Physics Letters B

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Contents lists available atScienceDirect

www.elsevier.com/locate/physletb

Search for a massive resonance decaying to a pair of Higgs bosons in the four b quark ﬁnal state in proton–proton collisions at √

s = 13 TeV

.The CMS Collaboration

CERN,Switzerland

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

Articlehistory:

Received13October2017

Receivedinrevisedform23March2018 Accepted29March2018

Availableonline4April2018 Editor: M.Doser

Keywords:

CMS Physics Extradimensions Graviton Radion

di-Higgsbosonresonance

AsearchforamassiveresonancedecayingintoapairofstandardmodelHiggsbosons,inaﬁnalstate consisting of two b quark–antiquark pairs, is performed. A data sample of proton–proton collisions at acentre-of-massenergy of13 TeV isused, collectedby the CMSexperiment atthe CERN LHCin 2016,andcorrespondingtoanintegratedluminosityof35.9 fb⁻¹.TheHiggsbosonsarehighlyLorentz- boosted andare eachreconstructedasasinglelarge-areajet. Thesignalischaracterizedbyapeakin thedijetinvariantmassdistribution,aboveabackgroundfromthestandardmodelmultijetproduction.

Theobservationsareconsistentwiththebackgroundexpectations,andareinterpretedasupperlimitson theproductsofthes-channelproductioncrosssectionsandbranchingfractionsofnarrowbulkgravitons andradionsinwarpedextra-dimensionalmodels.Thelimitsrangefrom126to1.4 fb at95%conﬁdence levelforresonanceswithmassesbetween750and3000 GeV,andarethemoststringenttodate,over theexploredmassrange.

©²⁰¹⁸^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

In the standard model (SM), the pair production of Higgs bosons(H) [1–3] inproton–proton(pp) collisionsat√

s=^{13 TeV} isarareprocess [4].However,theexistenceofmassiveresonances decaying to Higgs boson pairs (HH) in many new physics models mayenhancethisrateto a levelobservable attheCERN LHC using the current data. For instance, models with warped extra dimensions(WED) [5] containnewparticlessuchasthespin-0ra- dion [6–8] andthespin-2ﬁrstKaluza–Klein(KK)excitationofthe graviton [9–11],whichhavesizeablebranchingfractionstoHH.

TheWEDmodelshaveanextraspatialdimensioncompactiﬁed between two branes, with the region between (called the bulk) warpedviaanexponentialmetric

κ

l,

κ

beingthewarpfactorand l thecoordinateof theextra spatial dimension [12]. The reduced Planck scale (MPl≡^MPl/8

π

, MPl beingthe Planck scale) is con- sideredafundamentalscale.Thefreeparametersofthemodelare

κ

/M_PlandtheultravioletcutoffofthetheoryR≡√

6e⁻κlM_Pl[6].

In pp collisionsatthe LHC,the graviton andthe radionare pro- ducedprimarilythrough gluon–gluon fusionandarepredictedto decaytoHH [13].

Other scenarios, such as the two-Higgs doublet models [14]

(in particular, the minimal supersymmetric model [15]) andthe

E-mailaddress:cms-publication-committee-chair@cern.ch.

Georgi–Machacek model [16] predict spin-0 resonances that are produced primarily through gluon–gluon fusion, anddecay toan HH pair.TheseparticleshavethesameLorentzstructureandeffec- tive couplingstothe gluonsand, fornarrowwidths,resultinthe samekinematicdistributions asthoseforthebulk radion.Hence, theresultsofthispaperarealsoapplicabletothisclassofmodels.

Searches for a new particle X in the HH decay channel have beenperformedby theATLAS [17–19] andCMS [20–24] Collabo- rations inpp collisions at √

s=^{7 and}^{8 TeV.} ^More ^recently, ^the ATLAS Collaboration haspublished limitson the production of a KKbulkgraviton,decayingtoHH,inthebbbb ﬁnalstate,usingpp collisiondataat√

s=^{13 TeV,}correspondingtoanintegratedlumi- nosityof3.2 fb⁻¹[25].Becausethelongitudinalcomponentsofthe W and Z bosonscoupletotheHiggsfieldintheSM, aresonance decaying to HH potentially also decays intoWW and ZZ, with a comparablebranching fraction forX→^ZZ, ând^withâ ^branching fractionforX→^{WW that}îs^twiceâs^large.^Searches^for^X→^WW andZZ havebeenperformedbyATLASandCMS [26–35].

This letter reportson the search for a massive resonance decaying to an HH pair, in the bbbb final state (with a branching fraction≈^{33% [36]),}^performedûsingâ ^data^setcorresponding to 35.9 fb⁻¹ ofpp collisionsat√

s=^{13 TeV.}^The^search signiﬁcantly improves upon the CMS analysis performed using the LHC data collectedat√

s=8 TeV [24],andextendsthesearchedmassrange to 750–3000 GeV. This search is conducted for both the radion https://doi.org/10.1016/j.physletb.2018.03.084

0370-2693/©²⁰¹⁸^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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andthe graviton, whereas the earliersearch only considered the former.

In this search, the X→^{HH decay} ^would ^result ⁱⁿ ^highly Lorentz-boostedandcollimated decayproductsofH→^bb,^which are referred to asH jets. These are reconstructed using jet sub- structure and jet flavour-tagging techniques [37–39]. The background consists mostly of SM multijet events, and is estimated using several control regions defined in the phase space of the massesandflavour-tagging discriminatorsof the two H jets, and the HH dijet invariant mass,allowing thebackground to be predicted over the entire range of mX explored. The signal would appearasa peak inthe HH dijet invariant massspectrum above asmoothbackgrounddistribution.

