Combined measurement of differential and total cross sections in the H → γγ and the H → ZZ⁎ → 4ℓ decay channels at √s = 13 TeV with the ATLAS detector

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Combined measurement of differential and total cross sections in the H → γ γ ^and ^the ^H → ^{Z Z}

^∗

→ ⁴ ^decay ^channels ^at √

s = ^{13 TeV} ^with the ATLAS detector

.The ATLASCollaboration

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

Articlehistory:

Received28May2018

Receivedinrevisedform24August2018 Accepted11September2018

Availableonline17September2018 Editor:M.Doser

AcombinedmeasurementofdifferentialandinclusivetotalcrosssectionsofHiggsbosonproductionis performedusing36.1 fb⁻¹ of13 TeV proton–proton collisiondataproducedby theLHCand recorded bythe ATLASdetector in 2015 and 2016. Cross sections are obtained from measured H→γ γ ^and

H→^{Z Z}^∗→⁴êvent^yields,^whichâre ^combined^takingîntoâccount^detectorefficiencies,resolution, acceptances and branching fractions.The totalHiggs boson production cross section is measured to be57.0⁺₋⁶₅^._.⁰₉(stat.)⁺₋⁴₃^._.⁰₃(syst.) pb,inagreement withthe Standard Modelprediction. Differentialcross- sectionmeasurementsarepresentedfortheHiggsbosontransversemomentumdistribution,Higgsboson rapidity,numberofjetsproducedtogetherwiththeHiggsboson,andthetransversemomentumofthe leadingjet.Theresultsfromthetwodecaychannelsarefoundtobecompatible,andtheircombination agreeswiththeStandardModelpredictions.

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

1. Introduction

Differential cross-section measurements are important studies of Higgs boson production, probing Standard Model (SM) predictions. Deviations from the predictions could be caused by physics beyond the SM [1,2]. Both the ATLAS and CMS collaborations havemeasureddifferentialcrosssectionsinthe H→γ γ^,

H→Z Z^∗→4(where =e,μ⁾ ^and ^H→W W^∗→eνμν ^decay

channels [3–10].

This Letter describes the combination of two fiducial crosssection measurements in the H→γ γ ^{[11] and} ^H→^{Z Z}^∗→⁴ [12] decay channels, which were obtainedusing 36.1 fb⁻¹ of pp collisiondataproducedbytheLargeHadronCollider(LHC)in2015 and2016withacentre-of-massenergyof13 TeV andrecordedby the ATLAS detector [13]. Thecombined crosssection is extracted forthe total phasespace, increasing the degree ofmodeldepen- dencecomparedtotheindividualmeasurements,whichwereper- formedinafiducialphasespaceclosetotheselectioncriteriafor reconstructed events in the detector. Despite the additional sys- tematic uncertainties assigned to the extrapolation to the total phase space, the combination significantly reduces the measure- mentuncertaintycomparedto theresultsintheindividual decay channels.

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

The measured observables include the total production cross section, theHiggsboson’s transversemomentum p_T^H,sensitive to perturbativeQCDcalculations,andtheHiggsboson’srapidity|^y^H|^, sensitive to the parton distribution functions (PDF). Furthermore the numberof jets Njets is measured inevents witha Higgsbo- son andjet transverse momentum above 30 GeV, aswell as the leadingjet’stransversemomentum p^j1_T.BoththeNjetsandp^j1_T ob- servablesprobethetheoreticalmodellingofhigh-pTQCDradiation inHiggsbosonproduction.TheN_jetsobservableisalsosensitiveto thedifferentHiggsbosonproductionprocesses [14].

The cross sections are obtained from yields measured in the H→γ γ ând^H→^{Z Z}^∗→⁴^decay^channels,^whichâre^combined taking into account detector efficiencies, resolution, acceptances andbranchingfractions.Foreach decaychannel andeachobserv- able,thecrosssectionscanbewrittenas

σi= ^N

sig i

LB AiCi,

wherei istheiteratoroverthebinsoftheobservableofinterest,

σi is the crosssection inbin i, N^sig_i isthe number ofmeasured reconstructed signal events following the analysis selection, L is theintegratedluminosityandB^is^the^branching^fraction.^The^term Ciisthecorrectionfactorfromthenumberofeventsreconstructed tothenumberofeventsatparticlelevelproducedintherespective ﬁducialphasespace,andAi istheacceptancefactorextrapolating https://doi.org/10.1016/j.physletb.2018.09.019

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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Table 1

MonteCarlosamplesusedtosimulateHiggsbosonproduction,includingthegenerators,accuracyof calculationsinQCD,andPDFsets.

