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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Searches

for

exclusive

Higgs

and

Z boson

decays

into

J

γ

,

ψ (

2S

)

γ

,

and

ϒ(

nS

)

γ

at

s

=

13 TeV with

the

ATLAS

detector

.TheATLAS Collaboration

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

Articlehistory: Received3July2018

Receivedinrevisedform23August2018

Accepted12September2018

Availableonline14September2018 Editor: M.Doser

SearchesfortheexclusivedecaysoftheHiggsand Z bosonsintoa J/ψ, ψ(2S),or ϒ(nS)(n=1, 2, 3) meson and aphoton are performedwith a pp collision data samplecorresponding to an integrated luminosity of36.1 fb−1 collectedat√s=13 TeV withtheATLAS detectorattheCERNLargeHadron Collider.Nosignificantexcessofeventsisobservedabovetheexpectedbackgrounds,and95% confidence-levelupperlimitsonthebranchingfractionsoftheHiggsbosondecaysto J/ψγ, ψ(2S) γ,and ϒ(nS) γ

of3.5×10−4,2.0×10−3,and (4.9, 5.9, 5.7) ×10−4,respectively,areobtainedassumingStandardModel production. The corresponding 95%confidence-levelupper limits for thebranchingfractions ofthe Z

bosondecaysare2.3×10−6,4.5×10−6and (2.8, 1.7, 4.8) ×10−6,respectively.

©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Followingthe observationofa Higgsboson H with amass of approximately125 GeV bytheATLASandCMScollaborations [1,2], detailedmeasurementsof itspropertiesshow nodeviations from the Standard Model (SM) [3]. However, its role in fermionmass generationisstilltobeshownexperimentally.IntheSM,thismass generationisimplementedthroughYukawainteractions,andmany theories beyond the SM predict substantial modifications of the relevant Higgsboson couplings to fermions.The ATLAS and CMS collaborationshavereportedmeasurementsoftheHiggscoupling toathird-generationfermionwithasignificancegreaterthanfive standarddeviations inthe Hτ+τ− channel [3–5].In addition, progresshasbeenmadeinthethird-generationquark sectorwith indirect evidence of the coupling of the Higgs boson to the top quark [3]. Thiswas recently complementedby direct observation oftheassociatedproductionofthe Higgsboson witha top-quark pair(t¯t H ) [6,7].Evidence of Higgsbosondecays into bb has ¯ also beenfoundwitha significanceinexcessofthreestandard devia-tionsbybothATLASandCMS [8–10].Noexperimentalevidenceof Higgsbosondecaysintothefirst- andsecond-generationfermions hasyet beenfound, butdirect searcheswere recentlyperformed bytheATLAS CollaborationforHcc [11¯ ] and Hμ+μ−[12, 13] andbytheCMSCollaborationfor H→μ+μ− andHe+e− decays [14].

The Standard Model Higgs boson decays HJ/ψγ and H→ ψ(2S) γ offeran opportunity toaccessthe c-quark Yukawa

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

coupling [15,16] in a manner complementary to studies of the inclusive decay Hcc. ¯ The branching fraction for HJ/ψγ has been calculated within the SM to be B(HJ/ψγ) = (2.99+00..1615)×10−6 [17]. Other recent results on these calcula-tions are given in Refs. [18–20]. For H→ ψ(2S) γ the branch-ing fraction was calculated by the authors of Ref. [17] to be

B(H→ ψ(2S) γ)= (1.03±0.06)×10−6 usinganestimateforthe valueoftheorder-v2 NRQCDlong-distancematrixelement.

The corresponding decays in the bottomonium sector, H

ϒ(1S,2S,3S) γ,canprovide,incombinationwith H→bb decays, ¯ informationabouttherealandimaginarypartsofthe b-quark cou-pling to the Higgs boson [19], which could probe potential CP violation in the Higgssector. However, the expected SM branch-ingfractions,B(H→ ϒ(nS) γ)= (5.22+21..0270,1.42+00..7257,0.91+00..4838)×

10−9 (n=1,2,3) [17,18], are smaller due to a cancellation be-tweenthe“direct”and“indirect”amplitudes.Thedirectamplitude proceeds through the Hqq coupling ¯ with a subsequent pho-ton emission before the qq hadronisation ¯ to ϒ(nS). The indirect amplitude proceedsvia the Hγ γ coupling followed by the frag-mentation γ→ ϒ(nS).

Deviationsofthe c- and b-quark YukawacouplingsfromtheSM expectationscanleadtosignificantincreasesinthebranching frac-tions forexclusive decays. Thesedeviations can arise in beyond-the-SM theories; for example,the quark massesmight not origi-nateentirelyfromtheHiggsmechanismbutcouldalsobeinduced by other subdominant sources of electroweak symmetry break-ing [21]. Other scenarios include the minimal flavour violation framework [22], theFroggatt–Nielsenmechanism [23],the Higgs-dependent Yukawa couplings model [24], the Randall–Sundrum familyofmodels[25],andthepossibilityoftheHiggsbosonbeing

https://doi.org/10.1016/j.physletb.2018.09.024

0370-2693/©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

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The ATLAS Collaboration / Physics Letters B 786 (2018) 134–155 135

acompositepseudo-Goldstoneboson [26].Anoverviewofrelevant modelsofphysicsbeyond-the-SMisprovidedinRef. [27].