2. TheCMSdetectorandeventsimulations

TheCMSdetectorwithits coordinatesystemandtherelevant kinematic variables is described in Ref. [40]. The central feature of the CMS apparatus is a superconducting solenoid of 6 m in- ternal diameter, providing a magnetic ﬁeld of 3.8 T. Within the ﬁeld volume are siliconpixel andstrip trackers, alead tungstate crystalelectromagneticcalorimeter (ECAL), anda brass andscin- tillatorhadroncalorimeter(HCAL),eachcomposed ofabarreland twoendcapsections.The trackercoversa pseudorapidity

η

range from−².5 to 2.5 withthe ECAL andthe HCAL extending up to

|

η

|=^3. ^Forward calorimeters in the region up to |

η

|=^{5 pro-} vide almost hermetic detector coverage. Muons are detected in gas-ionization chambers embedded in the steel ﬂux-return yoke outsidethesolenoid,coveringaregionof|

η

_|<2.4.

Events ofinterest are selected usinga two-tieredtrigger system [41].The ﬁrstlevel(L1),composed ofcustom hardwarepro- cessors,uses informationfromthe calorimetersandmuon detec- torstoselecteventsatarateofaround100 kHz.Thesecondlevel, knownas thehigh-level trigger (HLT), consistsofa farm of pro- cessorsrunningaversionofthefulleventreconstructionsoftware optimizedforfastprocessing,andreducestheeventratetoaround 1 kHz beforedata storage.Eventsare selectedatthe triggerlevel bythepresenceofjetsofparticlesinthedetector.TheL1trigger algorithmsreconstructjetsfromenergydeposits inthecalorime- ters. At the HLT, physics objects (charged and neutral hadrons, electrons,muons,andphotons)arereconstructedusingaparticle- ﬂow(PF)algorithm [42].The anti-kT algorithm [43,44] isusedto clustertheseobjectswithadistanceparameterof0.8(AK8jets)or 0.4(AK4jets).

Bulkgravitonandradionsignaleventsaresimulatedatleading orderusing theMadGraph5_amc@nlo 2.3.3 [45] eventgenerator formassesintherange750–3000 GeV andwidthsof1 MeV (narrow width approximation). The NNPDF3.0 leading order parton distribution functions (PDFs) [46], taken from the LHAPDF6 PDF set [47–50], withthefour-ﬂavour scheme,isused.Theshowering andhadronizationofpartonsissimulatedwithpythia8.212 [51].

Theherwig++ 2.7.1 [52] generatorisusedforanalternativemodel toevaluatethesystematicuncertaintyassociatedwiththeparton showerandhadronization.The tuneCUETP8M1-NNPDF2.3LO [53]

is used forpythia 8, while the EE5C tune [54] is used forher- wig++.

Thebackgroundismodelledentirelyfromdata.However,sim- ulatedbackground samplesare used to develop and validate the background estimation techniques, prior to being applied to the data.These are multijetevents, generated atleading order using MadGraph5_amc@nlo,andtt+^jets, ^generated^atnext-to-leading orderusingpowheg2.0 [55–57].Boththesebackgroundsareinter- facedtopythia8forsimulatingthepartonshowerandhadroniza- tion.Studiesusingsimulations establishedthat themultijetcom-

ponentismorethan99%ofthebackground,withtherestmostly fromtt+jets production.

AllgeneratedsampleswereprocessedthroughaGeant4-based [58,59] simulationoftheCMSdetector.Multiplepp collisionsmay occur in the same oradjacent LHC bunch crossings(pileup) and contribute totheoveralleventactivityinthedetector.Thiseffect isincludedinthesimulations,andthesamplesarereweightedto matchthenumberofpp interactionsobservedinthedata,assum- ingatotalinelasticpp collisioncrosssectionof69.2 mb [60].

3. Eventselection

Events were collected using several HLT algorithms. The ﬁrst required the scalar pT sumof all AK4 jetsin the event (HT) to be greaterthan800or900 GeV,depending ontheLHCbeamin- stantaneous luminosity. A second trigger criterion required HT≥ 650 GeV, with a pair of AK4 jets with invariant mass above 900 GeV and a pseudorapidityseparation |

η

_|<1.5.A third set oftriggers selectedeventswiththescalar pT sumofallAK8jets greaterthan650or700 GeV andthepresenceofan AK8jetwith a “trimmedmass”above50 GeV,i.e.thejet massafterremoving remnants ofsoftradiationusingjet trimmingtechnique [61].The fourthtriggering condition wasbased onthe presenceofan AK8 jet with pT>360 GeV and trimmed mass greater than 30 GeV.

Thelast triggerselection acceptedeventscontainingtwoAK8jets having p_T>280 and200 GeV with atleast onehaving trimmed massgreaterthan30 GeV,togetherwithanAK4jetpassingaloose b-taggingcriterion.

The pp interaction vertex with the highest

p²_T of the associated clusters of physics objects is considered to be the one associatedwiththehardscatteringinteraction,theprimaryvertex.

Thephysicsobjectsarethejets,clusteredusingthejetﬁndingal- gorithm [43,44] withthe tracksassigned tothe vertexasinputs, and the associated missing transverse momentum, taken as the negative vectorsumofthe pT ofthosejets. Theotherinteraction verticesaredesignatedaspileupvertices.

