Observation of nuclear modifications in W± boson production in pPb collisions at √ s NN = 8.16 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Observation of nuclear modifications in W ^± boson production in pPb collisions at √

s _NN = ⁸ . 16 TeV

.The CMS Collaboration

^

CERN,Switzerland

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received4May2019

Receivedinrevisedform26September 2019

Accepted18October2019 Availableonline24October2019 Editor:M.Doser

Keywords:

CMS Heavyions Electroweak Wboson pPb nPDF

The productionofW^± bosonsisstudied inproton-lead (pPb)collisions atanucleon-nucleoncentre- of-mass energyof√

sNN=⁸.16 TeV. Measurementsare performedintheW^±→μ^±νμ channelusing a data samplecorresponding to an integrated luminosity of173.4±⁶.1 nb⁻¹,collected by the CMS Collaboration atthe LHC. The number of positively and negatively charged W bosons is determined separately in the muon pseudorapidity region in the laboratory frame |η^μ_lab|<2.4 and transverse momentum p^μ_T >25 GeV/c.The W^± boson differentialcross sections, muon chargeasymmetry, and theratiosofW^± bosonyields fortheproton-goingoverthePb-goingbeamdirectionsare reportedas afunctionofthemuonpseudorapidityinthenucleon-nucleoncentre-of-massframe.Themeasurements are comparedto the predictions from theoretical calculations based onparton distributionfunctions (PDFs) atnext-to-leading-order.The resultsfavour PDF calculationsthat includenuclear modifications andprovideconstraintsonthenuclearPDFglobalfits.

©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Theproductionofelectroweak(EW)gaugebosonsisconsidered tobeapowerfulprobeofthepartondistributionfunctions(PDFs) of the proton [1]. Most recent proton PDF sets include W and Z boson production data fromthe Tevatron and the CERN Large HadronCollider(LHC) intheir globalfitanalyses [2–4]. Similarly, themeasurementsofEWbosonproductioninproton-nucleusand nucleus-nucleus collisions, available for the first time at centre- of-massenergiesof theTeV scale, provideconstraintson nuclear modifications ofthe PDFs [5–8]. The presenceof a nuclear envi- ronmentmodifiesthepartondensitiesinthenucleusascompared tothoseinafreenucleon.ThenuclearPDFs(nPDFs)areexpected tobeenhanced forpartonscarryinga momentumfractioninthe range5×¹⁰⁻²^x^{10−1 inthe so-called}antishadowing region, andsuppressedforx^{10−2 inthe}shadowing region [9],withthe modificationsdepending on thescale Q².Because ofthelimited amount andtype ofexperimental data sets available for nuclear collisions, the determination of the nuclear parton densities is lessprecise than forthe free-proton case. As a consequence,the nPDFuncertaintiesareoneofthemainlimitationsoftheprecision

 E-mailaddress:cms-publication-committee-chair@cern.ch.

of quantumchromodynamics (QCD) calculationsdescribing hard- scatteringprocessesinnuclearcollisionsathighenergies [7].

Since W bosons are predominantly produced via qq annihila- tionthroughud→^W+anddu→^{W−processes,W bosonproduc-} tioncanbeusedtoprobethelightquarkPDFs,bothfortheproton and nuclei. In addition, the asymmetries of the separate yields of W⁺ andW⁻ bosons are known to be sensitive probes of the down-to-upquarkPDFratio [10–12].Consequently,theirmeasure- ment mayallow forthe flavour decompositionof u andd quark distributionsinnuclei [13].Amongthepossibledecaychannelsof theW boson, theleptonicdecaysare lessaffectedby background processesthanhadronicdecays.Anotheradvantageoftheleptonic decays is that any possible effect due to the QCD medium pro- ducedinnuclearcollisions shouldbenegligible,since leptonsare notsubjecttomedium-inducedenergylossthroughthestrongin- teraction [14,15].

Studies of the W and Z boson production in PbPb collisions ata nucleon-nucleon centre-of-mass energyof √

sNN=².76 TeV, performedby theATLAS [16–18] andCMS [19–21] Collaborations, have shown that the W and Z boson cross sections are con- sistent with no modification by the nuclear medium formed in these collisions. In pPb collisions, measurements of W produc- tionat√

sNN=⁵.02 TeV have beenperformedby ALICE [22] and CMS [13]. The comparisonwith next-to-leading-order (NLO) per- turbative QCD predictions favours the calculations that include https://doi.org/10.1016/j.physletb.2019.135048

0370-2693/©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

nPDFeffects. A similar observation is madefrom the analysisof theZ boson productioninpPbcollisions atthesameenergy [23, 24].These EW bosonmeasurements havebeen usedfor thefirst timeinaglobalfitanalysisofnPDFsets (EPPS16 [25]).Neverthe- less, a modest enhancement of the W⁻ boson production cross section inthemostbackwardregion (Pb-goingdirection) showed some difference with theoretical calculations (with and without nPDFeffects),possibly pointingtodifferentnuclear modifications oftheup anddownquarkPDFs [13].Moreprecisemeasurements arethusneededinordertoclarifytheoriginofthisdiscrepancy.

