Combination of searches for Higgs boson pairs in pp collisions at √s=13TeV with the ATLAS detector

Physics Letters B 800 (2020) 135103

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Combination of searches for Higgs boson pairs 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:

Received6June2019

Receivedinrevisedform13November2019 Accepted13November2019

Availableonline19November2019 Editor:M.Doser

ThisletterpresentsacombinationofsearchesforHiggsbosonpairproductionusingupto36.1 fb⁻¹of proton–protoncollisiondataatacentre-of-massenergy√

s=13 TeV recordedwiththeATLASdetectorat theLHC.ThecombinationisperformedusingsixanalysessearchingforHiggsbosonpairsdecayinginto thebbb¯ b,¯ bbW¯ ⁺W⁻,bb¯τ⁺τ⁻,W⁺W⁻W⁺W⁻,bb¯γ γ andW⁺W⁻γ γ finalstates.Resultsarepresented fornon-resonantand resonantHiggsbosonpairproductionmodes.Nostatisticallysignificantexcessin data above the StandardModel predictions is found.Thecombined observed (expected)limit at95%

confidence levelonthe non-resonantHiggsboson pairproductioncross-sectionis6.9 (10)times the predicted StandardModel cross-section.Limitsare alsoset ontheratio (κλ)ofthe Higgsbosonself- couplingto itsStandard Modelvalue. Thisratiois constrainedat95% confidencelevel inobservation (expectation) to −⁵.0<κλ<12.0 (−⁵.8<κλ<12.0).In addition, limits are set on the production ofnarrowscalarresonancesandspin-2Kaluza–KleinRandall–Sundrumgravitons.Exclusionregionsare alsoprovidedintheparameterspaceofthehabemusMinimalSupersymmetricStandardModelandthe ElectroweakSingletModel.

©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

ThediscoveryoftheHiggsboson(H ) [1,2] attheLargeHadron Collider(LHC) [3] in2012hasexperimentallyconfirmedtheBrout–

Englert–Higgs (BEH)mechanism ofelectroweak symmetry break- ingandmassgeneration [4–6].TheBEHmechanismnotonlypre- dicts theexistence ofa massive scalar particle,butalso requires thisscalarparticletocoupletoitself.Therefore,observingthepro- ductionofHiggsbosonpairs(H H )andmeasuringtheHiggsboson self-couplingλH H H isa crucialvalidationoftheBEH mechanism.

Any deviation from the Standard Model (SM) predictions would open awindow tonewphysics. Moreover, theform oftheHiggs fieldpotential,whichgeneratestheHiggsbosonself-couplingafter electroweaksymmetry breaking,canhaveimportantcosmological implications,involving,forexample,predictionsforvacuumstabil- ityormodelsinwhichthe Higgsboson actsastheinflation field [7–10].

In the SM, the gluon–gluon fusion pp→H H process (ggF) accountsfor more than 90% of the Higgs boson pair production cross-section,andonlythisproductionmodeisconsideredhere.It proceedsviatwoamplitudes:thefirst(A1)representedbythedia- grams(a)and(b),andthesecond(A2)representedbythediagram (c)inFig.1.Theinterferencebetweenthesetwoamplitudesisde-

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

structiveandyields an overall cross-sectionof σ_ggF^SM(pp→^{H H})= 33.5⁺₋²₂^._.⁴₈ fbat√

s=13 TeV [11],calculatedfirstatnext-to-leading order(NLO)inQCDwiththeheavytop-quarkapproximation [12], thennumericallywithfulltop-quarkmassdependence [13] (con- firmedlaterinRef. [14] andanalyticallycomputedwithsomeap- proximationinRef. [15])correctedatnext-to-next-to-leadingorder (NNLO) [16] in QCD matched with next-to-next-to-leading loga- rithmic(NNLL)resummationintheheavy top-quarklimit [17,18].

