Measurements Of Production Cross Sections of Polarized Same-Sign W √ Boson Pairs İn Association With Two Jets in Proton-Proton Collisions at s = 13 TeV

Contents lists available atScienceDirect

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

CMS

Collaboration



CERN,Geneva,Switzerland

a

r

t

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-proton collisions are reported. The measurements are based on a data sample collected with the CMS detector at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 137 fb−1. Events are selected by requiring 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 enhance the contribution of same-sign W±W± scattering events. An observed (expected) 95% confidence level upper limit of 1.17 (0.88) fb is set on the production cross section for longitudinally polarized same-sign W±W±boson pairs. The electroweak production of same-sign W±W± boson pairs with at least one of the W bosons longitudinally polarized is measured with an observed (expected) significance of 2.3 (3.1) standard deviations.

©2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

1. Introduction

Vectorbosonscattering(VBS)processesprobetheelectroweak (EW) symmetry breaking mechanism at high energy scales. The unitarity of thetree-level amplitudeof the scatteringof longitu-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± productionin as-sociation with two jets that proceeds via the EW interaction at treelevel,

O(

α

4

₎

_,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 backgroundcontributionofthequantum chro-modynamics(QCD)induced productionof W±W± boson pairsin associationwithtwojetswithtree-levelcontributionsat

O(

α

2

_α

2

S

)

,

where

α

Sisthestrongcoupling,issmall.Fig.1shows

representa-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].ThisLetterpresentsthefirst measure-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. Illustrative Feynmandiagrams 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,butthe cur-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

)coverageprovidedbythebarrelandendcap de-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 Geant_{4 [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(

α

6

₎

_{) 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-shellprojection tech-nique forthe predictions of the signal processes asdiscussed in Ref. [28].TheMadGraph5_amc@nlo predictions showsatisfactory agreement within the statistical uncertainties with the Phantom predictions in the relevant fiducial region, defined in Section 8, forthisanalysis.ComparisonsoftheMadGraph5_amc@nlo predic-tionswithpredictionsbasedon theon-shellprojection technique arereportedin Ref. [24]. The smallcontributionsofoff-shell and nonresonantproduction [28] arenotincludedinthesimulated sig-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.Thecorrectionsforthe un-polarized EW W±W± process at orders of

O(

α

S

α

6

)

and

O(

α

7

)

areappliedtotheMadGraph5_amc@nlo LOcrosssectionsforthe W±_TW±_T process. Only the corrections at order of

O(

α

S

α

6

)

are

applied to the MadGraph5_amc@nlo LO cross sections for the W±_LW±_L and W_L±W±_T processes because the corrections at order

O(

α

7

₎

_{areexpectedtobesmallerfortheW}±

LW±L andW±LW±T

pro-cesses comparedto the size ofthe corresponding corrections for theunpolarizedEW W±W± process [31].Thereisanegligible ef-fectin themeasured crosssectionsfromdifferencesinthe event kinematicalpropertiescausedbythetreatmentoftheNLO correc-tions.

The EW WZ background process is simulated with MadGraph5_amc@nlo 2.4.2atorder

O(

α

6

)

.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

α

S

α

5. 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,tt

¯

γ

,andtriplevectorboson(VVV)eventsis simu-latedatNLOaccuracyinQCDusingtheMadGraph5_amc@nlo 2.2.2 (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@nlo 2.3.3.ThetZq MC simulationisnormalized usingacrosssectioncomputedatNLOwithMadGraph5_amc@nlo in the five-flavor scheme, following the procedure described in Ref. [38].ThedoublepartonscatteringW±W±productionis gen-erated atLOusing pythia_{8.226 (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_Tmiss isdefinedasthe pro-jectionontotheplane perpendiculartothebeamaxisofthe neg-ativevectorsumofthemomentaofallreconstructedPFobjectsin anevent.Itsmagnitudeisreferredtoaspmiss_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 pmiss

T [49]. ThePVisdefined

asthevertexwiththelargestvalueofsummedphysics-object p2_T. The physics objects are derived from onlythe tracks assignedto thevertexasinputsbyclusteringthemintojets,includingleptons. The pmiss

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]. Electronandmuoncandidatesmustpasscertainidentification cri-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 parameterofthecandidateswithrespecttothePVandtheir iso-lationwithrespecttootherparticlesintheevent [9].

Forelectrons,thebackgroundcontributioncomingfroma mis-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

pjT >50 GeV |m−mZ| >15 GeV (ee)

m >20 GeV pmiss

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 pT

>

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 pj_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

and



η

refer tothe differencesin the azimuthal angle

φ

and

η

of the jet and the charged-lepton candidate,respectively.Becauseofthepresenceofundetected neu-trinosinthesignalevents,pmiss

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 boson

back-groundeventswherethechargeofoneoftheelectroncandidates ismisidentified.

The VBS topology istargeted by requiringthe two highest-pT

jetstohaveadijetmassmjj

>

500 GeV andapseudorapidity

sepa-ration

|

η

jj

|

>

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

|/|

_η

jj

|

isthe

Zeppenfeldvariable [56],

η

_{isthepseudorapidityofoneofthe}

se-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 tagging algorithm [57] is usedforthis se-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 bosonscaneachbeeither longi-tudinally or transversely polarized leading to different kinematic distributions, reflected in the kinematical properties of the two leptons,thetwojets,and



p_Tmiss.TheWLbosonstendtoberadiated

Table 2

ListanddescriptionofalltheinputvariablesforthesignalBDTtrainings. Variables Definitions

φjj Differenceinazimuthalanglebetweentheleadingand subleadingjets

pj1T pTof the leading jet

pj2T pTof the subleading jet

p1

T Leading lepton pT

p2

T Subleading lepton pT

φ Difference in azimuthal angle between the two leptons

m Dilepton mass

p

T Dilepton pT

mWW

T Transverse WW diboson mass

z∗1 Zeppenfeld variable of the leading lepton

z∗_

2 Zeppenfeld variable of the subleading lepton

Rj1, R between the leading jet and the dilepton system

Rj2, R between the subleading jet and the dilepton system

(p1 Tp 2 T)/(p j1 Tp j2

T) Ratio of pTproducts between leptons and jets

pmiss

T Missing transverse momentum

at a smaller anglewith respect to theincoming quark direction, resultinginasmaller WL boson pT comparedtothe radiatedWT

boson pT.Inaddition,therearedifferencesinthebehaviorofthe

scatteringamplitudesasafunctionofthe W±W± center-of-mass energyandthescatteringangle [58].

