Observation of photon-induced W+ W- production in pp collisions at √s=13 TeV using the ATLAS detector

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Observation

of

photon-induced

W

+

W

−

production

in

pp collisions

at

√

s

=

13 TeV

using

the

ATLAS

detector

.

The

ATLAS

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received9October2020

Receivedinrevisedform1March2021 Accepted2March2021

Availableonline4March2021 Editor:M.Doser

Thisletterreportsthe observationofphoton-inducedproductionof W -boson pairs,

γ γ

→W W . The analysis uses 139 fb−1 _{of LHC proton–proton collision data taken at} √_{s=13 TeV recorded by the}

ATLASexperimentduringthe years2015–2018.The measurementisperformedselectingone electron andonemuon,correspondingtothedecayofthedibosonsystemas W W→e±

νμ

∓

ν

finalstate.The background-onlyhypothesisisrejectedwithasignificanceofwellabove5standarddeviationsconsistent with the expectation from Monte Carlo simulation. A cross section for the

γ γ

→W W process of 3.13±0.31(stat.)±0.28(syst.) fbismeasuredinafiducialvolumeclosetotheacceptanceofthedetector, byrequiringan electronand amuonofoppositesignswithlargedilepton transversemomentumand exactly zero additional charged particles.This isfound to bein agreementwith the Standard Model prediction.

©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

Contents

1. Introduction . . . 1

2. ATLASdetector . . . 2

3. Dataandsimulatedeventsamples . . . 2

4. Eventreconstructionandselection . . . 3

5. Modellingofsignalandbackgrounds . . . 4

5.1. Modellingofadditional

pp interactions . . . .

4

5.2. Modellingoftheunderlyingevent . . . 5

5.3. Signalmodelling . . . 6

6. Eventcategoriesandbackgroundestimation . . . 7

7. Systematicuncertainties . . . 7

8. Results . . . 8

9. Conclusion . . . 10

Declarationofcompetinginterest . . . 10

Acknowledgements . . . 11

References . . . 11

TheATLASCollaboration . . . 12

1. Introduction

Thestudy of W -bosonpairproductionfromtheinteractionof incoming photons(

γ γ

→

W W ) inproton–proton(pp) collisions offers a unique window toa wide rangeof physicalphenomena. In the Standard Model (SM), the

γ γ

→

W W process proceeds

 _{E-mailaddress:atlas.publications@cern.ch.}

through trilinear and quartic gauge-boson interactions. This pro-cessisunique inthat, atleading order,it onlyinvolves diagrams with self-couplings of the electroweak gauge bosons, as shown in Fig. 1. Hence, a cross-section measurement directly tests the SU(2)

×

U(1)gaugestructureoftheSM.Atthesametime,asa pro-cessdrivenonlybyelectroweakbosonself-interactions,itis sensi-tive to anomalous gauge-boson interactions [1] as parameterised in effective field theory (EFT) with additional dimension-6 and dimension-8operators [2,3].Thus, cross-section measurementsof

https://doi.org/10.1016/j.physletb.2021.136190

0370-2693/©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Theleading-orderFeynmandiagramscontributingtotheγ γ→W W processarethet-channeldiagram(left)proceedingviatheexchangeofaW bosonbetweentwo

γW W verticesandadiagramwithaquarticγ γW W coupling(right).Inaddition,au-channeldiagramexists(notshown),whichalsoproceedsviatwoγW W vertices.

γ γ

→

W W caninfutureprovidevaluableinputfortheglobalEFT fits.

ThisletterpresentsameasurementintheW+W−

→

e±

νμ

∓

ν

channel that results in the observation of photon-induced W W production. Previously, the ATLAS and CMS Collaborations found onlyevidencefor

γ γ

→

W W productionwiththeRun-1data, AT-LASby using8 TeV pp collisions [4] andCMSby combiningtheir 7 TeV and8 TeV pp collisiondata [5,6].

The signal process proceeds through the pp

(

γ γ

)

→

p(∗)_W+_W−_p(∗) _{reaction,where p}(∗) _{indicates that thefinal-state}

proton either stays intact or fragments after emitting a photon. Whilsttheformeroccursthrough acoherentphotonradiationoff thewholeprotonwithoutdisintegration,forthelatteratleastone of the photons can be considered as being radiated off a par-ton in the proton. These contributions are classified as elastic, single-dissociative, anddouble-dissociative W W production. Elas-tic

γ γ

→

W W productionwithleptonicdecaysoftheW bosons resultsinafinalstate containingtwo chargedleptons andno ad-ditional charged-particle activity. Evenin the caseof dissociative photon-inducedproduction,thechargedparticlesfromtheproton remnants often falloutside theacceptance ofthe tracking detec-tor.

The suppressed activity in the central region of the detector in the

γ γ

→

W W signalgives the meansto control and signif-icantly reduce background from quark- and gluon-induced W W productionortop-quarkproductionwheretheleptonic finalstate is typically producedin association witha substantialamount of hadronic activity. The analysistherefore selects events that have no additionalcharged-particletracks reconstructedinthevicinity of the selectedinteraction vertex. The modelling ofthe hadronic activity in quark- and gluon-induced processes, as well as un-correlated activity fromadditional pp interactions, is constrained usingsame-flavouree and

μμ

Drell–Yan,DY(

→

ee

/

μμ

),eventsin data,reducingtheassociateduncertaintiesbyasignificantamount. Backgroundfromotherphoton-inducedprocesses,mainlydilepton production

γ γ

→ 

,isreducedbyselectingonlydifferent-flavour lepton pairs, e

μ

, leaving a smaller contribution from

γ γ

→

τ τ

production with leptonic

τ

decays. Since the contribution from the

γ γ

→

τ τ

processfalls offrapidlywith increasing transverse momentum of the dilepton system, pe_Tμ, it can be further sup-pressed by placing requirements on pe_Tμ. A fiducial cross sec-tionforthe pp

(

γ γ

)

→

p(∗)_W+_W−_p(∗) _{processthroughthedecay}

channelW+W−

→

e±

νμ

∓

ν

ismeasuredinafittothenumberof eventsinseveralkinematicregionswithdifferentsignaland back-groundcontributions.

2. ATLAS detector

TheATLAS detector [7] attheLargeHadronCollider(LHC)isa multipurposedetectorwithaforward–backwardsymmetric

cylin-dricalgeometryandnearly4

π

coverageinsolidangle.1Itconsists ofaninner trackingdetectorsurroundedbya thin superconduct-ingsolenoidprovidinga 2 Taxialmagneticfield,electromagnetic andhadroncalorimeters,andamuonspectrometer.

The inner tracking detector (ID) covers the pseudorapidity range

|η|

<

2

.

5 andiscomposedofthree subdetectors.The high-granularity silicon pixel detector covers the vertex region and typicallyprovides four measurementsper track, the firsthit nor-mally beingin the insertable B-layer [8,9]. It is followed by the siliconmicrostriptracker(SCT),whichusuallyprovideseight mea-surements per charged-particle track. These silicon detectors are complemented by the transition radiation tracker,which enables radially extended track reconstruction up to

|

η

|

=

2

.

0 and pro-vides electron identification information. The resolution of the z-coordinate of tracks at the point of closest approach to the beam line is about 0

.

170 mm for tracks with pT

=

500 MeV

andimproveswithhigher trackmomentum [10]. Fortracks with pT

<

1 GeV,thedominantcontributionto the z-resolutionis due

tomultiplescattering.

Lead/liquid-argon(LAr) samplingcalorimeters provide electro-magnetic (EM) energy measurements with high granularity. A steel/scintillator-tile hadron calorimeter covers the central pseu-dorapidity range(

|

η

|

<

1

.

7).The endcap andforwardregions are instrumented with LAr calorimeters for EM and hadronic en-ergymeasurements upto

|η|

=

4

.

