Search for Higgs boson pair production in the gamma gamma b(b)over-bar final state in pp collisions at √s=13 TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

Higgs

boson

pair

production

in

the

γ γ

bb final

state

in

pp

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

r

a

c

t

Articlehistory: Received1June2018

Receivedinrevisedform5October2018 Accepted29October2018

Availableonline1November2018 Editor:M.Doser Keywords: CMS Physics Higgs Photons b-Jets

A search is presented for the production of a pair of Higgs bosons, where one decays into two photons and the other one into a bottom quark–antiquark pair. The analysis is performed using proton–proton collision data at √s₌13 TeV recorded in 2016 by the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb−1. The results are in agreement with standard model (SM) predictions. In a search for resonant production, upper limits are set on the cross section for new spin-0 or spin-2 particles. For the SM-like nonresonant production hypothesis, the data exclude a product of cross section and branching fraction larger than 2.0 fb at 95% confidence level (CL), corresponding to about 24 times the SM prediction. Values of the effective Higgs boson self-coupling

κ

λare constrained to be within the range −11 <

κ

λ<17 at 95% CL, assuming all other Higgs boson couplings are at their SM value. The constraints on

κ

λare the most restrictive to date.

©2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

1. Introduction

Thediscoveryofaparticlewithamassofabout125 GeV,with propertiescompatiblewiththoseexpectedfortheHiggs(H)boson ofthe standard model(SM) [1–3], has stimulated interest inthe detailedexplorationandunderstandingoftheoriginoftheBrout– Englert–Higgs(BEH)mechanism[4,5]. Theproductionofa pairof Higgsbosons (HH)isarareprocess thatissensitive tothe struc-tureofthe BEHpotentialthrough theHiggsboson’sself-coupling mechanism. In the SM, the corresponding production cross sec-tion via gluon–gluon fusion in proton–proton (pp) collisions at

√

s

=

13 TeV ispredictedtobe

σ

gg→HH

=

33

.

5₋+2₂._.5₈fb [6–8],avalue

beyondthereach oftheanalysesbasedonthe currentintegrated luminosityoftheCERNLHCprogram.

Manytheories beyondthe SM (BSM)suggest the existence of heavy particles that can couple to a pair ofHiggs bosons. These particles could appear as a resonant contribution to the invari-ant mass of the HH system and induce a significant increase of theHH production cross section withrespect to theSM. For ex-ample,modelswithwarpedextradimensions(WED) [9] postulate theexistence ofcompactifiedextra spatial dimensions. They pre-dict new resonances decaying to a Higgs boson pair, including spin-0radionsR [10] andspin-2Kaluza–Kleingravitons(KK gravi-ton) [11]. The benchmark scenario considered in this paper, the

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

bulkRandall–Sundrum(RS)model [12],assumesthatallfieldscan propagateintheextradimension.ModelswithanextendedHiggs sectoralsopredictaspin-0resonancethatdecaystoapairofSM Higgsbosons,ifsufficientlymassive.Examplesofsuchmodelsare thesingletextensionoftheSM [13],thetwo-Higgs-doublet mod-els [14] (inparticular, the minimal supersymmetric model [15]), andtheGeorgi–Machacekmodel [16].Manyofthesemodels pre-dict that heavy scalar production occurs predominantly through the gluon–gluon fusion process. The Lorentz structure of the ef-fectivecouplingbetweenthescalarandthegluonisthesamefor aradionoraheavyHiggsboson.Therefore,thekinematicsforthe productionofaradionoranadditionalHiggsbosonareessentially thesame,providedthespin-0resonanceisnarrow.Theradion re-sultscanthereforebeappliedtoconstrainthisclassofmodels.

If the new particles are too heavy to be observed through a directsearch, they maycontribute to HH productionthrough vir-tual processes and lead to an enhancement of the cross section withrespecttotheSM prediction(asdiscussed,e.g.,inRef. [17]). In addition, different BSM models can modify the Higgs boson’s fundamental couplingsandimpactHH productioningluon–gluon fusion [18] (ggHH)andvectorbosonfusion(VBF) [6,8].

This letter describes a search for the production of pairs of Higgs bosons via pp

→

HH

→

γ γ

bb using a data sample of 35

.

9 fb−1 collected by the CMS experiment in 2016. Both non-resonant and resonant production are explored, with the search fora narrow resonance X conductedatmassesmX between260 https://doi.org/10.1016/j.physletb.2018.10.056

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

and900 GeV. The fully reconstructed

γ γ

bb final state combines the large SM branching fraction (

B

) of the H

→

bb decay with thecomparativelylowbackgroundandgoodmassresolutionofthe H

→

γ γ

channel,yieldingatotal

B(

HH

→

γ γ

bb

)

of0.26% [6].The search uses the mass spectra of the diphoton (mγ γ ), dijet (mjj),

andfour-body systems (mγ γjj), aswell asthe associatedhelicity

angles,toprovidediscriminationbetweentheHH production sig-naland theother SM processes. The ggHH production process is studiedin detailandthe sensitivityofCMS datato the nonreso-nantVBFproductionmechanismisinvestigatedforthefirsttime.

Searches in the same and complementary final states such as HH

→

bbbb or HH

→

τ

+

τ

−bb were performed in the past by the ATLAS [19–22] and CMS [23–28] Collaborations at

√

s

=

8 and 13 TeV.

2. TheCMSdetector

The CMS detector, its coordinate system, and the main kine-matic variables used in the analysis are described in detail in Ref. [29].The centralfeatureoftheCMSapparatusisa supercon-ductingsolenoid, of 6 minternal diameter, providing amagnetic fieldof 3

.

8 T.Asiliconpixel andstrip trackercoveringthe pseu-dorapidity range

|

η

|

<

2

.

5, anelectromagnetic calorimeter(ECAL) madeofleadtungstatecrystals,andabrassandscintillatorhadron calorimeterreside within the field volume. Forward calorimeters extend the pseudorapidity coverage above

|

η

|

=

3

.

0. Muons are detected in gas-ionization chambersembedded in thesteel flux-returnyokeoutsidethesolenoid.ThefirstleveloftheCMStrigger system,composedofspecialhardwareprocessors,usesinformation fromthecalorimeters andmuon detectorsto selectthemost in-terestingeventsinatimeintervaloflessthan4

μ

s.Thehigh-level triggerfurther decreases theeventrate, fromaround 100 kHz to lessthan1 kHz,beforedatastorage[30].

3. Simulatedevents

Signalsamplesaresimulatedatleadingorder(LO)using Mad-Graph5_amc@nlo 2.3.2[31–33] interfacedwithLHAPDF6[34].The next-to-leading-order(NLO) partondistributionfunction(PDF)set PDF4LHC15_NLO_MC is used [35–39]. The models describe the production through gluon–gluon fusion of particles with narrow width (set to 1 MeV) that decay to two Higgs bosons with the massofmH

=

125 GeV [40].Eventsaregeneratedeitherforspin-0

radionproduction,orspin-2 KK gravitonproduction,aspredicted bythebulkRSmodel.Foreachspinhypothesis16masspointsare generatedwithintherange260

≤

mX

≤

900 GeV instepsof10 GeV

formX between260and300 GeV,andinstepsof50 GeV formX

above300 GeV.