The Higgs boson mass used in these calculations andfor all re- sultsinthispaperismH=¹²⁵.09 GeV [19].Beyond-the-Standard- Model(BSM)scenarioscan bringsubstantialenhancement ofthis cross-sectionbymodifyingtherelativesignofA1andA2,andby increasingA2.TheA2 amplitudeisproportionaltotheHiggsself- couplingλH H H.TheHiggsbosonself-couplingmodifierduetoBSM scenariosisdefinedas κλ= λH H H/λ^SM_{H H H}.Inthisanalysis,allother Higgs boson couplings are assumed to have SM values. Indirect limitson κλhavebeenobtainedusingthemeasurementsofsingle Higgsbosonproductionanddecay [20] andelectroweakprecision observables [21,22],constraining κλ totherange−⁸<κλ<14 at 95% confidence level (CL). The Higgs boson self-coupling is dis- cussedinthecontextofBSMmodelsinRefs. [22,23].

SeveralBSMmodels alsopredict theexistence ofheavy parti- clesdecayingintoapairofHiggsbosons.Two-Higgs-DoubletMod- els[24],modelsinspiredbytheMinimalSupersymmetricStandard Model (MSSM) like habemus MSSM (hMSSM) [25–28], andElec- https://doi.org/10.1016/j.physletb.2019.135103

0370-2693/©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. Examplesofleading-orderFeynmandiagramsforHiggsbosonpairproduction:thediagrams(a)and(b)areproportionaltothesquareoftheheavy-quarkYukawa couplings,whilethediagram(c)isproportionaltotheproductoftheheavy-quarkYukawacouplingandtheHiggsbosonself-coupling.Hereκλistheratioofthebeyond- the-Standard-ModelHiggsbosonself-couplingtothatoftheSM.Thediagram(d)representstheproductionoftheHiggsbosonpairthroughanintermediateresonance( X ) thatcouplestogluonsthroughaneffectivecouplingandtotheSMHiggsboson.

troweakSingletModels(EWK-singlet) [11,29–31] predict, inaddi- tiontotheHiggsboson,asecond,heavier,CP-evenscalarthatcan decayinto two SM Higgs bosons. In the EWK-singlet model,the scalar statesare mixed, witha mixingangle α. The ratio ofthe vacuumexpectationvalue ofthe additionalsingletto that ofthe SM Higgs doublet, tanβ, is a free parameter. In the hMSSM, the CP-evenstatesalso mix, andthemodel’s phenomenology can be describedbythemass(mA)ofathird,CP-odd,resonanceandthe ratioofthevacuumexpectationvaluesofthetwoHiggsdoublets, tanβ. Alternatively, the Higgs boson pair can be produced reso- nantly throughthe decayof aspin-2 Kaluza–Klein (KK) graviton, aspredictedintheRandall–Sundrum (RS)modelofwarpedextra dimensions [32]. Aschematic diagram forproduction of a heavy resonancefollowedbyitsdecayintoaHiggsbosonpairisshown inFig.1(d).

This letter presents a combination of results from searches for both non-resonant and resonant Higgs boson pair produc- tion in proton–proton (pp) collisions at √

s=^{13 TeV. The data} were collected with the ATLAS detector [33–35] and correspond to an integrated luminosity of up to 36.1 fb⁻¹. The combination includes all published ATLAS H H search analyses using √

s= 13 TeV data, namely those studying the final states bbb¯ b [36],¯ bbW¯ ⁺W⁻ [37], bb¯τ⁺τ⁻ [38], W⁺W⁻W⁺W⁻ [39], bb¯γ γ [40]

andW⁺W⁻γ γ [41].

PreviouscombinationsofsearchesforH H pairproductionwere performed at √

s=^{8 TeV by the ATLAS experiment [42] and at}

√s=^{13 TeV by the CMS experiment} [43] combining the final statesbbb¯ b [44–47],¯ bbVV[48],bb¯τ⁺τ⁻[49] andbb¯γ γ [50].