9.Themuon spectrometer(MS) surrounds the calorimeters and is based on three large air-core toroidalsuperconductingmagnetswitheightcoilseach.Themuon spectrometer includes a system of precision tracking chambers (

|η|

<

2

.

7)andfastdetectorsfortriggering(

|η|

<

2

.

4).Atwo-level triggersystem [11] selectstheeventsusedintheanalysis.

3. Data and simulated event samples

The analysis uses proton–proton collision data recorded with the ATLAS detector during the Run-2 data-taking period (2015– 2018)at

√

s

=

13 TeV with thenumber ofinteractions,

μ

int,per

bunchcrossing(alsoreferredtoaspile-up)rangingfromabout10 to60withanaverageof33.7 [12].

Thesizeoftheregionwherethecollisionsoccur, theso-called beam spot, is a result of the operating parameters of the LHC. Ofspecific importance forthis analysisis its width along the z-direction, which determines the density of pp interactions. The widthisdeterminedbyfittingthedistributionofthez positionsof thereconstructedverticestoGaussianfunctionsusinganunbinned

1 _{ATLASusesaright-handedcoordinatesystemwithitsoriginat thenominal}

interactionpointinthecentreofthedetectorandthez-axiscoincidingwiththe axisofthebeam pipe.The x-axispoints fromtheinteractionpoint tothe cen-treoftheLHCring,andthe y-axispointsupward.Thepseudorapidityisdefined intermsofthe polarangleθ asη= −ln tan(θ/2), and

φ

is theazimuthal an-glearoundthebeampipe relativetothe x-axis.Theangulardistanceisdefined as



R=(η)2_{+ (φ)}2_.

likelihood fit.Itvaried between30and50mmduring theRun-2 data-takingperiod [13].Thedatacorrespondtoanintegrated lumi-nosityof

L

=

139.0

±

2.4 fb−1 afterdataqualityrequirements [14] havebeenapplied.Thisvalueisderivedfromthecalibrationofthe luminosityscalewiththemethodexplainedinRef. [12],usingthe LUCID-2detector [15] fortheprimaryluminositymeasurement.

Signal andbackground processes were modelled using Monte Carlo (MC) event generators to study kinematic distributions, to evaluate background contamination in the signal region and to interpret the results.Tosimulate thedetector response,the gen-erated events were passed through a detailed simulation of the ATLAS detector [16] based on Geant_{4 [17] or on a combination} of Geant4 and a parameterised calorimeter simulation [18]. The present measurement relies only on tracking information from charged hadrons, muons and electrons, which is simulated by Geant4 in either case, as well as the modelling of the calori-metric response ofelectrons which can be reliably parametrized. Multiple pp interactionsoccurringinthesameoradjacentbunch crossingsare includedinthesimulation byoverlaying several in-elastic pp collisionsmatchingthe averagenumberofinteractions perbunchcrossing.Theinelasticpp collisionsweregeneratedwith Pythia _{8.186 [19] using a set oftuned parameters calledthe A3} tune [20] andtheNNPDF2.3LO [21] setofpartondistribution func-tions (PDF).AllMCsamplesare correctedtothebeamconditions ofthedataasdescribedinSection5.1.Inallsamplesusing Pythia8 or Herwig7 to simulate the parton showering, underlying event andhadronisation,thedecaysofbottomandcharmhadronswere performedwithEvtGen1.2.0 [22].

The elastic component ofthe

γ γ

→

W W signalprocess was modelled at leading order (LO) using Herwig 7.1.5 [23,24] in-terfaced with the BudnevQED photon flux [25] through ThePEG software [26]. This sample isused to model the photon-induced processes in thefiducial region of themeasurement as it uses a photonflux,whichisdifferentialinbothx andvirtuality Q2.Itis correctedtomatchthecrosssection,includingthedissociativeas wellasnon-perturbativecomponents,usingadata-drivenmethod describedinSection5.3.Thisdata-drivenapproachisvalidated us-ing elastic anddissociative

γ γ

→

W W samples produced using MG5_aMC@NLO 2.6.7 [27] interfacedto Pythia 8.243.Thedefault photon flux in MG5_aMC@NLO andthe CT14QED [28] PDFwere usedto modelthephoton radiationfromprotons andquarks, re-spectively. The parametrizeddetectorsimulation was usedin the generation ofthe MG5_aMC@NLO samples. Theyare used when-ever regions with reconstructed track multiplicities larger than zeroarestudied.

The production of

γ γ

→ 

, with



=

e

,

μ

,

τ

, was modelled in the same way as for the

γ γ

→

W W signal process. Ad-ditional generators were used to validate the modelling of the

γ γ

→ 

dissociative events. The single-dissociative processes weremodelledusing LPAIR 4.0 [29].Alternative

γ γ

→ 

double-dissociative samples were produced with Pythia 8.240 using the NNPDF3.1NLOluxQED PDF set [30]. Diffractive QCD-processes and

γ γ

→

4



production were produced using Pythia 8.244 and MG_{5_aMC@NLO 2.6.7interfacedto Pythia 8.243andstudiedusing} particle-levelinformationonly.Thecontributionoftheseprocesses was found to be negligible in the signal region of the measure-ment.

The dominant background from quark-induced W W produc-tion, also referred to as qq

→

W W , was modelled at next-to-leading-order (NLO) accuracy using the Powheg-Box v2 [31–35] generatorinterfacedto Pythia8andalternativelyto Herwig7.The Powheg-Boxv2sampleemploystheCT10 [36] PDFforthematrix element calculation and is interfacedto Pythia 8.212 for parton showering and hadronisation employing the parameter values of the AZNLO tune [37] and the CTEQ6L1 [38] PDF. Samples using a set ofvariations in the tune parameters (eigentune variations)

sensitivetoinitial- andfinal-stateradiation,aswellasfurther vari-ationsrelatedtomultiplepartoninteractionsandcolour reconnec-tion,wereproducedto studythedescriptionoftheparton show-ers and hadronisation. Herwig 7.1.6 was used as an alternative partonshower, using the H7UE tune [24] andthe MMHT2014LO PDF set [39] foreventsgenerated withthe Powheg-Box v2 gen-erator. An alternative sample for quark-induced W W production was generated using the Sherpa [40,41] event generator in or-der to evaluate modelling uncertainties. The Sherpa 2.2.2 sam-ple usesmatrix elements at NLO accuracy inQCD forup to one additional parton and at LO accuracy for up to three additional partonemissions. The matrixelement calculationswere matched and merged with the Sherpa parton shower based on Catani– Seymour dipole factorisation [42,43] using the MEPS@NLO pre-scription [40,44–46].ThevirtualQCDcorrectionswereprovidedby the OpenLoops 1library [47–49].Thesample wasgeneratedusing theNNPDF3.0NNLOset [50],alongwiththededicatedsetoftuned parton-showerparametersdevelopedbythe Sherpa authors.

DY production, pp

→

Z

/

γ

∗

→ 

with



=

e

,

μ

,

τ

, was mod-elled using the same settings for Sherpa, Powheg+Pythia8 and Powheg+Herwig7 as for the quark-induced W W event genera-tiondescribedabove.DY( Z

/

γ

∗

→

τ τ

)wasmodelledwith Powheg interfaced to Pythia 8.186 using the NNPDF3.0NLO PDF set [50] andtheAZNLO tunetogetherwiththeCTEQ6L1PDFsetforparton showeringandhadronisation.