In thenonresonant casewe use theeffective field theory ap-proachandnotationsfromRefs. [6,41]. Firstwe considertwo SM coupling modifiers:

κ

λ

≡ λ

HHH

/λ

SMHHH, which measures deviations

ofthe Higgs boson trilinearcoupling

λ

HHH from its SM

expecta-tion,

λ

SM_HHH

≡

m2_H

/(

2v2

)

=

0

.

129;and

κ

t

≡

yt

/

ySMt ,whichmeasures

deviations ofthe top quark Yukawacoupling yt from its SM

ex-pectation ySM t

=

√

2 mt

/

v

≈

1

.

0. Here v

=

246 GeV denotes the

vacuumexpectationvalueoftheHiggsboson,mHitsmass,andmt

denotes the top quark mass. Second, we also consider couplings notfoundintheSMthatarederivedfromdimension-6operators: contactinteractionsbetweentwoHiggsbosonsandtwotopquarks (c2), betweenone Higgsbosonandtwo gluons(cg),andbetween

twoHiggsbosonsandtwogluons(c2g).Wedefinethesethree

pa-rametersinsuch awaythat their valuesarezerowithin theSM. Themostgeneralproductionisdescribedbyamodificationofthe

SMLagrangian,therelevantpartofwhich,labelledas

L

HH,isgiven

inthefollowingequation [42]:

L

HH

=

κ

λ

λ

SMHHHv H3

−

mt v



κ

tH

+

c2 v H 2

 

_t LtR

+

h.c.



+

1 4

α

S 3

π

v



cgH

−

c2g 2v H 2



_Gμν_G μν

,

(1)

where tL and tR are the topquark fieldswithleft andright

chi-ralities,respectively.TheH denotesthephysicalHiggsbosonfield,

Gμν isthegluon field strengthtensor, and

α

S is thestrong

cou-pling constant.The notation h.c. isusedforthe Hermitian conju-gate. FivemainFeynman diagrams,showninFig.1,contribute to ggHH atLO.

The crosssectionis expressedatLOasa functionoffiveBSM parameters(

κ

λ,

κ

t,c2,cg,andc2g)[6,41] andthisparametrization

is approximately extended to the next-to-next-to-leading order matchedtothenext-to-next-to-leadingloginquantum chromody-namics(QCD)usingaglobalk-factor[6,7,43] thathasuncertainties comingfromthePDF,missingorders,

α

S andfinitetopquarkmass

effects. Thereisa dependenceofthe k-factorsonmHH relatedto

thefinitetop quarkmasseffects[44]. Withintheregionof sensi-tivityofthisanalysis,mHH

<

900 GeV,anyeffectiscoveredbythe

total k-factor uncertainty. The departure of the parameters from theirSMvaluescanchangethetotalcrosssectionbyafeworders ofmagnitude.Furthermore,thekinematicpropertiesoftheHH fi-nal state are modified, whichaffects thefinal sensitivity through the modification of the acceptance and efficiency of the experi-mentalanalysis.

To avoid a prohibitively large numberof samples to simulate andtoanalyze,we usethe methodproposedinRefs. [6,41,45] to partition the parameter spaceinto 12regions withdistinct kine-matics, referred to as clusters. Each of the clusters with its HH kinematics can be represented by a point in the 5D parameter spacethatisreferredtoasabenchmarkhypothesis.Wesimulatethe 12benchmarkhypothesestogetherwithtwoadditionalones–one assuming all parametersto beSM ones(referredto asSM bench-markhypothesis)andtheotherusingidenticalassumptionsexcept fora vanishing Higgsboson self-coupling(referredto as

κ

λ

=

0). The list ofbenchmark hypotheses is provided inTable 1. An ad-ditionalHH sampleisproducedviatheVBFmechanismusingSM couplings.

The ensemble of events obtainedby combining all 14 gluon– gluon initiated samples covers the possible kinematic configura-tions of the effective field theory parameter space. These events canthereforesubsequentlybereweightedusingtheprocedure de-rivedinRef. [46] tomodelanydesiredpointinthefull5D param-eterspace. Inthisprocedure,an event-by-eventweight is analyt-ically calculated from the generator-level information on the HH system.

The dominant backgrounds to the

γ γ

bb finalstate are those inwhichtwoobjectsidentifiedasphotons(eitherpromptphotons orjetsmisidentified asphotons)areproducedinassociationwith jets(referredtoasn

γ

+

jets).Thesimulationofthesefinalstates ischallenging duetolargeeffectsfromhigherordersinQCD [47] andlimitedknowledgeoffragmentationeffectsinthecaseofajet misidentifiedasaphoton.Inthisanalysis, thesecontributions are modeledentirelyfromdata.

Single Higgsboson productioninthe SM,withtwo additional jetsandwithasubsequentdecayoftheHiggsbosontotwo pho-tons, is also considered. In some cases, additional jets can be effectively initiated by b quarks,but inothers they can be initi-atedbylighterquarksandmisidentifiedasab jet.Theconsidered processes – gluon–gluon fusion (ggH), VBF, and associated pro-duction with tt (ttH), bb (bbH), and vector bosons (VH) – are sources ofbackground in thisanalysis. Theyare simulated using

Fig. 1. FeynmandiagramsthatcontributetoggHH atLO.TopdiagramscorrespondtoSM-likeprocesses,referredtoasboxandtrianglediagrams,respectively.Thebottom diagramscorrespondtopureBSMprocesses:thefirstexploitsthecontactinteractionoftwoHiggsbosonswithtwotopquarksandthelasttwodescribecontactinteractions betweentheH bosonandgluons.

Table 1

ParametervaluesofnonresonantBSMbenchmarkhypotheses.ThefirsttwocolumnscorrespondtotheSMandκλ=0 samples,respectively,whilethenext12correspond

tothebenchmarkhypothesesidentifiedusingthemethodfromRef. [45].

SM κλ=0 1 2 3 4 5 6 7 8 9 10 11 12 κλ 1.0 0.0 7.5 1.0 1.0 −3.5 1.0 2.4 5.0 15.0 1.0 10.0 2.4 15.0 κt 1.0 1.0 1.0 1.0 1.0 1.5 1.0 1.0 1.0 1.0 1.0 1.5 1.0 1.0 c2 0.0 0.0 −1.0 0.5 −1.5 −3.0 0.0 0.0 0.0 0.0 1.0 −1.0 0.0 1.0 cg 0.0 0.0 0.0 −0.8 0.0 0.0 0.8 0.2 0.2 −1.0 −0.6 0.0 1.0 0.0 c2g 0.0 0.0 0.0 0.6 −0.8 0.0 −1.0 −0.2 −0.2 1.0 0.6 0.0 −1.0 0.0

MadGraph_{5_amc@nlo 2.2.2forVH and2.3.3forbbH,and powheg} 2.0 [48–51] atNLOforggH,VBF H,andttH.Allsingle-Higgs back-groundsamplesarenormalizedtotheSM crosssectionas recom-mendedinRef. [6].