Multivariatetechniquesareusedtoenhancetheseparation be-tween the different processes. We implement boosted decision trees (BDTs)withgradientboosting usingthe tmva package [59]. TwodifferentBDTs,referred toasthesignalBDTs,are trainedon simulatedevents toseparate eitherthe W±_LW±_L and W±_XW±_T pro-cessesortheW±_LW±_X andW±_TW±_T processes.Severaldiscriminating observablesare used asthe inputstothe BDTs, includingthejet andleptonkinematicalpropertiesandpmiss

T ,assummarizedin

Ta-ble 2. The distributions of these observables are taken from the SM predictions.Hypotheticalmodifications dueto beyondtheSM physics areassumedtoimpactonly theproductionrates,butnot thekinematicdistributionsofsensitivevariables.Angularvariables are included,such asthe difference in the azimuthal angles be-tween theleading andsubleadingjets(

φjj

) andleptons (

φ

),

andthe



R betweentheleading(subleading)jetandthedilepton system



Rj1,(



Rj2,).ThedileptonpT,m,andthetransverse

dibosonmassmWW

T asdefinedinRef. [15] arealsoconsidered.The

kinematic variable

(

p1 T p 2 T

)/(

p j1 Tp j2

T

)

proposed inRef. [58] is also

includedintheBDT inputs.A largersetofdiscriminating observ-ables was studied,butonlyvariables that improvethesensitivity andshow someseparationare retained.Thedistributions of

φjj

(upper),

φ

 (middle), and m (lower) at the generator level

for the W±_LW±_L, W±_LW±_T,and W±_TW±_T processes withthe helicity eigenstates definedintheparton-parton (left)andW±W± (right) center-of-mass reference frames are shown in Fig. 2. The signal extraction was also compared witha deep neural network using the Keras [60] deeplearning library,interfacedwiththe Tensor-Flow[61] library,whichledtoaconsistentlygoodperformance.

6. Backgroundestimation

A combination of methods based on control samples in data andsimulationisusedtoestimate backgroundcontributions. Un-certaintiesrelatedtothetheoreticalandexperimental predictions aredescribedinSection7.Theelectronchargemisidentificationin simulationiscorrectedtoreproducetheratemeasuredindata. Us-ingZ

→

ee events,themisidentificationrateisabout0.01%(0.3%) inthebarrel(endcap)region [50].Oppositelychargeddilepton fi-nalstatesfromt

¯

t,tW,W+W−,andDrell–Yanprocessescontribute tothebackgroundfromchargemisidentification.

Table 3

ListanddescriptionoftheinputvariablesfortheinclusiveBDTtraining. Variables Definitions

mjj Dijet mass

|ηjj| Difference in pseudorapidity between the leading and subleading jets φjj Difference in azimuth angles between the leading and subleading jets

pj1T pTof the leading jet

pj2_T pTof the subleading jet

p1

T Leading lepton pT

p

T Dilepton pT

z∗_

1 Zeppenfeld variable of the leading lepton

z∗2 Zeppenfeld variable of the subleading lepton

pmissT Missing transverse momentum

The nonprompt lepton backgrounds originating from leptonic decaysofheavyquarks,hadronsmisidentifiedasleptons,and elec-tronsfromphotonconversionaresuppressedbytheidentification andisolation requirementsimposed onelectrons andmuons. The remainingcontributionfromthenonpromptleptonbackgroundis estimateddirectlyfromdatafollowingthetechnique describedin Ref. [12], where theyield in a sample of data eventsdominated by jet productionis extrapolated to the signal region using effi-cienciesforlooselyidentifiedleptons to passthestandard lepton selection criteria. A normalizationuncertainty of 20% isassigned forthe nonprompt lepton background to include possible differ-encesinthecompositionofjetsbetweenthedatasampleusedto derivetheseefficienciesandthedatasampleintheW±W±SR [9]. Several background-enriched control regions (CRs), disjoint fromone anotherandfromtheSR, areusedtoselectevent sam-plesenrichedwithWZ,nonpromptlepton,tZq,andZZ background events. The WZ CR is defined by requiring three leptons where theopposite-signsame-flavorleptonsfromtheZ bosoncandidate have pT

>

25 and10 GeV withthedileptonmass within15 GeV

of the nominal Z boson mass. In events with three same-flavor leptons,theopposite-signleptonpairwiththedileptonmass clos-est to mZ is associated with the Z boson. The remaining lepton

withpT

>

20 GeV isassociatedwiththeW boson.Inaddition,the

trilepton mass m is required to be greater than 100 GeV and

max

(

z∗_

)

must belessthan 1.0. Distributionsofseveralkinematic variablesintheWZ CRarereportedinRef. [15].

ThenonpromptleptonCRisdefinedbyrequiringthesame se-lectionasfortheW±W± SR,butwiththeb jetvetorequirement inverted. The selected sample is enriched with events from the nonprompt lepton backgroundand dominatedby semileptonic t

¯

t events.Similarly,thetZq CRisdefinedbyrequiringthesame selec-tionastheWZ CR,butwiththeb quarkvetorequirementinverted. TheselectedsampleisdominatedbythetZq backgroundprocess. Finally, the ZZ CR requirements select events with four leptons withthe sameVBSrequirements asthe W±W± SR. ThefourCRs are used to estimate the normalization of the main background processesfromdata.Allotherbackgroundprocessesareestimated fromsimulationafterapplyingcorrectionstoaccountforsmall dif-ferencesbetweendataandsimulationasdetailedinSection7.

TodistinguishEWW±W±productionfromtheSMbackground processes before extractingthe individual polarizations, a BDT is trainedusing the TMVA package [59]. Several discriminating ob-servableslistedinTable3areusedasinputstothisBDT,whichwe willrefertoastheinclusiveBDT.The valuesofmjjand

|

η

jj

|

are

powerfulbecauseVBStopologiestypicallyhavelargevaluesforthe dijetmassandpseudorapidityseparation [15].TheSMbackground processes are dominated by the nonprompt lepton background contribution, which comes mainly from top quark production. A largetraining backgroundsample ofsimulatedeventsisobtained by usingoppositely chargeddilepton eventsfrom topquark pro-duction.

Fig. 2. Generatorleveldistributionsofφjj(upper),φ(center),andm(lower)inthefiducialregionfortheWL±W±L,W±LW±T,andW±TW±T processeswiththehelicity eigenstatesdefinedintheparton-parton(left)andW±W± (right)center-of-massreferenceframes.Thedistributionsarenormalizedtounitarea.Theerrorbarsrepresent theuncertaintiesassociatedwiththelimitednumbersofsimulatedevents.

7. Systematicuncertainties

Several sources of systematic uncertaintyin the cross section measurementscanaffecttheratesandshapesofthedistributions for the signal and background processes. Foreach source of un-certainty, the impact in differentbins of the final distribution is considered asbeingfullycorrelated, whereas differentsources of uncertaintyaretreatedasuncorrelated.

The uncertainties in the integrated luminosity measurements for the data used in this analysis are 2.5, 2.3, and 2.5% for the 2016, 2017, and2018datasamples [16–18], respectively.The

to-talintegratedluminosityhasanuncertaintyof1.8%becauseofthe uncorrelatedtimeevolutionofsomesystematiceffects.

The simulation of pileup events assumes a total inelastic pp crosssectionof69.2 mb,withanassociateduncertaintyof5% [62,

63]. The impact of the pileup on the expected signal and back-groundyieldsislessthan1%.

Discrepanciesintheleptonreconstructionandidentification ef-ficiencies between data andsimulation are adjusted by applying corrections to all MC simulation samples. The efficiency correc-tions,whichdependonthepTand

η

ofthelepton,aredetermined

de-Table 4

SystematicuncertaintiesoftheW±LW±L andW±XWT±,andW±LW±X andW±TW±T cross sectionmeasurementsinunitsofpercent.