This letterreports the results of measurements of W^± boson production in pPb collisions at √

sNN=⁸.16 TeV. The measure- ments are performed in the W^±→

μ

^±

ν

_{μ decay} channel using pPb data recorded with the CMS detector in 2016, correspond- ingtoatotalintegratedluminosityof173.4±⁶.1 nb⁻¹.Thisdata setisroughly fivetimeslargerthantheone availableforthepre- vious measurement at √

sNN=⁵.02 TeV [13,26,27]. The W^± bo- son differential cross sections are presented as functions of the muonpseudorapidityinthenucleon-nucleoncentre-of-mass(CM) frame,

η

CM.In orderto fullyexploit theinformationprovided by the data, two additional sets of observables are also measured asfunctionsof

η

CM: themuon charge asymmetry andthe muon forward-backwardratios (RFB).The measurement ofasymmetries hasacoupleofadvantages ascomparedto thatof thecrosssec- tions.First,asymmetriesaremoresensitivetomodificationsofthe quarkPDFs [7]. Second,uncertaintiesintheintegratedluminosity andthetheoreticalscaledependencecancelinthemeasurementof theseasymmetries.TheresultsoftheW^± bosondifferentialcross sectionsandasymmetriesarecomparedtoperturbativeQCDcalcu- lationsbasedonNLOPDFswithandwithoutnuclearmodifications.

Thetheoreticalpredictionsforfreeprotonsareobtainedusingthe CT14 [2] protonPDFset,whilethoseincludingnucleareffectsare derivedusingtwodifferentnPDFsetsforleadions:nCTEQ15 [28]

andEPPS16 [25].

2. Experimentalmethods

2.1. Data-takingconditionsandtheCMSdetector

During the data-taking period, the directions of the proton andlead beamswere swapped after an integrated luminosity of 62.6 nb⁻¹ wascollected.The beamenergieswere 6.5 TeVforthe protonsand2.56 TeVpernucleon forthelead nuclei.Byconven- tion, the proton-(Pb-)going side defines the positive (negative)

η

region,labelledastheforward(backward)direction.Becauseofthe asymmetric collision system, massless particles produced in the nucleon-nucleoncentre-of-massframeatan

η

CMarereconstructed at

η

lab=

η

CM+⁰.465 inthelaboratoryframe.TheW^±bosonmea- surements presentedin this letterare expressed in terms ofthe muonpseudorapidityintheCM,

η

_CM^μ .

Thecentralfeature oftheCMSapparatusisasuperconducting solenoidof6 minternal diameter,that provides a magneticfield of3.8 T.Withinthesolenoidvolume area siliconpixelandstrip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrass andscintillatorhadroncalorimeter(HCAL),eachcom- posedof abarrel andtwo endcapsections.Forwardcalorimeters extendthe

η

coverage providedby the barrelandendcap detec- tors. The hadron forward (HF) calorimeter uses steel as an ab- sorberandquartz fibresasthesensitive material.Thetwohalves of the HF are located 11.2 m from the interaction region, one on each end, and together they provide coverage in the range 3.0<|

η

_|<5.2. They also serve as luminosity monitors. Muons are measuredinthe range|

η

|<2.4,withdetection planesmade usingthreetechnologies:drifttubes,cathodestripchambers, and resistiveplatechambers. A moredetaileddescription ofthe CMS detector,togetherwitha definitionofthecoordinatesystemused andtherelevantkinematicvariables,canbefoundinRef. [29].

The particle-flow (PF)algorithm [30] aimsto reconstructand identify each individual particle in an event, with an optimised combinationofinformationfromthevariouselementsoftheCMS detector. The energyof photonsis obtainedfromthe ECALmea- surement. Theenergyofelectronsisdeterminedfromacombina- tion oftheelectronmomentum attheprimary interactionvertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sumof all bremsstrahlung photons spatially compatiblewithoriginatingfromtheelectron track.The charge and momentumof muonsis obtainedfromthe curvature ofthe corresponding track.The energyofchargedhadronsis de- termined from a combination of their momentum measured in the tracker (assuming the charged-pion mass) and the matching ECALandHCALenergydeposits,correctedforzero-suppressionef- fectsandfortheresponsefunctionofthecalorimeterstohadronic showers. Finally, the energyof neutral hadrons isobtained from thecorrespondingcorrectedECALandHCALenergies.

2.2. Eventselectionandmuonreconstruction

Collision events are required to have at least one interaction vertex reconstructed usingtwo ormore tracks within a distance from the nominal collision point of 25 cm along the beam axis and2 cmalongitstransverseplane.Thecontaminationfromback- groundeventsnotoriginatingfrominelastichadroniccollisions is further suppressed by requiring at leastone tower on each side of theHFcalorimeterwitha totalenergylarger than3 GeV. The lossofeventswithW^±bosonscandidatesduetothispPbcollision eventselectionhasbeendeterminedtobelessthan0.2%.

The main signature of the W^±→

μ

^±

ν

μ process is the pres- ence of an isolated high-pT muon. Events of interest for offline analysis are selected using a trigger algorithm [31] that requires the presence of at least one muon candidate of p_T>12 GeV/c.

