Evidence for electroweak production of two jets in association with a Zγpair in ppcollisions at √s=13 TeV with the ATLAS detector

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Evidence for electroweak production of two jets in association with a Z γ ^{pair in} pp collisions at √

s = 13 TeV with the ATLAS detector

.The ATLAS Collaboration

^

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

Articlehistory:

Received21October2019

Receivedinrevisedform11February2020 Accepted24February2020

Availableonline28February2020 Editor:M.Doser

EvidenceforelectroweakproductionoftwojetsinassociationwithaZγ pairin√

s=13 TeV proton–

proton collisions at the Large Hadron Collider is presented. The analysis uses data collectedby the ATLAS detector in2015 and 2016 that correspondsto an integrated luminosity of 36.1 fb⁻¹.Events thatcontaina Z bosoncandidate decayingleptonicallyintoeithere⁺e⁻ orμ⁺μ⁻,aphoton,andtwo jets are selected. The electroweak component is measured with observed and expected significances of 4.1 standard deviations. The fiducial cross-section for electroweak production is measured to be

σZγj j−^EW=⁷.8±².0fb,ingoodagreementwiththeStandardModelprediction.

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

1. Introduction

AttheLargeHadronCollider(LHC),theelectroweak(EW)sector ofthe StandardModel (SM) can be probed by studyingthe self- coupling of vector bosons, which is precisely predicted through theSU(2)L×^U(1)Ygaugesymmetry.Vector-bosonscattering(VBS), V V→^{V V with V} =^W/Z/

γ

,isone ofthemostinteresting pro- cesses to look atto study such effects, asit issensitive to both the triple andthe quartic gauge boson couplings, where physics beyondtheSMcansignificantlyaltertheSMpredictions [1–3].

Inhadroncollisions,VBS eventsarecharacterisedby thepres- enceoftwobosonsandtwojets,V V j j,thatarecreatedinapurely electroweak process [4], through the interaction of bosons that havebeenradiatedfromtheinitial-statequarks. Forsuchevents, thescatteredquarksare not colour-connectedandlittlehadronic activityisexpectedinthegapbetweenthetwojets.Theseevents are alsocharacterised by a large invariant massof the dijetsys- temanda large separationof thetwo jets inrapidity,while the decayproductsofthebosonsaretypicallyproducedinthecentral region.

The V V j j final states, however, are produced mainly through a combination ofstrong and electroweak interactions in pp col- lisions. The former are of order

α

²_S

α

²_EW at the Born level,where

α

S is the strong coupling constant and

α

EW is the electroweak couplingconstant.Inthefollowing,such processesare referredto asQCD-inducedbackgrounds,Z

γ

j j−^{QCD.TheproductionofV V j j}

 E-mailaddress:atlas.publications@cern.ch.

eventsthrough pure

α

_EW⁴ interactions atthe Born levelare more rare; they are referred to as electroweak processes, Z

γ

j j−^EW, in the following. It is not possible to study VBS diagrams inde- pendentlyfromotherelectroweakprocessesasonlytheensemble is gaugeinvariant [5].There is alsointerferencebetween theSM electroweakandQCD-inducedprocesses.Some exampleFeynman diagramsfortheseprocessesareshowninFig.1.

Amongallthepossibleelectroweakproductionmodes,onlythe W^±W^±j j andW Z j j productionprocesseshavebeenobserved [6–

9]. Evidence forthe Z

γ

j j channelhas beenreported [10], while limits on electroweak cross-sections have been reported for the Z Z j j channel [11], the W

γ

j j channel [12], and the V V chan- nel [13,14] whereat mostone of the two bosons decaysto two jets.

The Z

γ

j j channel [15] isparticularlyinterestingtostudysince itallowsthemeasurementoftheneutralquarticgaugecouplings, asforthe Z Z finalstatebutwitha largerexpectedcross-section.

The Z

γ

j j cross-sections have been computed at next-to-leading order(NLO)in

α

SforboththeQCD-inducedbackgrounds [16] and theelectroweaksignal [17]. TheNLO QCD correctionsarenot in- cluded in the following for either the electroweak signal or the QCD-inducedbackground,astheywerenotevaluatedforthephase spaceusedinthispaper.

ThisLetterreportstheevidencefor,andthemostprecisemea- surementsto dateof,electroweak Z

γ

j j production,wheerthe Z boson decays leptonically into either e⁺e⁻ or

μ

⁺

μ

⁻, exploiting the data collected withthe ATLAS detector in2015 and 2016 at acentre-of-massenergyof√

s=^{13 TeV,and}correspondingtoan integratedluminosityof36.1 fb⁻¹.

https://doi.org/10.1016/j.physletb.2020.135341

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

Fig. 1. RepresentativeFeynmandiagramsoftheprocessesrelevanttothisanalysis:(a)quarticgaugecouplingVBSsignal,(b)triplegaugecoupling,(c)electroweaknon-VBS signal,QCD-inducedbackgroundswith(d)gluonexchangeor(e)gluonradiation.

2. ATLASdetector

TheATLAS detector [18–20] isamultipurposedetectorwitha cylindricalgeometry¹andnearly4

π

coverageinsolidangle.

The collision point is surrounded by inner tracking detectors, collectively referred to as the inner detector (ID), located within a superconducting solenoid providing a 2 T axial magnetic field, followedbyacalorimetersystemandamuonspectrometer(MS).

Theinner detectorprovides precisemeasurements ofcharged- particle tracks in the pseudorapidity range |

η

_|<2.5. It consists ofthree subdetectors arranged in a coaxialgeometryaround the beam axis: a silicon pixel detector, a silicon microstrip detector andatransitionradiationtracker.

The electromagnetic (EM)calorimeter covers the region |

η

_|<

3.2 andisbasedonhigh-granularity,lead/liquid-argon(LAr)sam- plingtechnology.Thehadroniccalorimeterusesasteel/scintillator- tiledetectorin theregion |

η

_|<1.7 anda copper/LAr detectorin theregion1.5<|

η

_|<3.2.Themostforwardregionofthedetector, 3.1<|

η

|<4.9,isequippedwithaforwardcalorimeter,measuring electromagnetic and hadronic energies in copper/LAr and tung- sten/LArmodules,respectively.