Decays of the Higgs boson into a heavy, vector quarkonium state, QJ/ψ or ϒ(nS), and a photon were searched for by theATLASCollaborationwithup to19.2 fb−1 ofdatacollectedat √

s=8 TeV [28],resultingin95%confidencelevel(CL)upper lim-itsof1.5×10−3 forB (HJγ)and(1.3,1.9,1.3)×10−3 for

B (H→ ϒ(nS)γ) (n=1,2,3). The former decay mode was also searchedforbytheCMSCollaboration [29],yielding asimilar up-perlimit.Inaddition,theATLASCollaborationsearchedfortherare Higgsdecays H→ φγ and H→ρ γ [30,31].

Owing to the large Z boson production cross section at the LHC,rare Z boson decayscanbeprobedatmuchlowerratesthan forHiggsboson decaysinto the samefinal state. Branching frac-tions for ZQ γ decays have been calculated to be between 10−8 and 10−7 for both the ZJ/ψγ and Z→ ϒ(nS) γ de-cays [32–34]. Measurements ofthe branching fractions forthese decayswouldprovideasensitivetestoftheSMandthe factorisa-tionapproachinquantumchromodynamics(QCD),sincethepower correctionsin terms ofthe ratio of theQCD energyscale to the vector-bosonmassaresmall [33].ATLASsearchedfor Z boson de-caysinto J/ψ orϒ(nS)(n=1,2,3) andaphoton with20.3 fb−1 of data collected at √s=8 TeV [28], resulting in 95% CL upper limitsof2.6×10−6and(3.4,6.5,5.4)×10−6,respectively.ATLAS

alsosearchedforthedecaymodes Z→ φγ andZρ γ [30,31]. This Letter describes searches for Higgs and Z boson decays intothe exclusivefinal states J/ψγ,ψ(2S) γ,and ϒ(nS) γ (n= 1,2,3)with J/ψμ+μ−,ψ(2S)μ+μ−,andϒ(nS)μ+μ− using ATLAS data collected in 2015 and 2016 at √s=13 TeV. Throughoutthe remainder ofthis Letter, where no distinction is relevant,the J/ψ andψ(2S)statesare referredtocollectively as theψ(nS)states.

2. ATLAS detector

ATLAS [35] isamultipurposeparticledetectorwithaforward– backwardsymmetriccylindricalgeometryandnear4π coveragein solidangle.1 Itconsistsofan innertracking detector, electromag-neticandhadroniccalorimeters,andamuonspectrometer.

Theinnertrackingdetector(ID)coversthepseudorapidityrange |η|<2.5 and is surrounded by a thin superconducting solenoid providinga 2 T magnetic field. At small radii,a high-granularity silicon pixel detector surrounds the vertex region and typically provides four measurements per track. It is followed by a sili-conmicrostrip tracker,which provideseight measurement points per track.Thesilicon detectorsare complementedby a gas-filled straw-tubetransitionradiationtracker,which enablesradially ex-tendedtrackreconstructionupto|η|=2.0 withtypically35 mea-surementspertrack.

Electromagnetic(EM)calorimetrywithintheregion|η|<3.2 is provided by barreland endcaphigh-granularity lead/liquid-argon (LAr)EMcalorimeterswithanadditionalthinLArpresampler cov-ering|η|<1.8 tocorrectforenergylossinupstreammaterial;for |η|<2.5 theEMcalorimeterisdividedintothreelayersindepth. A steel/scintillator-tile calorimeter provides hadronic calorimetry for|η|<1.7.LArtechnology withcopperasabsorber isusedfor thehadroniccalorimetersintheendcapregion1.5<|η|<3.2.The solid-angle coverage is completed with forward copper/LAr and

1 ATLASusesaright-handedcoordinatesystemwithitsoriginatthe nominal

interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis pointsupward.Cylindricalcoordinates(r,φ)areusedinthe transverseplane,φ beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedinterms ofthepolarangleθas η= −ln tan(θ/2).

tungsten/LArcalorimetermodulesin3.1<|η|<4.9 optimisedfor EMandhadronicmeasurements,respectively.

The muon spectrometer surrounds the calorimeters and has separate triggerand high-precision tracking chambersmeasuring the deflection of muons in a magnetic field provided by three air-core superconductingtoroidalmagnets.The precisionchamber systemcoverstheregion|η|<2.7 withthreelayersofmonitored drift tubes, complementedby cathode strip chambersin the for-ward region.The muontrigger systemcoversthe range|η|<2.4 withresistiveplatechambersinthebarrelandthingapchambers intheendcapregions.

A two-level trigger and data acquisition system is used to record events for offline analysis [36]. The level-1 trigger is im-plemented inhardware andusesasubsetofdetectorinformation to reduce the eventrateto atmost100 kHz.It is followedby a software-basedhigh-leveltriggerwhichfilterseventsusingthefull detectorinformationandoutputseventsforpermanentstorageat anaveragerateof1 kHz.

3. Data and simulated data

The search is performed with a sample of pp collision data recorded at a centre-of-mass energy √s=13 TeV corresponding toanintegratedluminosityof36.1 fb−1.Theintegratedluminosity of thedata sample has an uncertaintyof 2.1% derived using the methoddescribedinRef. [37].Eventsareretainedforfurther anal-ysisonlyifthey werecollectedunderstableLHCbeamconditions andallrelevantdetectorcomponentswerefullyfunctional.