Moreover,toenhancethesignal purity [11,13],thefiducialregion of the analysis has been restricted to muons of pT>25 GeV/c with |

η

^μ_lab|<2.4.The muon candidatesare reconstructed inCMS withan algorithmthat combinestheinformationfromthe muon detectors and the tracker [32]. Muons are selected by applying thestandardtightselectioncriteriadescribedinRef. [32].Further, muonsarerequiredtobeisolatedfromnearbyhadronicactivityto reduce the jet background.The muon isolation parameter (Iμ)is definedasthepTsumofallPF-reconstructedphotons,chargedand neutral hadrons, in a cone of radius R=√

(

η

)²+ (φ)²=⁰.3 aroundthemuoncandidate,where

η

andφ arethepseudora- pidity andazimuthal (inradians)distancesto themuon.Amuon isconsideredisolatedifIμ islessthan15%ofthemuon pT.

Background processes yielding high-p_T muons can be classi- fiedasreducibleorirreducible.Thereduciblebackgroundincludes muon decays that can be tagged and removed from the signal.

These events are mainly composed of

μ

⁺

μ

⁻ pairs from Drell–

Yanevents(Z/

γ

^∗),andhigh-p_T muonsfromjetsproducedviathe strong interaction, referred to as QCD multijet events.To further suppresstheformerprocesses,eventscontainingatleasttwoiso- lated oppositely charged muons, each with pμ

T >15 GeV/c, are removed. The irreduciblebackgroundsources comprisemuonde- cays that passtheanalysisselection criteriaandthereforecannot betaggedevent-by-event,includingZ/

γ

^∗_→

τ

⁻

τ

⁺,W→

τ ν

τ ,and tt production. All backgrounds are estimated using Monte Carlo (MC) simulations, exceptQCD multijet,whichismodelled witha data-driventechniquedescribedbelow.

2.3. Signalyielddetermination

Leptonicdecaysof W bosonsincludeneutrinos,whichare not detected in CMS. Theirpresence isinferred fromtheoverall mo-

mentumimbalanceinthetransverseplane,knownasthemissing transverse momentum p^miss_T ; its magnitude(p^miss_T ) is defined as themagnitudeofthesumofthenegative p_T vectorsofallrecon- structedPFobjectsinanevent.Inthisanalysis,thep^miss_T distribu- tionisusedtoextractthesignalyieldsin24muon

η

^μ_CM bins,each 0.2 units wide, except for four in the most backward (−².86<

η

^μ_CM<−².60,−².20<

η

^μ_CM<−¹.93, −¹.93<

η

_CM^μ <−¹.80), and forward(1.80<

η

^μ_CM<1.93) regions, becauseof thedetector ge- ometryandtheunbalancedbeamenergies.

The p^miss_T distributions of the signal and EW backgrounds are described using templates from MC simulations. The MC samples were generated using the NLO generator powheg v2 [33–35]. To include EW corrections, the powhegbox packages W_ew-BMNNP [36] and Z_ew-BMNNPV [37] areusedto generate the pp→^W±→^l±

ν

l andpp→^Z/

γ

^∗→^{l+l− processes, respec-} tively.Events from the pp→^{tt processare generated using the} powhegboxpackagehvq[38],whichisaheavyflavourquarkgen- erator. The simulation of pPb collisions is performed using the CT14 [2] PDF setcorrectedwiththe EPPS16 nuclearmodification factors,definedastheratiosoftheboundprotonPDFtothatofa freeproton,derivedforPbions [25].The partondensities ofpro- tons andneutrons are scaled according to the mass andatomic numberoftheleadisotopes.

Thepartonshoweringis performedby hadronising theevents using pythia 8.212 [39] withtheCUETP8M1underlying-event(UE) tune [40,41]. To consider a morerealistic distributionof the un- derlyingenvironment presentinpPb collisions,the powheg sam- plesareembeddedinsimulatedpPbeventsgeneratedby epos lhc (v3400) [42],takingintoaccountthepPbboost.The epos lhc sim- ulation is tuned to reproduce the global eventproperties of the pPbdatasuchasthe

η

distributionsofchargedhadrons [43].The embedding of the signal andpPb UEs is performedby requiring thesamegeneratedinteractionpointwhensimulatingthedetector hits.Thetriggerdecisionsareemulatedandtheembeddedevents arereconstructedwiththesamealgorithmsasusedfordata.The detectorresponseissimulatedwith Geant4 [44].

The agreement between the EW simulations and the data is improved by weighting the EW boson pT distribution using a pT-dependentfunction derived fromthe ratioof theZ boson pT distributionsinZ→

μ

⁺

μ

⁻eventsindataandsimulation.Further- more,thepPbeventactivityisreweighedby matchingthesimu- latedtotalenergydistribution reconstructedon both sidesofthe HFcalorimetersto theone observedin dataina Z/

γ

^∗_→

μ

⁺

μ

⁻

sample.

TheshapeoftheQCD multijetbackgroundismodelledwitha functionalformdescribedbyamodifiedRayleighdistribution [45]

definedas:

f



p^miss_T

 =

^pmiss_T

exp



− 

p^miss_T



2



2



σ

0

+ σ

1p^miss_T

+ σ

2



p^miss_T



2



2

 ,

where

σ

0,

σ

1,and

σ

2 are free parametersto bedetermined. Itis foundtoreproducewellthe p^miss_T shapeofdataeventscontaining nonisolatedmuons,with

χ

² valuesdividedbythenumberofde- greesoffreedom(dof)closetoone.TheQCDshapeisextractedby fittingthedata infiverelative muon isolation (Iμ/pμ

T) bins with boundariesrangingfrom0.4to0.9.The

σ

0,

σ

1,and

σ

2 parameters extractedfromthefitsarefoundtolinearlydependontherelative muon isolation andare extrapolated to the isolated muon signal region.