The muon spectrometer comprises separate trigger and high- precision tracking chambers to measure the deflection of muons in a magnetic field generated by three large superconducting toroidal magnetsarranged withan eightfold azimuthal coilsym-

1 ATLASusesaright-handed coordinatesystemwith itsoriginat thenominal interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam direction.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y- axispointsupward.Cylindricalcoordinates(r,φ)areusedinthetransverse(x,y) plane,φbeingtheazimuthalanglearoundthebeamdirection.Thepseudorapidity isdefinedintermsofthepolarangleθasη= −^ln[^tan(θ/2)]^.

metryaroundthecalorimeters.Thehigh-precisionchamberscover the range |

η

_|<2.7. The muon trigger system covers the range

|

η

|<2.4 withresistive-platechambersinthebarrelandthin-gap chambersintheendcapregions.

Atwo-leveltriggersystem [21] is usedtoselecteventsinreal time. It consists of a hardware-based first-level (L1) trigger and a software-basedhigh-level trigger.Thelatteremploysalgorithms similartothoseusedofflinetoidentifyelectrons,muons,photons andjets.

3. Signalandbackgroundsimulation

Signal and background processes are modelled using Monte Carlo (MC) simulations. All MC events were passed through the Geant4-based [22] ATLAS detector simulation [23]. They are re- constructed and analysed usingthe same algorithm chainas the data. These events also include additional proton–proton inter- actions (pile-up) generated with Pythia 8.186 [24] using the MSTW2008LO [25] parton distribution functions (PDFs) and the A2 setoftuned parameters [26] (A2tune). The simulatedevents arereweightedtoreproducethemeannumberofinteractionsper bunch crossing observed during 2015 and 2016data-taking. The averagenumberof pp interactionsper bunchcrossingisfoundto bearound13in2015and25in2016.Scalefactorsareappliedto simulated eventsto correctforthe differencesobservedbetween data andMC simulation inthe trigger, reconstruction, identifica- tion,isolation andimpactparameter efficienciesofphotons, elec- tronsandmuons [27,28].Thephoton energy,electronenergyand muonmomentuminsimulatedeventsaresmearedtoaccountfor differencesinresolutionbetweendataandMCsimulation [28,29].

In this analysis, the signal is the electroweak production of Z(

γ

j j (with =e,

μ

), withjetsoriginating fromthe frag-

mentation of partons arising from electroweak vertices. Signal events (

γ

j j) were generated [30] at leading-order (LO) accu- racy(at order

α

_EW⁵ ) using MadGraph5_aMC@NLO 2.3.3 [31] with noextrapartoninthefinalstate.Thenominalrenormalisationand factorisationscalesweresettothetransversemassofthediboson system. The NNPDF30 LO PDF set [32] was used forthe genera- tionoftheevents,andthehadronisationandpartonshowerofthe eventswasmodelled using Pythia 8.212 withtheA14tune [33].

An alternative model of hadronisation and parton shower is ob- tainedbyre-showeringeventswithHerwig 7.0.1 [34,35] usingthe UEEE-5tunethatisbasedonthemodelsdiscussedinRefs. [36,37]

inconjunctionwiththe CTEQ6L1 LO PDFset [38].

Analternativesample ofsimulated eventsatLO accuracy was generated using Sherpa 2.2.4 [39] with Comix [40] and merged withthe Sherpa partonshower [41].Thefactorisation andrenor- malisation scales were set to the invariant mass of the diboson system. The NNPDF30 next-to-next-to-leading order (NNLO) PDF set [32] wasusedforthegenerationofthissample.

ThemainbackgroundcomesfromtheQCD-inducedproduction oftheZ(

γ

j j finalstate,whichisestimatedatleadingorder, i.e. at order

α

_S²

α

_EW³ . The MC sample used to model this back- ground was obtained with the Sherpa 2.2.2 event generator for the

γ

process with up to one parton at NLO generated with OpenLoops [42] andup to threepartons atLO using Comix. The different final-state multiplicities were merged with the Sherpa partonshowerusingthe ME+PS@NLO prescription [43].Thissam- plewasgeneratedusingthe NNPDF30 NNLOPDFset.

AnalternativeQCD samplewas usedtostudy thedependence of the kinematic distributions on the matrix-element generator.

Thissample was obtainedwith MadGraph5_aMC@NLO 2.3.3 with up to one parton at NLO for the

γ

process. The second jet is obtainedfromtherealemissionatmatrix-elementlevel,i.e.with LOaccuracy. The eventgenerator was interfacedto Pythia 8.212 forthe inclusion of the partonshower and hadronisation of the events;theFxFxmergingprescriptionwasused [44] withamerg- ingscaleof20 GeV.The NNPDF30 NLO PDFsetandtheA14tune wereusedforthegeneration.

Interferencebetweenthe electroweak andQCD processes was estimatedatLO accuracyinQCDusingthe MadGraph5_aMC@NLO 2.3.3 MCeventgeneratorwiththe NNPDF30 LO PDFsetincluding onlycontributionstothesquaredmatrix-elementatorder

α

S

α

⁴_EW. Theeventgeneratorwasinterfacedto Pythia 8.212 fortheparton showersandhadronisationoftheeventswiththeA14tune.These interferenceeffectsare found tobe positive andare oftheorder of3% of the Z

γ

j j−EW cross-section in the fiducialphase space studiedbythisanalysis.

Thesecond-largestbackgroundinthisanalysisisduetoZ+^jets processes.In thiscase, one ofthe jetsis misidentified asa pho- ton. This contribution is estimated using a data-driven method, as explained in Section 5. Cross-checks are performed using a Sherpa 2.2.1 MC sample [45], produced with up to two jets at NLO accuracyanduptofourjetsatLO accuracy,usingComixand OpenLoops,andmergedwiththe Sherpa partonshoweraccording tothe ME+PS@NLO prescription.The NNPDF30 NNLOPDF setwas usedforthegenerationofthissample.Thissampleisscaledtothe NNLOpredictionsforinclusiveZ productionusinganormalisation factor [45] derivedfrom FEWZ [46] andthe MSTW2008NNLO PDF set [25].