Allgeneratedeventsareprocessedwith pythia 8.212[52] with thetuneCUETP8M1[53] forshowering,hadronization,andthe un-derlyingeventdescription,and Geant4 [54] for thesimulationof theCMSdetectorresponse.Thesimulatedeventsincludemultiple overlappingpp interactionsoccurringinthesamebunch crossing (pileup)asobservedinthedata.

4. Datasetandeventselection

Events are selected using double-photon triggers, which re-quiretwo photons with transverse momenta pγ_T1

>

30 GeV and

pγ_T2

>

18 GeV for the leading and subleading photons, respec-tively.In addition, calorimeter-based isolation and shower shape requirementsareimposedonlineonthetwo photons.Finally,the diphotoninvariantmassisrequiredtoexceed90 GeV.

Intheofflineselection,eventsarerequiredtohaveatleastone well-identifiedpp collisionvertexwithapositionlessthan24 cm away from the nominal interaction point in the z-direction. The primary vertex is identified by a multivariate analysis that was trained for the measurement of H

→

γ γ

production [55]. This analysisuses the momenta ofthe charged particletracks associ-ated withthe vertex, andvariables that quantify the vector and scalarbalanceofpTbetweenthediphotonsystemandthecharged

particletracksassociatedwiththevertex.Thepresenceofatleast twojetsinthefinal stateofthisanalysishelpstocorrectly iden-tifytheprimaryvertexinmorethan99.9%ofthesimulatedsignal events.

4.1.TheH

→

γ γ

candidate

Photons are identified using a multivariate technique that in-cludesas inputsthe pT ofthe electromagneticshower, its

longi-tudinalleakageintothehadroncalorimeter,anditsisolationfrom jetactivityintheevent.Itwasdesignedduringthedatatakingat

√

s

=

8 TeV [55,56] and retrainedwith

√

s

=

13 TeV data. Identi-fied photoncandidates witha trackmatched tothe ECALcluster arerejected.Photonenergiesarecalibratedsubsequentlyandtheir energiesinsimulatedsamplesaresmearedtomatchtheresolution indata[55].

Events are required to have at least two identified photon candidates that are within the ECAL and tracker fiducial region (

|

η

|

<

2

.

5),butexcludingtheECALbarrel-endcaptransitionregion (1

.

44

<

|

η

|

<

1

.

57). The photon candidates are required to pass thefollowingcriteria:100

<

mγ γ

<

180 GeV; p_Tγ1

/

mγ γ

>

1

/

3 and

pγ_T2

/

mγ γ

>

1

/

4.Incaseswheremorethantwophotonsarefound, the photon pair with the highest transverse momentum pγ γ_T is chosen.

Foreventsthatpasstheaboveselections,thetriggerefficiency is measured to be close to 100% using data events containing a Z bosondecayingtoapairofelectrons,ortoapairofelectronsor muonsinassociationwithaphoton[56].

4.2. TheH

→

bb candidate

The particle-flow (PF) algorithm aims to reconstruct each in-dividualparticle (referredto asa PFcandidate) inan eventwith an optimized combination of information from the various ele-ments of the CMS detector [57]. Jets are clustered from these candidatesusing theanti-kT algorithmwithadistance parameter

Rj

=

0

.

4 [58,59].Jet candidatesare requiredtohave pT

>

25 GeV

and

|

η

|

<

2

.

4.Inaddition,identificationcriteriaareapplied to re-move spuriousjetsassociated withcalorimeternoise.Finally,jets must be separated from each of the two selected photon candi-dates by a distance



Rγj

≡

√

(

η

γj

)

2

+ (φ

γj

)

2

>

0

.

4, where

φ

isthe azimuthalangle inradians.The selectedjetsare combined intodijetcandidates.At leastonedijetcandidateis necessaryfor aneventtobeselected.Thecombinedsecondaryvertexalgorithm, optimizedfor13 TeV data, provides acontinuous b tagging score

Table 2

Summaryofthebaselineselectioncriteria.

Photons Jets

Variable Selection Variable Selection

pγ_T1 >mγ γ/3 pT[GeV] >25

pγ_T2 >mγ γ/4 Rγj >0.4

|η| <2.5 |η| <2.4

mγ γ [GeV] [100,180] mjj[GeV] [70,190]

Fig. 2. Comparisonof



MX(redline)withmγ γjj (purpledottedline)fordifferentspin-2resonancemasses.Alldistributionsareobtainedafterthefullbaselineselection

(Table2),andarenormalizedtounitarea.

definedbetween0and1.Itisusedtoquantifytheprobabilitythat a jet is a result ofa b quark hadronization [60]. In cases where morethantwojetsarefound,thedijetconstructedfromthetwo jetswiththe highestb tagging scoresisselected.An eventis ac-ceptedif 70

<

mjj

<

190 GeV.

The energies of the two selected jetsare corrected usingthe standardCMSalgorithm,whichisflavorblind [61].Inadditionto thiscorrection, a jet energy regression procedure is used to im-provethemjjresolution.Amultivariateanalysistechnique isused

tocorrecttheabsolutescaleoftheheavy-quarkjetsbytakinginto accounttheirspecificfragmentationfeatures,i.e.,alarger contribu-tionfrom chargedleptons andneutrinos thanin light-quarkjets. The approach we use inthis letteris similar to the one used in theCMS search fortheSM H

→

bb decays [62], andin addition, takesadvantageofvariablesrelatedtothemissingtransverse mo-mentumvector,



p_Tmiss,toestimatetheneutrinocontributiontothe heavy-quarkdecay.The



p_Tmiss is calculatedasthenegative ofthe vectorialsumofthetransversemomentaofallPFcandidates.The jetsforming the dijet candidateare ordered by pT, andan

opti-mizedenergyregression distinguishesthehigher pT jetfromthe

lower pT one.The improvementto themjj resolution duetothe

regression procedure depends on the b jet pT spectrum

charac-teristicofa givensignal hypothesis.Forexample, fortheSM-like searchitisoftheorderof15%.

4.3. TheHH system

Asummaryofthebaselineselectionrequirementsispresented in Table 2. After the diphoton and dijet candidates are selected, theyarecombinedtoforman HH candidate.