Process Generator Accuracy in QCD PDF set

ggF Powheg-Boxv2 (NNLOPS) [20–23] NNLOin|y^H|[24], p_T^HconsistentwithHqT (NNLO+NNLL) [26,27]

PDF4LHC [25]

VBF Powheg-Boxv2 [20–22,28] NLO PDF4LHC

V H Powheg-Boxv2 (MiNLO) [20–22,29] NLO PDF4LHC t¯t H Madgraph5_aMC@NLO(v.2.2.3) [30] NLO CT10nlo [31]

b_bH¯ Madgraph5_aMC@NLO(v.2.3.3) [30,32] NLO NNPDF23 [33]

Table 2

Cross-sectionpredictionsusedtonormalizethe MCsamples,theaccuracyofthe calculations(inQCDifnotnotedotherwise),andthecompositionoftheproduction modesintheSM.

Process Accuracy Fraction [%]

ggF N³LO, NLO EW corrections [37–50] 87.4 VBF NLO,NLOEWcorrections [51–53]

with approximateNNLOQCDcorrections [54]

6.⁸ V H NNLO [55,56], NLO EW corrections [57] 4.¹ tt H¯ NLO, NLO EW corrections [58–61] 0.9 b_bH¯ five-flavour: NNLO, four-flavour: NLO [62] 0.9 fromthefiducialtothetotalphase spacecontainedinthebinof interest.

Predictedbranchingratiosandproductioncrosssectionsareob- tainedfor mH=¹²⁵.09 GeV [15],as described inSection 2. The numberofsignaleventsineachbinofaprobedobservableisex- tracted in the H→γ γ ând ^H→^{Z Z}^∗→⁴ ^channels ^from ^fits tothemγ γ andm4invariantmassdistributions,respectively.The signalextractionandthecorrectionfactorsarediscussedindetail inRefs. [11,12].Thecorrectionfactorsareobtainedfromsimulated events,assumingSM Higgsboson production.In ordertoharmo- nize thepublished H→γ γ ^fiducial measurement [11] withthe H→^{Z Z}^∗→⁴ analysis [12],adjustments were madeto thebin boundaries andthe uncertainties ofthecorrection factors dueto thefractionsofdifferentHiggsbosonproductionprocessesinthe H→γ γ ^decay ^channel. ^Toextrapolate to the total phase space, acceptancefactorsanduncertaintiesare calculatedforthecombi- nation,asdiscussedinSection3.Section4presentsthecombina- tionmethodology.TheresultsarediscussedinSection5.

2. HiggsbosonMonteCarlosamples,crosssectionsand branchingfractions

PredictionsofSM Higgsbosonproductionareused inthecal- culation of the correction and acceptance factors, and are com- paredtothemeasuredcrosssections.TheMonteCarlo(MC)event generators that were used to simulate gluon–gluon fusion (ggF), vector-bosonfusion(VBF),associatedHiggsbosonproduction(V H, V =^W,^Z^), ^and ^Higgs ^boson ^production ⁱⁿ association with a heavy-quarkpair(tt H¯ ,b_bH¯ ₎_are_listed_in_Table_1._The _accuracy_of thecalculationsandthePDFsetsusedarealsogiven,withtheab- breviationsNLO fornext-to-leadingorder,NNLOfornext-to-next- to-leading order, andNNLLfor next-to-next-to-leadinglogarithm.

For ggF, VBF, V H, bbH¯ in both decay channels and tt H¯ in the H→γ γ ^decay ^channel,^Pythia8 [16,17] was used forthedecay, partonshower,hadronizationandmultiplepartoninteractions.For tt H¯ inthe H→^{Z Z}^∗→⁴ ^decay^channel, ^Herwig++[18,19] was used.