Source of uncertainty W±LW±L (%) W±XW±T (%) W±LW±X (%) W±TW±T (%) Integrated luminosity 3.2 1.8 1.9 1.8

Lepton measurement 3.6 1.9 2.5 1.8

Jet energy scale and resolution 11 2.9 2.5 1.1

Pileup 0.9 0.1 1.0 0.3

b tagging 1.1 1.2 1.4 1.1

Nonprompt lepton rate 17 2.7 9.3 1.6

Trigger 1.9 1.1 1.6 0.9

Limited sample size 38 3.9 14 5.7

Theory 6.8 2.3 4.0 2.3

Total systematic uncertainty 44 6.6 18 7.0 Statistical uncertainty 123 15 42 22

Total uncertainty 130 16 46 23

terminationofthetriggerefficiencyleadstoanuncertaintysmaller than1%intheexpectedsignal yield.The leptonmomentumscale uncertaintyiscomputedbyvaryingthemomentaoftheleptonsin thesimulationbytheiruncertainties,andbyrepeatingtheanalysis selection.Theresultinguncertaintiesintheeventyieldsareabout 1% forboth electrons andmuons.These uncertainties aretreated ascorrelatedacrossthethreedatasets.

The uncertainty in thecalibration of the jet energyscale and resolutiondirectlyaffectstheselectionefficiencyofthejet multi-plicityrequirementandthe pmiss_T measurement.Theseeffectsare estimated by changing the jet energy in the simulation up- and downwards by onestandard deviation. Theuncertainty inthejet energy scale and resolution is 2–5%, depending on the pT and

η

[47], and the impact on the expected signal and background yieldsis1–4%.

Discrepanciesintheb taggingefficiencybetweendataand sim-ulationareadjustedbyapplyingcorrectionstothesimulated sam-ples [57], whichare estimatedseparately forcorrectlyand incor-rectly identifiedjets.Eachsetofvaluesresultsinuncertainties in theb taggingefficiencyofabout1–4%,andtheimpactonthe ex-pectedsignalandbackgroundyieldsisabout1%.Theuncertainties in thejet energyscale andb taggingare treatedasuncorrelated acrossthethreedatasets.

The dominant theoretical uncertainties corresponding to the choiceoftheQCDrenormalizationandfactorizationscalesare es-timatedby varyingthesescales independentlyupanddownbya factoroftwo fromtheir nominalvalues.Thelargestcrosssection variation, while excluding thetwo extreme variations whereone scaleisvariedup andtheother onedown,istakenasthe uncer-tainty.ThePDFuncertaintiesareevaluatedaccordingtothe proce-duredescribedinRef. [64].ThescaleandPDFuncertaintiesforthe processesestimatedfromsimulationaretreatedasfullycorrelated across bins for the distributions used to extract the results. The effect of

O(

α

7

₎

_{correction for the unpolarized EW W}±_W±

pro-cessontheshapesofthedistributionsfortheW_L±W±_L andW±_LW±_T processesisconsideredasasystematicuncertainty.Thecorrection valuesareusedasasymmetricshapeuncertainty. The uncertain-tiesassociatedwiththelimitednumbersofsimulatedeventsand ofdataeventsusedtoestimatethenonpromptleptonbackground arealsoincludedassystematicuncertaintieswiththelatterbeing the dominant contribution. A summary ofthe systematic uncer-taintiesintheW±_LW±_L andW±_XW±_T,andintheW±_LW±_X andW±_TW±_T crosssectionmeasurementsisshowninTable4.

8. Results

Binnedmaximum-likelihoodfitsareperformedtodiscriminate between the signals and the remaining backgrounds using the W±W± SRandtheWZ,nonprompt lepton,tZq,andZZ CRs.Two

Table 5

ExpectedyieldsfromvariousSMprocessesandobserved dataeventsinW±W± SR.Thecombinationofthe statis-ticalandsystematicuncertaintiesisshown.Theexpected yieldsareshownwiththeirbest fitnormalizationsfrom thesimultaneousfitfortheW±_LW_L±andW±_XW±_T cross sec-tions.TheW±LW±T and W±TW±T yieldsareobtainedfrom theW±XW±T yieldassumingtheSMpredictionfortheratio oftheyields.ThetVx backgroundyieldincludesthe con-tributionsfromt¯tV andtZq processes.

Process Yields in W±W±SR W±LW±L 16.0±18.3 W±LW±T 63.1±10.7 W±TW±T 110.1±18.1 QCD W±W± 13.8±1.6 Interference W±W± 8.4±0.6 WZ 63.3±7.8 ZZ 0.7±0.2 Nonprompt 213.7±52.3 tVx 7.1±2.2 Other background 26.9±9.9 Total SM 522.9±60.7 Data 524

separate fits are performed, one for the simultaneous measure-ments of the W±_LW±_L and W±_XW±_T cross sections and a second for the simultaneous measurements of the W±_LW±_X and W±_TW±_T crosssections.Thesystematicuncertaintiesaretreatedasnuisance parameters andare profiled [65,66] with the shape and normal-ization of each distribution varying within the respective uncer-tainties inthe fit. The normalization uncertainties are treated as log-normalnuisanceparameters.Thenuisanceparameters arenot significantly constrained. The small QCD W±W± contribution is normalizedto the SM predictionand allowed tovary within the uncertainties. The normalizations of the tZq, ZZ, and WZ back-groundprocessesare freeparameters ofthemaximum-likelihood fits,togetherwiththesignalcrosssections.Atwo-dimensional dis-tributionisusedinthesimultaneous fitsfortheW±W± SRwith fivebins inthe inclusiveBDT andfive bins inthe corresponding signalBDT.ThemjjdistributionisusedfortheCRsinthefitwith

fourbins.The binboundariesare chosen to havesimilar W±_LW±_L andW±_LW±_X contributionsacrossthebins.

The interferencecontributions betweenthe EW andQCD dia-grams for the W±W± and WZ processes are normalized to the SM predictionswithin theuncertainties. Theimpact oftreatment of the interference contributions on the results is evaluated by performinga setofalternative fitswherethe interference contri-butionsbetweentheEWdiagramsfortheW±_LW±_L andW±_XW±_T or W±_LW±_X andW±_TW±_T processesandQCDdiagramsarescaled with thesquare rootofthemeasuredtothepredictedcrosssection ra-tios.Thetwoapproachesyieldconsistentresults.

The distributions ofmjj (upper left),

φjj

(upper right),

φ



(lowerleft),andtheoutputscoreoftheinclusiveBDT(lowerright) intheW±W±SRareshowninFig.3.Thedistributionsofthetwo signalBDToutputscoresareshowninFig.4.Thepredictedyields areshownwiththeir best fitnormalizationsfromthe simultane-ousfitfortheW±_LW±_L andW±_XW±_T crosssections.Thedatayields, together with the SM expectations with the best fit normaliza-tions, are given in Table 5. The background yields withthe best fit normalizations fromthe simultaneous fit for the W±_LW±_X and W±_TW±_T crosssectionsareconsistentwiththeyieldsshownin Ta-ble5withinafewpercent.

The fiducialregion for the cross section measurements is de-fined by requiring two same-sign leptons (electrons or muons) withpT

>

20 GeV,

|

η

|

<

2

.

5,andm

>

20 GeV,andtwojetswith

mjj

>

500 GeV and

|

η

jj

|

>

2

.