TohaveabetterestimateofmHHwecorrectmγ γjjusing



MX

=

mγ γjj

− (

mjj

−

mH

)

− (

mγ γ

−

mH

),

(2)

whichmitigates themγ γjj dependencyonthe dijetanddiphoton

energyresolutionswiththeassumptionthatthedijetanddiphoton

originatefromaHiggsbosondecay [63].Thisprocedurehasan ef-fectsimilartothekinematicfitusedpreviouslyinRef. [23].While forthedistanceparameterRj

=

0

.

5 usedinRef. [23] thekinematic

fitwas thebestoptiontoreconstructmHH,forthesmallerradius

usedinthispaper



MX appearstobemoreefficient.The

improve-ments in the mHH reconstruction are most striking for low-mX

hypotheses, as shown in Fig. 2, and have little impact on high

mX hypotheses. This effect can be understood by the fact that

the relative contribution to M



X of

|

mjj

−

mH

|

is much smallerat

high mX.

Withthefourreconstructedobjects fromthe HH decay, angu-lar correlations in the signal can provide important information to separate it from the background.In this analysiswe consider three helicity angles. The scatteringangle,

θ

_HHCS, is definedin the Collins–Soper(CS) frameofthefour-bodysystem [64], asthe an-glebetweenthemomentumoftheHiggsbosondecayingintotwo photons and the line that bisects the acute angle between the collidingprotons.SincethedirectionsofthetwoHiggsboson can-didatesarecollinearintheCSframe,thechoiceoftheHiggsboson decayingtophotonsasthereferencedirectionisarbitrary. There-fore,weusetheabsolutevalueofthecosineofthisangle

|

cos

θ

_HHCS

|

toobviatethisarbitrariness.TheH bosondecayanglesaredefined, ina waysimilarto Ref. [64], astheanglesofthedecayproducts in each Higgsboson’srest framewithrespect to thedirectionof motionofthebosonintheCSframe.Sincethetwophotonsfrom theHiggsbosondecayareindistinguishableandthechargesofthe b quarksarenotconsideredinthisanalysis,theabsolutevaluesof thecosinesoftheseanglesareused:

|

cos

θ

γ γ

|

and

|

cos

θ

jj

|

.

4.4. Backgroundproperties

The main kinematicdistributions ofthe

γ γ

bb final statethat areusedthroughouttheanalysis(invariantmassesandhelicity an-gles) are shown in Fig. 3, after the basic selections summarized in Table2.The datainFig.3 aredominated byn

γ

+

jets events, which aretheprimary contributionto thebackgroundinthis

re-Fig. 3. Data(dots),dominatedbynγ+jets background,comparedtodifferentsignalhypothesesandthreesingle-Higgsbosonsamples(ttH,VH,andggH)aftertheselections onphotonsandjetssummarizedinTable2forthekinematicdistributionsdescribedinSections1and4.3:MX(topleft)and

|

cosθHHCS|(topright);mγ γ (middleleft)and

|cosθγ γ|(middleright);mjj(bottomleft)and

|

cosθjj|(bottomright).Thestatisticaluncertaintiesonthedataarebarelyvisiblebeyondthemarkers.Theresonantsignalcross

sectionisnormalizedto500 fb andtheSM-likeggHH (VBFHH)processto104₍₁₀5_{)timesitscrosssection.}

gion ofphase space. The SM single-Higgs boson production pro-cesses,representedbycoloredareasinthefigure,arethreeorders ofmagnitudelowerthanthenonresonantn

γ

+

jets processes.Only single-Higgsbosonproductionprocesseswithasufficientnumber ofevents(ttH,VH,andggH)areshownforclarityofthefigure. Fi-nally,signal shapesareshowninthe figures,wherethe resonant oneshave beennormalized to a crosssection of500 fb and the

SM-like ggHH (VBF HH) signal to 104 (105) times its cross sec-tion.

As expected, the signals produce peaks in mγ γ and mjj. The

resonant di-Higgs boson signals peak sharply in M



X, while SM

HH processesexhibitbroadstructuresinducedbytheinterference patternofdifferentFeynmandiagramscontributingtotheHH pro-duction and shaped by the analysisselections. The data show a

smoothlyfallingmassspectrum,asexpectedforthen

γ

+

jets back-ground.Finally,thesingle-Higgsbosonbackgroundspeak inmγ γ ,

butnotinmjjorM



X (excepttheVH processwhichgivesapeakin

mjjaroundtheVmasses).

The

|

cos

θ

_HHCS

|

distributionissensitivetothetensorstructureof theproduction mechanism(see forexample Ref. [65]).It is rela-tivelyflat forggHH [66] andthespin-0 mediatedproduction.For the spin-2 mediated productionit decreases toward 1, while for VBFHH andthedataitrises toward1.Thedistributionofthe co-sine of the H

→

γ γ

helicity angle is expectedto be flat forthe sampleswithgenuineHiggsbosons.Thedecreasetoward1isdue tothe selectionson photon pT.In thedata thedistribution rises

upto 0.8andthen decreases.Thisshaperesultsfromthe combi-nationofmatrixelementpropertiesandtheasymmetricselections onthephoton pT.Inthesameway,the

|

cos

θ

jj

|

distributionisflat

forthesignal,butrisessignificantlytoward1forthedataandggH.

5. Eventclassificationandmodeling

Afterdijetanddiphotoncandidateselection,eventsareplaced into categories using the M



X variable and a multivariate (MVA)

classifier.Both variablesare designedto minimize thecorrelation betweenmγ γ and mjj. In each category, a parametric fit is

per-formed inthetwo-dimensional mγ γ –mjj plane forthe signal

ex-traction procedure using a product of probability densities (PDs) forsignal andbackgrounds. This 2D approach helpsto constrain the impactof the single-Higgs bosonbackground since its struc-tureinmjjdiffersfromthatofthesignal.Finally,allthecategories

are combinedtogether assuminga signal modelto maximizethe sensitivityoftheanalysis.

5.1. Eventclassification 5.1.1.



MXcategorization

In the nonresonant search, a categorization is performed us-ingtheM



X information.SincetheM



XspectrumforSM-like ggHH

productionhasa maximumataround 400 GeV andthen

γ

+

jets backgroundpeaks atthe kinematicthreshold of250 GeV

=

2mH,

the maximal sensitivity isachieved for M



X

>

350 GeV. However,

anomalouscouplingsmaychangetheM



X distributionforthe

sig-nal hypothesis. Therefore, instead of imposing a M



X selection,

eventsare categorizedin the nonresonant search into high-mass (HM)andlow-mass(LM)regionsthat areaboveandbelow



MX

=

350 GeV,respectively.

In the resonant search,



MX is used to define a unique

sig-nal region that depends on the mass of the resonance being sought.This masswindowtypically contains 60%ofthe signal at low mX, increasing gradually forhigher mX. The resonant search

starts just above the threshold at 260 GeV



2mH and extends

up to mX

=

900 GeV. In fact the Rj value used in this paper is

smallenoughtoreconstructthedecayproductsoftwo boostedb quarksproducedintheHiggsbosondecaysasseparatejetsupto

mX

≈

1

.