Tomitigatetheeffectofpileup,particles areassignedweights usingthepileupper particleidentiﬁcation(PUPPI)algorithm [62], withtheweightcorrespondingtoitsestimatedprobabilitytoorig- inatefromapileupinteraction.Chargedparticlesfrompileupver- ticesreceiveaweightofzerowhilethosefromtheprimaryvertex receiveaweightofone.Neutralparticlesareassignedaweightbe- tweenzeroandone,withhighervaluesforthoselikelytooriginate fromtheprimaryvertex.ParticlesarethenclusteredintoAK8jets.

Thevectorsumoftheweightedmomentaofallparticlesclustered inthejetistakentobethejetmomentum.Toaccount fordetec- tor response nonlinearity,jet energy correctionsare applied as a functionofjet

η

andpT[63,64].Ineachevent,theleadingandthe subleadingp_TAK8jets,j₁ andj₂,respectively,arerequiredtohave pT>300 GeV and|

η

_|<2.4.

Theremovalofeventscontainingisolatedleptons(electronsor muons) with p_T>20 GeV and|

η

|<2.4 helps suppresstt+^jets anddibosonbackgrounds.The isolationvariableis deﬁnedasthe scalar pT sum of the charged and neutral hadrons, and photons in a cone of R=⁰.3 for an electron or R=⁰.4 fora muon, whereR≡

(

η

)²+(φ)²,φbeingtheazimuthal angleinra- dians.Theenergyfrompileupdepositedintheisolationcone,and the pT oftheleptonitself,is subtracted [65,66].The isolation re- quirementremovesjetsmisidentiﬁedasleptons.Additionalquality criteria are applied to improve the purity of the isolated lepton samples.Electronspassingcombinedisolation andquality criteria correspondingtoaselectioneﬃciencyof90%(70%)aredesignated

“loose” (“medium”)electrons.Forthe “loose”(“medium”)muons, the totalassociated eﬃciencyis 100% (95%).The probability ofa jet to be misidentiﬁed as an electron ora muon is in the range

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0.5–2%,dependingonpT,

η

,andthechoiceofmediumorloosese- lectioncriteria.Eventscontainingonemediumlepton,ortwoloose leptonsofthesameﬂavour,butofoppositecharge,arerejected.

The H→^{bb system}îs reconstructed as a single high-p_T AK8 jet, where the decay products have merged within the jet, and thetwohighest pT jetsintheeventare assumedtobe theHiggs boson candidates. The jet is groomed [67] to remove soft and wide-angle radiation using the soft-drop algorithm [68,69], with the soft radiationfraction parameter z set to 0.1 andthe angu- lar exponent parameter β set to 0. The groomed jet is used to compute thesoft-drop jet mass,which peaksatthe Higgsboson massforsignaleventsandreducesthemassofbackgroundquark- andgluon-initiatedjets. Dedicated mass corrections [70], derived fromsimulationanddatainaregionenrichedwithtt eventswith merged W→^{qq decays,} âre âpplied ^to ^the ^jet ^mass ⁱⁿôrder ^to remove residual dependenceon thejet pT,andto matchthe jet massscaleandresolutionobservedindata.

Thesoft-dropmassesofj1 andj2arerequiredtobewithinthe range105–135 GeV, withan eﬃciency ofabout 60–70%,for jets arisingfromasignal ofmassm_X intherange750–3000 GeV.The

“N-subjettiness”algorithmisusedtodeterminetheconsistencyof the jet with two subjets froma two-pronged H→^{bb decay,} ^by computing the inclusive jet shape variables

τ

1 and

τ

2 [71]. The ratio

τ

21≡

τ

2/

τ

1 witha valuemuch lessthan oneindicates ajet with two subjets. The selection

τ

21<0.55 is used, having a jet p_T-dependenteﬃciencyof 50–70%,beforeapplying thesoft-drop massrequirement.

For background events, j1 and j2 are often well separated in

η

,especiallyathighinvariant mass(m_jj)ofj₁ andj₂.Incontrast, signaleventsthatcontain aheavyresonancedecayingtotwo en- ergetic H jets are characterized bya small separationofthe two jetsin

η

. Events are thereforerequired to havea pseudorapidity separation|

η

(j₁,j₂)|<1.3.

Theeﬃciencyofthetriggercombinationismeasuredinasam- ple of multijet events, collected with a control trigger requiring a single AK4 jet with p_T>260 GeV, and with the leading and the subleading pT AK8 jets, j1 and j2, respectively, passing the above selectionson pT,

η

,andthesoft-drop mass.The eﬃciency isgreater than99% form_jj≥^{1100 GeV,}^andⁱⁿ^the^range^40–99%

for750<m_jj<1100 GeV.The triggereﬃciencyofthe simulated samplesiscorrectedusingascalefactortomatchtheobservedef- ﬁciencyin the data. This scale factor isapplied asa function of

|

η

(j₁,j₂)|^becauseît^hasâ^mild^dependenceôn^this^variable.

Themainmethodtosuppressthemultijetbackgroundisb tagging: sincea true H→^{bb jet} ^contains ^two ^{b hadrons,} ^the ^{H jet} candidatesareidentifiedusingthededicated“double-b tagger”algorithm [72]. The double-b tagger exploits the presence of two hadronized b quarks inside the H jet, anduses variables related tob hadronlifetimeandmass todistinguishbetweenH jets and thebackgroundfrommultijetproduction;italsoexploitsthefact thattheb hadronflightdirectionsarestronglycorrelatedwiththe axesusedtocalculatetheN-subjettinessobservables.Thedouble-b tagger is a multivariate discriminator with output between −¹ and 1, with a higher value indicating a greater probability for the jet to contain a bb pair. The double-b tagger discriminator thresholds of 0.3 and 0.8 correspond to H jet tagging efficien- ciesof 80and 30%and are referred toas “loose”(L) and“tight”

(T)requirements, respectively. Events musthave the two leading p_T AK8jetssatisfyingtheloosedouble-b taggerrequirement.The data-to-simulationscale factor forthe double-b tagger eﬃciency ismeasured inan eventsample enriched in bb pairsfromgluon splitting [72],andappliedtothesignalstoobtainthecorrectsig- nalyields.

