Measurements of production cross sections of polarized same-sign W boson pairs in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Measurements of production cross sections of polarized same-sign W boson pairs in association with two jets in proton-proton collisions at

√ s = ^{13 TeV}

.The CMSCollaboration

CERN,Geneva,Switzerland

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

Articlehistory:

Received20September2020

Receivedinrevisedform18November2020 Accepted8December2020

Availableonline11December2020 Editor:M.Doser

Keywords:

CMS Diboson Electroweak Polarized Longitudinal

The first measurements of production cross sections of polarized same-sign W^±W^± boson pairs in proton-protoncollisions are reported. The measurements are based ona data sample collectedwith the CMS detector at the LHC at a center-of-mass energy of13 TeV, corresponding to an integrated luminosity of 137 fb⁻¹.Events are selected byrequiring exactly two same-sign leptons, electrons or muons, moderate missing transverse momentum, and two jets with a large rapidity separation and a large dijet mass to enhancethe contribution ofsame-sign W^±W^± scattering events. Anobserved (expected)95% confidencelevel upperlimitof1.17(0.88) fb isset ontheproductioncrosssectionfor longitudinallypolarizedsame-signW^±W^±bosonpairs.Theelectroweakproductionofsame-signW^±W^± bosonpairswithatleastoneoftheW bosonslongitudinallypolarizedismeasuredwithanobserved (expected)significanceof2.3(3.1)standarddeviations.

©^{2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Vectorbosonscattering(VBS)processesprobetheelectroweak (EW) symmetry breaking mechanism at high energy scales. The unitarity of thetree-level amplitudeof the scatteringoflongitu- dinallypolarizedgaugebosons athighenergies isrestoredinthe standard model (SM) by a Higgs boson with a mass lower than about1 TeV [1,2]. Theobservationofa Higgsbosonwitha mass of about 125 GeV [3–5] provides an explanation that W and Z gauge bosons acquire mass via the Brout–Englert–Higgs mecha- nism,butadditionalHiggsbosons maystill playaroleintheEW symmetrybreaking.ModificationsoftheVBS crosssectionforthe longitudinally polarized W and Z bosons are predicted in mod- els ofphysics beyondthe SM throughmodifications ofthe Higgs bosoncouplings togaugebosons orthroughthepresenceofnew resonances [6,7].Themeasurementsofthelongitudinallypolarized scattering ofthe W and Z bosons provide complementary infor- mation to direct measurements of the Higgs boson couplings to gaugebosons [8,9].ModelsofbeyondSMphysics thatmodifythe crosssectionsofVBSprocesseswithtransverselypolarizedW and Z bosonsarediscussedinRef. [10].

At the CERN LHC, VBS interactions are characterized by the presenceoftwogaugebosonsinassociationwithtwoforwardjets

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

that have a large rapidity separation. Theyare part ofa class of processescontributingtothesame-signW^±W^± productioninas- sociation with two jets that proceeds via the EW interaction at treelevel,O(α⁴),where α istheEW coupling,referred toasEW W^±W^± production.Theleptonic decaymode W^±W^±→^±ν ^±ν^, whereboth W bosonsdecayintoelectronsormuons,,=^e,μ^, is a promising final state to study the polarized scattering from gaugebosons.The backgroundcontributionofthequantumchro- modynamics(QCD)induced productionof W^±W^± boson pairsin associationwithtwojetswithtree-levelcontributionsatO(α²α²_S), where αSisthestrongcoupling,issmall.Fig.1showsrepresenta- tiveFeynmandiagramsofVBSprocessesinvolvingself-interactions betweengaugebosons throughtripleandquarticgaugecouplings andthet-channelHiggsbosonexchange.

The unpolarized EW W^±W^± production has been previously measuredattheLHC intheleptonic decaymodesat√

s=^{8 and} 13 TeV [11–15]. Thefirst differentialcross section measurements werereportedinRef. [15].ThisLetterpresentsthefirstmeasure- mentoftheEWproductioncrosssectionsforpolarizedsame-sign W^±W^± bosonpairs. Thedatasample ofproton-proton(pp) colli- sions at√

s=13 TeV correspondsto an integratedluminosity of 137 fb⁻¹ [16–18], collected withthe CMS detector [19] in three LHCoperatingperiodsduringtheyears2016,2017,and2018.The threedata setsare analyzedindependently, withappropriate cal- ibrations and corrections, because of the various LHC operating conditionsand the upgrades in the performance of theCMS de-

https://doi.org/10.1016/j.physletb.2020.136018

0370-2693/©^{2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. IllustrativeFeynmandiagrams ofVBSprocesses, whereW bosonsareradiated fromincoming quarks(q),contributingtotheEW-inducedproductionofevents containingtwoforwardjetsandW^±W^±bosonpairsdecayingtoleptons.Diagramswiththetriplegaugecouplingvertex(left),thequarticgaugecouplingvertex(center), andthet-channelHiggsbosonexchange(right)areshown.

tector. Candidate events contain exactlytwo identified same-sign leptons, moderate missing transverse momentum, and two jets withalargerapidityseparationandahighdijetmass.