25 TeV [67].However,forvaluesofmX

≈

1 TeV andlarger

theavailableamountofdataistoosmalltoperformthesignal ex-tractionprocedureasdefinedinthispaper.

5.1.2. MVAcategorization

AnMVAprocedureisusedtoselectthemostsignal-likeevents andtofurtherclassifythem.Withthisgoal,aboosteddecisiontree (BDT)istrainedwiththe TMVA package [68] usingthreetypesof variables:

•

b taggingvariables:theb taggingscoreofeachjetinthedijet candidate;

•

HelicityanglesasdefinedinSection4.3;

Fig. 4. DistributionsoftheBDToutput(classificationMVA)obtainedforthe high-massnonresonanttraining.Data,dominatedbynγ+jets background,arecompared todifferentsignalhypothesesandthreesingle-Higgsbosonsamples(ttH,VH,and ggH)aftertheselectionsonphotonsandjetssummarizedinTable2.Thestatistical uncertaintiesonthedataarebarelyvisiblebeyondthemarkers.Theresonant sig-nalcrosssectionisnormalizedto500 fb andtheSM-likeggHH (VBFHH)process to104₍₁₀5_{)timesitscrosssection.}

•

HH transverse balance variables: pγ γ_T

/

mγ γjj and pjjT

/

mγ γjj,

where pjj_T isthetransversemomentumofthedijetcandidate.

TheBDT istrainedwiththeensembleofggHH samplesasthe signal hypothesis in the nonresonant search separately for low-andhigh-masscategories.Fortheresonantcases,theensembleof resonant signals isused to train one BDT formX

<

600 GeV and

another one for mX

>

600 GeV. This training strategy maximizes

thesensitivitytomassiveresonances.Thebackgroundeventsused forthe training are obtainedfroma controlsample that was ex-tracted fromthe databyinverting theidentificationcondition on one ofthetwophotons. Thissampleisdominatedbyevents hav-ing aphotonproducedwiththreeaccompanyingjets. Weverified that afterexcludingtheeventswith120

<

mγ γ

<

130 GeV inthe signal andcontrol samples,thekinematicpropertiesofthesetwo samplesarewellmatched.

Fig. 4 shows the BDT output from one of the four trainings. The MVAefficientlyseparatesgluon–gluon producedsignalsfrom then

γ

+

jets backgroundthat representsthedominant contribu-tionto thedata.Themostpowerfuldiscriminatingvariables used in the BDT are the b taggingscores ofthe jets, followed by the kinematic variables.Therefore, the single-Higgsboson production samples withgenuine contributions from two b quarks (ttH and Z

(

→

bb

)

H) areclassifiedasmoresignal-like,whileggH andother VH processesareclassifiedasmorebackground-like.Finally,events fromtheVBFHH productionareselectedlessefficientlythanthose fromggHH production.

Foragivencategorythepurityisdefinedastheratiobetween the numberof events coming from a hypothetical signal witha production cross section normalized to 1 fb and the number of background events. For each of the four trainings, the output of the MVA classifier is used to define a category withthe highest purity(HPC)andanotherwithmediumpurity(MPC).The remain-ingeventsarerejected,becausetheydonotimprovethesensitivity ofthe analysis. Inthenonresonant low-



MX MPCregion,an

addi-tionalrequirementisplacedontheb taggingscore,corresponding to80%efficiencyforgenuineb jets[60].Thisreducesthe contribu-tionoftheeventswherethejetwithlowestb taggingscorecomes froma pileupevent. Table3 showstheHPCandMPC definitions forthedifferentregionsoftheresonantandnonresonantanalyses.

Table 3

Definitionofhigh-puritycategory(HPC)andmedium-puritycategory(MPC)fortheresonantandnonresonantanalyses.

Analysis Region Classification MVA MX

Nonresonant High-mass HPC: MVA>0.97 MX>350 GeV

MPC: 0.6<MVA<0.97

Low-mass HPC: MVA>0.985 MX<350 GeV

MPC: 0.6<MVA<0.985

Resonant mX>600 GeV HPC: MVA>0.5 Mass window

MPC: 0<MVA<0.5

mX<600 GeV HPC: MVA>0.96 Mass window

MPC: 0.7<MVA<0.96

Fig. 5. Consecutiveselection efficienciesfor differentanalysisstepsfor two res-onance hypotheses:spin-0 (top) and spin-2(bottom). Online selection includes thephotononlinepreselectionconditionsdescribedatthebeginningofSection4. Diphotonselectionsinclude photonidentificationand kinematicsselectionsfrom Table2.DijetselectionsarethosedescribedinTable2.

5.1.3. Signalacceptancetimesefficiency

Thetypical signal acceptance timesefficiency(A



) values ob-tained in the resonant analysis are shown in Fig. 5. Consecutive effects of the selections on A



for different analysis steps are shown:afterthetriggerselectionthatincludesalooseonline pre-selection on the photons, after the diphoton candidate selection, afterthedijet candidateselection,andafter theMVA categoriza-tion.ThefinalA



valuesrangefromapproximately20%(lowmass) to50% (highmass) forboththe spin-0andspin-2 resonance hy-potheses.ForanidenticalmXvalue,A



isabithigherforaspin-2

hypothesisthanforspin-0,becausetheHiggsbosonsare,on

aver-Fig. 6. Signalshapesformγ γ (top)andmjj (bottom)intheSMHH nonresonant

sampleafterfullanalysisselectioninthehigh-massandHPCregion.Thesolidline showsafittothesimulateddatapointswithadouble-sidedCrystalBallfunction. Thenormalizationoftheshapesisarbitrary.

age,producedmorecentrallyintheKKgravitonmodelconsidered inthisletter(seeFig.3).

The A



value is30(13)%forthe SM-likeggHH (VBF HH) sig-nalhypothesis,with25(10)%inthehigh-massregion and5(3)% inthe low-massone. Thedifference betweenthetwo production mechanismsmainlycomesfromthefactthattheMVAwastrained assumingaggHH signal.Forexample,oneofthemost discriminat-ing variables,

|

cos

θ

_HHCS

|

,showninFig.3,hasasimilar behaviorto then

γ

+

jets backgroundandfortheVBFHH process, whileitis verydifferentfortheggHH process.

