Measurements of W and Z boson production in pp collisions...

Eur. Phys. J. C (2019) 79:128 https://doi.org/10.1140/epjc/s10052-019-6622-x

Regular Article - Experimental Physics

Measurements of W and Z boson production in pp collisionsat

√s = 5.02 TeV with the ATLAS detector

ATLAS Collaboration�

CERN, 1211 Geneva 23, Switzerland

Received: 22 October 2018 / Accepted: 22 January 2019© CERN for the benefit of the ATLAS collaboration 2019

Abstract Measurements of fiducial integrated and differ-ential cross sections for inclusive W+, W− and Z bosonproduction are reported. They are based on 25.0 ± 0.5 pb−1of pp collision data at

√s = 5.02 TeV collected with the

ATLAS detector at the CERN Large Hadron Collider. Elec-tron and muon decay channels are analysed, and the com-bined W+, W− and Z integrated cross sections are foundto be σW+ = 2266 ± 9 (stat) ± 29 (syst) ± 43 (lumi) pb,σW− = 1401 ± 7 (stat) ± 18 (syst) ± 27 (lumi) pb, andσZ = 374.5 ± 3.4 (stat) ± 3.6 (syst) ± 7.0 (lumi) pb, in goodagreement with next-to-next-to-leading-order QCD cross-section calculations. These measurements serve as referencesfor Pb+Pb interactions at the LHC at

√sNN = 5.02 TeV.

1 Introduction

Measurements of W± and Z boson1 production at hadroncolliders provide a benchmark for the understanding of quan-tum chromodynamics (QCD) and electroweak (EW) pro-cesses. Predictions for the differential and fiducial crosssections are available up to next-to-next-to-leading-order(NNLO) accuracy in QCD and include EW corrections atnext-to-leading-order (NLO) accuracy [1–3]. The rapiditydistribution of EW boson production is sensitive to the under-lying QCD dynamics and, in particular, to the parton distri-bution functions (PDFs) which define the initial kinematicsof the hard process. Therefore, measurements of weak-bosonproduction offer an excellent opportunity to test models ofparton dynamics.

The ATLAS, CMS and LHCb collaborations have mea-sured W± and Z boson production in proton–proton (pp)collisions at centre-of-mass energies of

√s = 7, 8 and 13

TeV [4–7]. These measurements provide precision tests ofthe QCD theory and PDFs, which can be complemented

1 Throughout this paper, Z/γ ∗ boson production is referred to as Zboson production.

� e-mail: [email protected]

with measurements at the additional centre-of-mass energy√s = 5.02 TeV.This paper describes measurements of the production

cross sections times leptonic branching ratios for the inclu-sive W+ → �+ν, W− → �−ν and Z → �+�− (� = e, μ)processes. Integrated and differential cross sections are mea-sured in a fiducial phase space defined by detector accep-tance and lepton kinematics. ForW± bosons the decay leptoncharge asymmetry is also determined. All measurements areperformed with pp collision data corresponding to an inte-grated luminosity of 25.0 pb−1, collected at

√s = 5.02 TeV

with the ATLAS detector. The data were recorded during theautumn of 2015. The peak instantaneous luminosity deliv-ered by the LHC was L = 3.8 × 1032 cm−2 s−1 and themean number of pp interactions per bunch crossing (hardscattering and pile-up events) was 1.5. Therefore, this datasetis characterised by a relatively low pile-up contribution ascompared to the measurements of weak-boson productionperformed at higher centre-of-mass energies by ATLAS.

In addition, the measurement of W± and Z boson pro-duction in pp collisions at the centre-of-mass energy

√s =

5.02 TeV is an important reference for weak-boson produc-tion in heavy-ion collisions. The LHC has provided bothproton–lead (p+Pb) and lead–lead (Pb+Pb) collisions at thecentre-of-mass energy per nucleon pair

√sNN = 5.02 TeV.

Published results from the ATLAS and CMS collaborationsare currently available for W± and Z boson production [8–11] in Pb+Pb collisions at

√sNN = 2.76 TeV and Z boson

production [12,13] in the p+Pb system at√sNN = 5.02 TeV.

2 The ATLAS detector

The ATLAS experiment [14] is a multipurpose particle detec-tor with a forward–backward symmetric cylindrical geome-try.2 It consists of an inner tracking detector surrounded by a

2 ATLAS uses a right-handed coordinate system with its origin at thenominal interaction point (IP) in the centre of the detector and the z-axis

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128 Page 2 of 29 Eur. Phys. J. C (2019) 79:128

thin superconducting solenoid, electromagnetic and hadroniccalorimeters, and a muon spectrometer incorporating threelarge superconducting air-core toroid magnets with eightcoils each.