The main variable used in the search for a HH resonance is the “reduced dijet invariant mass” m_jj,red≡^mjj−(m_j₁ −^mH)−

Fig. 1.Thesoft-dropmass(upper),theN-subjettinessτ21(middle),andthedouble-b taggerdiscriminator (lower) distributions ofthe selectedAK8 jets.The multijet backgroundcomponentsfor thedifferentjet flavoursareshown:jetshavingtwo Bhadrons(bb)orasingleone(b),jetshavingacharmhadron(c),andallother jets(light).Alsoplottedarethedistributionsforthesimulatedbulkgravitonand radionsignalsofmasses1400and2500 GeV.Thenumberofsignalandbackground eventscorrespondtoanintegratedluminosityof35.9 fb⁻¹.Asignalcrosssection σ(pp→^X→^HH→^bbbb)=^{20 pb is}âssumed^forâll^the ^masshypotheses.The eventsarerequiredtohavepassedthetriggerselection,leptonrejection,theAK8 jet kinematicselectionspT>300 GeV and|η|<2.4,and |η(j1,j2)|<1.3.The reduceddijetinvariantmassmjj,redisrequiredtobegreaterthan750 GeV.TheN- subjettinessrequirementofτ21<0.55 isappliedtotheupperandlowerfigures.

Thesoft-dropmassesofthetwojetsarebetween105–135 GeV forthemiddleand lowerﬁgures.

(m_j₂−^mH), where m_j₁ and m_j₂ are the soft-drop masses of the leading and subleading H-tagged jets in the event, and mH= 125.09 GeV [73,74] is theHiggs bosonmass.The quantity m_jj,red is usedratherthanmjj sinceby subtractingthe soft-dropmasses of thetwo H-tagged jetsandaddingback the exactHiggs boson massm_H,ﬂuctuationsinm_j₁ andm_j₂ duetothejet massresolu-

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Fig. 2.Thejetseparation|η(j1,j2)|^(left)ând^the^reduced^dijetînvariant^mass^mjj,red(right)distributions.Themultijetbackgroundcomponentsforthedifferentjetflavours areshown:eventscontainingatleastonejetwithtwoBhadrons(bb)orasingleone(b),eventscontainingajethavingacharmhadron(c),andallotherevents(light).Also plottedarethedistributionsforthesimulatedbulkgravitonandradionsignalsofmasses1400and2500 GeV.Thenumbersofsignalandbackgroundeventscorrespondto anintegratedluminosityof35.9 fb⁻¹.Thesignalcrosssectionσ(pp→X→HH→bbbb)isassumedtobe20 pb forallthemasshypotheses.Theeventsarerequiredtohave passedtheonlineselection,leptonrejection,theAK8jetkinematicselectionspT>300 GeV,|η|<2.4.Thesoft-dropmassesofthetwojetsarebetween105and135 GeV, andtheN-subjettinessrequirementofτ21<0.55 andmjj,red>750 GeV areapplied.Themjj,reddistributions(right)require|η(j₁,j₂)|<1.3.

tionarecorrected,leadingto8–10%improvementinthedijetmass resolution.Arequirementofm_jj,red>750 GeV isappliedforselect- ingsignal-likeevents.

Thesoft-dropmass,

τ

21,anddouble-b taggerdiscriminatordis- tributionsofthetwo leading pT jetsare showninFig.1 forsim- ulatedevents after passing the onlineselection, lepton rejection, kinematicselection, andthe requirementm_jj,red>750 GeV. Also, the N-subjettiness requirement of

τ

21<0.55 is applied for the soft-drop mass and the double-b tagger distributions, while the soft-drop mass requirement is applied to the

τ

21, and double-b taggerdiscriminator distributions. Sincesome ofthe triggers im- poseatrimmedjetmassrequirement,thisaffectstheshapeofthe oﬄinesoft-dropjetmass,resultinginasteepriseabove∼^{20 GeV.}

The distributions of the |

η

(j₁,j₂)| ând ^the ^mjj,red variables are showninFig.2.Inthesefigures,themultijetbackgroundisshown fordifferentjet flavourcategories:jetshavingtwoBhadrons(bb) orasingle one (b),jetshavingacharm hadron(c),andall other jets(light).

Thedouble-b taggerdiscriminator ofthetwo leadingAK8jets mustexceed the loosethreshold. In addition,if both discrimina- torvaluesalsoexceedthetightthreshold,eventsareclassiﬁedin the“TT”category. Otherwise,they are classiﬁedin the“LL” category,which contains events withboth j1 andj2 failingthe tight thresholdaswell aseventswitheitherj₁ orj₂ passingthe tight thresholdwhiletheotherpassestheloosethresholdonly.

The backgrounds are estimated separately for each category, andthecombinationofthelikelihoodsfortheTTandLLcategories givestheoptimalsignalsensitivityoverawiderangeofresonance masses,accordingtostudiesperformedusingsimulatedsignaland multijetsamples.TheTTcategoryhasagoodbackgroundrejection form_X up to 2000 GeV. At higher resonance masses, where the backgroundissmall, theLLcategory providesbetter signalsensi- tivity. The full event selection eﬃciencies forbulk gravitons and radionsofdifferentassumedmassesare showninFig. 3. Thera- dion has a smaller eﬃciency than the bulk graviton because its

|

η

(j₁,j₂)| distributionis considerablywider than that ofa bulk gravitonofthesamemass,asshowninFig.2(left).