TheW Z and Z Z backgroundprocessesweremodelledatNLO using Sherpa aswellas Powheg-Box v2interfacedto Pythia 8.212 with the same settings as employed for the W W event gener-ation. W

γ

production,gluon-induced W W production including resonant and non-resonant contributions and W W j j production invector-boson scatteringwere simulatedusingthe Sherpa 2.2.2 generatorwiththeNNPDF3.0NNLOPDFset.Thesesamplesuse ma-trixelementsatNLOQCDaccuracyforuptooneadditionalparton andLO accuracy for up to three additional parton emissions for W

γ

andgluon-induced W W productionandLO-accuratematrix elementsforW W j j productioninvector-bosonscattering.

The t

¯

t and W t processes were simulated with the Powheg-Box _{[31–33,51,52] v2 generator at NLO with the NNPDF3.0NLO} PDF interfaced to Pythia 8.230using the A14tune [53] andthe NNPDF2.3LOsetofPDFs.FortheW t process,thediagramremoval scheme [54] wasappliedtoremoveinterferenceandoverlapwith tt production.

¯

4. Event reconstruction and selection

Candidate events from

γ γ

→

W W production are identified by thepresence ofan electron andamuon withhightransverse momentumandtheabsence ofadditionalreconstructed charged-particletracksassociatedwiththeinteractionvertex.

Tracksarereconstructed frompositionmeasurements (hits)in the ID caused by the passage of charged particles [55,56]. The trackreconstructionconsistsofaniterativetrack-findingalgorithm seededbycombinationsofatleastthreesilicon-detector hits fol-lowedbya combinatorialKalman filter [57] tobuild track candi-dates based on hits compatible withthe extrapolated trajectory. Ambiguities between the trackcandidates are then resolved and quality criteria are applied to suppresscombinations of hits un-likelytooriginate froma single chargedparticle.Atleastone hit inthe two innermost layers is required ifthe extrapolated track crossesthesensitiveregionofanactive sensormodule.The num-ber ofsilicon hitsin the pixel andSCT detectors must be larger than9for

|η|

≤

1

.

65 orlargerthan11for

|η|

>

1

.

65,withnomore thantwo missing SCThitson a trackifthe respectiveSCT mod-ules are operational. Additionally, a selection is imposed on the transverse impact parameter,

|

d0

|

<

1 mm, to reject tracks from

andbe within

|η|

<

2

.

5.Theseselection criteriaresultinan effi-ciency of 75–80% depending on the track pT. The largest source

ofinefficiency ishadronicinteractionswiththedetectormaterial. Insimulatedevents,reconstructedtrackscanbeclassifiedas orig-inating fromthe hard scatteror fromadditional pp collisions by matching the hitsthat contributed tothe track fitto the energy deposited by the charged particle inthe Geant4 simulation. The respectivetracksarecountedasnHS_trkandnPU_trk.

Electronsarereconstructedfromenergyclustersinthe electro-magnetic calorimeterthatare matchedto tracksreconstructed in theID [58,59].Thebest-matchingtrackisselectedusingascriteria track–clusterspatialdistanceandthenumberofhitsinthesilicon detectors [59].Furthertracksmaybeassignedtotheelectron can-didateiftheyarelikelytooriginatefrominteractionswithdetector material.The pseudorapidityofelectrons isrequiredtobewithin the range of

|

η

|

<

2

.

47, excluding the transition region between thebarrelandendcapsintheLArcalorimeter(1

.

37

<

|η|

<

1

.

52). Electron candidates are requiredto have transverse momenta pT

>

20 GeV.

Muons are built from tracks reconstructed using MS hits matched to ID tracks. A globalfit using the hitsfrom both sub-detectors is performed [60]. Each muon candidate is matched uniquelytoexactlyoneIDtrackandisrequiredtosatisfy

|η|

<

2

.

4 andpT

>

20 GeV.

Identificationandisolation criteriaareappliedto electronand muoncandidatestosuppressnon-promptleptonsfromhadron de-cays. Identificationcriteriaarebased onshower shapesandtrack parameters for the electrons, and on track parameters for the muons. Theisolation criteriauseinformationaboutID tracksand calorimeter energy deposits ina fixed cone of



R

=

0

.

2 around eachlepton.Electronsmustsatisfythe‘medium’identification cri-teria aswell asthe looseisolation criteriadescribed in Ref. [59], which have a combined efficiency of 75–85% depending on the electron pT.Muoncandidatesarerequiredtosatisfythe‘medium’

identification and loose isolation criteriaintroduced in Ref. [60], which have an efficiency of about 95%. The significance of the transverse impactparameter, definedastheabsolutevalue ofd0,

dividedbyitsuncertainty,

σ

d0,mustsatisfy

|

d0

|/

σ

d0

<

3 formuons

and

|

d0

|/σ

d0

<

5 forelectrons.

Thedecisiononwhetherornot torecordtheeventwasmade by single-electron orsingle-muon triggers with requirements on lepton identification and isolation similar to those applied of-fline.Thetransversemomentumthresholdsforthesetriggerswere 24 GeV for electrons [61] and 20 GeV for muons [62] in 2015, whilst during the 2016–2018 data-taking period the thresholds were both raisedto 26 GeV and requirementson lepton identifi-cationandisolationweretightened.Complementarytriggerswith higherpT thresholdsandnoisolationorlooseridentification

crite-riawereusedtoincreasethetriggerefficiency.

Events are required to contain exactly two leptons of oppo-siteelectricchargethat satisfythe abovecriteria. Oneofthe lep-tons musthave transversemomentum exceeding 27 GeV andbe matchedtoanobjectthatprovidedoneofthetriggersusedforthe read-outandstorageofthe event.The invariant massofthetwo selected leptons must exceed m

=

20 GeV. Both same-flavour

(ee

/

μμ

) anddifferent-flavour(e

μ

) eventsareacceptedeitherfor auxiliarymeasurementsorforthesignalextraction,respectively.

Theinteractionvertexisreconstructedfromthetwoleptonsin the event,



1 and



2, as the weighted average z-position of the

tracksextrapolatedtothebeamline:

z_vtx

=

z1sin 2

_θ

1

+

z2sin 2

_θ

2 sin2

θ

1

+

sin 2

_θ

2

,

where sin2

θ

 approximately parameterises the resolution of the

z-position [10].Thisdefinitionoftheinteraction vertexisnot

bi-ased by the presence of additional tracks from hadronicactivity inassociation withthe dilepton pairproduction orby additional tracksfromnearbypile-upinteractions.It resultsina30%higher efficiency than a primary vertex selection based on the sum of squaredtracktransverse momenta [63]. Requirements are placed oneachleptontofulfil

|(

z

−

zvtx

)

sin

θ

|

<

0

.

5 mm.

Awindow of



z

= ±

1 mm around z

vtx defines the regionin

whichIDtracksarematchedtotheinteractionvertex.Thenumber oftracksinthiswindow,excluding thoseused inthe reconstruc-tionofleptons,iscountedasntrk.Signal

γ γ

→

W W event

candi-datesare selectedusingtheexclusivityrequirementthatntrk

=

0.

Eventswithlowtrackmultiplicities,1

≤

ntrk

≤

4,areusedto

eval-uate backgrounds. The modelling ofntrk is therefore vital to the

extractionofthe

γ γ

→

W W signal,andthisisdiscussedfurther inthefollowingsection.