Thethird-largestbackgroundaffectingthisanalysisisfromtt¯+

γ

events.These eventswere generated atLO accuracy usingthe MadGraph5_aMC@NLO2.3.3generatorinterfacedto Pythia 8.212 forthepartonshoweringandhadronisation.The NNPDF23 LO PDF setandtheA14tunewere usedforthegeneration.The normali- sationofthepredictionsiscorrectedforNLO QCDeffects [47].

All other backgrounds are smallerand are obtained from MC simulations.ThemostimportantofthesearetheW Z background,

which was simulated with Sherpa 2.2.1and the NNPDF30 NNLO PDF set, andthe W t background, which was simulatedwith the Powheg-Box [48–50] generatorinterfacedto Pythia 6.428 [51] and the perugia 2012tune [52].The CT10 NLO PDF set [53] wasused forthegenerationofthissample.

4. Eventselection

Events are selected ifthey were recordedduring stablebeam conditions and if they satisfy detector and data quality require- ments, which include all relevant subdetectors functioning nor- mally. Events were collected using single-leptonor dileptontrig- gers [21,54] thatrequire,respectively,atleastoneortwoelectrons ormuons.

For single-lepton triggers, the transverse momentum (pT) thresholdin2015was24 GeV forelectronsand20 GeV formuons satisfyingalooseisolationrequirementbasedonlyonIDtrackin- formation. In 2016, due to the higher instantaneous luminosity, these thresholds were increased to 26 GeV for both the elec- tronsandmuons,andtighterisolationrequirementswereapplied.

Inefficiencies forleptons withlargetransverse momentawere re- ducedbyincludingadditionalelectronandmuon triggersthat do not includeanyisolation requirements; thesehadtransverse mo- mentum thresholdsof60 GeV and50 GeV,respectively.Finally,a single-electrontriggerrequiringpT>120 GeV withlessrestrictive electron identification criteriawas used to increase the selection efficiency for high-pT electrons. The threshold was increased to 140 GeV in 2016. In2015, the dileptontrigger pT thresholdwas 12 GeV for electrons, and either 10 GeV for muons in conjunc- tionwithtwomuonsproducingL1triggers,or18 GeV and8 GeV inthecasethatonlyone ofthetwomuonsproduced anL1trig- ger.In2016,thesethresholdswereraisedto17 GeV forelectrons, 14 GeV forthesymmetricdimuontrigger,and22 GeV and8 GeV fortheasymmetricmuontrigger.Thecombinedefficiencyofthese triggersiscloseto100% fortheeventsthatpassthekinematicre- quirementsdescribed below.Toensure that thetrigger efficiency iswelldetermined,theleptoncandidatesmustbematchedtothe leptonsthatareselectedbythetriggerandhaveatransversemo- mentumatleast1 GeV abovetheonlinethreshold.

Eventsmust havea primaryvertexwithatleasttwo charged- particletrackswhichmustbe compatiblewiththe pp interaction region. In cases where multiple vertices are reconstructed in a single event, the vertex with the highest sum of the p²_T of the associated tracks is selected as the productionvertex of the Z

γ

system.

Muonsarereconstructedbymatchingtracksinthemuonspec- trometer to tracks in the inner detector. Candidate muons are required tosatisfy the ‘medium’ setof identificationcriteria [28]

basedonthenumberofdetectorhitsandp_T measurementsinthe ID and the MS. The efficiencyof selecting such muonsaveraged over pT and

η

islarger than 98%. Both theID andMS measure- ments are usedto computethe muon momentum.The measure- ment alsotakesintoaccount the energylossinthe calorimeters.

Muons are used in the analysis if they satisfy pT>20 GeV and

|

η

|<2.5.

Electronsarereconstructedby matchingenergyclustersinthe electromagnetic calorimeter to an ID track. Candidate electrons are required to pass a ‘medium’ likelihood requirement that is builtfrominformationabouttheelectromagneticshowershapein the calorimeter, track properties and the track-to-cluster match- ing [27]. The efficiency of selecting such electrons is of about 90%.Calorimeterenergyandthetrack’sdirectionarecombinedto computetheelectronmomentum.Electronsarerequiredtosatisfy pT>20 GeV and|

η

_|<2.47.

Toensurethatelectronandmuoncandidatesoriginatefromthe primary vertex, the significance of the track’s transverse impact

parameterrelative to thebeamlinemustsatisfy |^d0/

σ

d0|<3 (5) formuons(electrons), andthe longitudinal impact parameter z0, thedifferencebetweenthevalueofz at thepointonthetrackat whichd0 isdefinedandthe longitudinal positionofthe primary vertex,isrequiredtosatisfy|^z0·^sin(θ )|<0.5 mm.

Electronsandmuonsarerequiredtobeisolatedfromhadronic activity by imposing maximum energy requirements in cones in the

η

–φ plane, defined using the R =

(

η

)²+ (φ)^{2 dis-} tance, around their direction of flight, using calorimeter-cluster and ID-track information, excluding the electron or muon mo- mentum.Theyare selectedfollowingthe ‘gradientloose’require- ments [27,28].Themuonisolationcriterionimposesafixedupper limit in a cone of size R=⁰.2 for calorimeter-based isolation andinacone ofsizeR=⁰.3 forID-based isolation,witha se- lectionefficiencyabove 90% for p_T>20 GeV andatleast99% for pT>60 GeV.Forelectrons,therequirementsvarywith pT,allow- ing a selection efficiencyof atleast 90% for pT>25 GeV and at least99% for pT>60 GeV.Forelectrons, both isolation variables areevaluatedwithaconeofsizeR=⁰.2.