5.Theleptonsatthegeneratorlevel

four-Fig. 3. Distributionsofthemjj(upperleft),φjj(upperright),φ(lowerleft),andoftheoutputscoreoftheinclusiveBDT(lowerright)intheW±W±SR.Thepredicted

yieldsareshownwiththeirbestfitnormalizationsfromthesimultaneousfit.ThehistogramsfortheW±W±processincludethecontributionsfromtheW±LW±L,W±LW±T, andW±_TW±_T processes(shownseparatelyassolidlines),QCDW±W±,andinterference.Thehistogramsforotherbackgroundsincludethecontributionsfromdoubleparton scattering,VVV,andfromoppositelychargeddileptonfinalstatesfromt¯t,tW,W+W−,andDrell–Yanprocesses.Theoverflowisincludedinthelastbin.Thebottompanel ineachfigureshowstheratioofthenumberofeventsobservedindatatothatofthetotalSMprediction.Thegraybandsrepresenttheuncertaintiesinthepredictedyields. Theverticalbarsrepresentthestatisticaluncertaintiesinthedata.

Fig. 4. DistributionsoftheoutputscoreofthesignalBDTusedfortheW±LW±L andW±XW±T crosssectionmeasurements(left)andoftheoutputscoreofthesignalBDTused fortheW±LW±X andW±TW±T crosssectionmeasurements(right).Thepredictedyieldsareshownwiththeirbestfitnormalizationsfromthesimultaneousfit.Thehistograms fortheW±W±processincludethecontributionsfromtheW±_LW±_L,W±_LW_T±,andW±_TW±_T processes(shownseparatelyassolidlines),QCDW±W±,andinterference.The histogramsforotherbackgroundsincludethecontributionsfromdoublepartonscattering,VVV,andfromoppositelychargeddileptonfinalstatesfromt¯t,tW,W+W−,and Drell–Yanprocesses.ThebottompanelineachfigureshowstheratioofthenumberofeventsobservedindatatothatofthetotalSMprediction.Thegraybandsrepresent theuncertaintiesinthepredictedyields.Theverticalbarsrepresentthestatisticaluncertaintiesinthedata.

Fig. 5. ProfilelikelihoodscanasafunctionoftheW±LW±L crosssection.Thered (blue)linerepresentstheexpectedvaluesinthebackground-onlyhypothesis,i.e., assumingnocontributionfromtheW±_LW±_L process,consideringallsystematic un-certainties (onlystatistical ones).The greenlineshowsthe expectedvalues for thesignal-plus-backgroundhypothesis.Theobservedvaluesarerepresentedbythe blackline.

Table 6

MeasuredfiducialcrosssectionsfortheW±LWL±andW±XW±T processes,andforthe W±LW±X andW±TWT± processesforthehelicityeigenstatesdefinedintheW±W± center-of-massframe.Thecombinationofthestatisticalandsystematic uncertain-tiesisshown.ThetheoreticalpredictionsincludingtheO(αSα6)andO(α7) cor-rectionstothe MadGraph5_amc@nlo LOcrosssections,asdescribedinthetext, arealsoshown.Thetheoreticaluncertaintiesincludestatistical,PDF,andLOscale uncertainties;BisthebranchingfractionforWW→ ν_ν[55].

Process σB(fb) Theoretical prediction (fb) W±_LW±_L 0.32+0.42 −0.40 0.44±0.05 W±XW±T 3.06+ 0.51 −0.48 3.13±0.35 W±LW±X 1.20+ 0.56 −0.53 1.63±0.18 W±_TW±_T 2.11+0.49 −0.47 1.94±0.21

momentum ofeach lepton afterfinal-statephoton radiationwith that ofphotonsfoundwithinaconeof



R

=

0

.

1 aroundthe lep-ton.Thejetsatgeneratorlevelareclusteredfromstableparticles, excluding neutrinos,usingtheanti-kT clusteringalgorithmwitha

distanceparameterof0.4,andarerequiredtosatisfy pT

>

50 GeV

and

|

η

|

<

4

.

7. Jetswithin



R

<

0

.

4 of theselected charged lep-tonsarenotincluded.Theoverallsignalselectionefficiencywithin the fiducial region is about 40%. Electrons and muonsproduced in the decay of a

τ

lepton are not included in the definition of the fiducialregion. Nonfiducial signal events,i.e.,events selected atthereconstructed levelthat donotsatisfy thefiducial require-ments, are scaled together with the fiducial signal events in the simultaneousfit.Therelativecontributionofthenonfiducialevents isapproximately20%. Thenonfiducialevents aretreatedas back-groundprocesses.

The fit results for the W±_LW_L± andW±_XW±_T cross sections are shown in Fig. 5 as scans of the negative profile log-likelihood,

−

2



ln

L

,asafunctionoftheW±_LW±_L crosssection.Theexpected distributions include the contribution from the W±_XW±_T process. The corresponding observed (expected)upperlimit at 95% confi-dence level(CL) is 1.17(0.88) fb. The fiducialcross section mea-surementsfortheW±_LW±_L andW±_XW±_T processesandthe theoret-icalpredictionsare showninTable6.Themeasuredcrosssection valuesagreewiththetheoreticalpredictionswithinuncertainties.

The fiducial cross section measurements for the W±_LW±_X and W±_TW±_T processes are extractedfrom a separate fitincluding the corresponding signal BDT. The measurements and thetheoretical predictions are summarized in Table 6. The significance of the measured W±_LW±_X yield is quantified using background-only

hy-Table 7

MeasuredfiducialcrosssectionsfortheW±LWL±andW±XW±T processes,andforthe W±LW±X and W±TW±T processesfor thehelicityeigenstatesdefinedinthe parton-partoncenter-of-massframe.Thecombinationofthestatisticalandsystematic un-certaintiesisshown.ThetheoreticalpredictionsincludingtheO(αSα6)andO(α7) correctionstothe MadGraph5_amc@nlo LOcrosssections,asdescribedinthetext, arealsoshown.Thetheoreticaluncertaintiesincludestatistical,PDF,andLOscale uncertainties;BisthebranchingfractionforWW

→ ν

ν[55].

Process σB(fb) Theoretical prediction (fb) W±LW±L 0.24+ 0.40 −0.37 0.28±0.03 W±XW±T 3.25+ 0.50 −0.48 3.32±0.37 W±_LW±_X 1.40+0.60 −0.57 1.71±0.19 W±TW±T 2.03+ 0.51 −0.50 1.89±0.21

pothesis,i.e., assumingno contributionfromtheW±_LW±_X process, underthe asymptoticapproximation [67] and corresponds to 2.3 standarddeviations.Theexpectedsignificanceisevaluatedwithan Asimovdataset [67] andcorrespondsto3.1standarddeviations.

The measurements are also performed for the polarized ob-servablesdefinedusingthe helicityeigenstatesintheinitial state parton-parton center-of-mass reference frame. Defining the po-larization vectors in the parton-parton center-of-mass reference framechangestherespectivecontributionsofW±_LW±_L,W±_LW±_X and W±_XW±_T, and the distributions of the input observables sensitive to thepolarization [68].The fiducial cross section measurements and the theoretical predictions are summarized in Table 7. The observed (expected) 95% CL upper limit of the production cross sectionis1.06(0.85) fb fortheW±_LW±_L process.Theobserved (ex-pected) significance of the W±_LW±_X process is 2.6 (2.9) standard deviations.