5. Modelling of signal and backgrounds

Correctionsareappliedtothesimulatedsignalandbackground eventsamplesto adjustthelepton trigger,reconstruction, identi-fication andisolation efficiencies, aswell asthe energyand mo-mentum resolutions, to those observed in data. The muon mo-mentumscale iscorrectedinthe MCsimulation,whilst the elec-tronenergyscaleiscorrectedindata [59–62].Accuratemodelling of the transverse momenta of the bosons is important because of its correlation with the expected charged-particle multiplicity fromhadronicactivity. The pW W

T distributionin theMC samples

forquark-induced W W production isreweightedtothe theoreti-calcalculationatnext-to-next-to-leading-order(NNLO)accuracyin perturbativequantum chromodynamicswithresummationofsoft gluon emissions up to next-to-next-to-next-to-leading-logarithm (N3LL)accuracyusingMATRIX+RadISH [48,49,64–72].Acorrection forthe transversemomentum distribution ofdilepton pairs from theDYprocess isderivedfromdatausingee and

μμ

finalstates with an invariant mass within 15 GeV of the nominal Z boson masscorrectedforbackground,andisappliedtoallDYsamplesas afunctionofthegenerator-levelp_TZ.Additionaldata-driven correc-tionsareneededforthisanalysistoaccountfor(i)mismodellingof theadditional pp interactionsproducedinthesamebunch cross-ing, (ii) mismodelling of the charged-particle multiplicity in the qq

→

W W background process, and (iii) second scatterings and thedissociativecontributiontothe

γ γ

→

W W signalprocess. 5.1. Modellingofadditionalpp interactions

Tracksfromnearbyadditional pp interactionscan bematched totheinteractionvertexand,thus,lower theefficiencyofthe ex-clusivity requirement. Their number depends on the density of additional pp interactions and the number of tracks originating fromtheseinteractions.Data-driven techniquesareusedtoderive correctionsto the simulated eventsto further improvetheir de-scriptionofthedata,targetingthedensityof pp interactionsand thenumberoftracksperinteractionseparately.

Thesimulatedeventsarereweightedsuchthatthedistribution ofthe average numberof pp interactions per bunchcrossing re-producestheone measuredinthedata.Thelongitudinalwidthof the beam spot,

σ

BS_{, determines the average density, along z, of}

additionalpp interactionsneartheinteractionvertex.Theaverage longitudinalwidthof thebeam spotvaried throughoutthe data-collectionperiod dueto changes in the LHC beamoptics. It was about44 mmin2015andbetween34and38 mmin2016–2018 compared to 42 mm in MC simulation. The photon-induced MC sampleswere producedwithboth,the nominalconditions inMC simulationandalsowithabeamspotwidthof35 mmtostudythe impactofthesesettings.Onlythelattersampleswereusedinthe final analysis. To account forthe different densities ofadditional

Fig. 2. Thenormaliseddistributionoftracksfromadditionalpp interactions,nPU trk,

associatedwiththeinteractionvertex,indataandsignalsimulatedwithabeam spotwidthofσBS

MC=42 mm.Fordata,nPUtrkisdeterminedusingarandomz-position

alongthebeamaxisawayfromtheinteractionvertex.Thesamequantityisshown forsimulatedγ γ→W W eventsbeforeandaftercorrectingthebeamspotwidth totheoneobservedindata.Theinverseratioofthebeam-spot-corrected simula-tiontodatacorrespondstothecorrectionappliedtonPU

trkinthesimulationusing

theGeant4-basedclassification.Todemonstratetheclosureofthecorrection,the numberoftracksreconstructedinelasticγ γ→W W signalMCsamplesisshown afterapplyingthefullsetofcorrections, namelytheσBS_{correctionandthen}PU trk

correction.Theshownuncertaintiesarestatisticalonly.

pp interactions in data and simulation, the beam spot width is effectivelycorrectedbymodifyingthematchingoftrackstothe in-teractionvertexinsimulation:tracksclassifiedasoriginatingfrom apile-upinteractionarecountedinntrkiftheyhavealongitudinal

impact parameterz within 1 mm

×

σ

BS

MC

/

σ

DataBS of zvtx. Thevalues

for

σ

BS

Data are sampledfromtheLHC runconditions during Run2

accordingtotheluminositytakenatagivenvalueof

σ

BS Data.

An ancillary datameasurement is used to determine the cor-rection for thenumber of tracks fromadditional pp interactions randomly matchedto theinteractionvertex, nPU_trk.In same-flavour Z

→ 

events,thiscorrection isobtained bycounting the num-ber oftrackssatisfyingthenominalselectioncriteriarelativetoa random position in z that is well separatedfrom the interaction vertex,

|

z

vtx

−

z

|

>

10 mm. Eacheventissampled multipletimes

using non-overlapping regions in z.Thisprocedure optimises the statisticalpower, butdoesnot consider theactual distribution of z

vtx along z.To correctforthe resultingbias,nPUtrk isextractedas

a functionofthe z-coordinate andweightedwiththenormalised beamspotdistribution.

Thismethodistestedusingsimulatedeventsandfound to re-producethenPU_trkdistributionindatawithin0.1–3.5%forlowtrack multiplicities,withlargerdisagreementforlargerntrk.Fig.2shows

theprobabilitydistributionofnPU_trkassociatedwithzvtx,extractedin

dataandsimulationbeforeandafterthecorrectionsforthebeam spotwidth.Thebottompanelshowstheratiotodata.Theinverse ratioofthebeam-spot-correctedsimulationtodatacorrespondsto thecorrection appliedasa functionofnPU_trk inthesimulation.The distributions ofthe numberofnPU_trk in

γ γ

→ 

and

γ γ

→

W W MCeventsareshownafterthebeamspotandthepile-up correc-tions. Before anycorrections, thedisagreement canbe up to15% dependingonthebeamspotconditionsinthesimulation.Afterthe

σ

BS _{correction,forlowtrackmultiplicitiesdisagreementsofabout}

10% persists because the

σ

BS _{correction only improvesthe}

mod-ellingofthe densityofthe pile-upverticesbutnotof theirtrack

multiplicity.ThisiscorrectedusingthenPU_trkcorrection.Thefullset ofcorrectionsisappliedtoallMCsamplesusedintheanalysis.

The presence of the additional tracks from pile-up will ran-domly lead to the rejection of signal events and therefore the distributionofnPU_trk canbe usedto extractthe signalefficiencyof theexclusivityrequirement(ntrk

=

0).Thisexclusiveefficiency

de-pendsstrongly onthenumber ofinteractions perbunch crossing and the general beam conditions. The average efficiency for the 2015–2018datasetwithanaverage

μ

intof33.7is52.6%.Itdrops

from60%at

μ

int

=

20 toabout30%at

μ

int

=

60.Whencomparing

thedata-driven efficiencywiththat obtaineddirectly fromsignal MCsamples,theresultsagreetobetterthan0.2%.

Thefulleffectofthedata-drivencorrectionfortracksfrom ad-ditional pp interactions is assigned as a systematic uncertainty, resultingin1%and3%uncertaintyintheefficiencytoselectevents withoutany additionalassociated tracks (ntrk

=

0) for signal and

background, respectively. The uncertainty of having a low num-ber of tracks associated with the vertex (1

≤

ntrk

≤

4) is 2% for

photon-inducedprocesses and10% for quark- and gluon-induced processes.

5.2.Modellingoftheunderlyingevent

Forquark-induceddibosonproduction,additionalcharged par-ticles can be produced from initial-state radiation or secondary partonicscattersin thesame pp collision,also calledthe under-lying event. However, for low values of the number of charged particles,thench distribution was foundto be notwell modelled

by many of the phenomenological models implemented in the generators [73–76]. The underlying event can be assumed to be similar for quark-induced production ofdifferent colourless final statesifthetransversemomentaofthesefinalstatesare compara-ble [76].Therefore,thecharged-particlemultiplicity inqq

→

W W eventscanbeconstrainedusingdatameasurementsofDY produc-tionof



pairs in pp collisions. Specifically, the charged-particle multiplicity is measured for Z

→ 

produced in slices of p

T.

This two-dimensional measurement is then used to correct the DY anddibosonsimulation. Thegeneral validity ofthisapproach has been tested using DY and diboson samples generated with Powheg+Pythia8, Sherpa and Powheg+Herwig7. The multiplicity spectraofcharged particlesare found tobe very differentinthe differentMCsamples,yetrelativelysimilarbetweentherespective DYanddibosonprocessesata constantvalue ofthe bosonor di-bosonpT withtheagreementbeingoftheorderto10-20%.