Because ofmomentum conservation, the production of Z and W bosonsisbalanced by a hadronicrecoilcomposed ofjets and particlesfromthepPbunderlyingactivity.The distributionofthe

hadronicrecoilsignificantlycontributestothep^miss_T resolution.Be- causeofthesimilarityoftheproductionprocessesoftheZ andW bosons,andtheirsimilarmasses,weassumethattherecoildistri- butionsarethesameforbothspecies.Therefore,thecorrectionof the simulatedrecoildistribution isderived in acontrol region of Z→

μ

⁺

μ

⁻ eventsusinga hadronicrecoiltechnique [46,47].The hadronicrecoilofZ→

μ

⁺

μ

⁻ events,uT, isdefinedasthevector p_T sumofall PFcandidates,excluding thedecayproducts ofthe Z boson.Thedistributionsofthehadronicrecoilcomponentsthat areparallel andperpendiculartothe Z bosontransversemomen- tum ^pZ_T^{arefittedinsimulationanddatausingaweightedsumof} twoGaussianfunctions.Themeanandresolutionvaluesextracted fromtherecoilfitsareusedtoscalethesimulatedhadronicrecoil distributionstomatchtheperformancemeasuredindata.Thecor- rectedp^miss_T distributionisthenderivedintheEWMCsamplesas thevectorsumofthecorrectedhadronicrecoil^ucorr_T ^andthepTof thereconstructedmuonsfromthedecayofZ andW bosons.

The number of W^±→

μ

^±

ν

μ events is extractedby perform- ing an unbinned maximum likelihood fit of the observed p^miss_T distribution in each muon

η

CM bin. The total fit modelincludes sixcontributions: thesignal W^±→

μ

^±

ν

μ template,theEWback- ground Z/

γ

^∗_→

μ

⁺

μ

⁻, W→

τ ν

_{τ and} Z/

γ

^∗_→

τ

⁺

τ

⁻ templates, the tt background template, and the QCD background functional formderivedfromcontroldatasamples.Whenfittingthedata,the QCD shape parameters (

σ

i) are fixed to the extrapolated values, whilethe ratioofthe EWand tt backgroundyields to thesignal yieldisfixedtotheresultsfromsimulation.Onlytwoparameters are left free inthe fit, the W boson signal and QCD background normalisations. Theobserved numbersofmuonscoming fromW bosondecaysovertheentire

η

^μ_CMrangeare:97971±³³²

μ

⁺and 81147±³⁰¹

μ

⁻,wheretheuncertaintyisstatistical.Examplesof theresultingp^miss_T distributionsinthemidrapidity(−⁰.2<

η

^μ_CM<

0.0)andforward(1.80<

η

^μ_CM<1.93)bins,areshowninFig.1,af- terapplying all analysiscorrectionsandselection criteria. The fit modelisfoundtogiveagooddescriptionofthedata,with

χ

²/dof valuesclosetoone.

ThesimulatedsampleofW^±→

μ

^±

ν

μ embeddedinto epos lhc isused toderive theefficiencyofthe muon trigger,isolation, re- construction, and selection criteria, as a function of

η

_CM^μ . These single-muonefficienciesarealsodirectlyestimatedfrompPbdata ina Z→

μ

⁺

μ

⁻ sample usingthe tag-and-probe (TnP)technique, asdescribedinRef. [48].ThedataandMCreconstructionefficien- cies are observed to be consistent with each other, whereas the triggerefficiencyislowerintheZ boson simulationby5%thanin data at|

η

^μ_lab|=¹.4.The muon isolation selection is found to re- jectfewermuonsinthesimulation,becauseofthesmallerpPbUE activity compared todata. In orderto correct forthe differences betweendataandsimulation,themuonefficiencycomputedfrom the W^±→

μ

^±

ν

μ MC sample is multipliedby theTnPcorrection factors event-by-event. Thesecorrection factors are computed, in binsofmuon pT and

η

lab,fromtheratioofthemuonefficiencies measured in data to those calculated from simulations. The TnP scalefactorsproducechangesinthemuonefficiencyrangingfrom

−^{3% inthe}mid-rapidityregion(|

η

_lab^μ_|<1.0)to+^{5% at}|

η

^μ_lab|=1.4.

The TnP-corrected efficiencies vary with

η

^μ_CM, from (81±¹)% to (92±²)%.