9. Summary

Thefirstmeasurements ofproductioncrosssectionsfor polar-ized same-sign W±W± boson pairs are reported. The measure-ments are based on a sample of proton-proton collisions at a center-of-massenergyof13 TeV collected bytheCMSdetectorat the LHC, corresponding to an integratedluminosity of 137 fb−1. Events are selected by requiring exactly two same-sign leptons (electrons or muons), moderate missing transverse momentum, and two jets with a large rapidity separation and a high dijet mass. Boosted decision trees are used to separate between the polarizedscattering processesby exploitingthe kinematic differ-ences.Anobserved(expected)95%confidencelevelupperlimiton theproductioncrosssectionforlongitudinallypolarizedsame-sign W±W± bosonpairs of1.17(0.88) fb isreportedwiththehelicity eigenstatesdefinedintheW±W±center-of-massreferenceframe. The electroweakproduction ofthe W±W± boson pairs where at leastone ofthe W bosonsislongitudinallypolarizedismeasured withanobserved(expected)significanceof2.3(3.1)standard devi-ations.Results arealsoreportedwiththepolarizationsdefinedin the parton-parton center-of-mass reference frame. The measured crosssectionvaluesagreewiththestandardmodelpredictions.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort.

Inaddition,wegratefullyacknowledgethecomputingcentersand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructure essentialto ouranalyses. Finally, we acknowledge the enduring support for the construc-tion andoperation oftheLHC andtheCMSdetectorprovided by the followingfundingagencies:BMBWF andFWF(Austria); FNRS and FWO (Belgium); CNPq, CAPES,FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (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);MOE andUM(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,andNRCKI (Rus-sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter,IPST,STAR, andNSTDA(Thailand);TÜBITAK andTAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOEand NSF (USA).

Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract Nos.675440, 752730,and765710 (EuropeanUnion);the Leventis Foundation; the AlfredP. Sloan Foundation;the Alexan-der vonHumboldt Foundation;theBelgianFederalScience Policy Office; the Fonds pour la Formation à la Recherche dans l’In-dustrieetdans l’Agriculture (FRIA-Belgium);the Agentschapvoor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S. - FNRS and FWO (Belgium) under the “Excellence of Sci-ence – EOS” – be.h project n. 30820817; the Beijing Municipal ScienceandTechnology Commission,No.Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic;theDeutscheForschungsgemeinschaft(DFG)under Ger-many’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sci-ences, the New National Excellence Program ÚNKP, the NK-FIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the Council of Science andIndustrial Research,India;theHOMING PLUSprogram ofthe Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of 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;theNationalPriorities Re-search Programby QatarNationalResearch Fund;theMinistryof ScienceandHigher Education,projectno.02.a03.21.0005(Russia); the Tomsk Polytechnic University Competitiveness Enhancement Program; the Programa Estatal de Fomento de la Investigación Científica yTécnica de Excelencia Maríade Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalisand Aristeia programs cofinanced by EU-ESF andtheGreek NSRF;theRachadapisekSompot Fundfor Postdoc-toralFellowship, ChulalongkornUniversity andthe Chulalongkorn AcademicintoIts2ndCenturyProject AdvancementProject (Thai-land);theKavliFoundation;theNvidiaCorporation;the SuperMi-cro Corporation;the WelchFoundation, contractC-1845; andthe WestonHavensFoundation(USA).

References

[1] B.W.Lee,C.Quigg,H.B.Thacker,Thestrengthofweakinteractionsatvery high-energiesand theHiggsboson mass,Phys. Rev.Lett.38(1977)883,https:// doi.org/10.1103/PhysRevLett.38.883.

[2] B.W.Lee,C.Quigg,H.B.Thacker,Weakinteractionsatveryhigh-energies:the roleoftheHiggsbosonmass,Phys.Rev.D16(1977)1519,https://doi.org/10. 1103/PhysRevD.16.1519.

[3] ATLASCollaboration,Observationofanewparticleinthesearchforthe stan-dardmodelHiggsbosonwiththeATLASdetectorattheLHC,Phys.Lett.B716 (2012)1,https://doi.org/10.1016/j.physletb.2012.08.020,arXiv:1207.7214. [4] CMSCollaboration,Observationofanewbosonat amassof125GeVwith

theCMSexperimentattheLHC,Phys.Lett.B716(2012)30,https://doi.org/10. 1016/j.physletb.2012.08.021,arXiv:1207.7235.

[5] CMSCollaboration,Observationofanewbosonwith massnear125GeVin ppcollisionsat√s =7and8TeV,J.HighEnergyPhys.06(2013)081,https:// doi.org/10.1007/JHEP06(2013)081,arXiv:1303.4571.

[6] D.Espriu,B.Yencho,LongitudinalWWscatteringinlightoftheHiggsboson discovery,Phys.Rev.D87(2013)055017,https://doi.org/10.1103/PhysRevD.87. 055017,arXiv:1212.4158.

[7] J.Chang,K.Cheung, C.-T.Lu,T.-C.Yuan,WWscatteringintheeraof post-Higgs-bosondiscovery,Phys.Rev.D87(2013)093005,https://doi.org/10.1103/ PhysRevD.87.093005,arXiv:1303.6335.

[8] G.Aad,etal.,ATLAS,CMS,MeasurementsoftheHiggsbosonproductionand decayratesandconstraintsonitscouplingsfromacombinedATLASandCMS analysisoftheLHCppcollisiondataat√s=7 and8TeV,J.HighEnergyPhys. 08(2016)045,https://doi.org/10.1007/JHEP08(2016)045,arXiv:1606.02266. [9] CMSCollaboration,MeasurementsofpropertiesoftheHiggsbosondecayingto

aWbosonpairinppcollisionsat√s=13TeV,Phys.Lett.B791(2019)96,

https://doi.org/10.1016/j.physletb.2018.12.073,arXiv:1806.05246.

[10] S.Brass,C.Fleper,W.Kilian,J.Reuter,M.Sekulla,TransversalmodesandHiggs bosonsinelectroweakvector-bosonscatteringat theLHC,Eur.Phys.J.C78 (2018)931,https://doi.org/10.1140/epjc/s10052-018-6398-4,arXiv:1807.02512. [11] ATLASCollaboration,EvidenceforelectroweakproductionofW±W±jjinpp collisionsat√s=8 TeVwiththeATLASdetector,Phys.Rev.Lett.113(2014) 141803,https://doi.org/10.1103/PhysRevLett.113.141803,arXiv:1405.6241. [12] CMSCollaboration,Studyofvectorbosonscatteringandsearchfornewphysics

ineventswithtwosame-signleptonsandtwojets,Phys.Rev.Lett.114(2015) 051801,https://doi.org/10.1103/PhysRevLett.114.051801,arXiv:1410.6315. [13] CMS Collaboration, Observation ofelectroweak production of same-signW

boson pairsinthetwojet andtwosame-sign leptonfinalstatein proton-protoncollisionsat√s=13TeV,Phys.Rev.Lett.120(2018)081801,https:// doi.org/10.1103/PhysRevLett.120.081801,arXiv:1709.05822.

[14] ATLASCollaboration,Observationofelectroweakproductionofasame-signW

bosonpairinassociationwithtwojetsinppcollisionsat√s=13 TeVwith theATLASdetector,Phys.Rev.Lett.123(2019)161801,https://doi.org/10.1103/ PhysRevLett.123.161801,arXiv:1906.03203.

[15] CMS Collaboration, Measurements ofproduction cross sectionsof WZ and same-signWWbosonpairsinassociationwithtwojetsinproton-proton colli-sionsat√s=13TeV,Phys.Lett.B809(2020)135710,https://doi.org/10.1016/ j.physletb.2020.135710,arXiv:2005.01173.