In the W^±W^± channel, each of the W bosons can be polar- ized either longitudinally (WL) or transversely (WT), leading to threedistinct contributions W^±_LW^±_L,W^±_LW^±_T,andW^±_TW^±_T.Ideally, wewouldmeasureallthreecontributionsseparately,butthecur- rent data sample size is too limited. Therefore, two maximum- likelihood fits are performed: one for W^±_LW^±_L and W^±_XW^±_T; and another forW^±_LW^±_X andW^±_TW^±_T.The index X indicates eitherof the two polarization states.The eventkinematical propertiesare used to extractthe various contributions. Twosets ofresultsare reported with the helicity eigenstates defined either in the WW center-of-massreferenceframeorintheinitial-stateparton-parton one.

2. TheCMSdetector

The central feature of the CMS apparatus is a superconduct- ing solenoidof6 m internal diameter,providinga magneticfield of3.8 T. Withinthe solenoidvolumeare asiliconpixel andstrip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrassandscintillatorhadroncalorimeter,each composedof abarrelandtwoendcapsections.Forwardcalorimetersextendthe pseudorapidity(η)coverageprovidedbythebarrelandendcapde- tectors. Muonsare detectedingas-ionizationdetectorsembedded inthesteelflux-returnyokeoutsidethesolenoid.Amoredetailed descriptionofthe CMSdetector,togetherwitha definitionofthe coordinate system used and the relevant kinematic variables, is giveninRef. [19].

Thefirst leveloftheCMStriggersystem,composed ofcustom hardware processors, uses informationfromthe calorimetersand muon detectorsto selecteventsofinterestwitha latencyofless than4 μs. Thesecondlevel,knownasthehigh-leveltrigger,con- sists of a farm of processors running a version of the full event reconstructionsoftwareoptimizedforfastprocessing,andreduces theeventratetoabout1 kHz beforedatastorage [20].

3. Signalandbackgroundsimulation

Several MonteCarlo(MC) event generators are used to simu- late the signal and backgroundcontributions. Three independent setsofsimulatedeventsforeachprocessareneededtomatchthe data-taking conditions inthe various years. All generated events areprocessedthrougha simulationoftheCMSdetectorbasedon Geant4 [21] andarereconstructedwiththesamealgorithmsused fordata.Additionalpp interactionsinthesameandnearbybunch crossings,referredtoaspileup,arealsosimulated.Thedistribution ofthenumberofpileupinteractionsinthesimulationisadjusted to match the one observed in the data. The average number of pileupinteractionswas23(32)in2016(2017and2018).

The SM EW W^±_LW^±_L, W^±_LW^±_T, and W^±_TW^±_T signal processes, where both bosons decay leptonically, are separately simulated using MadGraph5_amc@nlo 2.7.2, with the implementation of polarized parton scattering [22–24], at leading order (LO) with six EW (O(α⁶)) and zero QCD vertices. The NNPDF 3.1 next- to-next-to-leading-order(NNLO) [25] partondistributionfunctions (PDFs) are used. Signal processes are simulated with the helic- ity eigenstates defined either in the W^±W^± center-of-mass ref- erenceframe orinthe initial parton-partonreferenceframe. The Phantom1.5.1generator [26,27] usestheon-shellprojectiontech- nique forthe predictions of the signal processes asdiscussed in Ref. [28].TheMadGraph5_amc@nlopredictionsshowsatisfactory agreement within the statistical uncertainties with the Phantom predictions in the relevant fiducial region, defined in Section 8, forthisanalysis.ComparisonsoftheMadGraph5_amc@nlopredic- tionswithpredictionsbasedon theon-shellprojection technique arereportedin Ref. [24]. The smallcontributionsofoff-shell and nonresonantproduction [28] arenotincludedinthesimulatedsig- nalsamplesandamountto1–2%inthefiducialregion.