The data samples used in this analysis were collected by a combination of two triggers [36]. The first required an isolated photon withtransverse momentum T greater than 35 GeV and atleastone muon with pTμ greaterthan 18 GeV.The second re-quired an isolated photon with T >25 GeV and a muon with pTμ>24 GeV. The use of two triggers with differing transverse momentumthresholdsonthephoton andmuonobjects offersan increasedtriggerefficiencywithrespecttothecaseofeither trig-gerusedalone.

Higgs boson productionwas modelled using the Powheg-Box v2 Monte Carlo(MC) eventgenerator [38–42] with CT10 parton distribution functions [43] forthe gluon–gluon fusion (gg H )and vector-boson fusion (VBF) processes. Both processes were calcu-lated up to next-to-leading order (NLO) in αS. Powheg-Box was

interfacedwith Pythia 8.186 [44,45] to modelthe partonshower, hadronisation,andunderlyingeventwiththeAZNLOsetoftuned parameters [46].Additionalcontributionsfromtheassociated pro-ductionofaHiggsbosonanda W or Z boson (denoted W H and Z H , respectively) were modelled by the Pythia 8.186 event gen-erator [44,45] withNNPDF23LO partondistributionfunctions [47] andtheA14setoftunedparametersforhadronisationandthe un-derlying event [48].The productionratesfortheSM Higgsboson with mH=125 GeV, obtained fromthe compilation in Ref. [27],

areassumedthroughoutthisanalysis.The gg H production is nor-malised such that it reproduces the total cross section predicted by a next-to-next-to-next-to-leading-order QCD calculation with NLO electroweak corrections applied [49–52]. The VBF produc-tionisnormalisedtoanapproximatenext-to-next-to-leading-order (NNLO) QCD crosssection withNLO electroweak corrections ap-plied [53–55]. The production of W H and Z H is normalised to cross sections calculated atNNLO inQCD withNLO electroweak corrections [56,57] including the NLO QCD corrections [58] for ggZ H . The production of a Higgs boson in association with tt (t¯ ¯t H ) or bb (b¯ bH ) ¯ isaccountedforbyscalingthetotalcross sec-tionusedtonormalisethe gg H signal sample,assumingthesignal efficiencyoftheseprocessestobe equalto thatfor gg H . The

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ad-ditionof tt H and b¯ bH to ¯ the gg H signal changesthe acceptance bylessthan1%.

The Powheg-Box v2event generator was alsoused to model inclusive Z boson production. Pythia 8.186 [44,45] withCTEQ6L1 parton distribution functions [59] and the AZNLO set of hadro-nisation and underlying-event parameters [46] wasused to sim-ulatepartonshowering andhadronisation. The prediction is nor-malisedtothetotalcrosssectionobtainedfromthemeasurement inRef. [60],whichhasan uncertaintyof2.9%.Thisconservatively assumestheluminosity componentoftheuncertaintytobe com-pletelyuncorrelatedwiththatofthissearch.

TheHiggsand Z boson decayswere simulatedasacascadeof two-bodydecays,accountingforeffects ofthequarkonium helic-ityon the μ+μ− kinematics. The quarkonium state is simulated tobe transverselypolarisedinthecaseoftheHiggsboson decay andlongitudinallypolarisedinthecaseofthe Z boson decay [34]. ThebranchingfractionsforthedecaysQμ+μ−aretakenfrom Ref. [61].The simulatedeventswere passed throughthe detailed Geant4 simulation of theATLAS detector [62,63] and processed withthesamesoftwareusedtoreconstructthedata.

4. Event selection for ψ(n S) γμ+μγ and

ϒ(n S) γμ+μγ

Muonsare reconstructed fromID trackscombined with inde-pendent muon spectrometer tracks or track segments [64] and are requiredtohave pTμ>3 GeV and pseudorapidity|ημ|<2.5. CandidateQμ+μ− decaysarereconstructedfrompairsof op-positely charged muons consistent withoriginating from a com-mon vertex. The highest-pT muon in a pair, called the leading

muoninthefollowing,isrequiredtohave pTμ>18 GeV.Dimuons

with a mass +μ− within 2.0<+μ<4.2 GeV are identi-fiedasψ(nS)μ+μ− candidates.Dimuonswith8.0<mμ+μ<

12.0 GeV areconsideredtobeϒ(nS)μ+μ−candidates. SelectedQμ+μ− candidatesaresubjectedtoisolation and vertex-qualityrequirements.Inthiscase,theprimary pp vertex is definedasthe reconstructedvertexwiththe highest ip2Ti ofall associatedtracksusedtoformthevertex.Thesumofthe pTofthe

trackswithinR =(φ)2+ (η)2=10 GeV/pμ

T (witha

maxi-mumR of 0.3)oftheleadingmuonisrequiredtobelessthan6% ofthemuon pT[65].Tomitigatetheeffectsofmultiple pp

interac-tionsinthesameorneighbouringbunchcrossings,onlyIDtracks thatoriginate fromtheprimary vertexare considered.The trans-versemomentumoftheIDtrackassociatedwiththeleadingmuon issubtractedfromthesum,andthesubleadingmuonisalso sub-tractedifit fallswithin theisolation cone.To rejectbackgrounds fromb-hadron decays,thesignedprojection oftheQ candidate’s flightdistancebetweentheprimary pp vertex andthedimuon ver-texonto thedirectionofits transversemomentum isrequiredto belessthanthreetimesitsuncertainty.