[16] CMSCollaboration,CMSluminositymeasurementforthe2016data-taking pe-riod,CMSPhysicsAnalysisSummaryCMS-PAS-LUM-17-001,https://cds.cern.ch/ record/2138682,2017.

[17] CMSCollaboration,CMSluminositymeasurementforthe2017data-taking pe-riodat√s=13 TeV,CMSPhysicsAnalysisSummaryCMS-PAS-LUM-17-004,

https://cds.cern.ch/record/2621960,2017.

[18] CMSCollaboration,CMSluminositymeasurementforthe2018data-taking pe-riodat√s=13 TeV,CMSPhysicsAnalysisSummaryCMS-PAS-LUM-18-002,

https://cds.cern.ch/record/2676164,2018.

[19] CMSCollaboration,TheCMSexperimentattheCERNLHC,J.Instrum.3(2008) S08004,https://doi.org/10.1088/1748-0221/3/08/S08004.

[20] CMS Collaboration, TheCMS trigger system, J. Instrum. 12(2017) P01020,

https://doi.org/10.1088/1748-0221/12/01/P01020,arXiv:1609.02366. [21] S.Agostinelli,et al., Geant4,Geant4 —asimulationtoolkit, Nucl.Instrum.

MethodsA506(2003)250,https://doi.org/10.1016/S0168-9002(03)01368-8. [22] R.Frederix, S. Frixione, Mergingmeets matching inMC@NLO, J. High

En-ergyPhys.12(2012)061,https://doi.org/10.1007/JHEP12(2012)061,arXiv:1209. 6215.

[23] J.Alwall, R. Frederix,S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.S. Shao, T. Stelzer,P. Torrielli, M. Zaro, The automated computation of tree-levelandnext-to-leadingorderdifferentialcrosssections,andtheirmatching toparton shower simulations,J.High EnergyPhys. 07 (2014)079,https:// doi.org/10.1007/JHEP07(2014)079,arXiv:1405.0301.

[24] D.BuarqueFranzosi,O.Mattelaer,R.Ruiz,S.Shil,Automatedpredictionsfrom polarizedmatrixelements,J.HighEnergyPhys.04(2020)082,https://doi.org/ 10.1007/JHEP04(2020)082,arXiv:1912.01725.

[25] R.D.Ball,etal.,NNPDF,Partondistributionsfromhigh-precisioncolliderdata, Eur.Phys.J.C77(2017)663,https://doi.org/10.1140/epjc/s10052-017-5199-5, arXiv:1706.00428.

[26] A.Ballestrero,A.Belhouari,G.Bevilacqua,V.Kashkan,E.Maina,PHANTOM:a MonteCarloeventgeneratorforsixpartonfinalstatesathighenergycolliders, Comput.Phys.Commun.180(2009)401,https://doi.org/10.1016/j.cpc.2008.10. 005,arXiv:0801.3359.

[27] A. Ballestrero,D. BuarqueFranzosi,L. Oggero,E.Maina,Vectorboson scat-teringatthe LHC:countingexperimentsforunitarizedmodelsinafullsix fermionapproach,J.HighEnergyPhys.03(2012)031,https://doi.org/10.1007/ JHEP03(2012)031,arXiv:1112.1171.

[28] A.Ballestrero, E.Maina,G.Pelliccioli, W bosonpolarizationinvectorboson scatteringattheLHC,J.HighEnergyPhys.03(2018)170,https://doi.org/10. 1007/JHEP03(2018)170,arXiv:1710.09339.

[29] B. Biedermann,A.Denner, M.Pellen, Largeelectroweak correctionsto vec-torbosonscatteringattheLargeHadronCollider,Phys.Rev.Lett.118(2017) 261801,https://doi.org/10.1103/PhysRevLett.118.261801,arXiv:1611.02951. [30] B.Biedermann,A.Denner,M.Pellen,CompleteNLOcorrectionstoW+W+

scat-teringanditsirreduciblebackgroundattheLHC,J.HighEnergyPhys.10(2017) 124,https://doi.org/10.1007/JHEP10(2017)124,arXiv:1708.00268.

[31] A.Denner,S.Pozzorini,Oneloopleadinglogarithmsinelectroweakradiative corrections.1.Results,Eur.Phys.J.C18(2001)461,https://doi.org/10.1007/ s100520100551,arXiv:hep-ph/0010201.

[32] J.Alwall,S.Höche,F.Krauss,N.Lavesson,L.Lönnblad,F.Maltoni,M.L.Mangano, M.Moretti,C.G.Papadopoulos,F.Piccinini,S.Schumann,M.Treccani,J.Winter, M.Worek,Comparativestudyofvariousalgorithmsforthemergingofparton showersandmatrixelementsinhadroniccollisions,Eur.Phys.J.C53(2008) 473,https://doi.org/10.1140/epjc/s10052-007-0490-5,arXiv:0706.2569. [33] S.Frixione,B.R.Webber,MatchingNLOQCDcomputationsandpartonshower

simulations,J.HighEnergyPhys.06(2002)029,https://doi.org/10.1088/1126 -6708/2002/06/029,arXiv:hep-ph/0204244.

[34] P.Nason,A newmethodforcombiningNLOQCD withshowerMonteCarlo algorithms,J.HighEnergyPhys.11(2004)040,https://doi.org/10.1088/1126 -6708/2004/11/040,arXiv:hep-ph/0409146.

[35] S.Frixione,P.Nason,C.Oleari,MatchingNLOQCDcomputationswithparton showersimulations:thePOWHEGmethod,J.HighEnergyPhys.11(2007)070,

https://doi.org/10.1088/1126-6708/2007/11/070,arXiv:0709.2092.

[36] S.Alioli,P.Nason,C.Oleari,E.Re,NLOvector-bosonproductionmatchedwith showerinPOWHEG,J. HighEnergy Phys.07(2008) 060,https://doi.org/10. 1088/1126-6708/2008/07/060,arXiv:0805.4802.

[37] S.Alioli, P. Nason, C.Oleari,E. Re,A general framework for implementing NLOcalculationsinshowerMonteCarloprograms:thePOWHEGBOX,J.High EnergyPhys. 06(2010)043,https://doi.org/10.1007/JHEP06(2010)043,arXiv: 1002.2581.

[38] CMSCollaboration,Measurementoftheassociatedproductionofasingletop quarkandaZbosoninppcollisionsat√s=13 TeV,Phys.Lett.B779(2018) 358,https://doi.org/10.1016/j.physletb.2018.02.025,arXiv:1712.02825. [39] T. Sjöstrand,S.Ask,J.R. Christiansen,R.Corke,N.Desai,P.Ilten,S.Mrenna,

S.Prestel,C.O.Rasmussen,P.Z.Skands,AnintroductiontoPYTHIA8.2, Com-put.Phys.Commun.191(2015)159,https://doi.org/10.1016/j.cpc.2015.01.024, arXiv:1410.3012.

[40] R.D. Ball, et al., NNPDF, Parton distributions for the LHC Run II, J. High EnergyPhys. 04(2015)040,https://doi.org/10.1007/JHEP04(2015)040,arXiv: 1410.8849.

[41] P. Skands, S.Carrazza, J. Rojo,Tuning PYTHIA 8.1:the Monash 2013tune, Eur.Phys.J.C74(2014)3024,https://doi.org/10.1140/epjc/s10052-014-3024-y, arXiv:1404.5630.

