A search for the Zγ decay mode of the Higgs boson in pp collisions at s=13 TeV with the ATLAS detector

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

A

search

for

the

Z

γ

decay

mode

of

the

Higgs

boson

in

pp collisions

at

√

s

=

13 TeV with

the

ATLAS

detector

.TheATLASCollaboration

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

Articlehistory: Received13May2020

Receivedinrevisedform13August2020 Accepted31August2020

Availableonline8September2020 Editor:M.Doser

Asearchforthe Zγ decayoftheHiggsboson,with Z bosondecaysintopairsofelectronsormuonsis

presented.Theanalysisusesproton–protoncollisiondataat√s =13 TeVcorrespondingtoanintegrated

luminosityof139 fb−1recordedbytheATLASdetectorattheLargeHadronCollider.Theobserveddata

areconsistentwiththeexpectedbackgroundwithap-valueof1.3%.Anupperlimitat95%conﬁdence

level ontheproductioncross-sectiontimesthebranchingratio for pp→H→Zγ isset at3.6 times

theStandardModelpredictionwhile2.6 timesisexpectedinthepresenceoftheStandardModelHiggs

boson. The best-ﬁt value forthe signal yield normalised tothe Standard Model prediction is2.0+₋1₀._.0₉

wherethestatisticalcomponentoftheuncertaintyisdominant.

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Anew boson [1,2] was discovered in2012 by theATLAS and CMSCollaborations.The observed propertiesofthe particle,such asits couplingsto Standard Model(SM) elementary particles, its spin andits parity, are sofar consistent withthe predictions for a SM Higgsboson (H ) [3–7]. The massof thisboson was deter-minedbytheATLASandCMSCollaborationstobemH=125.09± 0.21(stat)±0.11(syst)GeV usingtheLHCRun1dataset[8]. Sub-sequentmeasurements,bybothcollaborationsduringtheLHCRun 2,arepublished [9–11] andareconsistentwiththisvalue.

The SM Higgs boson can decay into Zγ through loop dia-gramsand the branching ratio is predictedto be B(H→Zγ)= (1.54±0.09)×10−3 _at_m

H=125.09 GeV [12]. Itcandiffer from theSMvalueforseveralscenarios beyondtheSM,forexample,if theHiggsbosonwereaneutralscalarofdifferentorigin [13,14],or acompositestate [15].Differentbranchingratiosarealsoexpected formodels with additional colourless charged scalars, leptons or vectorbosonsthatcoupletotheHiggsboson,duetotheir contri-butionsvialoopcorrections [16–18].

Finalstateswhere the Z bosondecays into electronor muon pairs can be eﬃciently triggered and clearly distinguished from backgroundeventsproducedinpp collisions.Inaddition,the Z(→ )γ (=e or μ)ﬁnalstatecanbereconstructedcompletelywith goodinvariantmassresolutionandrelativelysmallbackgrounds.

Previous searches for the H→Z(→ )γ decay by the AT-LAS and CMS Collaborations use the full pp data sets collected at √s=7 and 8 TeV [19,20] and partial data sets collected at

_E-mail_address:_atlas_{.publications}_@cern_.ch_.

13 TeV [21,22]. Inall cases,no signiﬁcantexcess ofeventsabove the expected background is observed around the Higgs boson mass.Priortothepresentstudy,theATLASCollaborationreported anobserved(expectedassumingthepresenceofaSMHiggsboson signal)upperlimit ontheproductioncross-section times branch-ing ratiofor pp→H→Zγ of6.6(5.2) timesthe SM prediction at95%conﬁdencelevelforaHiggsbosonwithmH=125.09 GeV usinga samplecorresponding toan integratedluminosity of36.1 fb−1 [21]. TheCMSCollaboration reportedanobserved (expected assumingthepresenceofaSMHiggsbosonsignal)upperlimitof 7.4 (6.0) times the SM prediction for a Higgs boson withmH = 125 GeV usingasamplecorrespondingtoanintegratedluminosity of35.9fb−1 [22].

An updated search for decays of the Higgs boson into Zγ with the Z boson decaying into electron or muon pairs is de-tailed inthisletter.The searchuses pp collisiondatarecordedat √

s=13 TeV with the ATLAS detector at the LHC from 2015 to 2018, corresponding toa totalintegratedluminosity of139 fb−1. Thereareimportantimprovementsinthisanalysiscomparedwith thepreviousone [21],includinganincreaseinthesizeofthedata set, an improved eventcategorisation, andoptimised lepton and photonidentificationcriteria.Eventswithatleastonephotonand two electrons ormuonsof opposite charge areclassified intosix mutuallyexclusive categorieswhich are designedto enhance the sensitivity to the presence of the SM Higgsboson decaying into Zγ.Thedominantbackgroundistheirreduciblenon-resonant pro-ductionof Z bosonstogether withphotons. Asimultaneousfitto the reconstructed Zγ invariant massdistributions inall the cat-egories is performedto extract the overall H→Zγ signal yield.

https://doi.org/10.1016/j.physletb.2020.135754

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Table 1

HiggsbosonMCsamplesproducedwith Powheg-Box v2with thetechniquesusedtogeneratetheeventandtheirprecisioninαs fortheeventgeneration(gen.).The

versionof Pythia 8andthePDFsetusedformodellingtheHiggsbosonsdecay,partonshower,hadronisationandtheunderlyingeventarelisted.Theprecisionofthetotal cross-sectionusedinthesamplenormalisationisalsoreported.Thecross-sectionoftheqq¯→ZH sampleisnormalisedtotakeintoaccountcontributionsfrombothqq¯→ZH andgg→ZH.