Photons are reconstructed from clusters of energy in the electromagnetic calorimeter. Clusters without matching ID tracks are classified as unconverted photon candidates while clusters matched toID tracks consistent withthe hypothesis ofa photon conversion into e+e− are classified as converted photon candi-dates [66].Reconstructed photon candidates are requiredto have transverse momentum T >35 GeV and pseudorapidity |ηγ|< 2.37, excluding the barrel/endcap calorimeter transition region 1.37<|ηγ|<1.52, and to satisfy the “tight” photon identifica-tion criteria [66]. Isolation requirements are imposed to further suppressthe contamination fromjets. The sumof thetransverse momentaofalltracksoriginatingfromtheprimary vertex,within

R =0.2 ofthephotondirection,excludingthoseassociatedwith reconstructed photon conversions, is requiredto be lessthan 5% of T. In addition to this track isolation criterion, a

calorime-terisolation criterion isapplied wherethesumofthe transverse momenta of calorimeter energy clusterswithin R =0.4 of the photon direction, excluding the transverse energy of the recon-structedphoton,isrequiredtobelessthan2.45 GeV+0.022pγT. The effects ofmultiple pp interactions in theevents are also ac-countedforinthecalorimeterisolationmeasurements.

Combinations of a Qμ+μ− candidate and a photon sat-isfying φ (Q, γ)>π/2 are retained for further analysis. When multiplecombinationsare possible,a situationthatarisesinonly a few percent of the events, the combination of the highest-pT

photonandtheQcandidatewithaninvariantmassclosesttothe respectivequarkoniummassisretained.Toimprovethesensitivity oftheϒ(nS)γ analysisinresolvingtheindividualϒ(nS)states,the eventsareclassifiedintotwo exclusivecategoriesbasedupon the pseudorapidityofthemuons.Eventswherebothmuonsarewithin theregion|ημ|<1.05 constitutethe“barrel”(B)category. Events whereatleastoneofthemuonsisoutsidetheregion|ημ|<1.05 constitutethe“endcap”(EC)category.

Tomaintainasinglesearchregion,whileensuringnear-optimal sensitivity for both the Higgs and Z boson analyses, the trans-versemomentumoftheQcandidatepQT isrequiredtobegreater than a value that varies as a function of the invariant mass of the three-body system mQγ . Forthe ψ(nS)μ+μ− (ϒ(nS)

μ+μ−)selection, pQT thresholdsof40 GeV (34 GeV)and54.4 GeV (52.7 GeV)areimposedfortheregions mQγ≤91 GeV and m≥ 140 GeV, respectively. The thresholds are varied between their minimum andmaximum values as a linear function of mQγ in theregion91 GeV<mQγ<140 GeV.

5. Signal modelling

For the ψ(nS) γμ+μγ final state, the total signal effi-ciencies (kinematic acceptance, trigger, reconstruction, identifica-tion,andisolation efficiencies)are19%and11%fortheHiggsand Z boson decays, respectively. The corresponding efficiencies for the ϒ(nS) γμ+μγ final states are22–23% and15–16%, re-spectively. The difference in efficiency betweenthe Higgs and Z bosondecaysarisesprimarilyfromthesofter pγT and p

μμ

T

distribu-tions associatedwith ZQ γ production,asseenby comparing Figs. 1(a)and 1(b) forthe J/ψγ caseandFigs. 1(c)and 1(d) for theϒ(nS) γ case.

Accounting forquarkoniumhelicity effectsin theQμ+μ− decaysleadstoa3–4%decreaseoftheexpectedHiggsboson effi-ciencyandacorresponding6–9%increaseoftheexpectedZ boson efficiency,relativetotheefficiencyforanisotropicdecay.

The +μγ resolution is 1.6–1.8% for both the Higgs and Z boson decays. For each of the final states, a two-dimensional (mμ+μγ and+μ−)probabilitydensityfunction(pdf)isusedto modelthesignal.TheHiggsbosonsignalsaremodelledwith two-dimensional multivariate Gaussian distributions, which retain the correlation between+μγ and +μ− of the final states.For the Z boson decays, the +μγ distributions of the signal are modelled with Voigtian pdfs (a convolution of Breit–Wigner and Gaussian pdfs) corrected with mass-dependent efficiency factors, andthe+μ− distributionsaremodelledasGaussianpdfs.