5.2. Signalmodeling

The signal PD of each mass dimension is modeled with a double-sidedCrystalBall(CB)function,whichisamodifiedversion ofthestandardCBfunction [69] withtwoindependentexponential tails.Thismodelingisusefulinsituationsinwhichalower-energy tail mightbe createdby energy mismeasurements anda higher-energy tail by the mismatching of objects (for example when a

Fig. 7. BackgroundfitsfortheSMHH nonresonantanalysisselectionintheHMregion.Theplotsontheleft(right)showthedistributionsintheHPC(MPC)region.Topplots showthemγ γ spectraandbottomonesmjjones.Thegreendashedlinerepresentsthenonresonantpartoftheexpectedbackground;thesolidbluelinerepresentsthefull

backgroundmodelingPD,i.e.,thesumofnonresonantbackgroundandSMsingle-Higgsbosoncontributionsscaledtotheircrosssections;andthesolidredlinerepresents theSM-likeHH production,normalizedtoitsSMcrosssectiontimesascalingfactorspecifiedinthelegend.

jet from additional QCD radiation is misidentified as one of the jets from the H boson decay). The final two-dimensional signal model PD isthe product of the independentmγ γ and mjj

mod-els. The no-correlation hypothesis is checked by comparing the two-dimensional mγ γ –mjj distribution fromthe simulated signal

sampleswiththe two-dimensional PD builtasa product of one-dimensionalones.Forthetypicalexpectednumberofsignalevents inthisanalysis,theimpactofsuchcorrelationsisfoundtobe neg-ligible.

The PD parameters are obtained by fitting the simulated sig-nalsamples ineach analysis region.Foreach mX point andeach

nonresonant sample a dedicated fit is performed. The resolution isestimatedby the

σ

eff value,definedashalfofthewidthofthe

narrowestregioncontaining68.3%ofthesignalshape.Examplesof thesignalshapesinthenonresonantanalysis,assuminganSM-like signal,areshowninFig.6.Thediphotonresolutionisdetermined to be

≈

1

.

6 GeV and the dijet resolution is

≈

20 GeV. The mean oftheGaussiancoreoftheCB function,

μ

,isclosetomH,within

0.1–0.2%formγ γ and1–2%formjj.

5.3. Backgroundmodeling

Thetotalbackgroundmodelisobtainedasasumofthen

γ

+

jets backgroundcontinuumPDandsingle-Higgsbosonproduction

PDs,thelatterbeingnormalizedtotheirSMproductioncross sec-tions.

Forboth theresonant andnonresonant analyses then

γ

+

jets continuum is described using polynomialsin the Bernstein basis [55].The datacontrol sample described in Section 5.2isused to define the appropriate order of the polynomial function for the one-dimensional PDsofthen

γ

+

jets backgroundcontinuum.For each search we randomlyselectfrom thecontrol sample a num-ber of events equal to the total number of events observed in data. A second-order Bernstein polynomial fits the data well. In categorieswithfewerevents,occurringintheresonant analysis,a first-order Bernstein polynomial isused. Thischoice of the back-groundPDistestedforpossiblebiasesinthesignal extractionby comparing ittoother possible backgroundmodels,such as expo-nentialsandLaurentpolynomials.Thebiasfromthechosen PDis always found tobe smallerthanthe statisticaluncertainty inthe fit,andcanbe safelyneglected [2]. Thecorrelation betweenmγ γ

andmjjwasmeasuredinthedatacontrolsampleandfoundtobe

compatiblewithzero.

The SM single-Higgs boson background contribution is esti-mated usinga PD fittedto simulatedsamples.Forall production mechanisms, the mγ γ distributionis modeled by a double-sided CB function.Themjjmodelingdependsontheproduction

mecha-nism: forggH and VBF H productionmjj ismodeled witha

Fig. 8. BackgroundfitsfortheSMHH nonresonantanalysisselectionintheLMregion.Theplotsontheleft(right)showthedistributionsintheHPC(MPC)region.Topplots showthemγ γ spectraandbottomonesthemjj ones.Thegreendashedlinerepresentsthenonresonantpartoftheexpectedbackground;thesolidbluelinerepresents

thefullbackgroundmodelingPD,i.e.,thesumofnonresonantbackgroundandSMsingle-Higgsbosoncontributionsscaledtotheircrosssections;andthesolidredline representstheSM-likeHH production,normalizedtoitsSMcrosssectiontimesascalingfactorspecifiedinthelegend.

isexpected to describe the lineshape ofthe hadronic decaysof vectorbosons;forttH andbbH adouble-sidedCB functionisalso used.Like the signal modeling, the final 2D SM single-Higgs bo-sonmodel isan independent productof modelsof themγ γ and mjjdistributions.Thisbackgroundcontributionisexplicitly

consid-eredonlyforthenonresonantsearch,sincefortheresonantoneit isseverelyreducedbyatightselectionwindowon



MX.The

resid-ualeventsareaccountedforbythecontinuumbackgroundmodels forthemγ γ andmjj variables.Theone-dimensionalprojectionsof

thebackground-plus-signalfitsinthesignalregionsofthe nonres-onantanalysisareshowninFigs.7and

8

.

6. Fittingprocedureandsystematicuncertainties

AlikelihoodfunctionisdefinedbasedonthetotalPDincluding the backgrounds, signal hypothesis, and the data. Then an un-binned maximum likelihoodfit is performedto the 2D mγ γ –mjj

datadistribution.The parameters forthesignal yield andforthe background-onlyPD areconstrainedinthefit.Uniformpriorsare used to parametrize the nonresonant background PD and log-normalpriorsareassumedforthesingle-Higgsbosonbackground parameterizing ourdegreeofuncertaintyintheexactSM produc-tioncrosssection.When convertingthefittedyieldsinto produc-tion cross sections, we use simulation to estimate the selection efficiency for the signal. The difference between the simulation

andthedataistakenintoaccountthroughparametersincludedin the likelihood function. Parametersrelated to the systematic un-certainties(nuisanceparameters)arevariedinthefitaccordingto alog-normal PD functionandcanbe classifiedaccordingtotheir impact on the analysis. The uncertaintyin the estimation ofthe integrated luminosity modifies the total expected signal normal-izationandistakentobe2.5% [70].Othersystematicuncertainties modify theefficiency ofthe signal selectionor impactthe signal ortheHiggsbosonPD.

Thephoton-relateduncertaintiesarediscussedinRef. [55].The photonenergyscale(PES)isknownatasub-percentlevelandthe photon energyresolution(PER)isknown with5% precision.A2% normalizationuncertaintyisestimatedinthe offlinediphoton se-lectionefficiencyandinthetriggerefficiency,while1%isassigned toquantifytheuncertaintyonthephotonidentificationefficiency. The uncertainties inthe jet energyscale (JES) and jet energy resolution(JER)areaccountedforbychangingthejetresponseby onestandarddeviationforeachsource[61].Theyimpactthe aver-agemjjpeakpositionbyapproximately1%andthepeakresolution

by5%.Theeffectsonthesignalacceptancearealsoaccountedfor. Tousetheb taggingscoreasaninputtotheclassificationMVA, itssimulateddistributionismatchedtodatabyapplying differen-tialscalefactorsthatdependonthejet pT and

η

[60].The

uncer-tainty intheefficiencyofthecategorizationMVAis estimatedby varyingtheb taggingdifferentialscalefactorswithinonestandard

Table 4

Summaryofsystematicuncertainties.