Process Technique Pythia8 version & tune PDF set QCD (gen.) Normalisation

ggF NNLOPS [90,91]

& MiNLO [92–98]

8.186, AZNLO [87] NNPDF30 [75,76] NNLO NNNLO (QCD), NLO (EW) [33–44]

VBF Powheg[67–71] 8.186, AZNLO NNPDF30 NLO NNLO (QCD), NLO (EW) [45–47]

qq¯→VH MiNLO [98–100] 8.186, AZNLO NNPDF30 NLO NNLO (QCD), NLO (EW) [48–55]

tt H¯ Powheg 8.230, A14 [86] NNPDF23 [29] NLO NNLO (QCD), NLO (EW) [56–59]

2. ATLAS detector and data sample

The ATLAS detector [23,24] at theLHC isa multipurpose par-ticledetectorwithaforward–backward symmetriccylindrical ge-ometry andanear 4π coverage insolid angle.1 _It_consists _of_an

innertrackingdetector(ID)surroundedbyathinsuperconducting solenoid, electromagnetic (EM) and hadroniccalorimeters, and a muonspectrometer(MS)incorporatingthreelargeair-coretoroidal magnetswitheightcoilseach.

A two-level trigger system [25] was used during the √s= 13 TeV data-taking period. The ﬁrst-level trigger (L1) is imple-mentedinhardwareandusesasubsetofthedetectorinformation. Thisisfollowedbyasoftware-basedhigh-leveltriggerwhichruns algorithms similarto thoseinthe oﬄinereconstruction software, reducing the eventrate to approximately 1 kHz from the maxi-mumL1rateof100 kHz.

Theeventswerecollected withtriggersrequiringeitheroneor twoelectrons ormuonsintheevent.Duetotheincreasing lumi-nosity, thetransverse momentum (pT) thresholds were increased slightly during the data-taking periods. At the highest instanta-neousluminosityrecorded,thelowestpTthresholdforthe single-muontriggerwas 26 GeV.Forthedimuontrigger,asymmetric pT thresholds of 22 GeV and 8 GeV were used. The pT threshold was 26 GeV for the single-electron trigger and 17 GeV for both electronsinthedielectrontrigger.Theselowest-thresholdtriggers werecomplementedbytriggerswithhigherthresholdsbutlooser leptonidentificationcriteria.ForH→Zγ eventsthatpassthefull analysisselection, described inSection 4, thetrigger selection is 95.6% efficientfor the eeγ final state and92.2% efficient forthe μμγ final state. The trigger efficiencyhas been measured to an accuracy better than 2%. After applying trigger and data quality requirements, the integrated luminosity of the data used in this search correspondsto 139±2.4 fb−1.The averagenumberof pp interactionsperbunchcrossing (pile-up)rangedfromabout13in 2015toabout39in2018,withapeakinstantaneousluminosityof 2×1034_cm−2_s−1_.

3. Simulation samples

SimulatedMonteCarlo(MC)eventsofthesignalanddominant backgrounds are used to optimise the search strategy. The gen-erated MC events, unless stated otherwise, were processed with thedetailedATLASdetectorsimulation [26] basedon Geant4 [27]. The effects of pile-up were modelled by overlaying simulated inelastic pp events over the original hard-scattering event. The

1 _The_ATLAS_experiment_uses_a_right-handed_coordinate_system_with_its_origin_at

thenominalinteractionpoint(IP)inthecentreofthedetectorandthez-axisalong thebeampipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axispointsupward.Polarcoordinates(r,φ)areusedinthetransverseplane.The polarangle(θ)ismeasuredfromthepositivez-axisandtheazimuthalangle(φ) ismeasuredfromthepositivex-axisinthetransverseplane.Thepseudorapidity isdeﬁnedinasη= −ln tan(θ/2).AngulardistanceismeasuredinunitsofR=

(η)2_{+ (φ)}2_.

pile-up events were generated with Pythia 8.186 [28] using the NNPDF2.3LO setof parton distribution functions(PDFs) [29] and theA3parametertune [30].TheMC eventswereweighted to re-produce thedistributionofthenumberofinteractions per bunch crossingobservedinthedata.

In order to improve the description of the data, simulated events were corrected to ensure that the efficiencies for the re-construction and identification of objects match those measured in data. The corrections include those applied to trigger, recon-struction, identificationandisolationefficienciesforelectronsand muons,identificationandselectionefficienciesforphotons,and se-lectionefficiencyforjets [31,32].Similarly,momentumandenergy scale and resolution corrections for simulated objects were also takenintoaccount.

The mass of the Higgs boson for all simulated samples was chosen to be mH =125 GeV and the corresponding width is

H =4.1 MeV [12].Thesampleswere normalisedwiththelatest available theoreticalcalculationsofthecorrespondingSM produc-tion cross-sections at mH =125.09 GeV via gluon–gluon fusion (ggF) [12,33–44], via vector-bosonfusion (VBF)[12,45–47],in as-sociation with a vector boson (VH, where V isa W or a Z bo-son) [12,48–55] and witha top-quark pair(t¯t H ) [12,56–59]. The branching ratiois calculated at leading order inQCD [12,60–63] andit hasbeenshownthat higherorder QCDcorrectionshave a smallimpactontheestimatedcouplingstrength [64–66].

The production of the SM Higgs boson was modelled with the Powheg-Box v2 MonteCarloeventgenerator [67–71], as de-scribed in Ref. [72] and summarised in Table 1. Pythia 8 [28] was used to simulate the H→Zγ decay as well asto provide parton showering, hadronisation andthe underlyingevent. Other Higgsbosonproductionprocessesarenotconsideredastheir con-tributions to the total Higgs boson production cross-section are of the order of 0.1% or less. All four production modes of the Higgs boson considered contribute to the signal in this analysis andtheirrelative yieldswere fixedtotheSM predictions. Contri-butionsfromH→μμ(wherethereconstructedphotonoriginates fromQEDfinal-stateradiation)wereevaluatedusingsamples pro-ducedinthesamemannerandareconsideredasapotential back-groundinthisanalysis. TheimpactofinterferencebetweenHiggs bosons decays with the same final-state signature (H →γ∗γ, γ∗→e+e−/μ+μ− and H→μμ) isexpectedtobe negligiblein theStandardModel [73] andisneglected.