2. Analysisdescription

Theanalysisstrategiesforeachofthefinalstatesconsideredin thisletteraresummarisedbelow.

• ^Thebbb¯ b analysis¯ isperformedusing fouranti-k_t jetsrecon- structed with a radius parameter R=⁰.4 [51,52] (resolved analysis)ortwo large-R jetswith R=¹.0 (boostedanalysis).

The datasetof the resolved analysisis split accordingto the years 2015and 2016, andthen statisticallycombined taking intoaccountthedifferenttriggeralgorithmsusedin2015and 2016. In part of the 2016 data period, inefficiencies in the onlinevertex reconstruction affected b-jet triggers that were usedintheresolvedanalysis,reducingthetotalavailableinte- gratedluminosity to27.5 fb⁻¹.Theboostedanalysissearches fortwolarge-R jetscontainingtheb-quarkpairsfromthede-

cays of thetwo Higgsbosons. The large-R jets are identified asoriginatingfromb-quarks usinga b-taggingalgorithmap- plied to R=⁰.2 track-jets [53] associated with the large-R jet [54].The analysisisdividedintothreecategories:thefirst category selectseventsinwhicheachofthetwo large-R jets hasone b-taggedtrack-jet; thesecond category requiresthat onelarge-R jetcontainstwob-taggedtrack-jetsandtheother large-R jetcontains oneb-taggedtrack-jet;thethirdcategory requiresthatbothlarge-R jetscontaintwob-taggedtrack-jets.

FortheSM H H search,onlytheresolvedanalysisisused,with two categories, one for the 2015 and another for the 2016 dataset.Theresonantsearchisinsteadperformedwiththere- solved analysis formasses inthe range 260–1400 GeV, with the boostedanalysis formassesin the range800–3000 GeV, andwiththecombinationofthe twoformassesintheover- lappingrange800–1400GeV.

•^{The b}_bW¯ ⁺_W⁻ _{analysis looks for the W W} → νqq decay channel, where isan electronormuon, andq isa u,d,s,c quark oranti-quark.Theb_{b pair}¯ _{isselectedfromtwo R}=⁰.4 jets (resolved analysis) or one R=¹.0 large-R jet (boosted analysis), whilethejetsfromthe W decay are reconstructed withR=⁰.4 jets.TheresolvedanalysisisusedintheSM H H search, in thesearch fora scalarresonance witha mass be- tween500and1400GeV,andinthesearchforaKKgraviton inthemassrange500to800GeV.Theboostedanalysislooks forscalarresonancesinthemassrange1400to3000GeVand forKKgravitonsbetween800and3000GeV.Theresolvedand boostedanalyseseachuseonecategory.Thetwoanalysesare notstatisticallycombinedduetoasignificantoverlapbetween thetwosignalregions.

•^{The b}_b¯τ⁺τ⁻ analysislooks forfinal stateswithtwo R=⁰.4 b-tagged jets and two τ-leptons. One of the two τ-leptons of the τ⁺τ⁻ pair is required to decay hadronically, while the otherdecayseitherhadronically (τhadτhad) orleptonically (τlepτhad).Inthe τlepτhad channel,eventsaretriggeredbysin- gle lepton triggers (SLT), requiring an electron or a muon in the final state, or by the coincidence of a lepton trig- ger witha hadronic τ trigger(LTT). Inthe τhadτ_had channel, events are triggered by single hadronic τ triggers (STT) or doublehadronic τ triggers (DTT).Theanalysisisdividedinto threecategories:one selects τhadτhad events,asecond selects

τlepτhadeventstriggeredbytheSLT,andathirdselects τlepτhad eventstriggeredbytheLTT.The τhadτhad andtheSLT τlepτhad categoriesareusedforallmodelinterpretations,whiletheLTT