Photoncandidatesarereconstructedfromclustersofenergyde- posited in the electromagnetic calorimeter and are classified as unconverted(clusterswithoutamatchingtrackormatchingrecon- structedconversionvertexintheID)orconverted(clusterswitha matchingreconstructedconversionvertexoramatchingtrackcon- sistent with originating from a photon conversion). Photons are identified using a cut-based selection relying on shower shapes measuredwiththeelectromagneticcalorimeter.Ninediscriminat- ing variables are used, built from the distribution of energy in differentlayers ofthe EMcalorimeterand informationabouten- ergyleakingintothehadroniccalorimeter.Theshowershapeval- ues in the simulation are corrected to improve their agreement with the shower shapes in data. Photons must satisfy a ‘tight’

requirement [55]. Photons selected in this analysis must satisfy ET>15 GeV,where ET isthe photon transverse energy,andthe pseudorapidity ofthe cluster must be inthe range |

η

_|<1.37 or 1.52<|

η

_|<2.37, to avoid the transition region between barrel andendcapcalorimeters.Photoncandidatesarerequiredtobeiso- latedaccordingto calorimeter-clusterandID-trackinformationin aconeofsizeR=⁰.2,excludingthephotonenergy.Therequire- mentvarieswith ET following the‘fixed loose’requirement [55], providinganaverageefficiencyofabout95%.Thecalorimetricpho- tonisolationiscorrectedtoaccountforleakageandthecontribu- tionfromtheunderlyingeventandpile-uptransverseenergy [27].

Jetsarereconstructedfromclustersofenergydepositionsinthe calorimeter [56] usingtheanti-k_t algorithm [57,58] witharadius parameter R=⁰.4.Calibration ofthejet energyisbasedonsim- ulation andinsitu methods fromdata [59]. Jets originatingfrom non-collisionbackgroundsordetectornoiseareremoved [60].Pile- upjetsare suppressedusinga multivariatecombinationoftrack- basedvariablesintheIDacceptance(|

η

_|<2.5) [61].Alljetscon- sideredmusthave pT>25 GeV andmustbe reconstructedinthe pseudorapidityrange|

η

_|<4.5.

Jetscontainingab-hadronareidentifiedintheIDvolumeusing a multivariate algorithm [62,63] that uses theimpact parameters andsecondaryverticesofthetracks containedinthejet.The se- lection is done using a working point chosen to provide a 70%

selection efficiency for b-jets in an inclusive t¯t MC sample. The 70%workingpoint hasrejectionfactors of10and400forcharm and light-flavour jets, respectively. Correction factors are applied tothesimulatedeventsamplestocompensate fordifferencesbe- tween data and simulation in the flavour-tagging efficiencies for b-jets,c-jetsandlight-flavourjets.Thecorrectionforb-jetsisde- rivedfromtt events¯ withfinal statescontaining twoleptons, and thecorrectionsareconsistentwithunitywithuncertaintiesatthe levelofafewpercentovermostofthejetpTrange.

Toavoidcasesinwhichalepton,photon,orjetisreconstructed as two separate final-state objects, severalsteps are followed to remove such overlaps. Bremsstrahlung radiation by a muon can result inID tracks anda calorimeterenergy deposit that are re- constructedasanelectroncandidate.Therefore,incasesforwhich anelectroncandidateandamuoncandidateshareanIDtrack,the objectisconsideredtobeamuon,andtheelectroncandidateisre- jected. Theoverlapofobjectsismeasured usingthe R distance.

Due to the isolation requirements placed on electron candidates, anyjetsthat closelyoverlapan electroncandidatewithin a coni- calregionR<0.2 arelikelytobereconstructionsoftheelectron and so are rejected. When jetsandelectrons are found within a largerhollowconicalregion0.2<R<0.4,itismorelikelythat arealhadronicjetispresentandthattheelectronisanon-prompt constituent of the jet, arising from the decay of a heavy-flavour hadron. Hence an electron candidate found within R<0.4 of anyremainingjetisrejected.Muonscanbeaccompaniedbyahard photonduetobremsstrahlungorcollinearfinal-stateradiation,and themuon–photon systemcanthenbereconstructedasbothajet andamuon candidate.Non-promptmuonscanarisefromdecays of hadrons in jets; however, these muons are associated with a higherIDtrackmultiplicity thanthoseaccompaniedby hardpho- tons.Inordertoresolvetheseambiguitiesbetweennearbyjetand muon candidates,first anyjetshaving fewerthan threeID tracks and within R<0.4 of any muon candidate are rejected, then anymuoncandidateswithinR<0.4 ofanyremainingjetarere- jected.Theambiguitybetweenphotonsandleptonsisresolvedby rejecting anyphotonsfound tobe withinR<0.4 ofanelectron oramuon.JetsfoundwithinR<0.4 ofanyphotonsarerejected.

Events are required to contain exactly two lepton candidates (electrons or muons)with the sameflavour andopposite charge andatleastonephoton candidatesatisfyingthe selectioncriteria described above. When there are two ormore photons selected, theonewiththehighestET isusedforfurtherprocessing.

The invariant mass of the two leptons, m , must be at least 40 GeV. The sum of the dilepton mass and the three-body

γ

invariantmass(m +^m γ )isrequiredtobelargerthan182 GeV, which istwice the Z boson mass. Thisrequirementensures that the three-body invariant mass is larger than the Z boson mass, thussuppressingcaseswheretheZ bosondecaysinto

γ

[15,64].

Toselectelectroweakprocesses,eventsare furtherrequiredto include at least two ‘VBS-tagging’ jets. A symmetric selection of pT>50 GeV isusedtoselectbothtaggingjets,whichareclassified asleadingandsubleadingintransversemomentum.Thesetwojets arerequiredtohaveaninvariantmassm_{j j}>150 GeV,inorderto minimise the contamination from triboson background in which a hadronicallydecaying W or Z bosonisproduced inassociation witha Z bosonandaphoton,i.e. Z

γ

₊Z/W(→^{j j}).

