. The nominal fit is displayed with solid uncertaintybands, while a similar fit with 8TeV and 7TeV data decorrelated is displayed with hashed uncertainty bands. Thelower panel displays the ratio to the central value of the ATLASepWZ19U fit with theW + jets pWT spectrum included.

23

sr

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty



ATLAS Preliminary, x = 0.0132Z = m 2Q

(a)

sR

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty




(b)

)u - dx(

0.1− 0

ABMP16

CT14

MMHT2014

NNPDF3.1

ATLASepWZ16

ATLASepWZ19C

ATLASepWZ19U

ATLASepWZWjet19

exp. uncertainty




(c)

Figure 14: Summary plots of rs (a) and Rs (b) evaluated at x = 0.013, and x(d − u) evaluated at x = 0.1 (c),all evaluated at Q2

= m2Z , for the ATLASepWZWjet19 PDF set in comparison to global PDFs [2–5], and the

ATLASepWZ16, ATLASepWZ19U and ATLASepWZ19C sets. The experimental, model and parameterisationuncertainty bands are plotted separately for the ATLASepWZWjet19 results. All uncertainty bands are at 68%confidence level.

24

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