Additional samples of Higgs bosons produced by gluon–gluon fusion are used for studies of theoretical uncertainties. A sam-ple with multiple parton interactions disabled is used to study the uncertainties in the signal acceptance related to the mod-ellingofnon-perturbativequantumchromodynamics(QCD)effects. A sample generated with MadGraph5_aMC@NLO [74] using the NNPDF30PDF [75,76] set, whichincludesup totwo jetsat next-to-leading-order (NLO) accuracy in QCD using the FxFx merging scheme[74,77],isusedtostudytheggF acceptanceintheanalysis categories.

The background in this analysis originates mainly from non-resonant production of a Z boson and a photon ( Zγ), with a

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smaller contributionfrom the production of Z bosons in associ-ationwithjets( Z+jets),withonejetmisidentiﬁedasaphoton.

Alarge sample of background Zγ events was simulated with the Sherpa v2.2.2 [78] generator using a fast simulation of the calorimeter response [79]. It was produced at NLO precision in QCD for up to one additional parton and leading-order (LO) accuracy in QCD for up to three additional partons using the NNPDF3.0nnlo PDF set [76]. The matrix elements were matched and merged with the Sherpa parton shower [80,81] using the MEPS@LOprescription [82–85].

TheelectroweakproductionofZγj j withjetsoriginatingfrom thefragmentationof partonsarising fromelectroweak verticesis also considered. It was generated at LO accuracy in QCD using MadGraph5_aMC@NLO 2.3.3withnoadditionalpartonsinthe ﬁ-nalstate, whichisorthogonal tothe Zγ simulationwithSherpa. TheNNPDF30LO PDFset [76] wasusedforthegenerationofthe events,andthe hadronisation,parton shower andtheunderlying eventoftheeventswasmodelledusing Pythia 8.212withtheA14 parametertune [86].

Thebackgroundoriginatingfrom Z+jets isestimatedusinga data-driventechniquewhichisvalidatedusingasamplesimulated withthe Powheg-Box v1MC generator [68–70] atNLO accuracy in QCD. It was interfaced to Pythia 8.186 for the modelling of the partonshower, hadronisation and the underlying event with parameters setaccording to theAZNLO tune [87]. The CT10 PDF set [88] was used forthe hard-scatteringprocesses, whereas the CTEQ6L1PDFset [89] wasusedforthepartonshower.

4. Event selection, reconstruction and categorisation

Eventsarerequiredtohaveatleastonephoton candidateand atleasttwosame-ﬂavouropposite-chargeleptons,(=e, μ), asso-ciatedwithaprimaryvertexcandidate.Thisprimaryvertex candi-dateisreconstructedfromchargedparticles(tracks)intheIDwith transversemomentumpT>500 MeV,andisdeﬁnedtobetheone withthe largest sum of the squared transverse momenta of the associatedtracks.

Muon candidates are required to have a high-quality trackin the ID or the MS, satisfy the medium identification criteria, be within|η|<2.7 andhave pT>10 GeV [32].Electronandphoton candidates are reconstructed from topological clusters of energy deposits in the EM calorimeter, and in the case of an electron, a track in the ID matched to the cluster [31,101]. Electron and photoncandidatesinthetransitionregionbetweenthebarreland endcapEMcalorimeters,1.37<|η|<1.52,areexcluded.Electrons are required to satisfy loose likelihood-based identification crite-ria [31],havepT>10 GeV andbewithin|η|<2.47,whilephoton candidates are required to satisfy pT>10 GeV, |η|<2.37 and the tight identification criteria. Compared with the previous AT-LAS publication [21] the electron identification criteria is looser, improving signal acceptance, and the photon identification has beenupdated toimprove efficiencyinthetransverse momentum range 10 GeV−35 GeV. The lepton and photon candidates are alsorequiredtobeisolatedfromadditionalactivityinthetracking detectorandinthecalorimeters. Contributionstothe energy de-positedinthecalorimetersoriginatingfromtheunderlyingevents andpile-uparecorrectedforonanevent-by-eventbasisusingthe methoddescribedinRefs. [102–104].

In order to ensure that muon and electron candidates origi-natefromthe primary vertex, itis requiredthat thelongitudinal impact parameter, z0, computed relative to the primary vertex position,satisfies |z0 · sinθ|<0.5 mm, where θ is the polar angleof the track. Additionally, to suppress leptons from heavy-flavourdecaysthesignificanceofthetransverseimpactparameter d0 calculated relative to the measured beam-line position must

satisfy|d0|/σd0<3(5)formuons(electrons)where σd0 isthe

un-certaintyind0 obtainedfromthetrackﬁt.

Jetsarereconstructedfromtopologicalclusters [105] usingthe anti-kt algorithm [106] with a radius parameter of 0.4. Theyare requiredtohavepT>25 GeV and|η|<4.4.Jetsproducedin pile-up interactionsare suppressedby requiringthat thosewith pT< 60 GeV and|η|<2.4 passaselectionbasedonajetvertextagging algorithm [107],whichis92%eﬃcientforjetsoriginatingfromthe hardinteraction.

Anoverlapremovalprocedureisappliedtotheselectedlepton, photon andjetcandidates. Iftwoelectrons sharethe sametrack, or the separation between two electron energy clusters satisﬁes |η|<0.075 and|φ|<0.125,thenonlythehighest-pT electron isretained.ElectroncandidatesthatfallwithinR=0.02 ofa se-lectedmuoncandidatearealsodiscarded.Inordertosuppressthe eventsarising fromQED ﬁnal-stateradiation(FSR),photon candi-dateswithin aR=0.3 conearound theleptonsofthe Z boson candidatearerejected.Jet–lepton andjet–photon overlapremoval arealsoperformedbyremovingthejetifitsaxisiswithinacone ofsizeR=0.2 aroundoneoftheleptonsorthephoton.