The inner-detector system (ID) is immersed in a 2 Taxial magnetic field and provides charged-particle trackingin the pseudorapidity range |η| < 2.5. At small radii, ahigh-granularity silicon pixel detector covers the interactionregion and typically provides four measurements per track.It is followed by the silicon microstrip tracker, which usuallyprovides eight measurement points per track. These silicondetectors are complemented by a gas-filled straw-tube transi-tion radiation tracker, which enables track reconstruction upto |η| = 2.0. The transition radiation tracker also provideselectron identification information based on the fraction ofhits (out of ∼ 35 in total) with an energy deposit above athreshold indicative of transition radiation.

The calorimeter system covers the pseudorapidity range|η| < 4.9. Within the region |η| < 3.2, electromagnetic (EM)calorimetry is provided by high-granularity lead/liquid-argon(LAr) calorimeters, with an additional thin LAr presamplercovering |η| < 1.8 to correct for upstream energy-loss fluc-tuations. The EM calorimeter is divided into a barrel sec-tion covering |η| < 1.475 and two endcap sections covering1.375 < |η| < 3.2. For |η| < 2.5 it is divided into three lay-ers in depth, which are finely segmented in η and φ. Hadroniccalorimetry is provided by a steel/scintillator-tile calorime-ter, segmented into three barrel structures within |η| < 1.7and two copper/LAr hadronic endcap calorimeters covering1.5 < |η| < 3.2. The solid-angle coverage is completedwith forward copper/LAr and tungsten/LAr calorimeter mod-ules in 3.1 < |η| < 4.9, optimised for electromagnetic andhadronic measurements, respectively.

The muon spectrometer (MS) comprises separate triggerand high-precision tracking chambers measuring the deflec-tion of muons in the magnetic field generated by the toroidmagnets. The precision chamber system covers the region|η| < 2.7 with three layers of monitored drift tubes, com-plemented by cathode strip chambers in the forward region.The muon trigger system covers the range |η| < 2.4 withresistive plate chambers in the barrel, and thin gap chambersin the endcap regions.

In 2015, the ATLAS detector had a two-level trigger sys-tem [15]. The level-1 trigger is implemented in hardware anduses a subset of detector information to reduce the event rateto a value of at most 75 kHz. This is followed by a software-

Footnote 2 continuedalong the beam pipe. The x-axis points from the IP to the centre of theLHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ)are used in the transverse plane, φ being the azimuthal angle around thez-axis. The pseudorapidity is defined in terms of the polar angle θ asη = − ln tan(θ/2), while the rapidity is defined as y = 12 ln E+pzE−pz .

based high-level trigger which reduces the event rate to about1 kHz.

3 Simulated event samples

Samples of Monte Carlo (MC) simulated events are usedto evaluate the selection efficiency for signal events and thecontribution of several background processes to the analyseddataset. All of the samples are processed with the Geant4-based simulation [16,17] of the ATLAS detector. Dedicatedefficiency and calibration studies with data are used to derivecorrection factors to account for residual differences betweenexperiment and simulation, as is subsequently described.

The processes of interest, specifically events containingW± or Z bosons, were generated with the Powheg-Boxv2 MC program [18] interfaced to the Pythia 8.186 par-ton shower model [19]. The CT10 PDF set [20] was used inthe matrix element, while the CTEQ6L1 PDF set [21] wasused with the AZNLO [22] set of generator-parameter val-ues (tune) for the modelling of non-perturbative effects inthe initial-state parton shower. The Photos++ v3.52 pro-gram [23] was used for QED radiation from electroweakvertices and charged leptons. Samples of top-quark pair (t t̄)and single-top-quark production were generated with thePowheg-Box v2 generator, which uses NLO matrix ele-ment calculations together with the CT10f4 PDF set [24].Top-quark spin correlations were preserved for all top-quarkprocesses. The parton shower, fragmentation, and underly-ing event were simulated using Pythia 6.428 [25] with theCTEQ6L1 PDF set and the corresponding Perugia 2012 tune(P2012) [26]. The top-quark mass was set to 172.5 GeV. TheEvtGen v1.2.0 program [27] was used to model bottom andcharm hadron decays for all versions of Pythia. Dibosonprocesses were simulated using the Sherpa v2.1.1 genera-tor [28]. They were calculated for up to one (Z Z ) or zero(WW , WZ ) additional partons at NLO QCD accuracy andup to three additional partons at LO. In addition, the Sherpadiboson sample cross section is scaled to account for the crosssection change when the Gμ scheme [29] is used instead ofthe native one for the EW parameters, resulting in an effectivevalue of α ≈ 1/132. Multiple overlaid pp collisions weresimulated with the soft QCD processes of Pythia v8.186using the A2 tune [30] and the MSTW2008LO PDF set [31].For the comparison with data in differential distributions andthe evaluation of single-boson EW backgrounds for the cross-section calculations, the single-boson simulations are nor-malised to the results of NNLO QCD calculations obtainedwith a modified version of DYNNLO 1.5 [2,3] optimised forspeed of computation, with uncertainties of 3%. The simula-tions of all other processes are normalised to the predictionsof NLO QCD calculations, with uncertainties of 10% for thediboson and top-quark processes.