ThefinalVBSsignalregion(SR)isdefinedbyrequiringthatthe pseudorapidity difference between the two leading jets |

η

(j j)| belargerthan1;thatnob-taggedjetbepresentintheevent;and that the centralityofthe

γ

system relativeto thetagging jets, definedas

γ ) = 



^{y γ}

− (

^yj1

+

^yj2

)/

2

(

yj₁

−

yj₂

)

 ,

⁽¹⁾

be lowerthan5,where y correspondstotherapidity,and j1 and j₂ labeltheselectedleadingandsubleadingjets.

5. Backgroundestimation

IrreduciblebackgroundsaremodelledkinematicallybyMCsim- ulations, and their normalisation is evaluated from the data.Re- ducible backgrounds,inwhichaphoton originatesfromahadron decay, are determined using data-driven techniques. Events in

whichone ormoreleptons originatefroma hadronicjetaresup- pressed by the stringent lepton selection. They are found to be negligibleandarenotconsideredhere.

Themainreduciblebackgroundoriginatesfrom Z+^jetsevents, inwhichonehadronicjetismisidentifiedasaphoton.Thisback- ground is not well modelled by the MC simulation and, there- fore, is estimated with data using a two-dimensional sideband method [65] similar to that applied in a previous analysis with Run 1data [15].Theshapesofthedistributionsof Z+^jetsevents areobtainedusingdata,afterapplyingallthesignalrequirements, butreversingthephoton identificationandisolation criteria [55].

The normalisation of this background is estimated in a control region designed to maximise the number of events available in thedata while beingclose to thesignal region; all signal region requirements are applied, except the transverse momentum re- quirementforthejets, whichisloweredto 30 GeV,andthe dijet invariantmassrequirement,whichislessthan150 GeV.Theratio ofZ+^jetstoZ

γ

j j−^{QCD eventsiscomputedinthisregion,sinceit} isfoundtobethesameinthiscontrolregionandinthesignalre- gion,inbothdataandMCsimulation,andusedtoextrapolatethe normalisation of Z+^{jets eventsto the signal region. To estimate} boththeshapeandthenormalisationofthisbackground,thecon- taminationfromevents containing realphotons isestimatedand correctedusingMCpredictions.

Themostimportantbackgroundisirreducibleandcomesfrom theQCD-inducedproductionof Z

γ

eventsinassociationwithtwo jets. The normalisation of thisbackground is constrainedby the data,asexplainedinSection6.

The other main irreducible background arises from t¯t +

γ

events.Thisprocess isalsoconstrainedbythedatainadedicated controlregionwhichisreferredtoasb-ControlRegion(b-CR).This controlregionisobtainedbyimposingallSRselectionsbutrequir- ingthepresenceofatleastonereconstructed b-taggedjetinthe event.

The contribution of backgrounds due to the production of Z+^jetsand

γ

+^{jetseventsintwodifferentoverlaid}interactionsis evaluated usinga data-drivenestimate following themethod de- scribedinRef. [64] andfoundtobenegligible.

Backgroundsfromothersourcesarereducibleandareevaluated using MC simulations. The most important contribution comes from W Z events, in which a charged lepton is misidentified as aphoton,andfromW t events.

6. Signalextractionprocedure

A boosted decision tree (BDT), as implemented in the TMVA package [66], isused to separate the electroweaksignal fromall thebackgrounds. The BDT is trained andthe setof variables re- tained as input to the BDT is optimised on simulated events to separate Z

γ

j j−^{EW eventsfromallbackgroundprocesses,exclud-} ing Z+^{jets, and to maximise the} signal-to-background ratio. In total,13 kinematic variables are combinedinto one discriminant thatcan takeanyvalue intherange[−¹,1]^{.Thefinal binningof} theBDT discriminant,or BDT score, isoptimised to improvethe sensitivityoftheanalysis.

Some ofthe variables usedin the BDT training are relatedto the kinematic properties of the two tagging jets: the invariant massof thesetwo jets, mj j, the difference inpseudorapidity be- tweenthesetwojets, 

η

j j,andthepseudorapidityand pT ofthe leadingjet.Other variablesarerelatedtothekinematicproperties ofthe photon andthe Z boson: the transverse momenta of the leadinglepton,the systemandthe

γ

system,andthe and

γ

invariantmasses.Anothersetofvariablesisrelatedtothecor- relationofthetwo taggingjetsandthe Z

γ

system:thedistance inthe

η

–φplanebetweenthe Z

γ

systemandthetwo-jetsystem, R(Z

γ

,j j); the smallest distance in the

η

–φ plane between a

photonandajet,amongallpossiblecombinations,Min(R(

γ

,j));

thedifferenceinazimuthbetweenthe Z

γ

systemandthetwo-jet system,φ (Z

γ

,j j)andthecentrality

γ

)asdefinedinEq. (1).

The modelling by MC simulations of the distribution shapes and the correlations between all input variables for the BDT is verified in the signal region. Compatibility within the uncertain- ties is observed forall distributions, asexemplified by Figs. 2(a) and2(b),exceptforthehigh-masstailofm_{j j} asshowninFig.2(c), as was also observed in previous analyses of electroweak pro- cesses [67–69].Thismismodellingdoesnot impactthesignalsig- nificancenortheuncertaintyinthemeasurementreportedinSec- tion9.

TheBDTscoredistributioninthesignalregionisusedtomea- surethe Z

γ

j j−^{EW signalfiducial}cross-sectionwithamaximum- likelihood fit, andto determine the significance ofthe signal. In this fit the ee

γ

j j and

μμγ

j j final statesare combined. An ex- tended likelihood function is builtfromthe product of two like- lihoods corresponding to theBDT scoredistribution in the Z

γ

j j SR, andthe multiplicity of reconstructed b-jets in the b-CR. The yieldsofthett¯+

γ

simulatedeventsareconstrainedbydatausing this last distribution. The normalisation of the Z

γ

j j−^{QCD sam-} ple is also constrainedby the data, directly inthe signal region, sincethisbackgrounddominatesthedistributionatlowBDTscore values.Thenormalisationsofthesebackgroundsareintroducedin the likelihood fit asunconstrained nuisance parameters, labelled as

μ

Zγj j−^QCD and

μ

_{t¯t+γ for} the Z

γ

j j−^{QCD and t}¯t+

γ

back- grounds,respectively.Theseparameters arerelative normalisation factors,definedwithrespecttotheSMpredictions.Fortheseback- grounds,thekinematicdistributionsareobtainedfromMCsimula- tions.BoththeshapeandthenormalisationdistributionsofZ+^jets background are estimated from data, as described in Section 5.

