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

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Physics Letters B 800 (2020) 135103

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Physics Letters B

Combination of searches for Higgs boson pairs in pp collisions at

s = 13 TeV with the ATLAS detector


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



Receivedinrevisedform13November2019 Accepted13November2019

Availableonline19November2019 Editor:M.Doser

ThisletterpresentsacombinationofsearchesforHiggsbosonpairproductionusingupto36.1 fb1of proton–protoncollisiondataatacentre-of-massenergy

s=13 TeV recordedwiththeATLASdetectorat theLHC.ThecombinationisperformedusingsixanalysessearchingforHiggsbosonpairsdecayinginto thebbb¯ b,¯ bbW¯ +W,bb¯τ+τ,W+WW+W,bb¯γ γ andW+Wγ 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 (

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 ppH 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-

structiveandyields an overall cross-sectionof σggFSM(ppH 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 HSMH H H.Inthisanalysis,allother Higgs boson couplings are assumed to have SM values. Indirect limitson κλhavebeenobtainedusingthemeasurementsofsingle Higgsbosonproductionanddecay [20] andelectroweakprecision observables [21,22],constraining κλ totherange8<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-

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense( 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 fb1. 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+WW+W [39], bb¯γ γ [40]

andW+Wγ 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-kt 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 fb1.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 bbW¯ +W analysis looks for the W W νqq decay channel, where isan electronormuon, andq isa u,d,s,c quark oranti-quark.Thebb 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 bb¯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 τhadτhad 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 Hx¯x y¯y)indicatesthebranchingfractionofthe H H pair whereone H decaysinto xx and¯ theotherdecaysinto y¯y.ThebranchingfractionvaluesaretakenfromRef. [11] foraHiggsbosonmass mH=125.09 GeV.Lintindicatestheintegratedluminosityofthedatasetusedintheanalysis.“Categories”indicatesthenumber ofsignalcategories.“Discriminant”indicatesthedistributionusedinthefinallimit-settingfit(“c.e.”standsforcountingeventsand indicatesthatasimpleeventcountingwasusedinthefinalfitratherthanadistributionshape).“Model”indicateswhichmodels eachanalysistested:NRstandsforSMH H signalmodel,S foraspin-0scalarmodel,andG foraKKgravitonmodel.“mS/Ggives theprobedmassrangefortheresonantsearch.“Ref.”reportsthereferencetotheindividualfinalstatepapers.

bbb¯ b¯ bbW¯ +W bb¯τ+τ W+WW+W bb¯γ γ W+Wγ γ

B(H Hx¯x y¯y) 0.34 0.25 0.073 0.046 2.6·103 1.0·103

Lint[fb1] 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


The W+WW+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 bb¯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 pT 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+Wγ 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 bbb¯ b,¯ bbW¯ +W andbb¯γ γ analyses use the H H invariant mass (mH H) as the final discriminant, the W+Wγ γ analysis uses the γ γ invariant mass (mγ γ ), while W+WW+W uses sim- pleeventcounting.FortheSM H H search,thebbb¯ b analysis¯ uses themH H distribution asadiscriminant, profitingfromthediffer- encebetweentheshapesofthesignalandthedominantmulti-jet background.Thebb¯γ γ and W+Wγ γ analysesfitthemγ γ dis- tribution toextract boththe signal yieldandthe backgroundex- pectation,whilethebbW¯ +Wand W+WW+Wanalyses 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+Wγ γ and W+WW+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+τselection.Thiscon- tamination is less than 8% of the bb¯τ+τ selected events, and it is not taken into account in the bb¯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.




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