The ATLAS Collaboration / Physics Letters B 800 (2020) 135103 3

Table 1

Summaryofthemaincharacteristicsoftheanalysesusedinthenon-resonantandresonantsearches.Theresonantanalysischar- acteristicsareindicatedbetweensquarebrackets.“B(H H→x¯x y¯y)”indicatesthebranchingfractionofthe H H pair whereone H decaysinto xx and¯ theotherdecaysinto y¯y.ThebranchingfractionvaluesaretakenfromRef. [11] foraHiggsbosonmass mH=¹²⁵.09 GeV.“Lint”indicatestheintegratedluminosityofthedatasetusedintheanalysis.“Categories”indicatesthenumber ofsignalcategories.“Discriminant”indicatesthedistributionusedinthefinallimit-settingfit(“c.e.”standsforcountingeventsand indicatesthatasimpleeventcountingwasusedinthefinalfitratherthanadistributionshape).“Model”indicateswhichmodels eachanalysistested:NRstandsforSMH H signalmodel,S foraspin-0scalarmodel,andG foraKKgravitonmodel.“mS/G”gives theprobedmassrangefortheresonantsearch.“Ref.”reportsthereferencetotheindividualfinalstatepapers.

bbb¯ b¯ bbW¯ ⁺W⁻ bb¯τ⁺τ⁻ W⁺W⁻W⁺W⁻ bb¯γ γ W⁺W⁻γ γ

B(^{H H}→x¯x y¯y) 0.34 0.25 0.073 0.046 2.6·10⁻³ 1.0·10⁻³

Lint[fb⁻¹] 27.5 [36.1] 36.1 36.1 36.1 36.1 36.1

Categories 2 [2–5] 1 [1] 3 [2–3] 9 [9] 2 [2] 1 [1]

Discriminant mH H[mH H] c.e. [mH H] BDT [BDT] c.e. [c.e.] mγ γ [mH H] mγ γ [mγ γ]

Model NR [S/G] NR [S/G] NR [S/G] NR [S] NR [S] NR [S]

mS/G[TeV] [0.26–3.00] [0.50–3.00] [0.26–1.00] [0.26–0.50] [0.26–1.00] [0.26–0.50]

Ref. [36] [37] [38] [39] [40] [41]

τlepτhadcategoryisusedintheSM H H search(excludingthe

κλanalysis)andinresonantsearchesuptoamassof800GeV.

•^{The W+W−W+W− analysis looks for channels with lep-} tonicand/orhadronicW decays.Threechannelsareidentified:

νν4q,ννν2q,andνννν,withbeinganelectron or muon, q a quark, and ν a neutrino. The q momentum is reconstructed fromR=⁰.4 jets.Inordertosuppress Z+^jets and tt background,¯ dilepton eventsare required tohave two leptons ofthe samecharge. Events are categorisedaccording to the lepton flavour (ee, eμ and μμ). Three-lepton events are selectedifthesumofthe leptonchargesis±1.Theyare dividedintotwocategoriesaccordingtothenumberofsame- flavour,opposite-charge(SFOS) leptonpairs; onecategory se- lectszeroSFOSleptonpairsandasecondcategoryselectsone or two SFOS lepton pairs. Four-lepton events are categorised accordingtothenumberofSFOSlepton pairsandthe invari- ant mass(m₄) ofthefour-leptonsystem. Fourcategoriesare defined,requiringthatthenumberofSFOSleptonpairsisless than two or equal totwo, andm4 is smaller orlarger than 180 GeV. A total of nine categoriesare fit simultaneously in thesearchesforbothnon-resonantandresonant H H produc- tion.

•^{The b}b¯γ γ analysissearches for a H H pair decaying into bb¯ and γ γ.Two high-pT isolated photonsare requiredto have ET/_{mγ γ} > 0.35 and 0.25 respectively. The events are then analysed usingtwo selections:a ‘looseselection’ requiring a jetwith pT>40 GeVandasecondjetwithpT>25 GeV,and a ‘tightselection’wherethetwo jetsarerequiredtohave p_T larger than 100 and 30GeV. All jets have a radius parame- terR=⁰.4.Bothselectionsaresubdividedintotwocategories requiringone b-taggedjetortwob-taggedjets. Thetight se- lection is used in the SM H H search and in the search for resonanceswithmasseshigherthan500GeV,whiletheloose selection isusedinthe κλ analysisandinthesearchforres- onances with masses smaller than 500 GeV. The analysis is therefore divided into four categories, butonly two of them aresimultaneouslyfittoextracteachresult.