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Eur. Phys. J. C (2019) 79:128 Page 3 of 29 128

4 Object definitions and event selection

This section describes the reconstruction of electrons, muonsand hadronic recoil objects, and the selection of W and Zbosons. Candidate events are required to have at least one pri-mary vertex reconstructed from at least three tracks with pT >400 MeV and to pass a trigger selection, which requires a sin-gle electron or muon candidate with a pT threshold of 15 GeVor 14 GeV, respectively. In addition, a loose likelihood-basedidentification requirement [32,33] is applied in the electrontrigger.

Electron candidates are required to have pT > 20 (25)GeV in the Z (W ) boson analysis and |η| < 2.47. Candi-dates within the transition region between barrel and endcapcalorimeters (1.37 < |η| < 1.52) are rejected. In addition,medium likelihood-based identification and tight isolationrequirements are applied [32,33]. Muon candidates must sat-isfy pT > 20 (25) GeV in the Z (W ) boson analysis and|η| < 2.4 and pass the requirements of medium identifica-tion and tight isolation [34]; both criteria were optimised for2015 analysis conditions.

Additional requirements are imposed on the significanceof the transverse impact parameter, d0, such that |d0|/σd0 <5 (3) for electron (muon) candidates. To ensure that leptoncandidates originate from the primary vertex, a requirementis also placed on the longitudinal impact parameter, z0, mul-tiplied by the sine of the track polar angle, θ , such that theabsolute value is smaller than 0.5 mm.

Events with Z boson candidates are selected by requiringexactly two opposite-charge electrons or muons, at least oneof which is matched to a lepton selected at trigger level. Thedilepton invariant mass must satisfy the fiducial requirement66 < m�� < 116 GeV.

Events with W boson candidates are selected by requir-ing exactly one electron or muon that is matched to a leptonselected at trigger level. The (anti-)neutrinos from W± →�±ν decays escape direct detection. A measure of the neu-trino transverse momentum, pνT, can be inferred from infor-mation about the hadronic system recoiling against the Wboson. The hadronic recoil is the vector sum of all calorime-ter energy clusters excluding the deposits from the decaymuon or electron, and is further described below. The trans-verse projection of the recoil onto the r–φ plane, �uT, is usedtogether with the decay lepton transverse momentum �p �T forthe calculation of the missing transverse momentum vector,

�E missT = −(�uT + �p �T

),

whose magnitude is denoted EmissT . The transverse mass ofthe lepton-EmissT system is defined as mT =√

2p�TEmissT

(1 − cos �φ�,EmissT

)where �φ�,EmissT

is the

azimuthal angle between �p �T and �E missT . The W boson can-

didate events are selected by requiring EmissT > 25 GeVand mT > 40 GeV. These event selection requirements areoptimised to reduce background contributions from multi-jetprocesses.

The general structure of the algorithm used for hadronicrecoil reconstruction is introduced in Ref. [35], wherethree-dimensional topological clusters [36] calibrated at thehadronic scale are used as inputs to the algorithm. In thismeasurement, the hadronic recoil is reconstructed using par-ticle flow objects [37] as inputs. The ATLAS particle flowalgorithm provides an improved EmissT resolution comparedto the algorithm using only topological clusters, and makesthe measurement less sensitive to pile-up by separating thecharged-hadron contribution from the neutral hadronic activ-ity [37]. The charged activity is measured by the ID and therelated tracks from charged hadrons can be matched to avertex. From all charged hadrons, only calorimetric clustersassociated with a track originating from the reconstructedprimary vertex are retained as input to the hadronic recoilalgorithm. The neutral hadronic activity is represented byclusters without an associated track, and is also used in therecoil algorithm.

5 Detector performance corrections

5.1 Lepton calibration and efficiency

The electron energy calibration is primarily obtained from thesimulation by employing multivariate techniques [38]. Thesignal Z → ee MC simulation is used for deriving the dataenergy scale calibration and resolution corrections for thesimulation. The energy resolution is corrected with additionalfactors no larger than about 1% in the barrel and up to 2%in the endcap region of the detector in order to account fora slightly worse resolution observed in the data. The energyscale is corrected by applying a per-electron energy scalefactor to the data derived from a comparison of the electron-pair invariant mass between the simulation and the data. Thisprocedure was found to be sensitive to the pile-up distributionin data due to different settings used for the signal readoutfrom the EM calorimeters [39]. Therefore, a special set ofscale correction factors was derived for this dataset.

Measurements of muon momenta can be biased by thedetector alignment and resolution, distortions of the mag-netic field or imprecise estimates of the amount of passivematerial in the detector. Corrections of the muon momentumscale and resolution, which are applied to the simulation, arederived as a function of the muon η and φ using Z → μ+μ−events [34]. The correction factors are chosen such that theyminimise the χ2 between the muon-pair invariant mass dis-tributions in data and simulation.