The+μ− distributionforselectedψ(nS) γ candidates,which pass the background generation region criteriadescribed in Sec-tion 6,isshown inFig.2(a) andexhibitsclearpeaksatthe J/ψ

andψ(2S)masses.InFigs.2(b)and 2(c),thecorresponding distri-butionsfortheselectedϒ(nS) γ candidatesareshown,wherethe

ϒ(1S,2S,3S)peakscanbeobserved.Theψ(nS)andϒ(nS)peaks are fittedwithGaussianpdfs andareusedtocross-checkthe pa-rametersobtainedfromthefittosimulatedsignaleventsamples, while the background is modelled with a Chebychev polynomial function. Theexperimental resolution in+μ− isapproximately

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The ATLAS Collaboration / Physics Letters B 786 (2018) 134–155 137

Fig. 1. Generator-leveltransversemomentum(pT)distributionsofthephotonandofthemuons,orderedinpT,for(a)HJ/ψγ,(b)ZJ/ψγ,(c)H→ ϒ(nS)γ and

(d)Z→ ϒ(nS)γsimulatedsignalevents,respectively.TheleadingmuoncandidateisdenotedbyT1andthesubleadingcandidatebyp

μ2

T .Thehatchedhistogramsdenote

thefulleventselectionwhilethedashedhistogramsshowtheeventsatgeneratorlevelthatfallwithintheanalysisgeometricacceptance(bothmuonsarerequiredtohave

|ημ|<2.5 whilethephotonisrequiredtohave|ηγ|<2.37,excludingtheregion1.37<|ηγ|<1.52).Thedashedhistogramsarenormalisedtounity,andtherelative differencebetweenthetwosetsofdistributionscorrespondstotheeffectsofreconstruction,trigger,andeventselectionefficiencies.

54 MeV forthe J/ψγ candidates(43 MeV foreventsinthebarrel categoryand64 MeV foreventsintheendcapcategory).

6. Background modelling

The dominant source of background exhibits a non-resonant +μγ distribution and is composed of two distinct contribu-tions:genuineQμ+μ− decaysandnon-resonantdimuon pro-duction.Thedecay Zμ+μγ withfinal-stateradiation( Z FSR) constitutesafurther,smallerbackgroundcontributionexhibitinga characteristicresonantstructureinthe+μγ distribution.

The+μγ continuum background is modelledwith a non-parametric data-driven approach usingtemplates to describe the kinematicdistributions.Thenormalisationofthebackgroundis ex-tracteddirectlyfromafittothedata.Theshapeofthebackground modelinthefinaldiscriminant variableisalsoprofiledinthefit. Asimilar procedurewas used intheearliersearch forHiggsand Z boson decaysinto J/ψγ andϒ(nS) γ [28] andthesearchesfor HiggsandZ boson decaysintoφγ and ρ γ [30,31].

The background model uses a sample of 5500 ψ(nS) γ and 2300ϒ(nS) γ candidateevents.Theseeventspassallofthe kine-maticselectionrequirementsdescribedpreviously,exceptthatthe photonandQ candidatesare not requiredtosatisfy thenominal isolationrequirementsanda looserminimum pQT requirementof

30 GeV isimposed.Theseeventsdefinethebackground-dominated “generation region”(GR). From theseevents,pdfs are constructed todescribethedistributionsoftherelevantkinematicandisolation variables andtheir mostimportant correlations. The datacontrol samples are corrected for contamination from Zμ+μγ de-cays.

Thepdfsofthesekinematicandisolationvariablesaresampled togenerateanensembleofpseudocandidates,eachwithcomplete

Q and γ four-vectorsandtheassociated Q andphoton isolation values.Theimportantcorrelationsamongthekinematicand isola-tionvariablesofthebackgroundevents,inparticularbetweenpQT and T, are retained in the generation of the pseudocandidates throughthefollowingsamplingscheme:

• Initially, a value for pQT is sampled from the corresponding pdf.

• The distributionof T isparameterised inbinsof pQT, anda valueissampledfromthecorrespondingbingiventhe previ-ously sampledvalueof pQT .Themuon isolation variablesare parameterisedinbinsof pQT and pγT andsampledaccordingto thepreviouslyselectedvalues.

• Thedistributions ofthepseudorapiditydifferencebetweenQ and γ, η(Q, γ), the photon calorimeter isolation variable,

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Fig. 2. Distributionof μ+μ− invariantmassfor(a)ψ(nS)γ andϒ(nS)γ ((b)barreland(c)endcapcategories)candidates.Thecandidatessatisfytheeventselectionbut withoutthenominalisolationrequirementsandwithalooserminimumpTQrequirementof30 GeV.Theseeventsconstitutethebackground“generationregion”definedin

Section6.

and their correlations are parameterised in a binned two-dimensionaldistributionin thesamebins of pQT used to de-scribethe T andmuonisolationvariables.

• Giventheselectedvaluesofrelativephotoncalorimeter isola-tionandpQT ,avalue fortherelativephotontrackisolationis sampled.

• Giventheselectedvaluesofη(Q, γ)and pQT ,avalueis sam-pledfortheazimuthal angularseparationbetweenQ and γ,

φ (Q, γ).

• Valuesfor ηQ andφQ aresampledfromabinned histogram ofthecorresponding distributionsinthedatacontrolsample. Thesearecombinedwithη(Q, γ)andφ (Q, γ)togivethe valuesof ηγ and φγ .

• A value for mQ is sampledfrom within the required region of+μ−.Separate pdfsareusedtodescribe the+μ− dis-tributionsofresonant ψ(nS)andϒ(nS) productionand non-resonant dimuons, which is referred to as“combinatoric” in thefollowing.

The use of this procedure ensures a good description of the background and avoids any reliance on the accuracy or limited samplesizeofsimulatedbackgroundevents.

The nominalselection requirementsare imposed andthe sur-viving pseudocandidates are used to construct templates for the mQγ distributions which are then smoothed using a Gaussian kerneldensityestimation [67]. Potentialcontamination ofthe GR samplefromsignal eventsisexpectedtobenegligible,anditwas verified, through signal injection tests, that such a potential

sig-nal contamination would not affectthe shape ofthe background model.