The Z boson candidates are reconstructed from two same-ﬂavour opposite-charge leptons satisfying the selection criteria. Theleptons ofthe Z bosoncandidateareadditionallyrequiredto be consistent withbeingacceptedby atleast oneof thetriggers thattheeventpassed.Itisrequiredthatthe pToftheleptonsthat areassociatedwiththesingle-leptonordileptontriggersis1 GeV above the trigger threshold. The invariant mass of the Z boson candidatesisrequiredtobebetween50 GeV and101 GeV before applying themass resolutionimprovements described in the fol-lowing.

TheresolutionoftheinvariantmassoftheZ→μμcandidates isimprovedby3% bycorrectingthe muonmomentaforcollinear FSR(R<0.15),usingallphotonsidentifiedintheEM calorime-ter [72]. A constrained kinematic fit is applied to the dilepton invariant mass [108] for all Z boson candidates. This fit uses a lineshapemodelledbyaBreit-Wignerdistributionusingtheworld average values for Z bosons mass and width [109] and a single Gaussian to model the lepton momentum response. It improves the mass resolutionby 14% for the Higgsboson candidates with electronsinthefinal stateandby10%forfinalstateswithmuons whencombinedwiththeFSRcorrection.

AftertheFSRcorrectionandapplyingthekinematicﬁt,Z boson candidatesare requiredto haveaninvariant masswithin 10 GeV ofthe Z bosonmass,mZ=91.2 GeV. Ifaneventhasmultiple Z bosoncandidateswhichpassallrequirements,thecandidatewith themassclosesttothe Z bosonmassischosen.Fewerthan1%of thesimulatedsignal eventsthat passtheﬁnal H→Zγ selection have more than two leptons (dominated by events produced via VH andt¯t H )andlessthan0.1%ofthesignaleventshavea Z boson candidatethatdoesnotmatchatrueZ boson.

The Higgs boson candidate is reconstructed from the Z bo-son candidateandthe highest-pT photon candidatein theevent. The invariant mass of the ﬁnal-state particles, mZγ after cor-rection for FSR and by the kinematic ﬁt, is required to satisfy 105 GeV<mZγ <160 GeV. Finally, to reduce background con-taminationand simplifythe backgroundmodelling, an additional requirementisplacedonthetransversemomentumofthephoton suchthat pγ_T/mZγ>0.12.

ForSMH→Z(→ )γ events,thereconstructionandselection eﬃciency (including kinematicacceptance) is 20.4% varying by a maximumof2%dependingontheproductionmode.

Inordertoimprovethesensitivitytoa H→Zγ signal,the se-lected events are classifiedinto six mutuallyexclusive categories withdifferentexpectedsignal-to-backgroundratiosandmass res-olutions. Categories are defined according to the lepton flavour andeventkinematics. Additionally, a boosteddecisiontree(BDT)

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Table 2

Thenumberofdataeventsselectedineachcategoryandinthe Zγ massrangeof105–160 GeV.Inaddition,thefollowingnumbersaregiven:theexpectednumberof HiggsbosonsignaleventsinanintervalaroundthepeakpositionforasignalofmH=125.09 GeV containing68%oftheSMsignal(S68),themassresolutionquantiﬁed

bythewidthofthe S68 interval(w68)deﬁnedbythedifferencebetweenthe84thandthe16thpercentileofthe signalmassdistribution,thebackgroundinthe S68

interval(B68)isestimatedfromﬁtstothedatausingthebackgroundmodelsdescribedinSection5,theobservednumberofeventsintheS68interval(N68),theexpected

signal-to-backgroundratiointheS68window(S68/B68),andtheexpectedsignificanceestimatedefinedasS68/√S68+B68.Thefinalrowofthetabledisplaystheexpected

numberofeventsforananalysisperformedinasingleinclusivecategorycalculatedbysummingthenumberofeventsineachindividualcategory.

Category Events S68 B68 N68 w68[GeV] S68/B68[10−2] S68/√S68+B68

VBF-enriched 194 2.7 16.7 17 3.7 16.2 0.60 High relative pT 2276 7.6 108.5 118 3.7 7.0 0.70 High pTtee 5567 9.9 474.7 498 3.8 2.1 0.45 Low pTtee 76 679 34.5 6418.6 6505 4.1 0.5 0.43 High pTtμμ 6979 12.0 634.4 632 3.9 1.9 0.47 Low pTtμμ 100 876 43.5 8506.9 8491 4.0 0.5 0.47 Inclusive 192 571 110.2 16159.8 16261 4.0 0.7 0.86

trainedtoseparateVBFsignaleventsfromotherHiggsboson pro-duction modes and backgrounds is used to deﬁne a category of eventswithatleasttwojets.Iftherearemorethantwojetsinan event, the two highest-pT jets are used. The kinematic variables used in the categorisation andas input to the BDT, which have beenextendedwithrespecttotheRef. [21],are:

• ThepTofthehighest-pT jet, p_Tj1.

• Thepseudorapiditydifferencebetweenthetwojets,ηj j. • TheminimumR betweenthe Z bosonorphoton candidate

andeitherofthetwojets,Rmin

γor Z,j. • Theinvariantmassofthetwojets,mj j.

• Theabsolutevalueofthedifferencebetweenthe pseudorapid-ityof the Zγ systemand the average pseudorapidity ofthe twojets,|ηZγ− (ηj1+ηj2)/2|

[110].

• TheazimuthalseparationbetweentheZγ systemandthe sys-temformedbythetwojets, Zγ,j j.

• The azimuthal angle between the dilepton system and the photon, Z,γ .