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Fig. 1 Efficiencies ofreconstruction, identification,isolation and triggerrequirements as a function oflepton pseudorapidity fora electrons and b muonsmeasured using thetag-and-probe method. Theefficiency of each selection isdefined with respect to leptonsselected in the previous step

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Electron candidates used for the analysis are required tosatisfy selection criteria related to reconstruction, identifica-tion, isolation and trigger. For each of these requirements,the efficiency of the selection is measured in data with thetag-and-probe method in Z → e+e− events, as describedin Ref. [33], and compared with the simulation. Data-to-simulation ratios of efficiencies are used as scale factors tocorrect the simulation for the observed differences. Measure-ments are performed as a function of the electron pT and ηfor electrons selected in the analysis. All uncertainties relatedto efficiency are classified as either correlated or uncorre-lated, and are propagated accordingly to the final measure-ment uncertainty.

The electron reconstruction efficiency is in the range 95–99% both in the data and simulation and is typically mea-sured with a precision of 2%. The data-to-simulation ratiois up to 2% (5%) different from unity in the barrel (endcap)calorimeter and is measured typically with 2% precision forpT in the range ∼30 to 50 GeV and 5% for pT > 60 GeV.The efficiency of an electron to further pass the medium iden-tification definition varies from 85 to 95% and is measuredwith 2% precision. This efficiency differs from the efficiencymeasured in the MC simulation by up to 5%. The isolationefficiency is measured with a precision of 5% and agreeswith the simulated value within 2%. Data-to-simulation cor-rection factors for identification and isolation efficienciesare measured with a precision of 2–6%. Finally, the triggerefficiency data-to-simulation ratio is found to deviate fromunity by 0.5–3% and is measured with a precision of up to2%.

Various selection requirements related to muon trigger,reconstruction, identification and isolation are imposed onmuon candidates used in the analysis. The efficiency of theselection criteria is measured in data with the tag-and-probemethod in Z → μ+μ− events [15,34] and compared withthe simulation. Ratios of the efficiencies determined in dataand simulation are applied as scale factors to correct the sim-ulated events. For muons with pT > 20 GeV, the correctionfactors measured as a function of muon pT have typicallyan uncertainty of 1–2% and do not deviate from a constant

value by more than 3%. Therefore, the pT dependence of thescale factors is neglected, and they are evaluated only as afunction of muon η.

The muon trigger efficiency in the endcap region of thedetector (1.05 < |η| < 2.4) is measured to be around 90%,and the values obtained in data and simulation agree well.However, in the barrel region (|η| < 1.05) the trigger effi-ciency determined in the simulation varies from 70 to 85%,while the efficiency measured in data is lower by 5–15%,which results in sizeable scale factors. The combined recon-struction and identification efficiency for medium-qualitymuons typically exceeds 99% in both the data and simulationwith good agreement between the two measurements. Theefficiency of the isolation selection is found to be 97–98%in the MC simulation and it differs from the efficiency mea-sured in the data by about 2% in the most central (|η| < 0.6)and most forward detector regions (1.74 < |η| < 2.4).

All measurements of lepton efficiency corrections are lim-ited in their precision by the number of Z → �+�− candi-dates available in the

√s = 5.02 TeV dataset.

Figure 1 summarises the reconstruction, identification,isolation and trigger efficiencies for electron and muon can-didates obtained from the tag-and-probe method.

Figure 2 shows the invariant mass distribution of thedilepton system for electron and muon candidates fromZ → �+�− boson decays after applying scale factors to theMC simulation. The data points are compared with simula-tion including Z boson signal and background components.The electron candidates in the data, shown on the left panel,are calibrated using calorimeter settings and calibration cor-rection factors optimised for low-pile-up conditions. Goodagreement between the data and the simulation is found forboth channels.

5.2 Recoil calibration

In events with W or Z boson production, the hadronicrecoil gives a measure of the boson transverse momentum.The calibration of the recoil is performed using dilepton

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Fig. 2 Detector-level invariantmass distribution of a dielectronand b dimuon pairs from Zboson decays together with EWbackground contributions.Background contributions aretoo small to be visible on alinear scale. Only the statisticaluncertainties of the data areshown

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Fig. 3 Distributions ofa u‖ + pZT and b u⊥ in data andZ → μ+μ− MC simulationbefore (squares) andafter (circles) recoil calibration.The shaded band in the ratiopanels represents the statisticaluncertainty of the data sample,while the error bars representthe systematic uncertaintyassociated with the calibrationprocedure

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events from decays of Z bosons produced in pp collisionsat

√s = 5.02 TeV, as information about the Z boson trans-

verse momentum can be obtained with high precision fromthe measurements of lepton momenta and compared withthe measurement from hadronic recoil. The recoil resolutionis studied using u⊥, the projection of �uT onto the axis – inthe transverse plane – perpendicular to the Z boson �pT. Theresolution is given by the standard deviation of the u⊥ distri-bution, σu⊥ . The transverse momentum scale response of therecoil can be studied using the bias defined as u‖+ pZT , whereu‖ is the projection of �uT onto the axis defined by �pZT , andis quantified via the average of the bias distribution. Differ-ences between the responses in data and simulation are lessthan ∼2 GeV, while up to ∼20% differences in the resolutionare observed.