The Z

→ 

eventsare selectedusingthecriteriadescribedin Section 4 with an additional requirement on the dilepton mass (70 GeV

<

m

<

105 GeV) to suppresscontributions from

back-groundprocesses.The contributionof pile-uptracks isestimated fromdatabysamplingrandomz-positionswellseparatedfromthe dileptonvertexasdiscussedinSection5.1.Thebackgroundatlow trackmultiplicitiesisdominatedby

γ γ

→ 

events,which have adifferent p

T dependencethanDY events andamountto about

5%ofthetotaleventsselectedwith70 GeV

<

m

<

105 GeV and

ntrk

=

0 whiletheircontributionis0.5%orsmallerforhighertrack

multiplicities. The relative normalisations for the elastic, single-dissociative and double-dissociative

γ γ

→ 

as well asthe DY processaredeterminedinafittothemeasuredp_T distributionin am

>

105 GeV sideband,requiringntrk

=

0 andusingtheshapes

fromMCsimulation. Inthissideband,the

γ γ

→ 

process con-tributesabout60%tothetotaleventsample.Thecontributionfrom the

γ γ

→

W W process witha same-flavour final state amounts to less than 1% of the

γ γ

→ 

processes in thiskinematic re-gionand isneglected. The overall normalisationsof thedifferent

γ γ

→ 

contributions relative to the prediction are compatible within the statistical uncertainty with those from earlier ATLAS studies [77].

Fig. 3. Ontheleft,thenormalisednumberofeventswithagivennumberofchargedparticles,1/NevdNev/dnch,predictedbySherpa, Powheg+Pythia8,and Powheg+Herwig7 iscomparedwiththeunfoldeddata.Theratioonthebottomistheinverseoftheweightsthatareappliedatparticlelevelasafunctionofthenumberofchargedparticles. Theeffectofthecorrectionfortheunderlyingeventisillustratedforthenumberofreconstructedtracksontheright. Sherpa and Powheg+Pythia8areshownbeforeand afterthecorrectionandcomparedwithdata.Thetotaluncertaintyofthecorrectionisshownfor Powheg+Pythia8intheupperpanel,andasabandaroundunityforthe lowerpanel.Thetotaluncertaintiesfor Sherpa and Powheg+Pythia8areverysimilar.

After the

γ γ

→ 

andpile-upcontributionsaresubtractedas backgrounds,D’Agostiniunfolding [78,79] isusedtounfoldthe dis-tribution of the reconstructed track multiplicity, ntrk, to that of

the number of charged particles, nch, using four iterations.2 The

charged-particlemultiplicityisextractedasafunctionofthepTof

thedileptonsystem,whichcorrespondstothetransverse momen-tum of the recoil, using 5-GeV-wide intervals of pT. The largest

sources of uncertainty are the contributions from pile-up tracks and uncertainties in the distribution used as the prior, assessed by comparing Powheg+Pythia8 and Sherpa. Other uncertainties originate from theevent selection andthe

γ γ

→ 

background subtraction, assessed by varying the kinematic selection and the normalisation of the photon-inducedbackground within the un-certainties of the fit in the m sideband. Fig. 3 (left) compares

the unfolded charged-particle multiplicity distribution for differ-ent MC models and data. For low values of nch, the

charged-particlemultiplicity distributionismismodelledbyafactorof2.5 in Powheg+Pythia8 and by a factor of4 in Sherpa, whilst good agreement with the Powheg+Herwig7 model is found except at nch

=

0 where the Powheg+Herwig7 prediction exceedsthe data

yieldbyabout30%.

Thecharged-particlemultiplicityinsimulatedDYeventsis cor-rectedusingper-eventweightsdeterminedastheratioofthe un-folded data to the unfolded MC simulation as a function of the charged-particlemultiplicity,andoftheparticle-levelpTofthe

de-cay products ofthe Z boson. The impact ofthe charged-particle multiplicitycorrectionisshowninFig.3(right)forDYevents.The simulationisshownbothbeforeandafterthecorrectionfor pile-up modelling and underlying-event modelling in Z

→ 

events satisfying70 GeV

<

m

<

105 GeV.The correctionsbringtheMC

simulationintoagreementwithdatawithinthesystematic uncer-taintyofthecharged-particlemeasurement.Thecorrectionforthe underlying-event modellingisappliedto W W , W Z and Z Z pro-cessesasafunctionofthecharged-particlemultiplicity,andofthe particle-levelpTofthedecayproductsofthedibosonsystem.

2 _{SimilarlytoRef. [80],chargedparticlesaredefinedtobestableiftheyhavea}

meanlifetimeτ>30 psandsatisfypT>500 MeV and|η|<2.5.

5.3.Signalmodelling

After the initial

γ γ

→

W W process, the protons can un-dergoasecondinelasticinteraction.Theseadditionalrescatterings do not change the kinematics of the

γ γ

→

W W process, but leadto the productionofparticles such that the crosssection of

γ γ

→

W W productionwithoutassociatedtracksisreduced.This effectis not included in the modelling ofthe signal. The proba-bilitythatnosuch additionalparticlesareproduced iscommonly referred to as the survival factor. In addition, the

γ γ

→

W W signal when applyingthe exclusivityrequirement ismodelled by Herwig7,whichincludesonly theelasticcomponent. Toobtaina better estimate ofthe expectedsignal yield including the disso-ciativecomponentsandtocorrectforeffectsfromtherescattering ofprotons, a correction factor isobtained froma

γ γ

→ 

con-trolsampleindata,following aprocedure similartothat applied inRefs. [4,6] usingsame-flavourleptonfinalstates.Toenhancethe purityin

γ γ

→ 

productionandtomimicthekinematic thresh-oldof

γ γ

→

W W production,thedileptonmassisrequiredtobe largerthan160 GeV.Theexclusivityrequirementofntrk

=

0 is

ap-plied.In theregion, wherethe correction factor isextracted, the predicted eventyield from the

γ γ

→

W W process with same-flavourfinal statesisapproximately1.5%ofthe

γ γ

→ 

yieldso thatthederivedcorrectionfactorisessentiallyindependentofthe

γ γ

→

W W signalprocess.

Thebackground,dominatedbyDY production,isestimated us-ingadata-driventechnique.Theshapeofthem distributionfor

backgroundeventsisestimatedusingeventswithntrk

=

5,which

isacompromisebetweensmallsignalcontaminationandcloseness to the signal region. This template is normalised to the ntrk

=

0

selection using a narrow window around the nominal Z boson mass (83

.

5 GeV

<

m

<

98

.

5 GeV) where the contribution from

photon-inducedprocessesissmall.Them lineshapeinsimulated

DYeventsisfoundtobeindependentofntrk forlowmultiplicities.

Whentheexclusivityrequirementofntrk

=

0 isapplied,the

ra-tiooftheyield fromphoton-inducedprocessesindatatotheMC predictionfortheelasticprocessesisfoundtobe3

.

59

±

0

.

15(tot.). This agrees with the expectation of3.55 obtained using the MC prediction.Ithasbeenverifiedthatthesignalmodellingcorrection

Fig. 4. Thedistributionofmintheregionwherethesignalmodellingcorrection isextractedastheratiooftheyieldofγ γ→ andγ γ→W W processespassing theexclusivityrequirementofntrk=0 totheyieldofthesimulatedelasticprocess

only.Shownarethedata,wherearequirementofntrk=0 hasbeenapplied,and

thebackgroundtemplatesselectedfromdatausingntrk=2 andntrk=5.In

addi-tion,theγ γ→ andγ γ→W W MCpredictionsaredepicted,aswellasthesum ofthenominalbackgroundtemplate(ntrk=5)andtheγ γ→ andγ γ→W W

MCpredictionsscaledbythesignalmodellingcorrection.Thenormalisationregion aroundthenominal Z bosonmassisindicatedwithaverticaldashedline,asis theregionwherethesignalmodellingcorrectionisextracted(m>160 GeV).The excessindatarelativetotheelasticγ γ→  andγ γ→W W predictionis at-tributedtothedissociativephoton-inducedprocessesandusedtoextractthesignal modellingcorrectionthatisshowninthelowerpaneloftheplot.Theuncertainties shownarestatisticalonly.

doesnotvaryasa functionof pe_Tμ withintheboundariesusedto extractthesignal.