[42] CMSCollaboration,Eventgeneratortunesobtainedfromunderlyingeventand multipartonscatteringmeasurements,Eur.Phys.J.C76(2016)155,https:// doi.org/10.1140/epjc/s10052-016-3988-x,arXiv:1512.00815.

[43] CMSCollaboration, ExtractionandvalidationofanewsetofCMSPYTHIA8 tunesfromunderlying-eventmeasurements,Eur.Phys.J.C80(2020)4,https:// doi.org/10.1140/epjc/s10052-019-7499-4,arXiv:1903.12179.

[44] CMSCollaboration, Particle-flowreconstruction andglobalevent description withtheCMSdetector,J.Instrum.12(2017)P10003,https://doi.org/10.1088/ 1748-0221/12/10/P10003,arXiv:1706.04965.

[45] M.Cacciari,G.P.Salam,G.Soyez,Theanti-kTjetclusteringalgorithm,J.High EnergyPhys. 04 (2008)063,https://doi.org/10.1088/1126-6708/2008/04/063, arXiv:0802.1189.

[46] M.Cacciari,G.P.Salam,G.Soyez,FastJetusermanual,Eur.Phys.J.C72(2012) 1896,https://doi.org/10.1140/epjc/s10052-012-1896-2,arXiv:1111.6097. [47] CMSCollaboration,JetenergyscaleandresolutionintheCMSexperimentin

ppcollisionsat8TeV,J.Instrum.12(2017)P02014,https://doi.org/10.1088/ 1748-0221/12/02/P02014,arXiv:1607.03663.

[48] CMSCollaboration,Pileupmitigationat CMSin13TeVdata, J.Instrum. 15 (2020) P09018, https://doi.org/10.1088/1748-0221/15/09/P09018, arXiv:2003. 00503.

[49] CMSCollaboration,Performanceofmissingtransversemomentum reconstruc-tioninproton-protoncollisions at √s=13 TeV usingthe CMSdetector,J. Instrum.14 (2019)P07004,https://doi.org/10.1088/1748-0221/14/07/P07004, arXiv:1903.06078.

[50] CMSCollaboration,Performanceofelectronreconstructionandselectionwith the CMSdetectorinproton-protoncollisionsat √s=8 TeV,J. Instrum.10 (2015) P06005, https://doi.org/10.1088/1748-0221/10/06/P06005, arXiv:1502. 02701.

[51] CMSCollaboration, Electron and photon performance inCMSwith the full 2017datasampleandadditional2016highlightsfortheCALOR2018 Confer-ence,CMSDetectorPerformanceSummaryCMS-DP-2018-017,https://cds.cern. ch/record/2320638,2018.

[52] CMSCollaboration,PerformanceoftheCMSmuondetectorandmuon recon-structionwithproton-protoncollisionsat√s=13 TeV,J.Instrum.13(2018) P06015,https://doi.org/10.1088/1748-0221/13/06/P06015,arXiv:1804.04528. [53] CMSCollaboration, PerformanceofCMSmuonreconstructionincosmic-ray

events,J.Instrum. 5(2010)T03022,https://doi.org/10.1088/1748-0221/5/03/ T03022,arXiv:0911.4994.

[54] CMS Collaboration, Performanceof the reconstruction and identification of high-momentum muons in proton-proton collisions at √s= 13 TeV, J. Instrum. 15(2020) P02027,https://doi.org/10.1088/1748-0221/15/02/P02027, arXiv:1912.03516.

[55] ParticleDataGroup,P.A. Zyla,etal.,Reviewofparticlephysics,Prog.Theor. Exp.Phys.2020(2020)083C01,https://doi.org/10.1093/ptep/ptaa104. [56] D.L.Rainwater,R.Szalapski,D.Zeppenfeld,ProbingcolorsingletexchangeinZ

+2-jeteventsattheCERNLHC,Phys.Rev.D54(1996)6680,https://doi.org/ 10.1103/PhysRevD.54.6680,arXiv:hep-ph/9605444.

[57] CMSCollaboration,Identificationofheavy-flavourjetswiththeCMSdetectorin ppcollisionsat13TeV,J.Instrum.13(2018)P05011,https://doi.org/10.1088/ 1748-0221/13/05/P05011,arXiv:1712.07158.

[58] K.Doroba,J.Kalinowski,J.Kuczmarski, S.Pokorski,J. Rosiek,M.Szleper,S. Tkaczyk,TheWLWLscatteringat theLHC:improving theselection criteria, Phys. Rev.D 86(2012) 036011, https://doi.org/10.1103/PhysRevD.86.036011, arXiv:1201.2768.

[59]H. Voss,A.Höcker,J.Stelzer,F.Tegenfeldt,TMVA,the toolkitfor multivari-ate dataanalysiswith ROOT, in:XIthInternational Workshopon Advanced ComputingandAnalysisTechniquesinPhysicsResearch(ACAT),2007,p. 40, arXiv:physics/0703039 [PoS(ACAT)040].

[60] F.Chollet,etal.,Keras,https://keras.io,2015.

[61] M.Abadi, et al.,Tensorflow:large-scalemachinelearning onheterogeneous distributedsystems,http://tensorflow.org/,2016,softwareavailablefrom ten-sorflow.org.

[62] ATLASCollaboration,Measurementoftheinelasticproton-protoncrosssection at√s=13 TeVwiththeATLASdetectorattheLHC,Phys.Rev.Lett.117(2016) 182002,https://doi.org/10.1103/PhysRevLett.117.182002,arXiv:1606.02625. [63] CMSCollaboration,Measurementoftheinelasticproton-protoncrosssection

at√s=13 TeV,J.HighEnergyPhys.07(2018)161,https://doi.org/10.1007/ JHEP07(2018)161,arXiv:1802.02613.

[64] J.Butterworth,S.Carrazza,A.Cooper-Sarkar,A.DeRoeck,J.Feltesse,J.Forte, StefanoGao,S.Glazov,J.Huston,Z.Kassabov,PDF4LHCrecommendationsfor LHCRunII,J.Phys.G43(2016)023001,https://doi.org/10.1088/0954-3899/43/ 2/023001,arXiv:1510.03865.

[65] T.Junk,Confidencelevelcomputationforcombiningsearcheswithsmall statis-tics,Nucl.Instrum.MethodsA434(1999)435,https://doi.org/10.1016/S0168 -9002(99)00498-2,arXiv:hep-ex/9902006.

[66] A.L.Read,Presentationofsearchresults:theC Lstechnique,J.Phys.G28(2002)

2693,https://doi.org/10.1088/0954-3899/28/10/313.

[67] G.Cowan,K.Cranmer,E.Gross,O.Vitells,Asymptoticformulaefor likelihood-based tests of new physics, Eur. Phys. J. C 71 (2011) 1554, https://doi. org/10.1140/epjc/s10052-011-1554-0,arXiv:1007.1727,https://doi.org/10.1140/ epjc/s10052-013-2501-z(Erratum).

[68] A.Ballestrero,E.Maina,G.Pelliccioli,Differentpolarizationdefinitionsin same-signW W scatteringattheLHC,Phys.Lett.B810(2020)135856,https://doi. org/10.1016/j.physletb.2020.135856,arXiv:2007.07133.