2.4. Systematicuncertainties

The leading source of systematic uncertainty originates from the TnP efficiencycorrections. The uncertainties on the TnP cor- rections are determined by propagating the uncertainties on the muonefficienciesextractedfromdataandsimulation,derivedfrom thefitstotheinvariantmassofZ→

μ

⁺

μ

⁻candidates.Theseun- certaintiesincludeastatisticalcomponentduetothefinitesizeof

thedatasample available, aswellasa systematiccomponentes- timated from variations in the fittingprocedure (different signal

Fig. 1. The missing transverse momentum p^miss_T distribution for W⁻→μ⁻νμ eventswithinthe−0.2<η_CM^μ <0.0 (top)rangeandforW⁺→μ⁺νμeventswithin the 1.80<η^μCM<1.93 (bottom)range.Unbinnedfitstothe data (blackpoints) areperformed with six contributions, stacked frombottom to top:tt (orange), Z/γ^∗→τ⁺τ⁻(darkblue),W^±→τ^±ντ(red),Z/γ^∗→μ⁺μ⁻(green),QCDmulti- jet(lightblue)andW^±→μ^±νμ (yellow).Theη^μ_CMregionsaredefinedsuchthat theprotonismovingtowardspositivepseudorapidity.Errorbarsrepresentstatis- ticaluncertainties.Thelowerpanelsdisplaythedatadividedbytheresultofthe fit.

and backgroundfunctions, anddifferent massrange used forfit- ting). Additionally, uncertainties are included to account for: (1) possible differencesin the reconstruction of muon tracks (0.6%), and(2) theimpact ofpileup andUE activity (0.3%).Anotherim- portantsourceofsystematicuncertaintyarisesfromthemodelling ofthe QCDmultijet p^miss_T distributionin thesignal region,which isestimatedbyallowingtheQCDshapeparameterstovarywithin the root-mean-squareof the extrapolatedvalues in bins of

η

_CM^μ , andbychangingthep^miss_T modeltothatusedinRef. [13].

The uncertaintyinthenormalisationoftheEW backgroundis estimated fromthe nPDFuncertainty inthe Z over W boson in- clusivecross sectionsusingtheCT14protonPDF andtheEPPS16 nPDF for the lead ions, the uncertainty in the W and Z boson branching fractions to leptons [49], and the experimental uncer- tainty in the tt crosssection inpPb events [50]. The uncertainty in thevector boson pT reweighingisderived fromthe difference of the results obtained applying and not applying the boson p_T correction. The uncertainty inthe binning ofthe p^miss_T MC tem- plates is estimated by using a p^miss_T bin size of 1 GeV/c. The impact of EW corrections in powheg is estimated from the dif- ference in the efficiency when computed using powheg without EWcorrections [51].Theuncertaintyinthe p^miss_T recoilcorrection isdetermined bychangingthemodelusedtofitthehadronicre- coildistributionandtheprofileoftherecoilmeanandresolution as a function of p^Z_T. Finally, the mismodelling ofthe UE activity in the simulation is estimated by reweighing the distribution of the trackmultiplicity instead of the energy deposited in the HF calorimeters. The integratedluminosity measurement uncertainty (3.5%) [27] only affects the W boson differential cross sections andcancels out in theasymmetry measurements. The maximum relative uncertaintyofthedifferentialcrosssectionsandabsolute uncertaintiesontheasymmetriesarepresentedforeachsourceof systematicuncertaintyinTable1.

3. Results

The W^± bosondifferential productioncrosssections arecom- puted as functions of

η

^μ_CM. The differential W^±→

μ

^±

ν

μ cross sectionsaredeterminedfrom

d

σ

^{W±→μ±νμ}

d

η

^μ_CM

η

_CM^μ

=

^Nμ

η

^μ_CM

L

 η

^μ_CM

^,

⁽¹⁾

where Nμ

η

_CM^μ isthe efficiency-correctedmuon yield inbinsof

η

^μ_CM, L ^{is the recorded integrated} luminosity, and 

η

^μ_CM is the widthofthemeasuredbin.

The cross sections for the W→

μν

_{μ decays} for W⁺ and W⁻ bosons are compared in Fig. 2 with NLO perturbative QCD predictions calculated with the MC program mcfm v8.0 [52]

Table 1

Maximumuncertaintyinthemeasuredobservablesamongtheη^μ_CMbinsdeterminedforeachsource.Theuncertaintiesinthecrosssectionsarerelative,whereasthosefor theasymmetriesareabsolute.Theglobalintegratedluminosityuncertaintyof±^{3.5%isnotincludedinthetotalsystematic}uncertaintyinthecrosssections.

Source W⁻_d^d_η^σ

CM [%] W⁺_d^d_η^σ

CM[%] W⁻RFB W⁺RFB WRFB

N_μ⁺−N⁻_μ N_μ⁺+N⁻_μ

Boson pTreweighing 0.5 0.4 0.001 0.001 0.001 0.001

EW background 0.4 0.3 0.002 0.001 0.001 0.000

POWHEG EW correction 0.9 0.5 0.007 0.004 0.006 0.003

Efficiency 3.0 3.2 0.026 0.037 0.030 0.011

Event activity reweighing 0.6 0.4 0.002 0.002 0.001 0.002

p^miss_T template binning 0.1 0.1 0.002 0.001 0.001 0.001

QCD background 1.2 0.7 0.016 0.007 0.009 0.006

Hadronic recoil correction 0.2 0.3 0.002 0.004 0.002 0.002

Total systematic uncertainty 3.3 3.3 0.030 0.038 0.031 0.013

Statistical uncertainty 2.4 2.0 0.026 0.029 0.019 0.015

Fig. 2. Differentialproduction crosssectionsfor W⁺→μ⁺νμ (top)andW⁻→ μ⁻νμ(bottom),asafunctionofthemuonpseudorapidityinthecentre-of-mass frame.Thesmallhorizontallinesrepresentthestatisticalandsystematicuncertain- tiessummedinquadrature,whereastheerrorbarsshowthestatisticaluncertainties only.Theglobalintegratedluminosityuncertaintyof±3.5%isnotshown.TheNLO calculationswithCT14PDF,andCT14+EPPS16andCT14+nCTEQ15nPDFs,arealso displayed,includingtheir68%confidenceintervalPDFuncertaintybands.Thebot- tompanelsshowtheratioofdata,CT14+EPPS16andCT14+nCTEQ15withrespect toCT14.