• The component, pTt, of the transverse momentum of the

Zγ system, that is perpendicular to the difference of the 3-momenta of the Z boson and the photon candidate (pTt= |p_TZγ × ˆt|, where ˆt= (p_TZ− pγ_T)/|p_TZ− pγ_T|). This quantity is stronglycorrelatedwiththetransversemomentumofthe Zγ system,buthasbetterexperimentalresolution[111,112]. Events withtwo ormorejets withηj j>2 that havea BDT outputscorelargerthan0.87areclassifiedintoaVBF-enriched cat-egory.Oftheremainingevents,thosethatsatisfytherequirement on pγ_T/mZγ >0.4 are classified into a Highrelative pT category whilethe othersare separatedintofourcategoriesdepending on the lepton flavour anda cut at pTt=40 GeV.The boundaries of thecategoriesareselectedtomaximisetheexpectedsignal signif-icance.

VBF events are estimated to constitute 72% of the signal in the VBF-enrichedcategory. The HighrelativepT andHighpTt cate-goriesare expectedtobe enriched inVBF, VH andt¯t H eventsas theseproduction modes have on average higherHiggs boson pT than ggF production.Because thecontinuum Zγ background has on average lower Higgsboson candidate pT than the signal, the signal-to-backgroundratioisexpectedtobehigherinthese cate-goriesthanintheothercategories,asshowninTable2.Thetable alsosummarisestheobservednumberofeventsindatainthe Zγ mass range of 105-160 GeV and the expected number of signal (S68) andbackground (B68) eventsin a mZγ window containing 68% oftheexpectedsignal. In additionthe widthofthewindow containing68%oftheSMsignal (w68),whichquantifies themass resolutionandisdefinedasthedifference betweenthe84thand the16thpercentileofthesignalmassdistribution,isreported.B68 is estimated from fits to the data using the background models

described in Section 5. Thecategorisation improvesthe expected sensitivity,whichisdeﬁnedasS68/√S68+B68,byapproximately 50%.

5. Signal and background modelling

Thesignalandbackgroundyieldsareextractedfromaﬁttothe mZγ distributionobservedindatabyassumingparametricmodels forboth thesignal andbackgrounds.Forthesignal, theexpected acceptance and parameters that describe the shape are obtained from simulated signal samples in the same manner asRef. [21]. Forthebackground,themodelsare chosenusingsimulated back-groundsamplesandthevaluesoftheirparametersaredetermined byaﬁttothemassspectrameasuredindata.

ThesignalmassdistributionfortheHiggsbosondecayintoZγ iswellmodelledbyadouble-sidedCrystalBall(DSCB)function(a Gaussian function with power-lawtails onboth sides) [113,114]. The peakpositionandwidthoftheGaussian componentare rep-resented by μCB and σCB, respectively. The parameters of the DSCBaredeterminedineachcategorybyperforminga maximum-likelihoodﬁttothesignalMCsamples.

The parametric model used to describe the background mZγ distribution is selected using a template that is constructed from the simulated Zγ and electroweak Zγj j events, and a Z+jets contributionderived fromdata.Thesimulated Zγ events usea fastsimulationofthecalorimeterresponsewhichhasbeen confirmedtoproduceamZγ distributioncompatible,ineach cate-gory,with Zγ eventssimulatedwiththedetailedsimulation.The shape ofthe mZγ distribution for Z+jets events is constructed foreach categoryfromadatacontrol regiondefinedbyrequiring thephotoncandidatetonotsatisfythetightidentificationcriteria butstill passalooseridentificationcriteria.Tosmooththe statis-tical fluctuations ofthe mZγ distribution for Z+jets events, an analytic functionisfittedtotheratioofthemZγ distributionsfor Z+jets and Zγ events,in themZγ range of105–160 GeV. The smoothed mZγ distribution for Z+jets events is constructed by multiplying the Zγ distribution by the fitted ratio. The Z +jets and Zγ distributions have similar shapes, allowing a parametric function tobeused tofittheratio.2 Theuncertaintyinthefitted ratio isfound to have negligibleimpact on the background tem-plate.

The background composition in each category is determined using data and conﬁrms the dominance of the Zγ process over otherbackgroundswherejetsaremisidentiﬁedasphotons.A two-dimensional sideband technique [21,115] basedon the trackand calorimeter isolation of the photon candidate and whether the

2 _The_functional_form_used_is₍₁₋_x1/3₎f0_xp0+p1log(x) _where_x=_m_Z_γ_/√_{s (}√_s= 13TeV)wherefiandpiarethefreeparametersofthemodel.

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Table 3

Theselectedbackgroundfunctionandﬁtrangeineachanalysiscategory.

Category Function Type Fit range [GeV]

VBF-enriched Second-order power function 110–155 High relative pT Second-order exponential polynomial 105–155

ee high pTt Second-order Bernstein polynomial 115–145

ee low pTt Second-order exponential polynomial 115–160

μμhigh pTt Third-order Bernstein polynomial 115–160

μμlow pTt Third-order Bernstein polynomial 115–160

photoncandidatesatisﬁesthetightorthelooseridentiﬁcation cri-teriaisperformedineachcategory.ThefractionofZγ eventswith genuinephotons(including the Zγj j contribution),inclusiveover categories,is0.78+₋0₀._.04₀₉.

Toconstruct the ﬁnal background template foreach category, thenormalisationoftheelectroweak Zγj j eventsisbasedonthe predictedcross-sectionwhilethecombined Zγ andZ+jets distri-butionisnormalisedtothenumberofdataeventsinthatcategory aftersubtractingtheexpectednumberofelectroweakZγj j events. The background template is treated as a representative Asimov dataset [116] when choosing the functional form used to model it.