Fig. 4 illustrates the extraction of the signal modelling cor-rection from data. The signal modelling correction is only ap-plicable to events with ntrk

=

0. The simulated Herwig7 events

are used in conjunction with the signal modelling correction for predictions ofphoton-induced processes inevents where the ntrk

=

0 requirement is applied, while the event samples from

MG5_aMC@NLO+Pythia8 are usedforpredictionsinregions with largertrackmultiplicities.

Uncertaintiesare evaluatedby increasing themasswindow of the DY background normalisation region to 73

.

5 GeV

<

m

<

108

.

5 GeV and by changing the number of tracks used in the selection of the template, using ntrk

=

2 instead of the nominal

value. The resulting uncertainty in the signal modelling correc-tion amounts to 4.2%. When the signal modelling correction is applied to

γ γ

→

W W , an additional transfer uncertainty is in-cludedtoaccountforpotentialdifferencesbetween

γ γ

→ 

and

γ γ

→

W W events due to the fact that rescattering effects are mass-dependent.Itiscalculatedasthelargestvariationthatarises fromplacingdifferentlowerboundsontheevaluationregion;the lower boundonm was varied fromm

=

110 GeV to400 GeV

inintervalsof10 GeV.Theresultinguncertaintyamountsto 11%. Thisuncertaintyaffectsonlythescalingofthe

γ γ

→

W W process andthusthemeasuredsignal strengthandanycrosssection pre-diction derived usingthe signal correctionfactor, butcancelsout inthemeasurementofthefiducialcrosssection.

6. Event categories and background estimation

Onesignal regionandthree controlregions,enriched insignal andbackgroundeventsrespectively,aredefinedusingthedilepton

transversemomentum, pe_Tμ, andthe numberof additionaltracks associated with the interaction vertex, ntrk. The signal region is

defined by selecting pe_Tμ

>

30 GeV and ntrk

=

0. It has an

ex-pectedpurity of57% andan expectedbackground contamination fromqq

→

W W productionof33%.

Additionalkinematic regions withalternative requirementson pe_Tμandntrkareusedtocontrolthemodellingofbackground

pro-cesses. The first control region is defined by pe_Tμ

<

30 GeV and 1

≤

ntrk

≤

4 andhelpstoconstraintheDY( Z

/

γ

∗

→

τ τ

)

normalisa-tion,asthisprocesscontributes75%oftheselectedeventsinthis region. It also has non-negligible contributions from qq

→

W W eventsandnon-prompt leptons.The second control regionis de-fined by pe_Tμ

>

30 GeV and 1

≤

ntrk

≤

4 and is designed to be

enriched in qq

→

W W events, withan expected contributionof about70%fromthatprocessandminorcontributionsfromtheDY process andnon-prompt lepton events.An additional control re-gionisselectedwithpe_Tμ

<

30 GeV andntrk

=

0.Itbringssome

ad-ditionalcontrolforthemodellingofbackgroundsspecifictoevents withnotracks,howeverhasasignalcontaminationoftheorderof 10%.The boundariesbetweentheseregions are chosen such that goodsignal–backgroundseparationisachieved.Inaddition,the re-gions used to control the normalisation of the backgrounds are definedtobetopologicallyverysimilartothesignalregion,which helpstominimiseuncertaintiesinextrapolating thenormalisation fromthecontrolregionstothesignalregion.

Backgroundevents fromnon-prompt leptons contribute about 6%oftheselected signalcandidatesinthe signalregion.The pri-mary source of these backgrounds in dilepton events is W +jets production where one of the leptons is prompt and the other stems from light-hadron or heavy-flavour decays. Background eventsfromnon-prompt leptons areestimatedfroma control re-gionwhereexactlyoneoftheleptons mustfailtosatisfysomeof theleptonidentificationcriteriaofthenominaleventselection.All other kinematic selection criteriaare the same as for the signal selection.The contributionfromnon-promptleptons isthen esti-mated by scaling the number ofevents in the control region by theratioofthenumberofnon-promptleptonspassing all identi-ficationrequirementstothosefailingsomeoftheserequirements. Thisratioismeasuredindataselectedwithoneelectronandone muon with the same electric charge, and requiring 1

≤

ntrk

≤

4.

Contributionsfromprompt leptons aresubtracted usingMC sim-ulation.Forthe extrapolationto theevent samplesselected with ntrk

=

0 adedicateduncertaintyisassigned.

7. Systematic uncertainties

Uncertainties and their correlations are evaluated in each of thesignal andcontrol regions. Theuncertainties in the measure-mentof tracks originate fromuncertainties in the innerdetector alignment,thereconstructionefficiency,andtheprobability to in-correctlyreconstruct tracks by includinghits fromnoise or from severaltracks.Thecombineduncertaintyamountsto 5–7%ofthe eventyieldsforDYandqq

→

W W production,whilstfor photon-induced processes these uncertainties are

<

1% in the regions wheretheseprocessescontributesignificantly.

Systematicuncertaintiesintheeventyieldsduetoelectronand muonreconstruction,includingeffectsfromthetriggerand recon-structionefficiencies,energy/momentumscaleandresolution,and pile-upmodellingare0.5%andupto2%dependingontheprocess, inthesignalandcontrolregions,respectively[59–62].

The uncertainty in the background from non-prompt leptons is dominated by the uncertainty in the measurement of the ra-tioof non-prompt leptons passing all identificationrequirements tothosefailingsome,inparticularthesubtractionofcontributions fromgenuine leptons inthe numerator of that ratio.The result-inguncertaintyonthisbackgroundestimationrangesbetween50%

Table 1

Summaryofthedataeventyields,andthepredictedsignalandbackgroundeventyieldsin thesignalregionandcontrolregionsasobtainedafterthefit.Theuncertaintiesshown in-cludestatisticalandsystematiccomponents.Becausethefitintroducescorrelationsbetween systematicuncertainties,theuncertaintyinthetotalexpectedyieldissmallerthanits com-ponents.Theleftmostcolumnofvaluescorrespondstothe signalregionusedtomeasure

γ γ→W W inproton–protoncollisions.Thenumbersfor qq→W W alsocontainasmall contributionfromgluon-inducedW W andelectroweakW W j j production.Theeventyields forotherbackgroundsincludecontributionsfromW Z andZ Z dibosonproduction,top-quark productionandothergluon-inducedprocesses.

Signal region Control regions ntrk ntrk=0 1≤ntrk≤4

peTμ >30 GeV <30 GeV >30 GeV <30 GeV

γ γ→W W 174±20 45±6 95±19 24±5 γ γ→  5.5±0.3 39.6±1.9 5.6±1.2 32±7 Drell–Yan 4.5±0.9 280±40 106±19 4700±400 qq→W W (incl. gg and VBS) 101±17 55±10 1700±270 970±150 Non-prompt 14±14 36±35 220±220 500±400 Other backgrounds 7.1±1.7 1.9±0.4 311±76 81±15 Total 305±18 459±19 2460±60 6320±130 Data 307 449 2458 6332

and 100%depending onthe region. The statisticaluncertainty in thecontrolregionfortheestimationofbackgroundfrom misiden-tifiedleptonsisalsoasignificantsourceofuncertainty.