using the CT14 [2] proton PDF. Also shown are two calcu- lations that include nuclear modifications in the PDF, based on the nCTEQ15 [28] and EPPS16 [25] nPDF sets (labelled as CT14+nCTEQ15andCT14+EPPS16, respectively). Both EPPS16 and nCTEQ15areHessianNLOnPDFsets,buttheformerincludesmore measurementsinthefit(containingLHCEWboson [13,23,24] and dijet [53] data), aswell asmore free parameters (20 forEPPS16, 17 for nCTEQ15). In addition, nuclear modifications of valence andseaquarks areallowed to be differentinEPPS16 for upand down quarks, while nCTEQ15 assumes flavour independence for thesea quarks. The nPDFuncertainties are propagated using the PDF4LHCrecommendationsforHessiannPDFsetsasprescribedin Ref. [1]. As can be seen in Fig. 2, the predicted CT14+nCTEQ15 andCT14+EPPS16crosssectionsaresystematically belowthe cal- culation using CT14 PDF at large positive muon rapidities be- cause of the depletion of the antiquark PDF in nuclei at small x= (^MW/√

s_NN)exp(−^yW) (^MW/√

s_NN)exp(−

η

^μ_CM)≈^10−3.Con- versely, the predicted cross sections from calculations including nPDFmodificationsare above thoseusingCT14 PDFin thenega- tiverapidity region,becauseof theslightquark antishadowingat

large x≈⁰.1.Whencompared todata,all theoreticalcalculations reproduce the measurement at backward rapidity within uncer- tainties,whileatforwardrapidity thecalculationsincludingnPDF effectsappeartobefavoured.

The muon forward-backward ratios, defined as N^±μ(+

η

^μ_CM)/

N^±μ(−

η

_CM^μ ) for both positive and negative muons, are compared in the upper panel of Fig. 3 to the CT14 PDF, and CT14+EPPS16 andCT14+nCTEQ15nPDFcalculations.Theseobservablesprobethe ratioofthenuclearmodificationsofthequarkPDFsinthePbnu- cleusfromsmallto large x values.Theresultsformuonsofboth chargesfavourthepredictionsincludingnuclearmodificationsover thefree-protonPDFcalculations.Basedontheprecisionoftheex- perimentalresults,themeasurements provideconstraintsonboth theCT14+EPPS16andCT14+nCTEQ15nPDFsets, especiallyinthe proton-goingregion(smallx).

Theyields ofpositivelyandnegativelychargedmuonsarefur- ther combined to measure the forward-backward ratio for all muonsNμ(+

η

^μ_CM)/Nμ(−

η

^μ_CM).Thisobservablehasacoupleofad- vantages compared to N^±μ(+

η

^μ_CM)/N^±μ(−

η

^μ_CM): it is less sensitive to the quark content in the proton and nuclei, and it has bet- ter statistical precision. The results for this asymmetry are pre- sented in the right panel of Fig. 3, and they strongly deviate fromtheCT14PDF predictions,favouring theCT14+nCTEQ15and CT14+EPPS16nPDFsets.Moreover, theexperimentaluncertainties are significantly smaller than the theoretical nPDF uncertainties.

Consequently,thesemeasurements couldconstrain thequark and antiquark distributions innuclei, and will be valuable inputs for globalfitstothedata.

Themuonchargeasymmetry,definedasA≡ (^N+μ−^Nμ⁻)/(N⁺μ+ N⁻μ), reflects the differences in the production of W⁺ and W⁻ bosons.Fig.4showsthemeasurementofthemuoncharge asym- metryasafunctionof

η

_CM^μ comparedtothe mcfm [52] predictions calculated usingCT14 PDF aloneandincluding nuclear modifica- tionsdescribedbytheEPPS16andnCTEQ15nPDFs.Allcalculations reproduce the present measurements within uncertainties in the entiremuon

η

range,includingwhenthe CT14protonPDFset is used,because nuclearmodifications ofthePDFs mostlycancel in thisquantity.

Thetensionbetweendataandtheoreticalcalculationsreported atnegative muon

η

inpPb collisions at√

s_NN=⁵.02 TeV [13] is notobservedinthepresentmeasurements.Thepresentuseofthe CT14protonPDFsetdecreasesthevalueofthechargeasymmetry comparedtothepredictionsbasedonCT10inRef. [13].Moreover, thetheoreticaluncertaintiesarealsoenlargedintheEPPS16nPDF setsandthetheoreticalcalculationsusingtheCT14+EPPS16nPDF sets agree better with the measurements at √

sNN=⁵.02 TeV, as compared to the EPS09 nPDF sets used in the analysis at

√sNN=⁵.02 TeV. It has been shownin Ref. [54] that the mea- surements of the lepton charge asymmetry at different collision energies(√

s ) aresimplyrelatedbyashiftintheleptonpseudo- rapidity,A(

η

l,√

s )=A(

η

ref,√

s),where

η

ref=

η

l+^ln(√ s/√

s )if

η

_l>0 and

η

ref=

η

_l−ln(√ s/√

s )if

η

l<0.Theresultofthisshift isshowninFig.5,demonstratingthatthepresentresultsandthe measurementsperformedat√

sNN=⁵.02 TeV [13] obeythisscal- ingproperty.