Following the procedure described in Ref. [35], in situcorrections to the resolution and the scale of uT are obtainedin Z events and are applied to the W boson event candidates,as a function of pWT . The corrections applied to the simulationare obtained as a function of pZT :

uW,corr‖ =〈uZ‖ + pZT

〉data −〈uZ‖ + pZT

〉MC +〈uZ ,data‖

〉

+(uW,MC‖ −

〈uZ ,data‖

〉)· σ

datau⊥

σMCu⊥; (1)

uW,corr⊥ = uW,MC⊥ ·σ datau⊥σMCu⊥

. (2)

Equation (1) describes corrections applied to the recoilresponse in simulation. It includes a shift which brings theaverage value of u‖ in the simulation closer to the one in data,taking into account differences in the bias. In addition, it cor-rects the response distribution for resolution differences (lastterm in the equation). The resolution correction is directlydescribed by Eq. (2) where it is applied to the u⊥ distribu-tion in the simulation. The impact of the calibration on thescale and resolution in events where a Z boson decays to adimuon pair is shown in Fig. 3. The distributions are shownfor the simulation before and after applying the correctionsand for data. Agreement of the distributions from simulationwith data distributions is improved after applying the calibra-

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tion, and residual differences are covered by the systematicuncertainties described in Sect. 8.

6 Background determination

6.1 W channels

The reported cross-section measurements correspond toinclusive Drell–Yan production of single vector bosonswhich decay leptonically. Background processes that con-tribute to the W± boson production measurement are EWprocesses producing W± → τ±ν, Z → �+�−, Z → τ+τ−decays, EW diboson (WW , WZ , Z Z ) production, as well astop-quark production and multi-jet processes. The multi-jetbackground includes various processes such as semileptonicdecays of heavy-flavour hadrons or in-flight decays of kaonsand pions for the muon channel, as well as photon conver-sions or misidentified hadrons for the electron channel. Thebackground contributions from EW and top-quark produc-tion are evaluated using simulated event samples, while themulti-jet contribution is estimated with a data-driven methodsimilar to the one described in Ref. [5].

Although multi-jet background events are well rejectedby the lepton isolation requirements, their contribution to thesignal region is still sizeable because of the very large produc-tion cross sections for multi-jet processes. This contributionis estimated from template fits to data in kinematic distribu-tions: lepton pT, EmissT and mT. The fits are performed in aphase-space region defined by the full event selection witha looser lepton pT requirement of pT > 20 GeV and withthe requirements on EmissT and mT removed. An additionalrequirement on the transverse component of the hadronicrecoil, uT < 30 GeV, is placed to ensure better agreementof the event kinematics between the fit region and the signalregion.

Template distributions for signal, EW and top-quark back-ground processes are constructed by applying the fit-regionselection to samples of simulated events. Templates enrichedin contributions from multi-jet processes are built using

events in data with non-isolated leptons selected by invertingthe isolation requirement described in Sect. 4. The normal-isation factors of template distributions for signal, EW andtop-quark backgrounds, as well as the multi-jet background,are extracted from a fit to the data. The fits are repeated withmulti-jet background templates constructed from differentintervals in a track-based (muon channel) or calorimeter-based (electron channel) isolation variable. Finally, a lin-ear extrapolation to the signal region is performed as afunction of the selected isolation variable, accounting alsofor the difference in kinematic selections between the fitregion and the signal region. Examples of post-fit tem-plate EmissT distributions, which are used to extract multi-jetyields in the electron and muon channels, are presented inFig. 4.

Following this procedure, multi-jet background processesare estimated to contribute around 0.9% of the W+ →e+ν sample and 1.4% of the W− → e−ν sample, whilein the muon channel they represent around 0.1% of theW+ → μ+ν sample and 0.2% of the W− → μ−ν sam-ple.

The largest background contributions to the decay modesstudied come from the production of single EW bosonsdecaying via other decay channels. The Z → e+e− back-ground represents 0.1% of the W+ → e+ν sample and 0.2%of the W− → e−ν sample, while the Z → μ+μ− back-ground amounts to 2.8% and 3.8% in the W+ → μ+ν andW− → μ−ν samples, respectively. The W± → τ±ν back-ground contributes around 1.8% to the samples selected inboth channels and the Z → τ+τ− background contributesapproximately 0.1%. Contributions from top-quark produc-tion (t t̄ and single top quarks) are estimated to be at thelevel of 0.1–0.2% in both channels. Similarly, diboson pro-cesses represent approximately 0.1% of the selected eventsamples.