4. Signalandbackgroundmodelling

Themethodchosen forthebackgroundmodellingdependson whethertheresonancemassmXisbeloworabove1200 GeV,since atlow masses thebackground doesnot fall smoothly as a func-

Fig. 3.Thesignalselectioneﬃcienciesforthebulkgravitonandradionmodelsfor differentmasshypothesesoftheresonances,shownfortheLLandtheTTsignal eventcategories.Owingtothelargesamplesizesofthesimulatedevents,thesta- tisticaluncertaintiesaresmall.

tion of m_jj,red, because of the trigger requirements, while above 1200 GeV it does. The background estimation relies on a set of control regions to predict the total background shape and nor- malization in the signal regions. The entire range of the m_jj,red distributionabove750 GeV isusedfortheprediction.

For signals with m_X≥^{1200 GeV,} ^the ûnderlying ^background distribution falls monotonically with m_jj,red, thus allowing the background shape to be modelled by a smooth function, above which alocalized signal issearched for.This smooth background modellinghelpstoreduceuncertaintiesinthebackgroundestima- tionfromlocalstatisticalfluctuationsinm_jj,red,therebyimproving the signal search sensitivity. The parameters of the function and itstotalnormalizationareconstrainedbyasimultaneousfitofthe signal andbackgroundmodelsto thedatain thecontrol andthe signalregions.Form_X≥^{1200 GeV,}^the^mjj,reddistributionsforthe signalaremodelledusingthesumofaGaussianandaCrystalBall function [75],asshowninFig.4foronesignalcategory.Thesame modellingisusedfortheothersignalcategories,withdifferentpa- rametersfortheGaussianandtheCrystalBallfunctions.

Thesignalandcontrolregionsaredeﬁnedbytwovariablesre- latedtotheleading p_Tjetj₁:(i)itssoft-dropmassm_j₁ and(ii)the valueofthediscriminatorofthedouble-b tagger.Thebackground

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Fig. 4.Thebulkgravitonsignalmjj,reddistributionfortheLLcategory,modelledus- ingthesumofGaussianandCrystalBallfunctions.Thismodellingisperformedfor signalsintherange1100<mjj,red<3000 GeV,wherethebackgrounddistribution fallssmoothly.Noeventsareobservedwithmjj,redgreaterthan3000 GeV.

Table 1

Deﬁnitionofthesignal,the antitag,andthesidebandregionsusedfortheback- groundestimation.Theregionsaredeﬁnedintermsofthesoft-dropmassesofthe leadingpT(j1)andthesubleadingpT(j2)AK8jets,andtheirdouble-btaggerdis- criminatorvalues.

Event category Jet Soft-drop mass (GeV) Double-b tagger discriminator Signal (LL) j1

105–135

>0.3, but

j2 not both>0.8

Signal (TT) j1

>0.8 j2

Antitag (LL) j1

105–135

<0.3

j2 0.3–0.8

Antitag (TT) j1 <0.3

j2 >0.8

Sideband j1 <105 or>135 >0.3, but

(LL, passing) j2 105–135 not both>0.8

Sideband j1 <105 or>135

>0.8 (TT, passing) j2 105–135

Sideband j1 <105 or>135 <0.3

(LL, failing) j2 105–135 0.3–0.8

Sideband j1 <105 or>135 <0.3

(TT, failing) j2 105–135 >0.8

is estimatedin bins of the m_jj,red distribution. Considering these twovariables,severalregionsaredeﬁned.

The pre-tag region includes events fulﬁlling the selection requirements inSections 2–3 apart fromthose on m_j₁ andon the j1 double-b tagger discriminator. The signal region is the subset of pre-tag events where mj₁ is inside the H jet mass window of 105–135 GeV, and with the j₁ double-b tagger discriminator greaterthan0.3or0.8,fortheLLandTTregions,respectively.The antitagregionsrequirethej1 double-b taggerdiscriminatortobe lessthan0.3, withtherequirementonj₂ beingthesameasthat for the corresponding LL or TT signal regions. The m_j₁ sideband regionconsistsofeventsinthepre-tagregion,wheremj₁ liesout- side theH jetmass window.Based onwhetherj₁ passesorfails thedouble-b tagger discriminator threshold,the sidebandregion is divided into either “passing”or “failing”, respectively. The an- titagregionsare dominatedby themultijetbackground,andhave identicalkinematicdistributionstothemultijetbackgroundevents in the signal region, according to studies using simulations. The deﬁnitionsofthesignal,theantitag,andthesidebandregionsare giveninTable1.