The normalisation of the exclusive background from Z FSR is determined directly from the fit to the data. The shape of this background in the +μγ distribution is modelled with a Voigtian pdf, while the +μ− distribution is modelled with a first order polynomial.The parameters of theformer pdf are de-rivedfromthesimulated Z→Q γ signalsamples.Theparameters ofthelatterpdfaredetermineddirectlyinthefittodata.

To validate this background model with data, the mQγ dis-tributions in several regions defined by kinematic and isolation requirementslooserthanthenominalsignalrequirementsareused tocomparethepredictionofthebackgroundmodelwiththedata. Three validation regions are defined using the GR selection as the basis and adding either the pQT requirement (VR1), or the muon isolation requirements (VR2), or the photon isolation re-quirement (VR3). The mQγ distributions in these validation re-gions are shownin Fig.3 forthe ψ(nS) γ andthe ϒ(nS) γ final states.Thebackgroundmodelisfoundtodescribethedatawellin allvalidationregions.

7. Systematic uncertainties

The systematic uncertainties in the expectedsignal yields are summarisedinTable1.UncertaintiesintheHiggsproductioncross sectionsareobtainedfromRef. [27].The Z boson productioncross sectionuncertaintyistakenfromthemeasurementinRef. [60].

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The ATLAS Collaboration / Physics Letters B 786 (2018) 134–155 139

Fig. 3. Thedistributionof+μγ indatacomparedtothepredictionofthebackgroundmodelfor((a),(b)and(c))H(Z)→ ψ(nS)γ and((d),(e)and(f))H(Z)→ ϒ(nS)γ intheVR1,VR2andVR3validationregions. Z FSRreferstothe Zμ+μγ backgroundcontribution.Thebackgroundmodelisnormalisedtotheobservednumberof eventswithintheregionshown.Theuncertaintybandcorrespondstotheuncertaintyenvelopederivedfromvariationsinthebackgroundmodellingprocedure.

TheuncertaintyintheacceptanceoftheHiggsbosonsignaldue tomissinghigherordersinthegenerator,partondistribution func-tions,underlying-eventsetoftunedparameters,andparton show-eringisestimatedbystudyingtheeffectofthedifferentvariations ontheacceptanceatgenerator level.Thetotal uncertaintyinthe acceptanceduetotheseeffectsisestimatedtobe1.8%.Forthe Z boson,therespectiveuncertaintyisdeterminedtobe6%by com-paringthe generator-level acceptancepredictions ofthe nominal simulatedsamplewiththoseof Madgraph5_aMC@NLO v2.2.2 [68] and Sherpa 2.2.1 [69].

Trigger efficiencies for photons are determined from samples enrichedwith Ze+e− eventsindata [70].The systematic un-certainty inthe expectedsignal yieldassociated withthe trigger efficiencyisestimatedtobe2.0%.Photonidentificationefficiencies are determined using the enriched Ze+e− events, aswell as inclusivephotonevents and Z→ γ events [66,71].The impact ontheyields ofthephoton identificationefficiencyuncertainties, forboth theconvertedandunconvertedphotons, are1.4%forthe Higgsand Z boson signals. Theeffectofthemuon reconstruction andidentificationefficiencyuncertaintyis2.8% [65].

The photon energy scale uncertainty, determined from Ze+e− eventsandvalidatedusing Z→ γ events [72,73],is prop-agatedthroughthe simulatedsignal samplesasa function of ηγ andT.Theuncertaintyassociatedwiththedeterminationofthe photon energy scale and resolution in the simulation is 0.3% in

the yieldof theHiggsand Z boson signal. Similarly,the system-aticuncertaintyassociatedwiththescaleofthemuonmomentum measurement is 0.2% [65]. The effect of the energy/momentum scale andresolution uncertainties on the signal shape is negligi-blefortheHiggsand Z boson signals.Forthe Z FSR background shape,theeffectis0.2%onthemeanvalueofthe+μγ

distri-bution.Includingthecorrespondingnuisanceparameterresultsin a0.5% changeintheexpectedlimit ofthe Z→ ϒ(nS)γ channels withnegligibleimpactintheotherchannels.

Theshape ofthebackgroundmodelis allowedtovaryaround the nominal shape, and the parameters controlling these sys-tematic variations are treated as nuisance parameters in the maximum-likelihoodfit described inSection 8. Three suchshape variations are implemented through scale variations on the T distribution in the model, linear distortions of the shape of the φ (Q, γ) distribution, and a global tilt of the three-body mass distribution around a pivot point. The first two variations are straightforward alterations to the underlying kinematics of the pseudocandidates,which causecorresponding changes in the three-bodymass.Thethirdvariationisapplieddirectlytothefinal three-body mass template. These systematic uncertainties allow thebackgroundtemplatetoadjusttotheobserveddistributionin data.

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Table 1

Summaryofthesystematicuncertaintiesintheexpectedsignalyields.