Theuncertaintiesinthecorrectionofpile-upmodellingandthe underlying event as well as the uncertainty in the signal mod-elling correction are described in Section 5. The correction for the underlying-event modelling in the W W , W Z and Z Z pro-cesses is derived in bins of p_T, butapplied asa function of di-boson pT, utilising the fact that there are only relatively small

differences in charged-particle multiplicity between the DY and diboson processes. Residual differencesare evaluated at the par-ticle level and considered as systematic uncertainties. For the largestsourceofbackground,thequark-inducedW W process, fur-ther studies are made. The predicted event yields are compared for Powheg+Pythia8andvariationsofthe Pythia8parton-shower tunes, and for Powheg+Herwig7 and Sherpa, with each predic-tion using its dedicated underlying-event correction. The event yieldsagreewellfor1

≤

ntrk

≤

4,butdisagreeinthesignalregion,

ntrk

=

0.Thebackgroundyieldfromthequark-induced W W

pro-cessisestimatedastheaverageofthehighestandlowestvalueof thevarious predictions,thatisthemidpointofthemostextreme predictionsasnopreferenceforeithermodelcanbededucedfrom the data. The envelope of all predictions is taken as the upper andlowerone-standard-deviationboundary,amountingto

±

7%for events selectedwithntrk

=

0, andamounting tolessthan 1% for

events selected with 1

≤

ntrk

≤

4. The uncertainties in the total

quark-inducedW W crosssection andtheshapeofthe pW W T

dis-tribution are taken from the MATRIX+RadISH prediction used to reweighttheW W samples,amountingto5–6%.

Because of the specific event selection of the analysis, large uncertainties are applied to minor backgrounds, where the ntrk

modelling cannot be easily studied in data: the uncertainty in the W

γ

normalisation is taken to be

±

100%, whereas uncer-tainties of

±

30% are used for the normalisation of top-quark production and W W j j production through vector-boson scatter-ing (VBS) as well as gluon-induced resonant and non-resonant W W production. The numbers are informed by the size of the underlying-event correction in DY and W W events and studies oneventswithforwardjetsoutsidetheacceptanceoftheID.For the smaller backgroundcontributions from W Z and Z Z produc-tion the uncertainty is assessed by comparing the event yields predicted by Powheg+Pythia8 with those predicted in Sherpa after applying the underlying-event correction described in Sec-tion5.2.

Thesystematicuncertainty inthemeasured crosssection also includes a contribution due to differences in reconstruction effi-ciencybetweenelastic anddissociativephoton-inducedprocesses as well as an uncertainty due to missing spin correlations in Herwig7, which mainly affects the peμ

T modelling. These

uncer-tainties are evaluated separately by comparing the reconstruc-tion efficiency of the elastic-only prediction with that including all production mechanisms andby comparing the reconstruction efficiency between Herwig7 and MG5_aMC@NLO+Pythia8. Their combined effectis

±

2%. Uncertainties stemming from the signal modellingcorrection are appliedto the signal predictionandare discussedindetailinSection5.3.

8. Results

The

γ γ

→

W W signalinproton–protoncollisionsisextracted using a profile likelihood fit of the estimated signal and back-groundeventyieldstodata.Thefitusestheintegratedeventyields in the four kinematic regions introduced in Section 6, and the ee

+

μμ

eventsselectedasdescribedinSection 5.3.Itmaximises theproductofPoissonprobabilitiestoproducetheobserved num-berofdataevents,Nobs,ineachoftheseregions [81].

ThenormalisationofthebackgroundsfromDY andqq

→

W W processes are free parameters in the fit. The expected elastic

γ γ

→ 

and

γ γ

→

W W eventyieldsforntrk

=

0 aremultiplied

bythesignalmodellingcorrectiondiscussedinSection5.3,which isobtainedasdescribedwithinthefittopreservetheexperimental correlationscorrectly. The eventyield forthe

γ γ

→

W W signal processisalsomultipliedbyasignalstrengththatisafree param-eterinthe fit.Systematic uncertainties areincluded inthe fit as nuisanceparametersconstrainedbyGaussianfunctions.Thefitcan onlyconstrainthe sumofthe backgrounds,sincethebackground composition issimilar ineventsselected withntrk

=

0 andthose

selectedwith1

≤

ntrk

≤

4.Overall, theuncertainty inthesumof

theiryieldsisdominatedbythesystematicuncertaintiesassigned to events selected withntrk

=

0. In this fit, the background-only

hypothesis is expected to be rejected with a significance of 6

.

7 standarddeviations.

Table1gives anoverviewof thenumberofdata events com-paredto backgroundand signal event yields in the different re-gionsafterthefit.Thedatayieldinthesignalregionis307, com-paredwith132backgroundeventspredictedbythebest-fitresult. Thenormalisations of the W W andtheDY background are

con-Fig. 5. ThedistributionsofpeTμfor1≤ntrk≤4 (left)andntrk=0 (right)areshown.Thefittednormalisationfactorsandnuisanceparametershavebeenused.Theyields

forthelikelihoodfitaregivenbytheintegralsofthedistributionssplitatpTeμ=30 GeV,asindicatedbytheverticaldashedlines.Theγ γ→W W signalregionrequiresa

selectionofpeTμ>30 GeV withntrk=0,asindicatedbythearrow.Theqq→W W componentalsocontainsasmallcontributionfromgluon-inducedW W andelectroweak

W W j j production.Similarly,‘otherqq initiated’includescontributionsnotonlyfromW Z andZ Z dibosonproductionbutalsofromtop-quarkproductionandother gluon-inducedprocesses.Thetotaluncertaintiesareshownashatchedbands.Thelowerpanelsshowtheratioofthedatatotheprediction,withthetotaluncertaintydisplayedas ahatchedband.Anarrowindicatesthattheratioisoff-scale.Thelastbininbothdistributionsincludestheoverflow.

strainedwiththehelpofthecontrolregions tobe1

.

21+₋0₀._.19₂₃(tot.) and1

.

16+0₋₀._.10₁₂(tot.),respectively.

By fitting the signal and background event yields in the sig-nalandcontrolregions,thebackground-onlyhypothesisisrejected witha significance of8

.

4 standarddeviations, assuming that the systematicuncertainties areGaussian-distributed up to large val-ues. A signal strength of 1

.

33₋+₀0._.14₁₄(stat.)+₋0₀._.22₁₇(syst.) is measured relative to the yield of elastic

γ γ

→

W W events predicted by Herwig7 scaled bythe signalmodellingcorrectionto accountfor allphoton-inducedproductionmechanismsinaphase spacewith notracksassociatedwiththeinteractionvertex.Theseresults con-stitutethe observationofphoton-inducedW W productionin pp collisions, aprocessforwhichonlyevidencewithsignificancesof 3.0

σ

[4] and3.6

σ

[6] waspreviouslyreported.

Fig.5showstwo pe_Tμ distributions:ontheleftforeventswith 1

≤

ntrk

≤

4 associated with the interaction vertex, and, on the

right, for events with the exclusivity requirement of no tracks. The boundary betweenlow- and high-pe_Tμ control andsignal re-gions is at30 GeV. The distributions inFig. 5 include the fitted normalisations andnuisanceparameters described above; the re-sulting predictions are in good agreement with the data. Fig. 6

showsthe distribution ofthe numberof reconstructedtracks for pe_Tμ

>

30 GeV.

The fiducial phase space used for the cross-section measure-ment is defined to be close to the acceptance of the detector. The leptons must at particle level satisfy the pseudorapidity re-quirement

|η|

<

2

.

5. One of the leptons is required to have a transverse momentum ofat least27 GeV, whilst the other must have pT

>

20 GeV. Theyare required tobe prompt leptons from

W decays. Photons in a cone of



R

=

0

.