The functional form used to model the background is se-lected from the following families of functions: Bernstein poly-nomials,exponentialpolynomialfunctions(e(Ni=0pimiZγ)_),_a_sum_of power functions (N_i₌₁fimZpiγ ), and a class of functions given by

(1−x1/3₎f_xN

i=0pilog(x)i _where _x=_m

Zγ/√s (√s=13 TeV)where fi and pi are the free parameters of the models. The choice of analytical modelof the backgroundand themZγ range used for the final fit is optimised in each category using the background templatementionedearlier.Theoptimisationprocedure,whichhas been updated when compared to Ref. [21], includes a limit on theamount ofbiasin theextracted signalyield (also referred to as spurious signal) and a requirement on the fit quality, and it prefersmodels with fewer free parameters to maximisethe sta-tisticalsensitivity to the expectedsignal. For each category used intheanalysis,thebiasduetothespurioussignalisestimatedby performing a signal-plus-background fit to the mZγ background-only distribution estimated as explained above, with mH varied between 123 GeV and 127 GeV. The maximum number of sig-nal events derived from these fits in each category constitutes thespurious-signalsystematicuncertainty.Arequirementthatthe spurious signal be less than 50% of the expected statistical un-certainty in the signal yield is applied when selecting the back-groundmodellingfunction.Stricter requirements onthe spurious signal are not possible due to the statistical uncertainty in the mZγ background template. Inaddition, the χ2 probability ofthe background-onlyfitisrequiredtobelargerthan1%.Thefitrange is optimised in each analysis category by varying the lower and upperboundsin5 GeV stepswithintheranges105–115 GeV and 140–160 GeV,respectively.The optimalfitrangeandfunctionare selectedtoachievethehighestsignalsignificancewhilefittingthe expectedmassdistributionofbackgroundplusSMsignal.The sig-nificance evaluation also includes the spurious-signal systematic uncertainty.Theselectedbackgroundfunctionalformandfitrange ineachcategoryaredetailedinTable3.

6. Systematic uncertainties

The dominant experimental uncertainty in the signal yield is thespurioussignalfromthechoiceofbackgroundmodel.The spu-rioussignalcorresponds toasmuchas50%ofthestatisticalerror inthe expectedsignal yield per category, due toa limited num-berofsimulatedbackgroundevents.Itintroducesa28%systematic uncertaintyinthesignal strength,deﬁnedastheratioofthe ob-servedtoexpectedsignalyield;however,itonlyincreasesthetotal

uncertainty in the expected signal strength by 5.6% because of the large statistical uncertainty. The contribution from H→μμ isestimatedusingsimulatedeventsandamountstoabout1.7% in-clusively,andupto3.3%inindividualcategories.Anuncertaintyin thiscontributiontakenfromthelatestATLAS measurement[117] resultsinan uncertaintyof2.1% intheexpectedsignalyield.The combined uncertainty in the signal yield in any category due to the reconstruction, identification, isolation, and trigger efficiency measurements [31,32] is no more than 2.6%, 2.4% and 1.6% for photons,electronsandmuons,respectively.Pile-upalsoaffectsthe lepton andphoton identificationefficiencybutcontributesa neg-ligible amount to the uncertainty (0.2%). The uncertainty in the combined2015–2018integratedluminosityis1.7% [118,119].

Thetheoreticaluncertaintiesinthepredictedsignalyield origi-natefromuncertaintiesinthepredictedbranchingratio(5.7%) [12] aswell as fromuncertainties in themodelling ofthe production cross-section andkinematics of the Higgs boson due to missing higher-orderQCDcalculations(5.3%),thataredominatedby uncer-taintiesintheQCDrenormalisationandfactorisationscales(5.2%). Smaller effects originate from the parton shower modelling un-certainty (1.3%), PDFs (2.5%) and αs (1.9%). The uncertainties in the Higgs boson event kinematics due to missing higher-order QCDcalculationsimpactthedistributionofsignaleventsamongst the analysiscategories.They are evaluated usingan extension of the Stewart–Tackmann method [12,120], based on inputs from Refs. [121–123].Detailsofhowtheuncertaintyin theacceptance ofggF eventsintheVBF-enrichedcategoryandallothercategories is evaluated can be found in Refs. [124] and [21], respectively. Additionally, to account forthe uncertainties in themodelling of jetkinematics inggF eventsthecategory acceptanceiscompared withtheacceptancederivedfromthe MadGraph5_aMC@NLO sam-ple.TheHiggsbosonandjetkinematicsparticularlyaffecttheggF signalacceptanceintheVBF-enrichedcategory(37%)andHigh rel-ative pT category (21%). The effect of parton shower modelling, PDFsand αsonthedistributionofsignaleventsamongstthe anal-ysiscategories is lessthan 11%, 1% and2%, respectively. The ex-pected signal yield in the VBF category is alsoaffected (14%) by thejetenergyscale,jetenergyresolutionandvertextagging eﬃ-ciency [125].

Theuncertaintyinthemodellingofthesignalshapevaries be-tween analysis channels. The uncertainty in the mass resolution (σCB) isdominatedby theuncertaintyintheelectron andphoton energy resolution (<3.4%) and in the muon momentum resolu-tion (<3.6%). The uncertainty in the signal position (μCB) from theuncertaintyinelectron,photonandmuoncalibration(<0.15%) islessthan theuncertainty inthe assumedHiggsbosonmass of 0.19% [8].Theimpactofthesignalmodeluncertaintyonthesignal strengthislessthan2%.

7. Results

A profile-likelihood-ratio test statistic [116] is used to search foralocalisedexcessofeventsabovetheexpectedbackgroundby performing a fit to themZγ spectra in thevarious categories. In the samemanneraswas done in previous searchesfor H→Zγ [21],thelikelihoodisbuiltfromtheproductofPoissonprobability terms across all categories withtwo contributions: non-resonant background,andHiggsbosonsignal.Thelikelihoodincludesterms for the systematic uncertainties discussed in Section 6 imple-mentedasnuisanceparameters.Thenuisanceparametersdescribe thesystematicuncertainties,whichareparameterisedasGaussian orlog-normal priorsandare correlatedacross analysiscategories where appropriate. Upperlimitsare set onthe Higgs boson pro-ductioncross-sectionat95%confidencelevel(CL)usingthe mod-ified frequentist formalism [126]. The results are derived using closed-formasymptoticformulae [116].