Source of systematic uncertainty Yield uncertainty H(Z)→ Qγ

Total H(Z)cross section 7.0% (2.9%)

Integrated luminosity 2.1%

H(Z)QCD modelling 1.8% (6%)

Trigger efficiency 2.0%

Photon identification 1.4%

Muon identification and reconstruction 2.8%

Photon energy scale 0.3%

Muon momentum scale 0.2%

8. Results

Thedataarecomparedwithbackgroundandsignalpredictions usinga two-dimensional (2D)simultaneous unbinned maximum-likelihood fit to the+μγ and+μ− distributions. A simul-taneous 2D fit is required to distinguish the Z FSR background fromthe Z signal andthe non-resonant background.The parameters ofinterest arethe Higgsand Z boson signal normal-isations. Systematic uncertainties are modelled using additional nuisanceparameters inthefit;inparticular, thebackground nor-malisations are free parameters. The fit uses the selected events with mQγ<300 GeV.

In total, 1033 events were observed in the ψ(nS) γ and 906 in the ϒ(nS) γ signal regions. The expected and observed num-bersofbackgroundeventswithin the mQγ ranges relevanttothe Higgs and Z boson signals are shown in Table 2. The results of thebackground-onlyfitsfortheψ(nS) γ andϒ(nS) γ analysesare showninFig.4.

Thesystematicuncertainties describedinSection 7resultina 1.0%increase of theexpected 95% CLupper limiton the branch-ing fraction of the H→ ψ(nS) γ decays. For the Z→ ψ(nS) γ decays,theeffectislarger,2.6%,mostly duetothesystematic un-certainty inthe backgroundshape. Similar behaviour isobserved intheϒ(nS) γ analysiswithsystematicuncertaintiesresulting in a2.5–2.7%deteriorationinthesensitivitytothe H→ ϒ(nS) γ de-cays and a 2.8–2.9% deterioration in the sensitivity to the Z

ϒ(nS) γ decays,also mostlydueto thesystematicuncertaintyin thebackgroundshape.

On the basis of the fit to the observed data, the largest ex-cessobservedis 2.2σ inthesearch for ZJ/ψγ.Upperlimits areseton thebranchingfractionsfortheHiggsand Z boson de-cays into Q γ using the CLs modified frequentist formalism [74]

withtheprofile-likelihood-ratiotest statistic [75] andthe asymp-totic approximations derived in Ref. [76]. The expected SM pro-duction crosssection isassumed fortheHiggs boson [27],while theATLAS measurementoftheinclusive Z boson crosssectionis used forthe Z boson signal [60], asdiscussed in Section 3.The results are summarised in Table 3. The observed 95% CL upper limits on the branching fractions for Higgs and Z boson decays into J/ψγ andψ(2S) γ are(3.5,20)×10−4and(2.3,4.5)×10−6,

Table 3

Expectedandobservedbranchingfractionupperlimitsat95%CLfortheH(Z)J/ψγ,H(Z)→ ψ(2S)γ,andH(Z)→ ϒ(nS)γ(n=1,2,3)analyses,assumingSM productionfortheHiggsand Z bosons.The±1σ intervalsoftheexpectedlimits arealsogiven.

Branching fraction limit (95% CL) Expected Observed

B (HJ/ψγ)[10−4] 3 .0+1.4 −0.8 3.5 B (H→ ψ (2S)γ)[10−4] 15.6+7.7 −4.4 19.8 B (ZJ/ψγ)[10−6] 1.1+00..53 2.3 B (Z→ ψ (2S)γ)[10−6] 6 .0+2.7 −1.7 4.5 B (H→ ϒ(1S)γ)[10−4] 5.0+2.4 −1.4 4.9 B (H→ ϒ(2S)γ)[10−4] 6 .2+3.0 −1.7 5.9 B (H→ ϒ(3S)γ)[10−4] 5.0+2.5 −1.4 5.7 B (Z→ ϒ(1S)γ)[10−6] 2.8+10..28 2.8 B (Z→ ϒ(2S)γ)[10−6] 3.8+1.6 −1.1 1.7 B (Z→ ϒ(3S)γ)[10−6] 3.0+10..38 4.8

respectively. The corresponding limits for the Higgs and Z bo-sondecaysintoϒ(nS) γ (n=1,2,3)are(4.9,5.9,5.7)×10−4and

(2.8,1.7,4.8)×10−6,respectively. Upperlimitsat95% CLon the product of the production cross section times branching fraction are determinedfortheHiggsbosondecays,yielding19 fb forthe HJ/ψγ decay,110 fb forthe H→ ψ(2S) γ decay,and(28,33, 32) fb forthe H→ ϒ(nS) γ (n=1,2,3)decays.

9. Summary

Searches for the exclusive decays of Higgs and Z bosons into J/ψγ, ψ(2S) γ, and ϒ(nS) γ have been performed with a √s=13 TeV pp collision data sample collected with the AT-LAS detector at the LHC corresponding to an integrated lumi-nosity of 36.1 fb−1. No significant excess of events is observed above the background expectations. The obtained 95% CL upper limits are B (HJ/ψγ) <3.5×10−4 and B (ZJ/ψγ) <

2.3×10−6 for the J/ψγ final state. The corresponding upper limitsareB (H→ ψ(2S)γ) <2.0×10−3 andB (Z→ ψ(2S)γ) <

4.5×10−6 for the ψ(2S) γ final state. The 95% CL upperlimits

B (H→ ϒ(nS)γ) < (4.9,5.9,5.7)×10−4 andB (Z→ ϒ(nS)γ) < (2.8,1.7,4.8)×10−6 are set for the ϒ(nS) γ (n=1,2,3) final

states. These upperlimits representan improvement by a factor of approximately two relative to the earlier H(Z)J/ψγ and H(Z)→ ϒ(nS) γ resultsfromtheATLASCollaborationusingupto 20.3 fb−1of√s=8 TeV pp collisiondatawiththeadditionofthe firstupperlimitsonthe H/Z→ ψ(2S) γ decays.