1 arounda lepton and notoriginatingfromthedecaysofhadronsareaddedtothe four-momentumofthelepton,thatisleptonsare“dressed”.Eventswith exactlytwoleptons areselectedwithopposite-signand different-flavourfinal states.DecaysofeitherW bosonintoa

τ

-leptonand neutrinoareexcluded.Theinvariantmassofthedileptonsystemis requiredto bem

>

20 GeV andits transversemomentum must

be pe_Tμ

>

30 GeV.The numberofchargedparticles, nch,with pT

>

500 MeV andwithin

|η|

<

2

.

5,excludingtheselectedleptons,is requiredtobezero.

Fig. 6. Thedistributionofthenumberoftracksassociatedwiththeinteraction ver-texisshown.Thefittednormalisationfactorsandnuisanceparametershavebeen used.Theγ γ→W W signalregionrequiresaselectionofntrk=0,asindicatedby

theverticaldashedline.Theqq→W W componentalsocontainsasmall contribu-tionfromgluon-inducedW W andelectroweakW W j j production.Similarly,‘other qq initiated’includescontributionsnotonlyfromW Z and Z Z dibosonproduction butalsofromtop-quarkproductionandothergluon-inducedprocesses. Thetotal uncertaintiesareshownashatchedbands.Thelowerpanelshowstheratioofthe datatotheprediction,withthetotaluncertaintydisplayedasahatchedband.

Withoutrequirements on the numberofreconstructed tracks, the selection efficiency after reconstruction is 75% for elastic

γ γ

→

W W events in the fiducialregion. The full selection effi-ciencyafterapplyingntrk

=

0 is39%.Thepredictednumberof

sig-naleventsincludesa

∼

5%contributionofleptonsfromW

→

τ ν

τ ,

τ

→ 

ν



ν

τ ,whichisestimatedusingtheMCsimulationandwhich is removed from the measured fiducial cross section using this fractionalcontribution.

Table 2

Theimpactofdifferentcomponentsofsystematicuncertaintyonthemeasuredfiducialcross sec-tion,withouttakingintoaccountcorrelations.Theimpactofeachsourceofsystematicuncertainty iscomputed byfirstperformingthefitwith thecorrespondingnuisanceparameterfixedtoone standarddeviationupordownfromthevalueobtainedinthenominalfit,thenthesehighandlow variationsaresymmetrised.Theimpactsofseveralsourcesofsystematicuncertaintyareaddedin quadratureforeachcomponent.

Source of uncertainty Impact [% of the fitted cross section] Experimental

Track reconstruction 1.1

Electron energy scale and resolution, and efficiency 0.4 Muon momentum scale and resolution, and efficiency 0.5 Misidentified leptons, systematic 1.5 Misidentified leptons, statistical 5.9 Other background, statistical 3.2 Modelling

Pile-up modelling 1.1

Underlying-event modelling 1.4

Signal modelling 2.1

W W modelling 4.0

Other background modelling 1.7

Luminosity 1.7

Total 8.9

Theobservedsignalstrengthtranslatesintoafiducialcross sec-tionof

σ

meas

=

3

.

13

±

0

.

31 (stat.)

±

0

.

28 (syst.) fb

for pp

(

γ γ

)

→

p(∗)_W+_W−_p(∗) _{production with W}+_W−

_→

e±

νμ

∓

ν

. The uncertainties correspond tothe statisticaland sys-tematicuncertainties,respectively.Table2givesanoverviewofthe sources of systematic uncertainties, which are discussed in Sec-tion7andpresentstheireffectonthemeasuredcrosssection.To evaluate the impact of one source of systematic uncertainty, the fitisperformedwiththecorrespondingnuisanceparameterfixed onestandarddeviationupordownfromthevalueobtainedinthe nominalfit,thenthesehighandlowvariationsaresymmetrised.

Thedatameasurementcanbecomparedwithtwotypesof pre-dictions. The first, used in the definition of the signal strength and thecalculation ofthe expected significance,is based on the Herwig7 prediction for elastic

γ γ

→

W W events scaled by the data-drivensignalmodellingcorrectiontoincludethedissociative processesandrescatteringeffectsasdescribedinSection 5.3.Itis foundtobe

σ

theo

× (

3

.

59

±

0

.

15 (exp.)

±

0

.

39 (trans.)

)

=

2

.

34

±

0

.

27 fb

,

wheretheuncertaintycontains allexperimentaluncertaintiesand receives an additional component due to the transfer from the

γ γ

→ 

tothe

γ γ

→

W W processdescribedabove.The uncer-tainties in the theory prediction are negligible because the scale uncertainty in the calculation of elastic production based on a photon-flux is smallandpartially cancels withthe signal correc-tionthat iscalculatedwithrespecttothesamephoton-flux com-paredto thedata.Astandalone theoryprediction forthe fiducial crosssectioniscomputedwith MG5_aMC@NLO+Pythia8 usingthe appropriate elastic or inelastic MMHT2015qed PDF sets [82] for eachofthecontributionsbyapplyingthefiducialrequirementsto all photon-inducedcontributions, whichyields 4

.

3

±

1

.

0(scale)

±

0

.

1(PDF) fb. The scale uncertainty is determined by varying the factorisation scale by factors of 2 and0.5 and symmetrising the effect.Thecontributionstothiscross-sectionpredictionfrom elas-tic and single-dissociative production are 16% and 81%, respec-tively. Double-dissociative production contributes only 3%. Using CT14qed [28] asthe central PDF set yields a predictionwhich is 26%smallerandamountsto3

.

2 fb.

The MG5_aMC@NLO+Pythia8 prediction does not include re-scatteringeffects that areexpected to decreasethe fiducialcross section.Forelastic

γ γ

→

W W production,asurvivalfactorof0.65 was estimated in Ref. [83]. In Ref. [84] a survival factor of 0.82 wascalculatedinatwo-channeleikonalmodelalsoaccountingfor thehelicity structureof thehard scatteringprocess.3 Multiplying the MG5_aMC@NLO+Pythia8 predictionby these survival factors resultsintheoreticalpredictionsof2

.

8

±

0

.

8 fband3

.

5

±

1

.

0 fb, re-spectively,withthetotaluncertaintiescalculatedasthequadratic sumofscaleandPDFuncertainties.Thesepredictionsarein agree-mentwiththemeasurement.

9. Conclusion

Thephoton-inducedproductionprocess,

γ γ

→

W W ,was stud-iedinproton–protoncollisions at

√

s

=

13 TeV recordedwiththe ATLASdetectorattheLHCcorrespondingtoanintegrated luminos-ityof139fb−1.EventswithleptonicW bosondecaysintoe±

νμ

∓

ν

finalstateswereselectedbyrequiringthat notracksexceptthose of the two charged leptons are associated with the production vertex. The background-onlyhypothesis is rejectedwitha signif-icance of 8

.

4 standard deviations whereas well above 5

σ

was expected.Thismeasurementconstitutestheobservationof photon-induced W W production in pp collisions, a process for which only evidence was previously reported. The signal strength and thecrosssectionforthesumofelasticanddissociativeproduction mechanisms are measured. The cross section for the pp

(

γ γ

)

→

p(∗)_W+_W−_p(∗)_{processinthedecaychannel W}+_W−

_→

_e±

_νμ

∓

_ν

ina fiducialphase spaceclose tothe experimental acceptanceis measuredtobe3

.

13

±

0

.

31(stat.)

±

0

.

28(syst.) fb.Thisresultisin agreementwiththetheoreticalpredictionsandmayserveasinput intoEFTinterpretations.

Declaration of competing interest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

3 _{Morerecentcalculationspredictslightlylowerabsorptionvaluesforthe}