The samples are normalized to the cross-section predictions takenfromRefs. [14,34–36].These predictions were obtainedas- sumingaHiggsbosonmassof125.09 GeV [15] tocalculatecross sectionsandbranchingratios.DetailsaregiveninTable2,including the accuracy of the calculations, and the composition of the

productionmodesintheSM.N³LOistheabbreviationfornext-to- next-to-next-to-leadingorder,andEWstandsforelectroweak.

In additionto theNNLOPS sample (see Table 1) scaled tothe N³LO cross section with a K-factor of 1.1, further SM ggF predictions are compared withthe measurements. Ifnot mentioned otherwise, thecross sectionspredictedby the respectivecalcula- tions are used. Forthecomparison withdata,the non-ggF Higgs bosonproductionprocessesareaddedusingthesamplesandcross sectionsdescribedabove.

• ^The ^p_T^H distribution is compared with the predictions from HRes[63,64],RaDISH+^NNLOJET^[65],^and^Madgraph⁵^_aMC@

NLO.HResincludesresummationtoNNLLandcomputesfixed- order cross sections for ggF Higgs boson production up to NNLO inQCD. Itdescribesthe p_T^H distribution atNLO. Finite t-,b-,andc-quarkmasses are includedatNLO accuracy.The RaDISH+^NNLOJET ^predictionîncludes resummationto NNLL andmatchingtotheone-jet NNLOdifferentialspectrumfrom NNLOJET [66,67].Itincludescorrectionsfromthefinitet- and b-quark masses.The predictions fromMadgraph5_aMC@NLO are scaled tothe N³LOcross section witha K-factorof1.47.

This generator provides NLO accuracy in QCD for zero, one, and two additional jets, merged with the FxFx scheme [68]

andincludestheﬁnitetopquarkmasseffects [30,69,70].

• ^The |^y^H| measurement is compared with predictions from Madgraph5_aMC@NLO merged with the FxFx scheme and SCETlib+^MCFM8 ^[71,72], ^which^achieves^NNLO+^NNLL_ϕ ^accuracy¹ by applyinga resummationofthevirtual corrections tothegluonformfactor.TheunderlyingNNLOpredictionsare obtained using MCFM8 with zero-jettiness subtractions [73, 74].

• Thep^j1_T measurementiscomparedwithSCETlib,withNNLL+ NNLO0 accuracy²[72,75].

• MultiplepredictionsexistfordifferentbinsoftheNjets distribution.Consideredhereare theSTWZ-BLPTWprediction [14, 75,76], whichincludes NNLL+NNLO resummationforthe pT of the leading jet, combined witha NLL+^NLO resummation forthesubleadingjet,andtheJVE-N³LOprediction [77],which includesNNLLresummationofthe pT oftheleading jetwith small-Rresummationandismatched totheN³LOtotal cross section. In addition,predictions fromMadgraph5_aMC@NLO, arecomparedwiththefullNjetsdistribution.

ForggF, VBF and V H,the PDF4LHC setisvaried according toits eigenvectors [25],andtheenvelopeofthevariationsisusedasthe systematicuncertainty.TheeffectofPDFuncertaintiesont¯t Hand b_bH¯ _is_negligible _and_not_included. _Therenormalization andfac-

1 TheprimeindicatesthatimportantpartsoftheN³LL(next-to-next-to-next-to- leadinglogarithm)contributionareincludedalongwiththefullNNLLcorrections andthesubscriptϕindicatesthatresummationisappliedtothegluonformfactor.

2 NNLO0referstotheNNLOcorrectionsrelativetotheLOgg→Hprocesswith 0additionalpartons.

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torizationscalesarevaried byfactorsof2.0and0.5. ForNNLOPS, insteadoftheinternalscale uncertainties,thesameschemeasin Refs. [11,12,78] isused:fourparametersaccountforuncertainties inthecrosssectionsforeventswithdifferentjetmultiplicities [14, 75,76,79], andthree parameters account for the uncertainties in themodellingofthep^H_T distributions.