Intheabsence ofacorrelation betweenm_j₁ andthe double-b tagger discriminator values, one could measure in the mj₁ sideband the ratio of the number of events passing and failing the

Fig. 5.Thepass-failratioRp/foftheleadingpTjetfortheLL(upper)andTT(lower) signalregioncategoriesasafunctionofthedifferencebetweenthesoft-dropmass oftheleadingjetandtheHiggsbosonmass,mj₁-mH.Themeasuredratioindiffer- entbinsofmj₁−^mHisusedinthefit(redsolidline),exceptintheregionaround mj₁−^mH=^0,^whichcorrespondstothesignalregion(bluetriangularmarkers).The fittedfunctionisinterpolatedtoobtainRp/finthesignalregion.Thehorizontalbars onthedatapointsindicatethebinwidths.(Forinterpretationofthecoloursinthe figure(s),thereaderisreferredtothewebversionofthisarticle.)

double-b tagger selection, R_p/f≡^Npass/N_fail,i.e.the“pass-fail ratio”.Theyieldintheantitagregion(ineachm_jj,redbin)couldthen bescaledby R_p/f toobtainanestimateofthebackgroundnormal- ization inthesignal region.However, thereis asmallcorrelation betweenthedouble-b taggerdiscriminatorandmj₁,whichistaken intoaccountbymeasuring thepass-failratio R_p/f asafunctionof mj₁.Thesignalfractionwasfoundtobelessthan10⁻³intheside- bandregionsusedtoevaluate Rp/f,assumingasignalcrosssection

σ

(pp→^X→^HH→^bbbb)of10 fb.

The Rp/ffortheLLsignalregionismeasuredusingratioofthe numberofeventsinthe“LL,passing”and“LL,failing”sidebandregions, asdeﬁned in Table 1.Likewise, the R_p/f for the TT signal regionusestheratioofthenumberofeventsinthe“TT,passing”

tothe“TT,failing”sidebandregions.ThevariationofRp/fasafunc- tionofmj₁ ineachmj₁sidebandisﬁttedwithaquadraticfunction.

Theﬁttothepass-failratioisinterpolatedtotheregionwherem_j₁ lieswithintheH jetmasswindowof105–135 GeV.Analternative ﬁtusingathirdorderpolynomialwas foundtogivethesamein- terpolatedvalueofRp/fintheHiggsjetmasswindow.Everyevent in theantitagregionisscaled by thepass-failratio evaluatedfor them_j₁ ofthat event,to obtainthebackground predictioninthe signalregion.

Fig.5showsthequadraticﬁtinthem_j₁ sidebandsofthepass- fail ratio Rp/f as a function ofmj₁, as obtained in the data. The backgroundpredictionusingthismethod,alongwiththenumber ofobservedeventsinthesignalregionisshowninFig.6.

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Fig. 6.Thereducedmass distributionsmjj,red for theLL(upper)and TT(lower) signalregioncategories.Thepointswithbarsshowthedata,thehistogramwith shaded band shows the estimated background and associated uncertainty. The mjj,redspectrumforthebackgroundisobtainedbyweightingthemjj,red spectrum intheantitagregionbytheratioRp/fofFig.5.Thesignalpredictionsforabulk gravitonofmass1000 GeV,areoverlaidforcomparison,assumingacrosssection σ(pp→X→HH→bbbb)of10 fb.Thelastbinsofthedistributionscontainall eventswithmjj,red>3000 GeV.Thedifferencesbetweenthedataandthepredicted background,dividedbythedatastatisticaluncertainty(dataunc.)asgivenbythe Garwoodinterval [76],areshowninthelowerpanels.

Forresonancemassesof1200 GeV andabove,thebackground estimation is improved by simultaneously fitting a parametric model for the background and signal to the data in the signal andtheantitagregions form_jj,red≥^{1100 GeV.}În^the^fit,^the^ratio R_p/f obtainedfromthesidebandsisusedtoconstrain therelative numberofbackground eventsin thetwo regions. Toaccount for possible Rp/fdependenceonmjj,redathighmjj,red values,the Rp/f obtainedfromthefitsshowninFig.5isalsoparametrizedasalin- earfunctionofmjj,red.Thesignalnormalizationisunconstrainedin thefit,while theuncertaintiesintheparameters ofthe functions used to model the background and R_p/f are treated asnuisance parameters. For the background modelling, a choice among an exponentialfunction Ne⁻^{a m}^jj,red,a “levelled exponential” function Ne⁻^{a m}^jj,red^/(¹⁺^{a b m}^jj,red⁾,anda“quadraticlevelled exponentialfunction”Ne^[−^{a m}^jj,red^/(¹⁺^{a b m}^jj,red^)]−[−^{c m}²^jj,red^/(¹⁺^{b c m}²^jj,red^)] wasmade,using aFisher F-test [77]. Ataconfidencelevel of95%,thelevelledex- ponentialfunctionwasfoundtobeoptimal. Sincethebackground shapes in the signal regions, as predicted using the antitag re-

gions,werefoundtobesimilar(Fig.6),theparametricbackground modellingwas tested usingthe antitagregion inthe databefore applyingittothesignalregion.

The simultaneous fits to the antitag and the signal regions are shown in Figs. 7 and 8, respectively, using the background modelonly.Thesearelabelledas“post-fit”curveswiththesignal region background yields constrained to be R_p/f times the background yields from the antitag regions. The “pre-fit” curves, obtained by fitting the antitagandthe signal regions separately to thebackground-onlymodel,withthebackgroundeventyieldsun- constrained,arealsoshownforcomparison.Inthepost-fitresults, the R_p/fdependenceonm_jj,redwasfoundtobenegligible.

Amongthefourfittedregions,correspondingtotheantitagand thesignalregionsintheLLandTTcategories, theeventswiththe highestvalueofm_jj,redoccur intheantitagregionoftheLLcate- gory,ataroundmjj,red=^{2850 GeV.} Âs^the ^parametric^background model is only reliable within the range of observed events, the likelihoodis onlyevaluated uptomjj,red=^{3000 GeV.}^This^results inatruncationofthesignaldistributionforresonanceshavingm_X of2800 GeV andabove,withsignalefficiencylossesincreasingto 30%formX=^{3000 GeV,}âs^shownⁱⁿ^Fig.^4.