Figures 5 and 6 show detector-level lepton pseudorapid-ity distributions for positive and negative electron and muoncandidates from W boson decays. Good agreement is foundbetween the data and the sum of signal and background con-tributions.

Fig. 4 Distributions of EmissTused to extract multi-jet yieldsin the a electron and b muonchannels after performing thetemplate fits. Only the statisticaluncertainties of the data areshown

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Fig. 5 Distribution ofdetector-level leptonpseudorapidity fora W+ → e+ν andb W− → e−ν. Only thestatistical uncertainties of thedata are shown

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Fig. 6 Distribution ofdetector-level leptonpseudorapidity fora W+ → μ+ν andb W− → μ−ν. Only thestatistical uncertainties of thedata are shown

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Fig. 7 Detector-levellepton-pair rapidity distributionsin the a electron and b muonchannels. Backgroundcontributions are negligibleusing a linear scale. Only thestatistical uncertainties of thedata are shown

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Table 1 Background contributions as a percentage of the total for the W+, W− and Z candidate samples in the electron (muon) channels

Background W+ → e+ν (W+ → μ+ν) W− → e−ν (W− → μ−ν) Z → e+e−(Z → μ+μ−)[%] [%] [%]

Z → �+�−, � = e, μ 0.1 (2.8) 0.2 (3.8) –W± → �±ν, � = e, μ – –


Table 2 Correction factors CW [Z ] used to calculate integrated and dif-ferential W and Z boson production cross sections. The integratedCW [Z ] factors are shown with the sum in quadrature of statistical and

systematic uncertainties. For the differential CW [Z ] factors, the spreadof values across lepton |η| or |y��| intervals is shown, while their uncer-tainties are described in the text

Channel CW (W+ → �+ν) CW (W− → �−ν) CZIntegrated cross-section measurements

Electron channel 0.657 ± 0.006 0.667 ± 0.005 0.522 ± 0.007Muon channel 0.723 ± 0.011 0.720 ± 0.010 0.780 ± 0.007

Differential cross-section measurements

Electron channel 0.55–0.80 0.52–0.62

Muon channel 0.55–0.85 0.60–0.82

Uncertainties in CW [Z ] of theoretical origin compriseuncertainties induced by the PDFs, by the description of theW and Z boson transverse momentum distributions, by theimplementation of the NLO QCD matrix element and itsmatching to the parton shower, and by the modelling of theparton shower, hadronisation and underlying event. Theseuncertainties are discussed in Ref. [4], where they are eval-uated to be smaller than 0.2% and thus are negligible at thepresent level of precision. The size of acceptance correctionsincluded in the integrated correction factors is 7% (3%) forthe W boson measurements and 14% (5%) for the Z bosonmeasurements in the electron (muon) channel. In the caseof differential W boson measurements, only the CW factorin the interval 2.18 < |η�| < 2.5 includes an acceptancecorrection of 9% for W± → e±ν processes and 40% forW± → μ±ν processes. On the other hand, all differentialCZ factors include an acceptance correction which variesfrom 6% to 28% for the Z → e+e− channel and up to 53%for the Z → μ+μ− channel.

8 Measurement uncertainties

8.1 Lepton calibration and efficiency corrections

Uncertainties in the determination of lepton trigger, recon-struction, identification and isolation efficiency scale fac-tors affect the measurements through the correction factorsCW [Z ].

The uncertainties of the electron efficiency measurementsare divided into contributions correlated across electron ηand pT intervals and uncorrelated ones, and are propa-gated to the cross-section measurements accordingly. Forthe W± → e±ν channels the efficiency determination con-tributes a systematic uncertainty of 0.8% to the fiducial cross-section measurements, while for the Z → e+e− channel thiscontribution is 1.3%. Systematic effects related to the elec-tron pT scale and resolution are subdominant, yielding anuncertainty at the level of 0.3% for the W± → e±ν channelsand less than 0.2% for the Z → e+e− channel. Uncertainties

in the modelling of the electron charge identification are atthe level of 0.1%, and neglected for the cross section mea-surements. Their impact on the asymmetry measurements ishowever sizeable and included in the final results.

In the muon channels, the statistical components of thescale factor uncertainties are propagated to the measurementsvia MC pseudo-experiments, while systematic componentsare propagated as a single variation fully correlated across allmuon |η| intervals. The single largest contribution to the sys-tematic uncertainty of fiducial cross-section measurements inthe W± → μ±ν channels is 1.4% and comes from the deter-mination of the muon trigger efficiency. For measurements inthe Z → μ+μ− channel the largest systematic uncertaintyis contributed by the muon isolation efficiency measurementand amounts to 0.7%. Uncertainties coming from the muonpT scale and resolution are below 0.2% for both W± → μ±νchannels and the Z → μ+μ− channel.