Sources of systematic uncertainties Type Value (%)

Integrated luminosity Normalization 2.5

Photon related uncertainties

Diphoton selection (with trigger uncertainties and PES) Normalization 2.0

Photon identification Normalization 1.0

PES (mγ γ

mγ γ ) Shape 0.5

PER (σγ γ

σγ γ ) Shape 5.0

Jet related uncertainties

Dijet selection (JES+JER) Normalization 0.5

JES (mjj

mjj) Shape 1.0

JER (σj j

σj j ) Shape 5.0

Resonant analysis specific uncertainties

Mass window selection (JES+JER) Normalization 3.0

Classification MVA – b tagging (HPC) Normalization 10–19

Classification MVA – b tagging (MPC) Normalization 3–9

Nonresonant analysis specific uncertainties 

MXClassification Normalization 0.5

Classification MVA – b tagging (HPC) Normalization 10–19

Classification MVA – b tagging (MPC) Normalization 3–9

Theoretical uncertainties in the SM single-Higgs boson production

QCD missing orders (ggH, VBF H, VH, ttH) Normalization 0.4–5.8 PDF andαSuncertainties (ggH, VBF H, VH, ttH) Normalization 1.6–3.6

Theoretical uncertainty bbH Normalization 20

Theoretical uncertainties in the SM HH boson production

QCD missing orders Normalization 4.3–6

PDF andαSuncertainties Normalization 3.1

mteffects Normalization 5

deviationoftheir uncertainties[60].The impactsofPES,PER,JES, andJERon the MVAclassification procedure havebeenfound to benegligible.Thosefoursourceshave,nevertheless,amildimpact onthe



MX-basedcategorization.

Theoretical uncertainties havebeen applied to the normaliza-tionofthesingle-Higgsbosonbackground,butnotonBSMsignals. When we consider the SM-like search and parametrize the BSM crosssection

σ

BSM gg→HHbytheratio

μ

HH

=

σ

BSM gg→HH

/

σ

SM gg→HH,the the-oretical uncertainties on

σ

SM

gg→HH are included in the likelihood.

Thefollowingsourcesare consideredcorrelatedforallthe single-Higgs boson channels (except bbH) and the double-Higgs boson channelinlinewiththerecommendationsfromRef. [6]:thescale dependenceofhigher-orderterms;theimpactfromthechoice of PDFquadraticallysummedwiththeuncertaintyon

α

S;and,inthe

caseofthe HH channel,theuncertainties relatedtotheinclusion ofmt intothecrosssectioncalculations.Finally,forthebbH

chan-nelallsourcesaresummedtogetherincludingalsotheuncertainty ontheb quarkmass.

The systematic uncertainties are summarized in Table 4. The correlations between different categories are taken into account. Theanalysisislimitedbythestatisticalprecision.Forexample,the systematicuncertainties worsentheexpectedcross section limits by3%forthesearchperformedassumingaSM-likesignal.

7. Results

NoevidenceforHH productionisobserved inthedata.Upper limitson the production cross section ofa pair of Higgs bosons timesthebranchingfraction

B(

HH

→

γ γ

bb

)

are computedusing themodifiedfrequentistapproachforconfidencelevels(CLs),

tak-ingtheprofilelikelihood asatest statistic [71–74] inthe asymp-toticapproximation.Thelimitsaresubsequentlycomparedto the-oreticalpredictionsassumingSMbranchingfractionsforHiggs bo-sondecays.

7.1. Resonantsignal

The observed and medianexpected upper limits at 95% con-fidence level (CL) are shownin Fig. 9, forthe pp

→

X

→

HH

→

γ γ

bb processassumingspin-0andaspin-2resonances.Thedata excludeacrosssectionof0.23to4

.

2 fb dependingonmX andthe

spinhypothesis.

The results are compared withthecross sections forbulk ra-dion and bulk KK graviton production in WED models. In anal-ogy with the Higgs boson, the hypothesized bulk radionfield is expected tobe predominantlyproduced through gluon–gluon fu-sion [75] and the cross section is calculated at NLO accuracy in QCD, using the recipe suggested in Ref. [76]. The theoretical in-putusedinthisletterisidenticaltotheonefromapreviousCMS analysis[23]. Moredetails canbefound inRef. [77].The produc-tioncrosssectioninthismodelisproportionalto1

/

2_R,where



R

is the scale parameterof the theory.The analysisat

√

s

=

8 TeV [23] alreadyexcluded a radionresonance up to 980 GeV for the scaleparameter



R

=

1 TeV,buthadnosensitivityfor



R

=

3 TeV.

Inthisanalysistheobservedlimitsareabletoexcluderadion res-onances,assuming



R

=

2 TeV,forallpointsbelowmX

=

840 GeV

and,assuming



R

=

3 TeV,belowmX

=

540 GeV.Thecouplingsof

the gravitons to matter fields are defined by

κ

/

MPl, with MPl

≡

MPl

/

√

8

π

beingthereducedPlanckmassand

κ

thewarpfactorof the metric.Assuming

κ

/

MPl

=

1

.

0,gravitons are excluded within

the range290

<

mX

<

810 GeV,while assuming

κ

/

MPl

=

0

.

5,the

exclusionrangeis350

<

mX

<

530 GeV.

Theeventsinasignalregiondefinedby122

<

mγ γ

<

128 GeV and90

<

mjj

<

160 GeV areshownasafunctionofmX inFig.10

andcompared to threedifferent resonantsignal hypotheses with theory parameters choseninsuch a waythat their crosssections are close tothe excluded ones. The vertical linesshow the mass windowsthatareusedtoselectinmX andsetthelimitsshownin

Fig. 9. Observedandexpected95%CL upperlimitsontheproductofcrosssection andbranchingfractionσ(pp

→

X)B(X→HH→γ γbb)obtainedthrougha com-binationofthetwoanalysiscategories(HPCandMPC)forspin-0(top)andspin-2 (bottom)hypotheses.Thegreenandyellowbandsrepresent,respectively,theone andtwostandarddeviationextensionsbeyondtheexpectedlimit.Alsoshownare theoreticalpredictionscorrespondingtoWEDmodelsfor bulkradions(top)and bulkKKgravitons(bottom).Theverticaldashedlinesshowtheboundarybetween thelow- andhigh-massregions.ThelimitsformX=600 GeV areshownforboth

methods.

7.2.Nonresonantsignal

The observed (expected) 95% CL upper limit on the SM-like pp

→

HH

→

γ γ

bb process is 2.0 (1

.

6 fb), and 0.79 (0

.