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Fig. 1. TheZγ invariantmass(mZγ)distributionsofeventssatisfyingtheH→Zγselectionindataforthesixeventcategories:(a)VBF-enriched,(b)HighrelativepγT,(c)

HighpTt ee,(d)LowpTt ee,(e)HighpTt μμ,and(f)LowpTt μμ.Theblackpointsrepresentdata.Theerrorbarsrepresentonlythestatisticaluncertaintyofthedata.

Thesolidbluelinesshowthebackground-onlyﬁtstothedata,performedindependentlyineachcategory.Thedashedredhistogramcorrespondstotheexpectedsignalfor aSMHiggsbosonwithmH=125 GeV decayingintoZγ multipliedbyafactorof20.Thebottompartoftheﬁguresshowstheresidualsofthedatawithrespecttothe

background-onlyﬁt.

Theinvariant massdistributionsofthe Zγ eventsforthe var-ious categoriesare shown inFig. 1 withthe background-onlyfit superimposed.The expectedHiggsbosonsignal normalisedto20 times the SM prediction for mH =125 GeV is also shown. At mH=125.09 GeV, the observed (expected with a SM Higgs bo-son) p-value under the background hypothesis is 1.3% (12.3%), which corresponds to a significance of2.2 σ (1.2 σ). A weighted sumofallcategorieswiththefittedsignal-plus-backgroundmodel superimposed is shown in Fig. 2. The events are weighted by ln(1+S68/B68),where S68andB68aredefinedinSection4.

The best-ﬁt value for the H→Zγ signal strength, deﬁned asthe ratio of the observed to the predicted SM signal yield, is found to be 2.0±0.9(stat.)+₋0₀._.4₃(syst.)=2.0₋+1₀._.0₉(tot.)with an ex-pectedvalueof1.0±0.8(stat.)±0.3(syst.)assumingthepresence of the SM Higgs boson. The measured signal strength amongst

all categories arecompatible within their total uncertainties. The largest measured signal strength is 4.7₋+3₂._.0₇(tot.) in the High pTt

ee category. The total uncertainty isdominated by the statistical componentfromthedata.The systematiccomponentofthe total uncertaintyisdominatedbythespurious-signaluncertainties.

The observed 95% CL limit on the H→Zγ signal strength is found to be 3.6 times the SM prediction compared with an ex-pected value of 1.7 (2.6) assuming no (SM) Higgs boson decays into Zγ.Theobservedupperlimiton σ(pp→H)·B(H→Zγ)is 305 fbat95%CL.AssumingtheSMHiggsbosonproduction cross-section, theupperlimit at95%CL on B(H→Zγ)is foundto be 0.55%.

Thisresultrepresentsanimprovementofabouta factorof2.4 in expectedsensitivity comparedwith theprevious ATLAS publi-cation[21].Ofthisimprovement,afactorofapproximatelytwois

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Fig. 2. Weighted Zγ invariant mass (mZγ)distribution ofeventssatisfying the H→Zγselectionindata.Theblackpointsrepresentdata.Theerrorbarsrepresent onlythestatisticaluncertaintyofthedata.Eventsareweightedbyln(1+S68/B68),

where S68 and B68 are the expected signaland backgroundevents ina mZγ windowcontaining68%ofthe expectedsignal.The solidbluecurve showsthe combinedﬁttedsignal-plus-backgroundmodelwhenﬁttingallanalysiscategories simultaneously,thedashedlineshowsthemodelofthebackgroundcomponent. duetothelargeranalyseddatasetandtheadditional20% improve-mentcanbeattributedtotheimprovementsintheanalysis.

8. Conclusion

Asearchfor Zγ decaysoftheSMHiggsbosonin139 fb−1 of pp collisions at √s=13 TeV is performed with the ATLAS ex-periment atthe LHC. The observed data are consistent with the expectedbackground witha p-value of1.3%, while theexpected p-value in the presence ofa SM Higgs boson is12.3%. These p-values correspond to a signiﬁcance of 2.2 and 1.2 standard de-viations, respectively. The observed 95% CL upper limit on the σ(pp→H)·B(H→Zγ) is 3.6 times the SM prediction for a Higgsbosonmassof125.09 GeV. Theexpectedlimit on σ(pp→ H)·B(H→Zγ)assumingeithernoHiggsbosondecayinto Zγ or thepresenceoftheSMHiggsbosondecayis1.7 and2.6 timesthe SMprediction,respectively. The best-ﬁtvalue forthesignal yield normalised to the SM prediction is 2.0₋+₀1._.₉0 where the statistical componentoftheuncertaintyisdominant.

Declaration of competing interest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

We thankCERN for thevery successful operation ofthe LHC, aswell asthe support stafffromour institutions without whom ATLAScouldnotbeoperatedeﬃciently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia;ARC,Australia;BMWFW andFWF,Austria;ANAS, Azerbai-jan;SSTC,Belarus;CNPqandFAPESP,Brazil;NSERC,NRC andCFI, Canada;CERN;CONICYT,Chile;CAS,MOSTandNSFC,China; COL-CIENCIAS,Colombia;MSMTCR,MPOCRandVSCCR,Czech Repub-lic; DNRF andDNSRC, Denmark; IN2P3-CNRSand CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC andHong Kong SAR, China; ISF andBenoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco;

NWO, Netherlands; RCN, Norway;MNiSW andNCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russia Federation;JINR;MESTD, Serbia;MSSR,Slovakia; ARRSandMIZŠ, Slovenia;DST/NRF,SouthAfrica; MINECO,Spain;SRCand Wallen-berg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOEandNSF,UnitedStatesofAmerica. Inaddition, in-dividualgroupsandmembershavereceived supportfromBCKDF, Canarie, Compute Canada and CRC, Canada; ERC, ERDF, Horizon 2020,MarieSkłodowska-CurieActionsandCOST,EuropeanUnion; Investissementsd’AvenirLabex,Investissementsd’AvenirIdex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-ﬁnanced by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana,Spain;GöranGustafssons Stiftelse,Sweden;The Royal SocietyandLeverhulmeTrust,UnitedKingdom.