8.2 Hadronic recoil corrections

The uncertainty assigned to the hadronic recoil calibration isconservatively defined from the full size of the corrections,which are derived using events with Z boson production.In these events, the impact of the correction on the u⊥ andu‖+pZT distributions varies between a few percent and ∼20%in the range [−15,+15] GeV, which dominates the reportedcross-section measurements. After applying this correctionto events with W+ and W− production, the resulting uncer-tainties on the cross-section measurements are at the level of0.5% for both the muon and electron channels.

8.3 Background evaluation

Uncertainties in the evaluation of EW and top-quark back-grounds in the W± → e±ν and W± → μ±ν channelsare estimated by varying the respective normalisation crosssections. For single-boson production, the size of the cross-section variations is obtained from higher-order QCD cal-culations, while for diboson and top-quark processes theuncertainty in the cross sections is conservatively taken as

123


Table 3 Measured fiducial W+ → �+ν differential and integrated cross sections for electron and muon channels|η�|min |η�|max W+ → e+ν W+ → μ+ν

dσ/d|η�| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb] dσ/d|η�| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb]0.00 0.21 448 8 10 8 473 9 15 9

0.21 0.42 463 8 10 9 472 8 11 9

0.42 0.63 453 8 10 9 493 8 11 9

0.63 0.84 460 8 10 9 460 9 12 9

0.84 1.05 466 9 11 9 478 9 13 9

1.05 1.37 469 7 10 9 478 6 10 9

1.37 1.52 – – – – 482 9 12 9

1.52 1.74 460 9 14 9 482 7 10 9

1.74 1.95 454 9 14 8 472 8 10 9

1.95 2.18 453 9 14 8 443 7 10 9

2.18 2.50 370 7 14 7 371 7 9 7

0.00 2.50 2243 13 27 42 2303 12 36 44

10%. The resulting uncertainties in the measurements inboth the W± → e±ν and W± → μ±ν channels are below0.2%. Uncertainties related to the multi-jet background eval-uation arise from the statistical precision of the multi-jettemplates and uncertainty in the normalisations of the sub-tracted EW and top-quark contamination. These contribu-tions are propagated through linear extrapolations over theisolation variables to the signal region. The related uncer-tainties in the measurements are evaluated to be 0.7–0.8%in the W± → e±ν channels and not more than 0.2% in theW± → μ±ν channels.

In both the Z → μ+μ− and Z → e+e− channels, theuncertainty associated with the background subtraction isnegligible, since all individual background contributions arebelow 0.2% of the selected data sample.

8.4 Luminosity calibration

Luminosity measurements in ATLAS are calibrated usingdedicated van der Meer scans [40]. The analysis of data fromthe scan performed in pp collisions at

√s = 5.02 TeV,

which uses the LUCID-2 detector for the baseline luminositymeasurements [41], yields a relative systematic uncertaintyof 1.9% in the measured luminosity. The largest sources ofuncertainty are systematic effects related to the van der Meerscan procedure and the long-term stability of the luminositycalibration

9 Results

9.1 Channel combination

Results of measurements in the electron and muon channelsare summarised in Table 3 for W+ boson production, Table 4

for W− boson production and Table 5 for Z boson pro-duction. In these tables, the statistical uncertainty is definedfrom the variance of the background-subtracted number ofobserved events, and the systematic uncertainty includesall uncertainty components described above, except for theluminosity uncertainty, which is given separately. The sys-tematic uncertainties coming from lepton efficiency correc-tions are measured as a function of lepton η and pT, andinclude a significant statistical component due to the numberof Z events used to derive the corrections. This statisticalcomponent is substantially reduced for the integrated crosssections compared to the differential ones.

The data tables provided in this paper contain compactsummaries of the measurement uncertainties. A completebreakdown of systematic uncertainties and their correlatedcomponents is provided in HEPData [42].

The electron and muon channel measurements are com-bined using the Best Linear Unbiased Estimate (BLUE)method [43], accounting for the correlations of the systematicuncertainties across the channels and measurement bins. The|η�| and |y��| distributions for the electron channel, muonchannel and combined results are shown in Figs. 8 and 9for W and Z bosons, respectively, and the results are listedin Tables 6, 7 and 8. In the interval 1.37 < |η�| < 1.52,only the muon channel measurements for W boson produc-tion are used. The combination yields χ2/d.o.f= 19.3/10for the W+ boson results, χ2/d.o.f= 15.1/10 for the W−boson results, and χ2/d.o.f= 3.0/5 for the Z boson results. Asimultaneous combination of all measurements, accountingfor the correlation of the experimental systematic uncertain-ties between the W and Z measurement results for a givenlepton flavour, gives χ2/d.o.f = 37.5/25, corresponding toa probability of 5.2%. In view of this remaining discrepancyand of the general trend of the muon channel cross sectionsto be higher than the electron channel ones, the systematic