•^{The W+W−}γ γ analysissearchesfora H H pairdecayinginto

γ γ andW W .Theanalysisusesthesamephotonselectionas thebb¯γ γ channel andlooksforone W decayingleptonically and a second W decaying hadronically (W W → νqq). The hadronicW decayisreconstructedfromR=⁰.4 jets.Onlyone category is used in the searches for both non-resonant and resonant H H production.

Asummaryofthemain analysischaracteristicsisgiveninTa- ble1.All analysesimpose a seriesofsequential requirementson kinematic variables to select signal events and suppress back-

grounds. The bb¯τ⁺τ⁻ analysis uses a boosted decision tree (BDT) [55] distributionasthefinaldiscriminantforboththenon- resonant and resonant searches. For the resonant searches, the b_bb¯ _b,¯ _bbW¯ ⁺_W⁻ _andbb¯γ γ analyses use the H H invariant mass (m_{H H}) as the final discriminant, the W⁺W⁻γ γ analysis uses the γ γ invariant mass (mγ γ ), while W⁺W⁻W⁺W⁻ uses sim- pleeventcounting.FortheSM H H search,thebbb¯ b analysis¯ uses themH H distribution asadiscriminant, profitingfromthediffer- encebetweentheshapesofthesignalandthedominantmulti-jet background.Theb_b¯γ γ and W⁺W⁻γ γ analysesfitthemγ γ dis- tribution toextract boththe signal yieldandthe backgroundex- pectation,whilethebbW¯ ⁺W⁻and W⁺W⁻W⁺W⁻analyses use eventcounting.

3. Statisticaltreatment

The statisticalinterpretationof thecombinedsearch results is basedonasimultaneousfittothedataforthecross-sectionofthe signalprocessandnuisanceparametersthatencodestatisticaland systematicuncertainties,usingtheCLS approach [56].Theasymp- toticapproximation [57] isused inthe analysisofall final states andtheircombination.

Allsignalregions consideredinthesimultaneousfitare either orthogonal by construction or have negligible overlap. The over- lap due to object misidentification between bb¯γ γ and bb¯τ⁺τ⁻, andbetweenW⁺W⁻γ γ and W⁺W⁻W⁺W⁻,whicharenot or- thogonalby construction,is evaluated by running the signal and datasamplesfromeachchannel throughtheanalysisselection of eachotherchannel.Lessthan0.1%ofsimulatedsignaleventsover- lap between analyses, and no overlap is found in data. There is someirreduciblecontaminationfrombbW¯ ⁺W⁻ andbb Z Z events¯ with τ’sinthefinalstatepassingthebb¯τ⁺τ⁻selection.Thiscon- tamination is less than 8% of the b_b¯τ⁺τ⁻ selected events, and it is not taken into account in the b_b¯τ⁺τ⁻ analysis, note that including this contribution would increase the analysis sensitiv- ity therefore the results obtained here are slightly conservative.

The detectorsystematicuncertainties,such asthose injet recon- struction,b-jettagging,electron,muonandphotonreconstruction andidentification,aswellastheuncertaintyontheintegratedlu- minosity [58], are correlated across all final states. Uncertainties on the signal acceptance derived by varying the renormalisation andfactorisationscales,the partondistributionfunctionsandthe partonshower are correlatedtoo. Theoretical andmodelling sys- tematicuncertainties ofthebackgrounds derived usingsimulated events are not correlated across different analyses because the overlapamongtheircontributionstothedifferentanalysesisneg- ligible.