63 pb) for the total ggHH production cross section assuming SM Higgs bosonbranching fractions.The results can also be interpreted in termsofobserved(expected)upperlimitson

μ

HH of24(19).The

constrainton

μ

HHisafactorofthreemorerestrictivethatthe

pre-vioussearch[23].

Anadditional study isperformed includingboth VBF HH and ggHH productionmechanismsinthedefinitionofthescalingfactor

μ

ext HH

=

σ

BSM gg→HH

+

σ

VBF HHBSM

σ

SM gg→HH

+

σ

VBF HHSM (3) where

σ

SM VBF HH

=

1

.

64+ 0.05

−0.06 fb [6]. The expectedsensitivity ofthe

analysis for

μ

ext

HH improves by 1.3% compared to

μ

HH. The

im-provement is smaller than the relative contribution of the VBF productioncrosssectiontothetotaloneintheSMbecauseofthe nonoptimalselectionefficiencyofthisanalysisfortheVBFevents, asexplainedinSection5.

Fig. 10. Data(dots)withstatistical uncertainties(vertical blacklinesaroundthe dots)histogrammedinbinsofMXareoverlaidontoexpectedMonteCarlo

simu-lateddistributionsforthreesingle-Higgsbosonssamples(ttH, VH,andggH)and three different resonant signalhypotheses. The data-driven backgrounds, domi-natedbynγ+jets,arenotshownandarespecifictotheanalysiscategories.The eventsareselected inthe signalregion definedby 122<mγ γ <128 GeV and 90<mjj<160 GeV andusethephotonsandjetsselectionssummarizedin

Ta-ble2.TheMPandHPcategoriesaremergedtogether.Thesignalsarenormalizedto thetheorycrosssectioncalculatedwiththeparametersshowninthefigureand as-suminganarrowwidthapproximation.Theverticallinesshowthe masswindows thatareusedtoselectinmXandsetthelimitsshowninFig.9.

The resultsare alsointerpreted in thecontext ofHiggs boson anomalous couplings.LimitsonthedifferentBSMbenchmark hy-potheses(listedin Table1) are showninFig.11 (top).Using the limits on the benchmark hypotheses and the map between the clustersandthepointsinthe5DBSMparameterspace,onecan es-timatetheconstraintsprovided bythesedataindifferentregions of phase space. It is important to stress that the same analysis categoriesareusedfortheSM-likesearchandforallBSM nonres-onantsearches.Thedifferencesbetweenthelimitscomeonlyfrom thekinematicpropertiesofthebenchmarksignal hypotheses.For instance,thetightestconstraintisplacedonthebenchmark2 hy-pothesis,whichfeaturesamHHspectrumthatextendsabove1 TeV

owingtolargecontributionsfromdimension-6operators.Theleast restrictiveconstraintisonbenchmark7thatdescribesmodelswith largevaluesof

κ

λ,wherethemHHspectrumpeaksbelow300 GeV.

Forbenchmark2mostoftheeventswouldbeobservedintheHM categories,whileforbenchmark7mosteventsfallintheLM cate-gories.Assumingequalcrosssections,benchmarkhypothesis2has a much better signal-over-background ratio than benchmark hy-pothesis 7.Intheintermediate caseofSM-like production itwas observedthattheHMcategorieshavethebestsensitivity.

Wereweightthebenchmarksamplestomodeldifferentvalues oftheSMcouplingmodifier

κ

λ,with

κ

tandotherBSMparameters

fixedtotheirSM values.InFig.11(bottom),95%CL limitsonthe nonresonantHiggsbosonpairproductioncrosssectionsareshown asafunctionof

κ

λ.Assumingthatthetopquark Yukawacoupling is SM-like (

κ

t

=

1), the analysis constrains

κ

λ tovalues between

−

11 and17.

8. Summary

A search isperformedby the CMSCollaboration forthe reso-nantandnonresonant productionofapairofHiggsbosonsinthe decaychannelHH

→

γ γ

bb,basedonan integratedluminosity of 35

.

9 fb−1 of pp collisions collected at

√

s

=

13 TeV in 2016. No statistically significant deviations from the standard model (SM) predictions are found. Upper limits at a 95% CL are set on the crosssectionsfortheproductionofnewparticlesdecayingtotwo

Fig. 11. Expectedandobserved95%CL upperlimitsontheSM-likeHH production crosssectiontimesB(HH→γ γbb)obtainedfordifferentnonresonantbenchmark models(definedinTable1)(top);fordifferentvaluesoftheκλ(bottom).Thegreen

andyellowbandsrepresent,respectively,theoneandtwostandarddeviation ex-tensionsbeyond theexpectedlimit. Theredlineinthebottom plotshowsthe predictionoftheorywiththeassociateduncertaintiesshownastheorangeband.

Higgs bosons in the mass range between250 and 900 GeV, un-der the spin-0and spin-2 hypotheses.In the caseofbeyond SM predictions,basedontheassumptionoftheexistenceofawarped extradimension,weexcludetheradion(spin-0)signalhypothesis, assuming the scale parameter



R

=

3 TeV, forall masses below

mX

=

540 GeV, and the KK graviton (spin-2) hypothesis for the

massrange290

<

mX

<

810 GeV,assuming

κ

/

MPl

=

1

.

0 (MPl

be-ingthereducedPlanckmassand

κ

thewarpfactorofthemetric). For nonresonant production with SM-like kinematics, a 95% CL upperlimitof2

.

0 fb isseton

σ

(

pp

→

HH

→

γ γ

bb

)

, correspond-ingtoabout24timestheSM prediction.Anomalouscouplings of the Higgs boson are also investigated, as well as the vector bo-son fusion HH production process. Values of the effective Higgs boson self-coupling

κ

λ are constrained to be within the range

−

11

<

κ

λ

<

17 at 95% CL, assuming all other Higgs boson cou-plingstobeattheirSM values.Thedirectconstraintsreportedon

κ

λarethemostrestrictivetodate. Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentersand

personneloftheWorldwideLHCComputingGridfordeliveringso effectively thecomputinginfrastructure essentialto our analyses. Finally, we acknowledge the enduring support for the construc-tion andoperationofthe LHCandtheCMSdetectorprovided by 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);MOE andUM (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);NASU andSFFR (Ukraine);STFC(United Kingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract No. 675440 (European Union);the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’A-griculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science - EOS” - be.h projectn. 30820817;the MinistryofEducation,YouthandSports (MEYS) of theCzech Republic; theCouncil of Scienceand Indus-trial Research, India; the HOMING PLUS program of the Foun-dation for Polish Science, cofinanced from European Union, Re-gional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-search Program by Qatar National Research Fund; the Programa Severo Ochoa del Principado de Asturias; the Thalisand Aristeia programscofinancedbyEU-ESFandtheGreekNSRF;the Rachada-pisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University andthe ChulalongkornAcademic intoIts 2nd Century Project Advancement Project (Thailand); the Welch Foundation, contractC-1845;andtheWestonHavensFoundation(USA).

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