TheotherirreduciblebackgroundsaredeterminedfromMC simu- lations.Backgroundnormalisationsandshapescanvarywithinthe uncertainties,constrainedbyGaussiandistributionsasdescribedin Section7.

The fiducial cross-section is derived using the signal strength parameter

μ

Zγj j−EW:

μ

Zγj j−^EW

=

^N

data Zγj j−EW

N^MC_{Zγj j−EW}

,

where N^data_Zγj j−^EW isthe numberofsignal eventsmeasuredin the data,whileN^MC_Zγj j−^EW isthenumberofsignaleventspredictedby the MadGraph5_aMC@NLO 2.3.3MCsimulation.

The observed cross-section (

σ

_Z^fid_γ^{. ,}_{j j}^data_−EW) is then obtained by multiplying the signal strength

μ

Zγj j−EW by the MadGraph5_aMC@NLO 2.3.3 MC cross-section prediction in the fiducial region (

σ

_Z^fid_γ^.,_{j j}^MC_−EW). Because the effectof interferencebe- tween the Z

γ

j j−^{QCD and the Z}

γ

j j−EW processes is not ac- counted for in the Z

γ

j j−QCD contribution, the observed cross- section

σ

^fid_Zγ^._{j j−EW}formally corresponds toelectroweakproduction plustheinterferenceeffects.

7. Systematicuncertainties

Several sources of systematic uncertainty in the signal and background processes can affect the cross-section measurement.

Forthebackgroundandsignalprocesses,allsystematicuncertain- tiesthataffecttheshapesoftheBDTscoreandN_b-jetsdistributions areconsidered.Inaddition,allsystematicuncertainties thataffect theacceptance andnormalisationofthedistributions are consid- ered forall processes,except for the theory uncertainties in the signalprocess, whereonlytheeffectontheacceptanceisconsid- ered.Systematicuncertaintiesintheshapesofdistributionsarenot appliediftheyareconsistentwithstatisticalfluctuations.

Fig. 2. Post-fitdistributionsof(a)thetransversemomentumofthe γ system,(b)thecentralityofthe γ systemrelativetothetaggingjets,and(c)mj jinthesignal region.Theuncertaintybandaroundtheexpectationincludesallsystematicuncertaintiesandtakesintoaccounttheircorrelationsasobtainedfromthefit.Eventsbeyond theupperlimitofthehistogramareincludedinthelastbinofthedistribution.

Theuncertaintiesinthetheoreticalmodellingofthesignaland backgroundsthatareestimatedfromMCsimulationscanaffectthe cross-section measurement. The uncertainties due to the knowl- edgeofthePDFandthe

α

SvalueusedinthegenerationoftheMC samplesaredeterminedusingthe PDF4LHC prescription [70].They arefoundtobeoftheorderof2%forthenormalisationoftheQCD and tt¯

γ

samples. The uncertainties due to missing higher-order QCDcorrectionsareevaluatedusinganenvelopeofthelargestde- viationsobtainedbyvaryingtherenormalisationandfactorisation scalesindependentlybyfactorsoftwoandone-half.Theseuncer- taintiesarelarge forthe Z

γ

j j−^{QCD andt}t¯+

γ

backgroundsand theirimpactonthenormalisationis⁺₋³⁰₂₀%.Theshapeuncertainties dueto themissing higher-orderQCD correctionsare of2–4% for thesignalandthe Z

γ

j j−^{QCD andt}t¯+

γ

backgrounds.

Forthesignal andt¯t+

γ

background,uncertainties duetothe partonshower andunderlying-event modelling are evaluated us- ingdedicatedtunevariations [33] andbyre-showeringeventswith Herwig 7.0.1insteadof Pythia 8.212.Theseuncertaintiesaffectthe

shapeofthedistributionbyatmost5% atlargevaluesoftheBDT scoreandarenegligibleatlowvaluesoftheBDTscore.Forthesig- nalthisuncertaintytakesintoaccounta problemwithcolorflow connection in VBS-like topology that was observed andreported inRefs. [71,72] in thepartonshower modelsof Pythia 8.212 and Sherpa 2.2.4. Forthe Z

γ

j j−QCD background, the modelling un- certainties dueto the partonshowers, underlying-event and ma- trix elements are estimated by comparing the predictions of the Sherpa2.2.2and MadGraph5_aMC@NLO 2.3.3MCgenerators.The difference betweenthesetwopredictionsistakenasasystematic uncertaintyappliedasbothapositiveandanegativevariation.The effects in the BDT score distribution and the Nb-jets distribution duetothesetwoset-upsaretakenasuncertainties.Themainim- pactisonthe BDTscoredistribution withan effectrangingfrom

−^{5% to20% atlowandhighvaluesoftheBDTscore,}respectively.

As discussed inSection 6, the interference betweenthe elec- troweak signal and the Z

γ

j j−QCD process is not included in the fit. However, this interference can distort the shape of the

Z

γ

j j−EW template. This effect is estimated using the Mad- Graph5_aMC@NLO2.3.3 MCgeneratoratLOinQCD,andistaken asasystematicuncertaintyintheshapeofthesignal.Thesizeof thiseffectrangesfrom5% to2% atlowandhighvaluesoftheBDT score,respectively.

Anothersource ofuncertaintyarisesfromthesizes ofthe MC samples anddata sample in the regions used in the analysis to modelthe BDT score and N_b-jets distributions. The statistical un- certainty in the shape of the BDT score for Z

γ

j j−^{QCD events} rangesfrom 5% to 13% atlow andhighvaluesof theBDT score, respectively,andisabout2% forZ

γ

j j−^{EW events.FortheZ}+^jets background,thestatisticaluncertaintydominatestheshapeuncer- taintydueto thesize ofthe datasample;itis about10% atlow BDTscore values,andup to 50% athighvalues,whileuncertain- tiesfromothersourcesarenegligible.Thestatisticaluncertaintyin theshapeof Nb-jets isabout25% for Z

γ

j j−^{QCD and isabout3%}

fortt¯

γ

events.