123


Table 4 Measured fiducial W− → �−ν differential and integrated cross sections for electron and muon channels|η�|min |η�|max W− → e−ν W− → μ−ν

dσ/d|η�| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb] dσ/d|η�| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb]0.00 0.21 322 7 7 6 341 8 10 6

0.21 0.42 316 7 7 6 314 7 6 6

0.42 0.63 303 7 7 6 327 7 6 6

0.63 0.84 294 7 7 6 303 7 7 6

0.84 1.05 300 7 7 6 306 7 8 6

1.05 1.37 280 5 6 5 290 5 5 6

1.37 1.52 – – – – 276 7 6 5

1.52 1.74 270 7 9 5 272 6 5 5

1.74 1.95 260 7 9 5 245 6 5 5

1.95 2.18 255 7 9 5 253 5 5 5

2.18 2.50 220 6 10 4 219 5 5 4

0.00 2.50 1393 10 17 26 1412 9 22 28

Table 5 Measured fiducial Z → �+�− differential and integrated cross sections for electron and muon channels|y��|min |y��|max Z → e+e− Z → μ+μ−

dσ/d|y��| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb] dσ/d|y��| [pb] δσstat [pb] δσsyst [pb] δσlumi [pb]0.0 0.5 99.9 2.5 1.6 1.9 105.2 2.4 1.1 2.0

0.5 1.0 100.3 2.7 1.6 1.9 101.9 2.3 1.0 1.9

1.0 1.5 89.2 2.7 1.4 1.7 89.8 2.1 0.8 1.7

1.5 2.0 59.6 2.4 1.2 1.1 61.0 1.8 0.6 1.1

2.0 2.5 19.6 1.3 0.7 0.4 20.3 1.2 0.2 0.4

0.0 2.5 369.0 5.3 4.7 6.9 377.9 4.4 3.4 7.1

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| [pb

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Acknowledgements We thank CERN for the very successful oper-ation of the LHC, as well as the support staff from our institutionswithout whom ATLAS could not be operated efficiently. We acknowl-edge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC,Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada;CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIEN-CIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Repub-lic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU,France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT,Greece; RGC, Hong Kong SAR, China; ISF and Benoziyo Center,Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO,Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portu-gal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federa-tion; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slove-nia; DST/NRF, South Africa; MINECO, Spain; SRC and WallenbergFoundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva,Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOE and NSF, United States of America. In addition, individual groupsand members have received support from BCKDF, CANARIE, CRCand Compute Canada, Canada; COST, ERC, ERDF, Horizon 2020, andMarie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Ger-many; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCAProgramme Generalitat de Catalunya, Spain; The Royal Society andLeverhulme Trust, United Kingdom. The crucial computing supportfrom all WLCG partners is acknowledged gratefully, in particular fromCERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Den-mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany),INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Tai-wan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide andlarge non-WLCG resource providers. Major contributors of computingresources are listed in Ref. [52].

Data Availability Statement This manuscript has no associated dataor the data will not be deposited. [Authors’ comment: All ATLAS sci-entific output is published in journals, and preliminary results are madeavailable in Conference Notes. All are openly available, without restric-tion on use by external parties beyond copyright law and the standardconditions agreed by CERN. Data associated with journal publicationsare also made available: tables and data from plots (e.g. cross sectionvalues, likelihood profiles, selection efficiencies, cross section limits,...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional materialrelated to the paper available that allows a reinterpretation of the datain the context of new theoretical models. For example, an extendedencapsulation of the analysis is often provided for measurements in theframework of RIVET (http://rivet.hepforge.org/). This information istaken from the ATLAS Data Access Policy which is a public docu-ment that can be downloaded from http://opendata.cern.ch/record/413[opendata.cern.ch].]

Open Access This article is distributed under the terms of the CreativeCommons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate creditto the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made.Funded by SCOAP3.

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http://arxiv.org/abs/hep-ph/0201195http://arxiv.org/abs/1406.3660http://arxiv.org/abs/1011.0937http://arxiv.org/abs/1007.2241http://arxiv.org/abs/hep-ph/0603175http://arxiv.org/abs/1005.3457http://arxiv.org/abs/0811.4622https://cds.cern.ch/record/1474107http://arxiv.org/abs/0901.0002http://arxiv.org/abs/1612.01456https://cds.cern.ch/record/2157687http://arxiv.org/abs/1603.05598http://arxiv.org/abs/1701.07240http://arxiv.org/abs/1603.02934http://arxiv.org/abs/1703.10485http://arxiv.org/abs/1407.5063http://arxiv.org/abs/1608.03953http://arxiv.org/abs/1704.05473http://arxiv.org/abs/1506.07443http://arxiv.org/abs/1706.00428http://arxiv.org/abs/1412.3989http://arxiv.org/abs/1506.06042http://arxiv.org/abs/1701.05838http://arxiv.org/abs/1612.03636https://cds.cern.ch/record/2202407


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Measurements of W and Z boson production in pp collisions...

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