The crucial computingsupport from all WLCG partnersis ac-knowledged gratefully,in particularfromCERN, theATLAS Tier-1 facilities atTRIUMF(Canada),NDGF (Denmark,Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany),INFN-CNAF (Italy), NL-T1 (Netherlands), PIC(Spain), ASGC(Taiwan), RAL (UK) and BNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Majorcontributorsofcomputingresourcesare listedin Ref. [127].

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M.C. Chu63a,X. Chu15a,15d, J. Chudoba140, J.J. Chwastowski85, L. Chytka130,D. Cieri115,K.M. Ciesla85, D. Cinca47,V. Cindro92, I.A. Cioar˘a27b, A. Ciocio18, F. Cirotto70a,70b, Z.H. Citron179,j, M. Citterio69a, D.A. Ciubotaru27b, B.M. Ciungu166, A. Clark54, M.R. Clark39,P.J. Clark50,S.E. Clawson101,

C. Clement45a,45b,Y. Coadou102,M. Cobal67a,67c, A. Coccaro55b,J. Cochran79,R. Coelho Lopes De Sa103, H. Cohen160, A.E.C. Coimbra36, B. Cole39, A.P. Colijn120, J. Collot58,P. Conde Muiño139a,139h,

S.H. Connell33c,I.A. Connelly57,S. Constantinescu27b, F. Conventi70a,am,A.M. Cooper-Sarkar134, F. Cormier174,K.J.R. Cormier166, L.D. Corpe95,M. Corradi73a,73b, E.E. Corrigan97,F. Corriveau104,ab, M.J. Costa173,F. Costanza5, D. Costanzo148, G. Cowan94, J.W. Cowley32, J. Crane101,K. Cranmer125, R.A. Creager136, S. Crépé-Renaudin58,F. Crescioli135, M. Cristinziani24,V. Croft169, G. Crosetti41b,41a, A. Cueto5, T. Cuhadar Donszelmann170,H. Cui15a,15d,A.R. Cukierman152, W.R. Cunningham57, S. Czekierda85,P. Czodrowski36, M.M. Czurylo61b, M.J. Da Cunha Sargedas De Sousa60b,

J.V. Da Fonseca Pinto81b,C. Da Via101, W. Dabrowski84a, F. Dachs36,T. Dado47, S. Dahbi33e, T. Dai106, C. Dallapiccola103,M. Dam40, G. D’amen29,V. D’Amico75a,75b, J. Damp100, J.R. Dandoy136,

M.F. Daneri30,M. Danninger151,V. Dao36, G. Darbo55b, O. Dartsi5,A. Dattagupta131, T. Daubney46, S. D’Auria69a,69b,C. David167b,T. Davidek142, D.R. Davis49, I. Dawson148,K. De8, R. De Asmundis70a, M. De Beurs120,S. De Castro23b,23a,N. De Groot119, P. de Jong120,H. De la Torre107, A. De Maria15c, D. De Pedis73a, A. De Salvo73a,U. De Sanctis74a,74b, M. De Santis74a,74b,A. De Santo155,

J.B. De Vivie De Regie65,C. Debenedetti145, D.V. Dedovich80,A.M. Deiana42, J. Del Peso99,

Y. Delabat Diaz46, D. Delgove65, F. Deliot144,C.M. Delitzsch7, M. Della Pietra70a,70b,D. Della Volpe54, A. Dell’Acqua36,L. Dell’Asta74a,74b, M. Delmastro5,C. Delporte65, P.A. Delsart58, D.A. DeMarco166, S. Demers182, M. Demichev80,G. Demontigny110, S.P. Denisov123,L. D’Eramo121, D. Derendarz85, J.E. Derkaoui35d,F. Derue135, P. Dervan91,K. Desch24, K. Dette166,C. Deutsch24,M.R. Devesa30, P.O. Deviveiros36,F.A. Di Bello73a,73b,A. Di Ciaccio74a,74b,L. Di Ciaccio5, W.K. Di Clemente136, C. Di Donato70a,70b, A. Di Girolamo36, G. Di Gregorio72a,72b,B. Di Micco75a,75b, R. Di Nardo75a,75b, K.F. Di Petrillo59, R. Di Sipio166,C. Diaconu102,F.A. Dias120, T. Dias Do Vale139a,M.A. Diaz146a, F.G. Diaz Capriles24, J. Dickinson18,M. Didenko165, E.B. Diehl106,J. Dietrich19,S. Díez Cornell46, C. Diez Pardos150,A. Dimitrievska18,W. Ding15b, J. Dingfelder24, S.J. Dittmeier61b, F. Dittus36, F. Djama102,T. Djobava158b,J.I. Djuvsland17, M.A.B. Do Vale81c,M. Dobre27b, D. Dodsworth26, C. Doglioni97,J. Dolejsi142,Z. Dolezal142, M. Donadelli81d,B. Dong60c, J. Donini38,A. D’onofrio15c, M. D’Onofrio91,J. Dopke143, A. Doria70a,M.T. Dova89,A.T. Doyle57,E. Drechsler151,E. Dreyer151, T. Dreyer53, A.S. Drobac169, D. Du60b, T.A. du Pree120,Y. Duan60d,F. Dubinin111,M. Dubovsky28a,