The agreement between data and theoretical calculations is quantifiedthrougha

χ

² testperformedforeachobservabletaking into account both experimental (including luminosity) and theo- reticaluncertaintiesandtheirbin-to-bincorrelations,obtainedfol- lowingtheprescription forHessianPDFsets [55] and rescaledto 68% confidence intervals. The results of the

χ

² test and the dof of each observable are shown in Table 2. The CT14+EPPS16 and CT14+nCTEQ15nPDFpredictions provecompatiblewiththe data, whiletheCT14PDFcalculationsdonotdescribethemeasurements well. These experimental results thus provide for the first time

Fig. 3. Forward-backwardratios,N^±_μ(+η_CM^μ)/N^±_μ(−η_CM^μ),forthepositively(left)andnegatively(middle)chargedmuons,andtheforward-backwardratioformuonsofboth signs,Nμ(+η^μ_CM)/Nμ(−η^μ_CM)(right),asafunctionofη^μ_CM.Thesmallhorizontallinesrepresentthestatisticalandsystematicuncertaintiessummedinquadrature,whereas theerrorbarsshowthestatisticaluncertaintiesonly.TheNLOcalculationswithCT14PDF,CT14+EPPS16nPDF,andCT14+nCTEQ15nPDF,arealsodisplayed,includingtheir 68%confidenceintervalPDFuncertaintybands.

clearevidenceofthenuclearmodificationofquarkPDFsfromthe measurements ofEWbosonproductioninnuclear collisions.Bin- to-bincorrelationshavebeenfoundtohavealargeimpactonthe obtained

χ

² values,especiallyfromnPDFuncertaintiesintheNLO calculations,whicharestronglycorrelatedinsideeachoftheshad- owing (positive

η

^μ_CM) and antishadowing (negative

η

_CM^μ ) regions, andanticorrelatedbetweenthesetworegions.

Furthermore,thepossible sources ofdifferencesbetweendata and the (n)PDFs are investigated. In the Hessian representation, a central PDF is given along witherror sets, each of which cor- respondstoan eigenvectorofthecovariancematrixinparameter space [56].Thevaluesof

χ

²/dofcorrespondingtothecompatibility betweenthe crosssectionmeasurements andthecalculationsus- ingeachoftheindividualsetsofCT14,nCTEQ15,andEPPS16(57, 33 and41 error sets, respectively) havebeen determined. Fig. 6 showsthedistributionofthe

χ

²/dofvaluesforthecentralander- rorsets.The

χ

²/dofvaluesobtainedareforindividualsets,thusig- noringtheoreticaluncertaintiesandtheircorrelations.Whilemost oftheEPPS16individualsets leadtoagoodagreementwithdata (with

χ

²/dof aroundunity),onlythose nCTEQ15setsthat exhibit thesmallerquarkshadowingatsmallx aremorecompatiblewith the data, yet with

χ

²/dof^{2. All CT14 PDF sets lead to a nar-} rowdistributioncentredaround

χ

²/dof^{3,becauseofthestrong} constraints imposed by the large experimental data sets used to extractthem.ThecurrentmeasurementsofW^± bosonproduction inpPbcollisionswillpermit furtherconstraintsonthequark and antiquarknPDFsandtheamountofquarkshadowinginthenuclei.

4. Summary

AstudyofW^±bosonproductioninpPbcollisionsatanucleon- nucleon centre-of-mass energy of √

s_NN =⁸.16 TeV is reported, using the muon decay channel for muons with transverse mo- mentagreaterthan25 GeV/c andforabsolutevaluesofthepseu- dorapidity in the laboratory frame |

η

^μ_lab|<2.4. The differential production cross sections for positively and negatively charged W→

μν

μ decays, the muon charge asymmetry, and the muon forward-backwardratios, are measured asfunctionsofthe muon pseudorapidityinthecentre-of-massframe,intherange−².86<

η

_CM^μ <1.93.

The measurements are compared to theoretical predictions frombothprotonpartondistributionfunctions(PDFs)(CT14)and nuclear PDF (CT14+EPPS16 , CT14+nCTEQ15) sets. The cross sec- tions and the forward-backward asymmetries exhibit significant deviations from the CT14 prediction,revealing nuclear modifica- tions of the PDFs unambiguously for the first time in the pro- duction of electroweak bosons in nuclear collisions. Both the

Fig. 4. Muonchargeasymmetry,(N⁺_μ−N⁻_μ)/(N⁺_μ+N⁻_μ),asafunctionofthemuon pseudorapidityinthecentre-of-massframe.Thesmallhorizontallinesrepresentthe statisticalandsystematicuncertaintiessummedinquadrature,whereastheerror barsshowthestatisticaluncertaintiesonly.TheNLOcalculationswithCT14PDF, CT14+EPPS16 nPDF, andCT14+nCTEQ15 nPDF, arealso displayed,including their 68%confidenceintervalPDFuncertaintybands.