The full next-to-leading-order (NLO) QCD and EW corrections fortheleptonicunpolarized W^±W^± scatteringprocesshavebeen computed [29,30], and they reduce the LOcross section for the EW W^±W^± process by approximately 10–15%, with the correc- tionincreasinginmagnitudetoupto25%withincreasingdilepton and dijet masses. The NLO corrections for the W^±_LW^±_L, W^±_LW^±_T, andW^±_TW^±_T processesarenotknown.Thecorrectionsfortheun- polarized EW W^±W^± process at orders of O(αSα⁶) and O(α⁷) areappliedtotheMadGraph5_amc@nloLOcrosssectionsforthe W^±_TW^±_T process. Only the corrections at order of O(αSα⁶) are applied to the MadGraph5_amc@nlo LO cross sections for the W^±_LW^±_L and W^±_LW^±_T processes because the corrections at order O(α⁷)areexpectedtobesmallerfortheW^±_LW^±_L andW^±_LW^±_T pro- cesses comparedto the size ofthe corresponding corrections for theunpolarizedEW W^±W^± process [31].Thereisanegligibleef- fectin themeasured crosssectionsfromdifferencesinthe event kinematicalpropertiescausedbythetreatmentoftheNLOcorrec- tions.

The EW WZ background process is simulated with MadGraph5_amc@nlo2.4.2atorderO(α⁶).TheQCD-inducedWZ processissimulatedatLOwithupto threeadditionalpartonsin the matrix element calculations using the MadGraph5_amc@nlo generatorwithatleastoneQCDvertexattreelevel.Thedifferent jetmultiplicitiesaremergedusingtheMLMscheme [32] tomatch matrixelementandpartonshowerjets.TheMadGraph5_amc@nlo generatoris alsoused to simulatetheQCD-induced W^±W^± pro- cess.

The interference betweenthe EW and QCD diagrams for the W^±W^±andWZ processesisgeneratedwithMadGraph5_amc@nlo including the contributions of order αSα⁵. The relative contri- butions in the fiducial region of the interference term between the EW and the QCD diagrams for the W^±_LW^±_L, W^±_LW^±_T, and

W^±_TW^±_T processes arecomparable to therelative contributions of the W^±_LW^±_L, W^±_LW^±_T, and W^±_TW^±_T processes to the EW W^±W^± cross section. The interferences betweenthe signal processesare expected to be small [24], and good agreement is observed be- tweentheincoherentsumofthepolarizedcrosssectionsandthe unpolarizedcrosssectionsforthedistributionsoftheobservables.

The powheg v2 [33–37] generator is used to simulate the t¯t, tW,andotherdibosonprocessesatNLO accuracyinQCD.Produc- tionoft¯tW,t¯tZ,t¯tγ,andtriplevectorboson(VVV)eventsissimu- latedatNLOaccuracyinQCDusingtheMadGraph5_amc@nlo2.2.2 (2.4.2) generator for 2016(2017 and 2018) [22,23] samples. The tZq process is simulatedat NLO in the four-flavor scheme using MadGraph5_amc@nlo2.3.3.ThetZq MC simulationisnormalized usingacrosssectioncomputedatNLOwithMadGraph5_amc@nlo in the five-flavor scheme, following the procedure described in Ref. [38].ThedoublepartonscatteringW^±W^±productionisgen- erated atLOusing pythia8.226 (8.230) [39] for 2016 (2017and 2018)samples.

The NNPDF 3.0 NLO [40] (NNPDF 3.1 NNLO [25]) PDFs are used for generating all 2016 (2017 and 2018) background sam- ples. For all processes, the parton showering and hadronization are simulated using pythia 8.226 (8.230) for 2016 (2017 and 2018). The modeling of the underlying event is done using the CUETP8M1 [41,42] (CP5 [43]) tune for simulated samples corre- spondingtothe2016(2017and2018)data.

4. Eventreconstructionandselection

EventsarereconstructedusingtheCMSparticle-flow(PF)algo- rithm [44] that reconstructsandidentifieseachindividualparticle withanoptimizedcombinationofallsubdetectorinformation.The missingtransversemomentumvector p_T^miss isdefinedasthepro- jectionontotheplane perpendiculartothebeamaxisoftheneg- ativevectorsumofthemomentaofallreconstructedPFobjectsin anevent.Itsmagnitudeisreferredtoasp^miss_T .

Jets are reconstructed by clustering PF candidates using the anti-kTalgorithm [45,46] withadistanceparameterof0.4.Jetsare calibratedinthesimulation,andseparatelyindata,accountingfor energydepositsofneutralparticlesfrompileupandanynonlinear detector response [47]. The effect of pileup is mitigated through a charged-hadron subtraction technique, which removes the en- ergy ofcharged hadronsnot originatingfromthe primary vertex (PV) [48] oftheevent.Correctionstojetenergiestoaccountforthe detectorresponseare propagatedto p^miss_T [49]. ThePVisdefined asthevertexwiththelargestvalueofsummedphysics-object p²_T. The physics objects are derived from onlythe tracks assignedto thevertexasinputsbyclusteringthemintojets,includingleptons.