Other systematic uncertainties originate from the reconstruc- tion, identification, and energy calibration of electrons, photons, muons, andjets. The largestof theseuncertainties is dueto the jetenergyscalecalibration.Theuncertaintiesduetothejetenergy resolutionandto thesuppression ofpile-upjetsare alsoconsid- ered,asdescribedinRef. [73].Thetotaleffectoftheuncertainties relatedtojet reconstruction andcalibrationon thenormalisation ofthe Z

γ

j j−QCD background isabout8%,anditisabout4% for Z

γ

j j−^{EW eventsinthesignalregion.Theimpactontheshapeis} largestfor the Z

γ

j j−^{QCD events andranges from 2% to18% at} lowandhighBDTvalues,respectively.Theuncertaintyduetothe heavy-flavourtaggingefficiencyamountsto9% (2%)innormalisa- tioninthesignal(b-CR)regionforthet¯t+

γ

background,whereas the impact on other backgrounds andon the shape ofthe tem- platedistributions is found to be negligible. Uncertaintiesin the lepton identification, reconstruction, isolation requirements, trig- gerefficiencies,energyscaleandenergyresolutionaredetermined by using Z events [27,28,74]. The largest experimental un- certaintyassociatedwiththephotonsis thephotonidentification efficiency [55].Thephotonandleptonuncertaintiesaffectonlythe normalisationof Z

γ

j j−^{EW, Z}

γ

j j−^{QCD, andt}¯t+

γ

processes.In total,theseeffectsareof3% to4% inthesignalregion.

A 20% yield uncertainty is assigned to the Z+^{jets reducible} backgroundestimate.Thisuncertaintyaccountsforthenumberof events in the control regions used in the two-dimensional side- bandmeasurement,andforthecorrelationbetweenphotoniden- tification and isolation requirements. A 20% yield uncertainty is assignedtotheotherbackgroundsestimatedfromsimulations.

AvariationinthepileupreweightingofMCsamplesisincluded tocover the uncertaintyon the ratiobetweenthe predicted and measuredinelasticcross-section [75].The resultinguncertaintyin themeasuredfiducialcross-sectionis5%.

The uncertaintyin the combined 2015–2016 integrated lumi- nosityis 2.1% [76], obtainedusing theLUCID-2 detector[77] for theprimaryluminositymeasurements.

Theeffectofeach oftheseuncertainties onthefiducialcross- sectionmeasurement isshownin Table1.The individual sources aregroupedintoeithertheoreticalorexperimentalcategories.The largestuncertaintiesare duetothejetreconstructionandcalibra- tion,followedbytheuncertaintyarisingfromthesizesoftheMC samples,andthetheoreticaluncertainties inthe modellingofthe Z

γ

j j−^{EW signal and of the Z}

γ

j j−QCD background. Uncertain- ties affecting only the normalisation of the Z

γ

j j−^{QCD and t}t¯

γ

backgroundhavealmostnoimpactonthe Z

γ

j j−EW cross-section measurement since the corresponding normalisation parameters areconstrainedbythefittothedataasexplainedinSection6.

Table 1

Relativeuncertaintiesinthemeasuredfiducialcross-sectionσ_Z^fid_γ^._{j j−EW}.Theuncer- taintiesareexpressedinpercentages.Thecorrelationsbetweentheseuncertainties aretakenintoaccountinthecomputationofthetotaluncertainty.

Source Uncertainty [%]

Statistical ⁺₋¹⁹₁₈

Zγj j−EW theory modelling ⁺₋¹⁰₆

Zγj j−QCD theory modelling ±⁶

t¯t+γtheory modelling ±2

Zγj j−EW and Zγj j−QCD interference ⁺₋³₂

Jets ±⁸

Pile-up ±⁵

Electrons ±1

Muons ⁺₋³₂

Photons ±¹

Electrons/photons energy scale ±1

b-tagging ±²

MC statistical uncertainties ±⁸

Other backgrounds normalisation (including Z+^{jets) +}−⁹8

Luminosity ±2

Total uncertainty ±²⁶

8. Phasespaceforcross-sectionmeasurements

The Z

γ

j j electroweak cross-section is measured ina fiducial phasespacethatisdefinedtocloselyfollowtheselectioncriteria ofthesignal regiondescribed inSection 4. Thisregionisdefined at the particle level, using stable particles (with a proper decay length c

τ

>10 mm)which are produced fromthe hard scatter- ing,includingthosethat aretheproductsofhadronisation,before theirinteractionwiththedetector.Leptonsproducedinthedecay of a hadron,a

τ

-lepton,or their descendants are not considered inthe definitionof thefiducial phasespace. Prompt-leptonfour- momenta are obtainedfroma sumof the leptons four-momenta andthefour-momentaofphotonsnotoriginatingfromhadronde- cays withina coneofsizeR=⁰.1 aroundtheleptons (‘dressed leptons’). Jetsare reconstructed using the anti-k_t algorithm with radius parameter R=⁰.4 using stable particles, excluding elec- trons, muons, neutrinos, and photons associated with the decay ofa W or Z boson. Photonisolation isdefinedasthetransverse momentumofthesystemofstableparticleswithinaconeofsize R=⁰.2 aroundthephoton,excludingmuons,neutrinos,andthe photonitself.

Thefollowingselectionrequirementsareimposedtodefinethe fiducialphasespace.Thechargedleptonsfromthe Z bosondecay arerequiredtohavetransversemomentumpT>20 GeV and|

η

_|<

2.5,andtheinvariantmassofthetwoleptonsmustbelargerthan 40 GeV. The photon is required to have transverse momentum p_T>15 GeV and |

η

|<2.37. Photons isolated fromany hadronic activityareselectedbyrequiringthatthephoton isolation,asde- finedabove,divided bythephotontransversemomentum beless than5%.Theangulardistancebetweeneachofthechargedleptons fromthe Z decayandthephotonisrequiredtobeR>0.4.The sum ofthe two-lepton invariant mass and two-lepton plus pho- toninvariantmassmustsatisfy(m +^m γ )>182 GeV inorderto excludefinal-stateradiationevents.