The predicted Higgs boson decay branching ratios are (0.227

± ^0.007)% ând ^(0.0125 ± ^0.0003)% ^for ^the ^H→γ γ ând ^H→ Z Z^∗→⁴ ^decays, respectively [14]. Both branching ratio calculations include the complete NLO QCD and EW corrections. For H→^{Z Z}^∗→⁴^, ^the interference effects betweenidentical final- statefermionpairsareincluded.Thecorrelationsofthebranching ratio uncertainties and the dependence of the predicted branching ratiosontheHiggsbosonmassare takenintoaccountinthe combination. For the H→^{Z Z}^∗→⁴ ^decay ^channel, ^which ^has the largerdependence, this corresponds toa relative variation of

∼2%inthe branchingratiowhen varyingthe assumedHiggsbo- sonmassby±⁰.24 GeV [15].

3. Acceptancecorrection

The acceptance factors that extrapolate at particle-level from the H→γ γ ^and ^H→^{Z Z}^∗→⁴ ^ﬁducial^phase^space^to^the^full phase space are estimated usingthe MC samples andcross sections described in Section 2. Theirevaluation assumesSM Higgs boson productionfractions anda Higgs boson massof 125 GeV;

the90 MeV differencefrom125.09 GeV has negligibleimpacton theHiggsboson kinematicsandiscoveredby thesystematicun- certaintyfromtheHiggsbosonmassmeasurement.

In the H→γ γ ^ﬁducial ^phasespace [11], theselected events havetwophotonswithpseudorapidity³ |η|<¹.^{37 or}^1.52 <|η|<

2.37andpTγ1>⁰.^35mγ γ, pTγ2>⁰.^25mγ γ,where pTγ1(2) refersto thetransversemomentumofthe(sub)leadingphotonandmγ γ is theinvariantmassofthetwophotons.Thephotonsarerequiredto beisolated:the p_T ofthesystemofchargedgenerator-levelparti- cleswithin R=⁰.^{2 of}^the^photonîs^required^to^be^less^than^0.05 timesthe pT ofthephoton. Inthe H→^{Z Z}^∗→⁴^fiducial^phase space [12], the selected events have four muons, four electrons, or two electrons and two muons. The three leading leptons are requiredto have p_T>20, 15, 10 GeV.The lowest-p_T muon (elec- tron)has to fulfil pT>^{5 (7) GeV.}^The ^muons ^have^to ^be ^within

|η|<².^{7 and} ^the ^electrons ^within |η|<².^47. ^Following ^the ^se- lectionof eventsindata, requirementsare placed onthe masses ofthetwo same-ﬂavour opposite-chargepairs,onthe R ofany two leptons, and the invariant mass of the four-lepton system, 115 GeV<^m4<^{130 GeV.}

Inthetotal phasespace, thequantities p^H_T and|^y^H| âre^com- puted directly from the simulated Higgs boson momentum in- stead ofitsdecay products,asinthe fiducialanalyses. Simulated particle-level jets are built from all particles with cτ >^{10 mm} excluding neutrinos, electrons and muons that do not originate fromhadron decays.Photonsareexcludedfromjetfindingifthey originate directlyfrom theHiggs bosondecayor areradiated off leptons fromthe Higgsboson decay. Jetsare reconstructed using the anti-kt algorithm [80] with a radius parameter R=⁰.^4, ând arerequiredtohavepT>^{30 GeV.}

3 ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominalin- teractionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeampipe.

Thex-axispointsfromtheIPtothecentreoftheLHCring,andthey-axispoints upwards.Cylindricalcoordinates(^r,φ)âreûsedⁱⁿ^the ^transverse^plane,φ^being theazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedintermsof thepolarangleθas η= −ln tan(θ/2).Angulardistanceismeasuredinunitsof

R≡

( η)²+( φ)².