The p^miss_T is also recalculated only from those jets by summing theirnegative pT vectors.

Electrons and muonsare reconstructed by associating a track reconstructed in the tracking detectors with either a cluster of energy in the ECAL [50,51] or a track inthe muon system [52].

Electronandmuoncandidatesmustpasscertainidentificationcri- teria to be further selected in theanalysis. Forthe “loose” iden- tification, they must satisfy pT>10 GeV and |η_|<2.5 (2.4) for electrons (muons). At the final stage of the lepton selection the

“tight” workingpoints criteriafollowing the definitions provided inRefs. [50,52] arechosen,includingrequirementsonthe impact parameterofthecandidateswithrespecttothePVandtheiriso- lationwithrespecttootherparticlesintheevent [9].

Forelectrons,thebackgroundcontributioncomingfromamis- measurement of the track charge is not negligible. The sign of thischarge isevaluatedusingthreeobservablesthatmeasure the electron curvatureapplyingdifferentmethods; requiringall three charge evaluations toagree reducesthis backgroundcontribution

Table 1

SummaryoftherequirementsdefiningtheW^±W^±SR.The|m− mZ|requirementisappliedtothedielectronfinalstateonly.

Variable Requirement

Leptons Exactly 2 same-sign leptons,pT>25/20 GeV p^j_T >50 GeV

|m−mZ| >15 GeV (ee)

m >20 GeV

p^miss_T >30 GeV b quark veto Required Max(z^∗) <0.75 mjj >500 GeV

|ηjj| >2.5

byafactoroffivewithanefficiencyofabout97% [50].Thecharge mismeasurementisnegligibleformuons [53,54].

Collision events are collected using single-electron (single- muon)triggersthatrequirethepresenceofanisolatedleptonwith p_T>27(24)GeV.Inaddition,asetofdileptontriggerswithlower pTthresholds,withathresholdof23 GeV orlowerfortheleading lepton andwitha threshold of 8 GeV for the subleadinglepton, isused.Thisensuresatriggerefficiencyabove99%foreventsthat satisfythesubsequentofflineselection.

Severalselection requirementsare used to isolatethe W^±W^± topology defining the signal region (SR) whilereducing the con- tributions of backgroundprocesses. Candidate events contain ex- actly two isolated same-sign charged leptons and at least two jetswith p^j_T>50 GeV and |η_|<4.7. Jets that are within R=

√(φ)²+(η)²<0.4 of one of the identified leptons are not usedintheanalysis. Here φ andηrefer tothe differencesin the azimuthal angle φ and η of the jet and the charged-lepton candidate,respectively.Becauseofthepresenceofundetectedneu- trinosinthesignalevents,p^miss_T isrequiredtoexceed30 GeV.

TheW^±W^± SRselectionrequiresoneofthesame-signleptons tosatisfypT>25 GeV andtheotherpT>20 GeV.Themassofthe dileptonpairm mustbegreater than20 GeV.Candidateevents inthedielectronfinalstatewithin15 GeV ofthenominalZ boson massmZ[55] arerejectedtoreducethenumberofZ bosonback- groundeventswherethechargeofoneoftheelectroncandidates ismisidentified.

The VBS topology istargeted by requiringthe two highest-pT jetstohaveadijetmassmjj>500 GeV andapseudorapiditysepa- ration|ηjj|>2.5.TheW bosonsintheVBStopologiesaremostly produced in the central rapidity region with respect to the two selected jets. The candidate W^±W^± events are required to sat- isfy max(z^∗)<0.75,where z^∗= |η−(η^j1+η^j2)/2|/|ηjj| ^isthe Zeppenfeldvariable [56], ηisthepseudorapidityofoneofthese- lectedleptons,and η^j1 and η^j2 arethepseudorapiditiesofthetwo candidateVBSjets.

CandidateeventswithoneormorejetswithpT>20 GeV and

|η_|<2.4 that are consistentwith thefragmentation ofa bottom quarkarerejectedtoreducethenumberoftopquarkbackground events.The DeepCSV b taggingalgorithm [57] is usedforthisse- lection. For the chosen working point, the efficiency to select b quark jets is about 70% and the rate for incorrectly tagging jets originatingfromthe hadronization ofgluons oru, d, s quarks is about1%.Therateforincorrectlytaggingjetsoriginatingfromthe hadronizationofc quarksisabout10%.Theselectionrequirements todefinethesame-signW^±W^±SRaresummarizedinTable1.

5. Extractingpolarizationinformation

IntheW^±W^±channel,theW bosonscaneachbeeitherlongi- tudinally or transversely polarized leading to different kinematic distributions, reflected in the kinematical properties of the two leptons,thetwojets,andp_T^miss.TheWLbosonstendtoberadiated