Inaddition totheserequirements,atleasttwo jetswith pT>

50 GeV and |

η

_|<4.5 arerequired.The angulardistancebetween each of the charged leptons from the Z boson decay and each of the jets is required to be R(j,)>0.3. The angular dis- tance between the photon and each of the jets is required to be R(j,

γ

)>0.4. Theinvariant massmj j ofthe twohighest-pT

Fig. 3. Post-fitdistributionsof(a)theBDTscoreinthesignalregionandof(b)Nb-jetsintheb-CR.Theuncertaintybandaroundtheexpectationincludesallsystematic uncertaintiesandtakesintoaccounttheircorrelationsasobtainedfromthefit.EventsbeyondtheupperlimitofthehistogramareincludedinthelastbinoftheNb-jets distribution.

Table 2

Expected and observed numbers of events in the signal and control re- gions, after the fit. The expected number of Zγj j−^{EW events from Mad-} Graph5_aMC@NLO2.3.3andtheestimatednumberofbackgroundeventsfromthe otherprocessesareshown. Totalpost-fituncertainties,asdescribedinSection7, areshown.Theuncertaintyinthetotalexpectedyieldissmallerthanthequadratic sumoftheuncertaintiesineachprocessduetothesebeing anti-correlatedafter thefit.

SR b-CR

Data 1222 388

Total expected 1222 ±^{35 389} ±¹⁹

Zγj j−EW (signal) 104 ±^{26 5} ±¹

Zγj j−^{QCD 864} ±^{60 82} ±⁹

Z+^{jets 200} ±^{40 19} ±⁴

tt¯+γ 48 ±10 280 ±21

Other backgrounds 7 ±^{1 4} ±¹

jetsisrequiredto bem_{j j}>150 GeV,andthedifference between the pseudorapidities of these two leading jets is required to be

|

η

j j|>1.Finally,thecentralityofthe

γ

systemrelativetothe taggingjetsmustsatisfy

γ

)<5.

9. Cross-sectionmeasurements

Aprofile-likelihood-ratio test statistic [78] is used tomeasure thesignalstrength

μ

Zγj j−^EWanditsassociateduncertainties.The systematic uncertainties are treated as nuisance parameters and are constrainedwithGaussian distributions inthe fit.The statis- tical uncertainty is determined after having fixed each nuisance parameter to the conditional maximum-likelihood estimator [78]

alsocalledprofiledvalue. Fig.3showsthe BDTscoredistribution inthesignal region,andtheb-taggedjetmultiplicity intheb-CR, afterhavingappliedthebackgroundandsignalnormalisationsand havingsetthenuisanceparameters tothevaluesadjusted bythe profile-likelihood fit.The yield of events obtainedafter the fitis detailedinTable2.

Thesignalstrengthismeasuredtobe:

μ

Zγj j−^EW

=

1

.

00

±

0

.

19

(

stat

.) ±

0

.

13

(

syst

.)

⁺₋⁰₀^._.¹³₁₀

(

mod

.)

=

¹

.

00

±

⁰

.

26

,

with“stat.”correspondingtothedatastatisticaluncertainty,“syst.”

totheexperimental systematicuncertainties andsizeofMCsam- ples, and “mod.” to the theoretical modelling of the signal and background MC samples. This corresponds to a statistical signif- icance of 4.1 standard deviations both observed and expected.

The expected significance is obtained after having applied the backgrounds normalisations, which are found tobe

μ

Zγj j−QCD= 0.78⁺₋⁰₀^._.²⁶₂₀ and

μ

_t¯t+γ=1.49⁺₋⁰₀^._.⁴⁰₃₄.The uncertaintyinthe normali- sationparametervaluesincludesthetheoreticaluncertainties,such asuncertaintiesderivedfromQCDscalevariations.Thenormalisa- tionofthet¯t+

γ

backgroundagreeswithresultsfromotherstud- ies performedwithATLAS Run2data [79] in thisfinalstate. The normalisation of the Z

γ

j j−QCD background is compatible with results obtainedin the W Z j j final state [7]. It was checked that thesignal strengthobtainedinthecombinationoftheee

γ

j j and

μμγ

j j final states is consistent with the results obtained sepa- ratelyforeachchannel.

The fiducialcross-section ismeasuredbycomputingtheprod- uct ofsignalstrengthandthepredictedcross-sectionusedto de- fineit:

σ

_Z^fid_γ^._{j j−EW}

=

7

.

8

±

1

.

5

(

stat

.) ±

1

.

0

(

syst

.)

⁺₋¹₀^._.⁰₈

(

mod

.)

fb

=

7

.

8

±

2

.

0 fb

.

Thiscross-sectioncorrespondstotheelectroweakZ

γ

j j particle- levelcross-sectioninthefiducialphasespacedefinedinSection8 usingdressed leptons,andincludingconstructiveinterferencebe- tweenthesignalandtheQCD-inducedprocesses.

Thismeasurement canbe comparedwiththeLOcross-section predictedby MadGraph5_aMC@NLO 2.3.3:

σ

_Z^fid_γ^.,_{j j}^MadGraph_−EW

=

⁷

.

75

±

⁰

.

03

(

stat

.) ±

⁰

.

20

(

PDF

+ α

S

)

±

0

.

40

(

scale

)

fb

.

Thecross-sectionpredictedby Sherpa 2.2.4issomewhatlarger thanthatpredictedby MadGraph5_aMC@NLO 2.3.3:

σ

_Z^fid_γ^.,_{j j}^Sherpa_−EW

₌

8

.

94

±

⁰

.

08

(

stat

.) ±

⁰

.

20

(

PDF

+ α

S

)

±

⁰

.

50

(

scale

)

fb

.