Acknowledgements

We thank CERN forthe very successful operation ofthe LHC, as well asthe supportstaff fromour institutions withoutwhom ATLAScouldnotbeoperatedefficiently.

Table 2

Thenumberofobservedeventsandthemeanexpectedbackground,withitstotaluncertainty,forthemQγ rangesofinterest.TheexpectedZ andHiggsbosoncontributions areshownforbranchingfractionvaluesof10−6 and10−3,respectively.Thesevaluesaremotivatedbytheexpectedsensitivityofthesearchtotherespectivebranching

fractions.

+μ−mass range [GeV]

Observed (expected background) Z signal forB=10−6 H signal forB=10−3

+μγ mass range [GeV]

81–101 120–130 J/ψγ 2.9–3.3 92 (89±6) 20 (23.6±1.3) 13.7±1.1 22.2±1.9 ψ(2S)γ 3.5–3.9 43 (42±5) 8 (10.0±0.8) 1.82±0.14 2.96±0.25 ϒ(1S)γ 9.0–10.0 115 (126±8) 9 (13.6±1.2) 7.8±0.6 10.7±0.9 ϒ(2S)γ 9.5–10.5 106 (121±8) 8 (12.6±1.4) 5.9±0.5 8.1±0.7 ϒ(3S)γ 10.0–11.0 112 (113±8) 7 (10.6±1.2) 7.1±0.6 9.2±0.8

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The ATLAS Collaboration / Physics Letters B 786 (2018) 134–155 141

Fig. 4. The+μγ and+μ− distributionsfortheselected(a)ψ(nS)γ and ϒ(nS)γ ((b)barreland(c)endcapcategories)candidatesalongwiththeresultsofthe maximum-likelihoodfitswithbackground-onlymodels.Z FSRreferstotheZμ+μγ backgroundcontribution.Thesolidbluelinedenotesthefullfitresultandthe dashedbluelinescorrespondtoits±1σuncertaintyband.Theratiosofthedatatothebackground-onlyfitsarealsoshown.(Forinterpretationofthecoloursinthefigure(s), thereaderisreferredtothewebversionofthisarticle.)

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WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq andFAPESP, Brazil; NSERC, NRC and CFI,Canada; CERN; CONICYT,Chile; CAS, MOSTandNSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic;DNRFandDNSRC,Denmark;IN2P3-CNRS,CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece;RGC,HongKongSAR,China;ISF,I-COREandBenoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN,Norway; MNiSW and NCN, Poland;FCT, Portugal; MNE/IFA, Romania; MES of Russia andNRC KI, Russian 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-dividualgroupsandmembershavereceivedsupport fromBCKDF, theCanadaCouncil,Canarie,CRC,ComputeCanada,FQRNT,andthe OntarioInnovation Trust,Canada; EPLANET,ERC,ERDF,FP7, Hori-zon 2020 and Marie Skłodowska-Curie Actions,European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne andFondationPartagerleSavoir,France;DFGandAvHFoundation, Germany;Herakleitos,ThalesandAristeiaprogrammesco-financed byEU-ESFandtheGreekNSRF;BSF,GIFandMinerva, Israel;BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana,Spain;theRoyalSocietyandLeverhulmeTrust,United Kingdom.

The crucial computingsupport fromall WLCG partners is ac-knowledged gratefully,in particularfrom CERN,the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Majorcontributorsofcomputingresourcesarelisted in Ref. [77].

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M. Aaboud34d, G. Aad99, B. Abbott124,O. Abdinov13,∗,B. Abeloos128,D.K. Abhayasinghe91, S.H. Abidi164, O.S. AbouZeid39,N.L. Abraham153,H. Abramowicz158,H. Abreu157,Y. Abulaiti6,

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The ATLAS Collaboration / Physics Letters B 786 (2018) 134–155 145

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F. Conventi67a,av,A.M. Cooper-Sarkar131, F. Cormier172,K.J.R. Cormier164, M. Corradi70a,70b,

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Figure

Fig. 1. Generator-level transverse momentum (p T ) distributions of the photon and of the muons, ordered in p T , for (a) H → J /ψ γ , (b) Z → J /ψ γ , (c) H → ϒ( nS ) γ and (d) Z → ϒ( nS ) γ simulated signal events, respectively
Fig. 2. Distribution of μ + μ − invariant mass for (a) ψ( nS ) γ and ϒ( nS ) γ ((b) barrel and (c) endcap categories) candidates
Fig. 3. The distribution of m μ + μ − γ in data compared to the prediction of the background model for ((a), (b) and (c)) H ( Z ) → ψ( nS ) γ and ((d), (e) and (f)) H ( Z ) → ϒ( nS ) γ in the VR1, VR2 and VR3 validation regions
Fig. 4. The m μ + μ − γ and m μ + μ − distributions for the selected (a) ψ( nS ) γ and ϒ( nS ) γ ((b) barrel and (c) endcap categories) candidates along with the results of the maximum-likelihood fits with background-only models

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