CT14+EPPS16, and the CT14+nCTEQ15 calculations show a good overall agreement withthe data, withthe measurements favour- ingtheformernPDFset.Inthelattercase,onlytheindividualsets that exhibit the smallestnuclear PDF modifications atsmall val- uesofx (intheshadowingregion)turnouttobecompatiblewith experimentalmeasurements.Thesmallexperimentaluncertainties allowforasignificantreductioninthecurrentuncertaintiesonthe quarkandantiquarknuclearPDFsintherange10⁻³x10⁻¹. Acknowledgements

WecongratulateourcolleaguesintheCERNacceleratordepart- ments for the excellent performance of the LHC and thank the technical andadministrativestaffs atCERNand atother CMSin- stitutes for their contributions to the success of the CMS effort.

Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectively thecomputinginfrastructure essentialto our analyses.

Finally, we acknowledge the enduring support for the construc- tion andoperationofthe LHCandtheCMSdetectorprovided by the followingfundingagencies: BMBWFandFWF(Austria);FNRS

Table 2

Resultsoftheχ²statisticaltestbetweenthemeasurementsandthenPDFcalculationsfromtheCT14PDF,CT14+EPPS16nPDF,andCT14+nCTEQ15nPDFsets.Thevalueof theχ²,thenumberofdegreesoffreedom(dof)andtheχ²probability(Prob.),arepresentedfortheW^±bosondifferentialcrosssections,themuonchargeasymmetries, thechargedmuonforward-backwardratios,andtheforward-backwardratiosofallmuons,respectively.

Observable CT14 CT14+EPPS16 CT14+nCTEQ15

χ² dof Prob. [%] χ² dof Prob. [%] χ² dof Prob. [%]

dσ^{W±→μ±νμ}(η^μ_CM)/dη^μ_CM 135 48 3×10⁻⁸ 32 48 96 40 48 79

(N⁺_μ−N_μ⁻)/(N⁺_μ+N_μ⁻) 23 24 54 18 24 80 29 24 23

N^±_μ(+η^μ_CM)/N^±_μ(−η^μ_CM) 98 20 3×10⁻¹⁰ 11 20 95 14 20 83

Nμ(+η^μCM)/Nμ(−η^μCM) 87 10 2×^{10−12 3 10 99 5 10 90}

Fig. 5. Comparisonofthemuonchargeasymmetrymeasuredat√

sNN=8.16 TeV (circles)andat√

sNN=⁵.02 TeV [13] (squares).Themuonpseudorapidityofthe measurementsat 5.02 TeV hasbeenshifted(seetextfor details) [54].Thesmall horizontallinesrepresentthe statisticalandsystematicuncertaintiessummed in quadrature,whereastheerrorbarsshowthestatisticaluncertaintiesonly.TheNLO calculationswithCT14+EPPS16nPDFat8.16 TeV andat5.02 TeV,arealsodisplayed, includingtheir68%confidenceintervalPDFuncertaintybands.

Fig. 6. Distributionoftheχ²/dofvaluesfromthecomparisonofdata(crosssection measurements)andtheoreticalcalculations,fortheCT14,nCTEQ15,andEPPS16in- dividualerrorsets.Theverticaldashedlinesrepresentthepredictioncorresponding tothecentralsetofCT14,nCTEQ15,andEPPS16.

and FWO(Belgium); CNPq,CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China);

COLCIENCIAS (Colombia); MSES andCSF (Croatia); RPF (Cyprus);

SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia);

AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NK- FIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland);

INFN(Italy);MSIPandNRF(RepublicofKorea);MES(Latvia);LAS (Lithuania);MOEandUM(Malaysia);BUAP,CINVESTAV,CONACYT, LNS,SEP,andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu- gal);JINR (Dubna);MON, RosAtom, RAS, RFBR,and NRCKI (Rus- sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies(Switzerland); MST (Taipei);

ThEPCenter,IPST,STAR,andNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro- gramme and the European Research Council and Horizon 2020 Grant, contract Nos. 675440 and 765710 (European Union); the Leventis Foundation; the AlfredP. Sloan Foundation;the Alexan- der von Humboldt Foundation; the Belgian Federal Science Pol- icy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium);

the F.R.S.-FNRSand FWO(Belgium) underthe “Excellence ofSci- ence – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z181100004218003; the MinistryofEducation, YouthandSports(MEYS) ofthe CzechRe- public; the Lendület (“Momentum”) Programme and the János Bolyai Research Scholarship of the Hungarian Academy of Sci- ences, the New National Excellence Program ÚNKP, the NKFIA researchgrants123842,123959,124845,124850,125105,128713, 128786, and 129058 (Hungary); the Council of Science and In- dustrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional DevelopmentFund, the MobilityPlusprogrammeof the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/

02861,Sonata-bis2012/07/E/ST2/01406;theNationalPrioritiesRe- search Program by Qatar National Research Fund; the Programa Estatal de Fomento de la Investigación Científica y Técnica de ExcelenciaMaríade Maeztu,grant MDM-2015-0509andthePro- grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF andthe Greek NSRF;

theRachadapisekSompotFundforPostdoctoralFellowship,Chula- longkornUniversityandtheChulalongkornAcademic intoIts2nd CenturyProjectAdvancementProject(Thailand);TheWelchFoun- dation,contractC-1845;andtheWestonHavensFoundation(USA).