TheCMSCollaboration

A.M. Sirunyan

†

,

A. Tumasyan

YerevanPhysicsInstitute,Yerevan,Armenia

W. Adam,

T. Bergauer,

M. Dragicevic,

J. Erö,

A. Escalante Del Valle,

R. Frühwirth

1

,

M. Jeitler

1

,

N. Krammer,

L. Lechner,

D. Liko,

I. Mikulec,

F.M. Pitters,

N. Rad,

J. Schieck

1

,

R. Schöfbeck,

M. Spanring,

S. Templ,

W. Waltenberger,

C.-E. Wulz

1

,

M. Zarucki

InstitutfürHochenergiephysik,Wien,Austria

V. Chekhovsky,

A. Litomin,

V. Makarenko,

J. Suarez Gonzalez

InstituteforNuclearProblems,Minsk,Belarus

M.R. Darwish

2

,

E.A. De Wolf,

D. Di Croce,

X. Janssen,

T. Kello

3

,

A. Lelek,

M. Pieters,

H. Rejeb Sfar,

H. Van Haevermaet,

P. Van Mechelen,

S. Van Putte,

N. Van Remortel

UniversiteitAntwerpen,Antwerpen,Belgium

F. Blekman,

E.S. Bols,

S.S. Chhibra,

J. D’Hondt,

J. De Clercq,

D. Lontkovskyi,

S. Lowette,

I. Marchesini,

S. Moortgat,

A. Morton,

Q. Python,

S. Tavernier,

W. Van Doninck,

P. Van Mulders

VrijeUniversiteitBrussel,Brussel,Belgium

D. Beghin,

B. Bilin,

B. Clerbaux,

G. De Lentdecker,

B. Dorney,

L. Favart,

A. Grebenyuk,

A.K. Kalsi,

I. Makarenko,

L. Moureaux,

L. Pétré,

A. Popov,

N. Postiau,

E. Starling,

L. Thomas,

C. Vander Velde,

P. Vanlaer,

D. Vannerom,

L. Wezenbeek

UniversitéLibredeBruxelles,Bruxelles,Belgium

T. Cornelis,

D. Dobur,

M. Gruchala,

I. Khvastunov

4

,

M. Niedziela,

C. Roskas,

K. Skovpen,

M. Tytgat,

W. Verbeke,

B. Vermassen,

M. Vit

GhentUniversity,Ghent,Belgium

G. Bruno,

F. Bury,

C. Caputo,

P. David,

C. Delaere,

M. Delcourt,

I.S. Donertas,

A. Giammanco,

V. Lemaitre,

K. Mondal,

J. Prisciandaro,

A. Taliercio,

M. Teklishyn,

P. Vischia,

S. Wertz,

S. Wuyckens

UniversitéCatholiquedeLouvain,Louvain-la-Neuve,Belgium

G.A. Alves,

C. Hensel,

A. Moraes

CentroBrasileirodePesquisasFisicas,RiodeJaneiro,Brazil

W.L. Aldá Júnior,

E. Belchior Batista Das Chagas,

H. Brandao Malbouisson,

W. Carvalho,

J. Chinellato

5

,

E. Coelho,

E.M. Da Costa,

G.G. Da Silveira

6

,

D. De Jesus Damiao,

S. Fonseca De Souza,

J. Martins

7

,

D. Matos Figueiredo,

M. Medina Jaime

8

,

C. Mora Herrera,

L. Mundim,

H. Nogima,

P. Rebello Teles,

L.J. Sanchez Rosas,

A. Santoro,

S.M. Silva Do Amaral,

A. Sznajder,

M. Thiel,

F. Torres Da Silva De Araujo,

A. Vilela Pereira

UniversidadedoEstadodoRiodeJaneiro,RiodeJaneiro,Brazil

C.A. Bernardes

a

,

L. Calligaris

a

,

T.R. Fernandez Perez Tomei

a

,

E.M. Gregores

a

,

b

,

D.S. Lemos

a

,

P.G. Mercadante

a

,

b

,

S.F. Novaes

a

,

Sandra S. Padula

a

a_{UniversidadeEstadualPaulista,SãoPaulo,Brazil} b_{UniversidadeFederaldoABC,SãoPaulo,Brazil}

A. Aleksandrov,

G. Antchev,

I. Atanasov,

R. Hadjiiska,

P. Iaydjiev,

M. Misheva,

M. Rodozov,

M. Shopova,

G. Sultanov

InstituteforNuclearResearchandNuclearEnergy,BulgarianAcademyofSciences,Sofia,Bulgaria

A. Dimitrov,

T. Ivanov,

L. Litov,

B. Pavlov,

P. Petkov,

A. Petrov

UniversityofSofia,Sofia,Bulgaria

BeihangUniversity,Beijing,China

M. Ahmad,

G. Bauer,

Z. Hu,

Y. Wang,

K. Yi

9

,

10 DepartmentofPhysics,TsinghuaUniversity,Beijing,China

E. Chapon,

G.M. Chen

11

,

H.S. Chen

11

,

M. Chen,

T. Javaid

11

,

A. Kapoor,

D. Leggat,

H. Liao,

Z.-A. Liu

11

,

R. Sharma,

A. Spiezia,

J. Tao,

J. Thomas-wilsker,

J. Wang,

H. Zhang,

S. Zhang

11

,

J. Zhao

InstituteofHighEnergyPhysics,Beijing,China

A. Agapitos,

Y. Ban,

C. Chen,

Q. Huang,

A. Levin,

Q. Li,

M. Lu,

X. Lyu,

Y. Mao,

S.J. Qian,

D. Wang,

Q. Wang,

J. Xiao

StateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing,China

Z. You

SunYat-SenUniversity,Guangzhou,China

X. Gao

3

InstituteofModernPhysicsandKeyLaboratoryofNuclearPhysicsandIon-beamApplication(MOE)–FudanUniversity,Shanghai,China

M. Xiao

ZhejiangUniversity,Hangzhou,China

C. Avila,

A. Cabrera,

C. Florez,

J. Fraga,

A. Sarkar,

M.A. Segura Delgado

UniversidaddeLosAndes,Bogota,Colombia

J. Jaramillo,

J. Mejia Guisao,

F. Ramirez,

J.D. Ruiz Alvarez,

C.A. Salazar González,

N. Vanegas Arbelaez

UniversidaddeAntioquia,Medellin,Colombia

D. Giljanovic,

N. Godinovic,

D. Lelas,

I. Puljak

UniversityofSplit,FacultyofElectricalEngineering,MechanicalEngineeringandNavalArchitecture,Split,Croatia

Z. Antunovic,

M. Kovac,

T. Sculac

UniversityofSplit,FacultyofScience,Split,Croatia

V. Brigljevic,

D. Ferencek,

D. Majumder,

M. Roguljic,

A. Starodumov

12

,

T. Susa

InstituteRudjerBoskovic,Zagreb,Croatia

M.W. Ather,

A. Attikis,

E. Erodotou,

A. Ioannou,

G. Kole,

M. Kolosova,

S. Konstantinou,

J. Mousa,

C. Nicolaou,

F. Ptochos,

P.A. Razis,

H. Rykaczewski,

H. Saka,

D. Tsiakkouri

UniversityofCyprus,Nicosia,Cyprus

M. Finger

13

,

M. Finger Jr.

13

,

A. Kveton,

J. Tomsa

CharlesUniversity,Prague,CzechRepublic

E. Ayala

EscuelaPolitecnicaNacional,Quito,Ecuador

E. Carrera Jarrin

UniversidadSanFranciscodeQuito,Quito,Ecuador

S. Abu Zeid

14

,

S. Khalil

15

,

E. Salama

16

,

14