Closuretestsofthebackgroundestimationmethodswere performed using simulated multijet samples withsignals of various crosssections.Thetestsindicatedagoodconsistencybetweenthe expectedandtheassumedsignalstrengths.

5. Systematicuncertainties

The following sources ofsystematicuncertainty affectthe ex- pectedsignalyields. Noneoftheseleadtoa signiﬁcantchangein thesignalshape.

Trigger response modelling uncertainties are particularly im- portant form_jj,red<1200 GeV,where thetriggerefficiency drops below99%.Ascalefactorisappliedtocorrectforthedifferencein efficiencyobservedbetweenthe dataandsimulation.Thecontrol triggerusedtomeasurethisscalefactorrequiresasingle AK4jet withpT>260 GeV,andittooissubjecttosomeinefficiencywhen m_jj,rediscloseto750 GeV,becauseofadifferencebetweenthejet energyscaleusedinthetriggerandthatusedintheofflinerecon- struction.Thisinefficiencyismeasuredusingsimulations,andhas anassociatedtotaluncertaintyofbetween1%and15%.

Thejetenergyscaleandresolutionuncertaintyisabout1% [63, 64].Thejetmassscaleandresolution,and

τ

21selectionefficiency data-to-simulation scale factor are measured using a sample of mergedW jetsinsemileptonictt events.Thecorrespondinguncer- taintiesareextrapolatedtoahigher pT rangethanthatassociated withtt events,usingsimulations.Acorrectionfactorisappliedto account forthe difference in the jet shower profile of W→^qq and H→^{bb decays,} ^by ^comparing ^the ^ratio ôf ^the êfficiency ôf H and W jets using the pythia 8 and herwig++ shower gener- ators. The jet mass scale and resolution has a 2% effect on the signal yields becauseof a changeinthe meanof theH jet mass distribution. The

τ

21 selection eﬃciency uncertainty amounts to a +³⁰/−^{26% change} ⁱⁿ ^the ^signal ^yields. ^The uncertainty in the H tagging correction factor is in the range 7–20% depending on theresonancemassmX.The double-b taggereﬃciencyscalefac- toruncertainty isabout2–5%,depending onthe double-b tagger requirementthreshold andjet p_T, andis propagated to the total uncertaintyinthesignalyield.

Theimpact ofthePDFsandthetheoretical scaleuncertainties areestimatedtobe0.1–2%,usingthePDF4LHCprocedure [50],and affecttheproductofthesignalacceptanceandtheeﬃciency.The PDF and scale uncertainties have negligibleimpact on the signal m_jj,red distributions.Additionalsystematicuncertaintiesassociated

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Fig. 7.Thereducedmassmjj,reddistributionsintheantitagregionfortheLL(left)andTT(right)categories.Theblackmarkersarethedatawhilethecurvesshowthepre-fit andpost-fitbackgroundshapes.Thedifferencesbetweenthedataandthepre-fitbackgrounddistribution,dividedbythestatisticaluncertaintyinthedata(dataunc.)as givenbytheGarwoodinterval [76],areshowninthelowerpanels.

Fig. 8.Thereducedmassmjj,red distributionsinthesignalregionfortheLL(left)andtheTT(right)categories.Theblackmarkersarethedatawhilethecurvesshow thepre-fitandpost-fitbackgroundshapes.Thecontributionofbulkgravitonsofmasses1600and2500 GeV inthe signalregionareshownassumingacross section σ(pp→X→HH→bbbb)of10 fb.Thedifferencesbetweenthedataandthepre-fitbackgrounddistribution,dividedbythestatisticaluncertaintyinthedata(dataunc.)as givenbytheGarwoodinterval [76],areshowninthelowerpanels.

withthepileupmodelling(2%)andtheintegratedluminosityde- termination(2.5%) [78],areappliedtothesignalyield.

Themainsource ofuncertaintyforthe multijetbackgroundin theregion mjj,red<1200 GeV is duetothe statisticaluncertainty in the ﬁt to the R_p/f ratio performed in the H jet mass side- bands. This uncertainty, amounting to 2.6% for the LL, and 6.8%

for the TT signal categories, is fully correlated between all bins ofaparticularestimate.Furthermore,thestatisticaluncertaintyin the antitag region is propagated to the signal region when the estimate is made. This is uncorrelated from bin to bin,and the Barlow–Beeston Lite [79,80] method is used to treat the bin-by- bin statistical uncertainty in the data. These uncertainties affect both the shape of the background in the m_jj,red distribution and thetotalbackgroundyield.

For mjj,red≥^{1200 GeV,} ^the ^overall ^background uncertainty is obtainedfrom the uncertainty in the four simultaneous ﬁts performed for the antitag andthe signal regions in the LL andthe

Table 2

Summaryofsystematicuncertaintiesinthesignalandbackgroundyields.

Source Uncertainty (%)

Signal yield

Trigger eﬃciency 1–15

H jet energy scale and resolution 1 H jet mass scale and resolution 2

H jetτ21selection +^30/−²⁶

H-tagging correction factor 7–20 Double-b tagger discriminator 2–5

Pileup modelling 2

PDF and scales 0.1–2

Luminosity 2.5

Background yield

Rp/fﬁt 2.6 (LL category) 6.8 (TT category)

TT categories. The dependenceof Rp/f onmjj,red isaccountedfor, althoughthiswasfoundtobenegligible.

AcompletelistofsystematicuncertaintiesisgiveninTable2.