TheoryuncertaintiesinthesignalacceptancerelatedtothePDF, higher-ordercorrections,andthepartonshowerareconsideredfor the acceptancefactorsandare correlatedbetweenthe twochan- nels. Uncertainties due to the PDF and scales are estimated as describedinSection2.Uncertaintiesduetothepartonshowerare evaluated by comparing the ggF default showeringPythia8 with Herwig7. The uncertainty is derived fromthe full difference between the two cases.The Higgsboson massis varied within the uncertaintyoftheATLAS–CMScombinedmeasurement [15].Toac- count for model dependence, the fractions of production modes are varied within the uncertainties from the dedicated measurements by the ATLAS and CMS collaborations [81]. For tt H¯ , the 13 TeV ATLASresultsareused [82]. ThebbH¯ crosssectionisvar- iedwithin theuncertaintiesduetothePDFandhigher-ordercorrections [14].Thetotal systematicuncertainties oftheacceptance factors rangebetween0.4% and5%,depending on theobservable andbin.Thepartonshoweruncertaintydominates.

Theinclusiveacceptancefactorsare50%fortheH→γ γ ^chan-

nel and42% for the H→^{Z Z}^∗→⁴ ^channel ^(relative^to ^the ^full phase spaceof H→Z Z^∗→22,where,=e orμ^). ^The^ac-

ceptanceislowerforH→^{Z Z}^∗→⁴^than^for^H→γ γ ^since^it^is

lesslikelyforfourleptonstofulfilthefiducialrequirements.Fig.1 shows theacceptancefactorsusedforthedifferentialobservables andtheirsystematicuncertainties.Thefiducialacceptancefallsoff steeplyastheHiggsbosonrapidity increases,asbothfiducialdef- initions include pseudorapidity requirementson the Higgs boson decay products. The fiducial acceptance in the H→γ γ ^channel

asa functionof p^H_T isshaped by the pT selection criteriaon the photons.

4. Statisticalprocedure

The combined measurement is based on maximizing the proﬁle-likelihoodratio [83]:

(σ)=^L(σ,θ(ˆˆ σ)) L(σˆ,θˆ) .

Here σ âre ^the ^parameters ôf înterest, θ âre ^the ^nuisance ^parameters, andL^represents ^the ^likelihood^function. ^The σˆ ând θ^ˆ terms denote the unconditionalmaximum-likelihood estimate of theparameters,whileθ(ˆˆ σ)istheconditionalmaximum-likelihood estimateforgivenparametervalues.

The likelihood function L ^includes ^the ^signal extraction, the correctiontoparticlelevel,andtheextrapolationtothetotalphase spaceineachchannel.Therefore,thetotalcrosssectionaswellas thecrosssectionsindifferentbinsforeachobservablecanbede- rived directlyasparameters ofinterest σ ^based^on^the^combined

datasetfromthe H→γ γ ^and^H→^{Z Z}^∗→⁴^channels.

Thedistributionshapeandnormalizationsystematicuncertain- ties ofall components are included inthe likelihood function as nuisanceparameters θ withconstraintsfromsubsidiarymeasure- ments.Thisallowstheuncertaintiestobecorrelatedbetweenbins, decaychannels,andcorrectionandacceptancefactors.Theuncer- taintycomponentsofthepredictedbranchingratiosarecorrelated between the decay channels, as well as the uncertainties in the acceptance and correction factors due to production mode vari- ations, PDF andhigher-order corrections, andthe partonshower.

The uncertaintyin the Higgs boson mass,including its effect on thepredictedbranchingratio,isalsocorrelatedbetweenchannels.

Experimentaluncertaintiesinthecorrectionfactorsandthesignal extraction in the H→^{Z Z}^∗→⁴ ^decay^channel, ^like ^the ^energy scaleandresolutionofelectrons,photons, andjets,andinthelu- minositymeasurementandpileupmodellingarealsocorrelated.

Combined measurement of differential and total cross sections in the H → γγ and the H → ZZ⁎ → 4ℓ decay channels at √s = 13 TeV with the ATLAS detector

Physics Letters B

Combined measurement of differential and total cross sections in the H → γ γ and the H → Z Z

→ 4 decay channels at √

s = 13 TeV with the ATLAS detector

Combined measurement of differential and total cross sections in the H → γγ and the H → ZZ⁎ → 4ℓ decay channels at √s = 13 TeV with the ATLAS detector

Combined measurement of differential and total cross sections in the H → γ γ ^and ^the ^H → ^{Z Z}

→ ⁴ ^decay ^channels ^at √

s = ^{13 TeV} ^with the ATLAS detector