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Fig. 9.Thelimitsforthespin-0radion(upper)andthespin-2bulkgraviton(lower) models.Theresultfor mX<1200 GeV usesthebackgroundpredictedusingthe controlregions,whileformX≥1200 GeV thebackgroundisderivedfromacom- binedsignalandbackgroundﬁttothedatainthecontrolandthesignalregions.

Thepredictedtheoreticalcrosssectionsforanarrowradionorabulkgravitonare alsoshown.

6. Results

AsshowninFigs.6and8,forthesignalregions,theobserved m_jj,red distribution is consistent with the estimated background.

Theresultsare interpreted intermsof upperlimitsontheprod- uct of the production cross sections andthe branching fractions

σ

(pp→X)B(X→HH→bbbb)forradionandbulkgravitonofvar- iousmasshypotheses.Theasymptoticapproximationofthemod- ifiedfrequentist approachforconfidence levels,takingtheprofile likelihoodasateststatistic [81–83],isused.Thelimitsareshown inFig.9fora narrowwidth radionorabulk graviton. Theseare comparedwiththe theoretical valuesofthe productof thecross sectionsandbranchingfractionsforthe benchmarks

κ

/M_Pl=⁰.5 and R=^{3 TeV,} ^where ^the ^narrow ^width approximation for a signal is valid, and where the corresponding HH decay branching fractions in the mass range of interest are 10 and 23%, for thegraviton andtheradion,respectively [13].Theexpectedlimits onthebulkgraviton aremorestringentthanthoseontheradion becauseof thehigher eﬃciencyofthe |

η

(j₁,j₂)| ^separation^re- quirementfortheformersignal.

The upperlimits on the productionof the cross sectionsand branchingfractionliesin therange126–1.4 fb fora narrowreso- nanceX ofmass 750<m_X<3000 GeV.Assuming R=^{3 TeV,} ^a bulkradionwithamassbetween970and1400 GeV isexcludedat 95%conﬁdencelevel,exceptina smallregion closeto1200 GeV, wheretheobservedlimit is11.4 pb,thetheoreticalpredictionbe- ing11.2 pb.

7. Summary

A search for a narrow massive resonance decaying to two standardmodelHiggsbosonsisperformedusingtheLHCproton–

proton collision data collected at a centre-of-mass energy of 13 TeV by theCMS detector,and corresponding to an integrated luminosityof35.9 fb⁻¹.Thefinalstateconsistsofeventswithboth Higgs bosons decaying to b quark–antiquark pairs, which were identifiedusingjetsubstructureandb-taggingtechniquesapplied to large-area jets. The data are found to be consistent withthe standard model expectations, dominated by multijet events. Up- perlimitsaresetontheproductsoftheresonantproductioncross sections ofa Kaluza–Klein bulk graviton anda Randall–Sundrum radion, and their branching fraction to HH→^bbbb. ^The ^limits range from 126 to 1.4 fb at 95% confidence level for bulk gravi- tonsandradionsin themassrange 750–3000 GeV.Forthe mass scale R=^{3 TeV,} â ^radionôf ^mass ^between⁹⁷⁰ ând^{1400 GeV} (except in a small region close to 1200 GeV) is excluded. These limitson the bulk graviton andthe radiondecaying to a pair of standardmodelHiggsbosonsarethemoststringenttodate,over themassrangeexplored.

Acknowledgements

WecongratulateourcolleaguesintheCERNacceleratordepart- ments for the excellent performance of the LHC and thank the technicalandadministrative staffsatCERN andatother CMS in- stitutes for their contributions to the success of the CMS effort.

Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses.

Finally, we acknowledge the enduring support for the construc- tionandoperation oftheLHC andtheCMSdetectorprovidedby thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil);

MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIEN- CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin- land,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun- gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN(Italy);

MSIPandNRF(RepublicofKorea);LAS (Lithuania);MOEandUM (Malaysia); BUAP, CINVESTAV,CONACYT, LNS, SEP, andUASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland);FCT(Portugal);JINR(Dubna);MON,ROSATOM,RAS,RFBR andRAEP(Russia);MESTD (Serbia);SEIDI,CPAN, PCTIandFEDER (Spain);SwissFundingAgencies(Switzerland);MST(Taipei);ThEP- Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro- gramme and the European Research Council and Horizon 2020 Grant,contract No. 675440 (EuropeanUnion);the Leventis Foun- dation;the A. P. Sloan Foundation; the Alexandervon Humboldt Foundation; the Belgian Federal Science Policy Oﬃce; the Fonds pourlaFormationàlaRecherchedansl’Industrieetdansl’Agricul- ture (FRIA-Belgium); the Agentschapvoor Innovatie door Weten- schap en Technologie (IWT-Belgium); the Ministry of Education, YouthandSports(MEYS)oftheCzechRepublic;theCouncilofSci- enceandIndustrialResearch,India;theHOMINGPLUSprogramme of the Foundation for Polish Science, coﬁnanced from European Union,Regional DevelopmentFund, theMobilityPlusprogramme oftheMinistryofScienceandHigherEducation,theNationalSci- ence Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/

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B/ST2/02861,Sonata-bis2012/07/E/ST2/01406; the NationalPrior- itiesResearchProgrambyQatar NationalResearchFund;thePro- grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes coﬁnanced by EU-ESF andthe Greek NSRF;

theRachadapisekSompotFundforPostdoctoralFellowship,Chula- longkornUniversityandtheChulalongkornAcademicintoIts 2nd CenturyProjectAdvancement Project(Thailand);theWelchFoun- dation,contractC-1845;andtheWestonHavensFoundation(USA).

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