Constraints on non-Standard Model Higgs boson interactions in an effective Lagrangian using differential cross sections measured in the H → γγ decay channel at √s=8 TeV with the ATLAS detector

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Physics Letters B

www.elsevier.com/locate/physletb

Constraints on non-Standard Model Higgs boson interactions in an effective Lagrangian using differential cross sections measured in the H → γ γ decay channel at √

s = ^{8 TeV with the ATLAS detector}

.ATLASCollaboration^

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

Articlehistory:

Received12August2015

Receivedinrevisedform30November2015 Accepted30November2015

Availableonline2December2015 Editor:W.-D.Schlatter

The strengthand tensorstructure oftheHiggsboson’sinteractionsare investigatedusingan effective Lagrangian, whichintroducesadditional CP-even and CP-oddinteractions that leadto changesin the kinematicpropertiesoftheHiggsbosonandassociatedjetspectrawithrespecttotheStandardModel.

The parameters of the effective Lagrangian are probed using a fit to five differential cross sections previously measured by the ATLAS experiment in the H→γ γ decay channel with an integrated luminosityof20.3 fb⁻¹at√_s

=^{8 TeV.In ordertoperforma}simultaneousfittothefivedistributions, thestatisticalcorrelationsbetweenthemaredeterminedbyre-analysingthe H→γ γ candidateevents intheproton–proton collisiondata.Nosignificantdeviationsfromthe StandardModelpredictionsare observedand limitsontheeffectiveLagrangianparametersare derived.Thestatisticalcorrelationsare madepubliclyavailabletoallowforfutureanalysisoftheorieswithnon-StandardModelinteractions.

©^{2015CERNforthebenefitoftheATLAS}Collaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Thediscovery ofaHiggsbosonattheATLAS andCMSexperi- ments[1,2]offersanewopportunitytosearchforphysicsbeyond the Standard Model (SM) by examining the strength and struc- ture ofthe Higgs boson’s interactions with other particles. Thus far, the interactions of the Higgs boson have been probed using the κ-framework[3],in whichthestrengthofagivencouplingis allowedtovaryfromtheSMpredictionbyaconstantvalue.In this approach,thetotal rateofa givenproductionanddecay channel candifferfromtheSMprediction,butthekinematicpropertiesof theHiggsbosonineachdecaychannelareunchanged.

An alternative framework for probing physics beyond the SM istheeffectivefieldtheory(EFT)approach[3–8],wherebytheSM Lagrangianisaugmentedbyadditionaloperators ofdimensionsix orhigher.Some oftheseoperatorsproducenewtensorstructures fortheinteractionsbetweentheHiggsbosonandtheSMparticles, whichcanmodifytheshapesoftheHiggsbosonkinematicdistri- butionsaswellastheassociatedjetspectra.Thenewinteractions ariseasthelow-energymanifestationofnewphysicsthatexistsat energyscalesmuch largerthanthe partoniccentre-of-massener- giesbeingprobed.

InthisLetter,the effectsofoperators thatproduce anomalous CP-even and CP-odd interactions between the Higgs boson and

 E-mailaddress:[email protected].

photons,gluons,W bosonsandZ bosonsarestudiedusinganEFT- inspiredeffectiveLagrangian.Theanalysisisperformedusingasi- multaneousfittofivedetector-correcteddifferentialcrosssections in the H→γ γ decay channel,which were previously published bytheATLASCollaboration[9].Thesearethedifferentialcrosssec- tions asfunctions of the diphoton transverse momentum (pγ γ

T ), thenumberofjetsproducedinassociationwiththediphotonsys- tem (Njets), the leading-jet transverse momentum (p_T^j1), and the invariant mass (m_{j j}) anddifference in azimuthal angle(φj j) of theleadingandsub-leadingjetsineventscontainingtwoormore jets.Theinclusionofdifferentialinformationsignificantlyimproves thesensitivitytooperators thatmodifytheHiggsboson’sinterac- tions with W and Z bosons.To performa simultaneous analysis ofthese distributions, thestatisticalcorrelations betweenbins of different distributions need to be included in the fit procedure.

These correlations are evaluated by analysing the H→γ γ can- didateeventsinthedata,andarepublished aspartofthisLetter toallowfuturestudiesofnewphysicsthatproducesnon-SMkine- maticdistributionsforH→γ γ.

2. HiggseffectiveLagrangian

The effective Lagrangian used in this analysisis presented in Ref. [8].In thismodel,the SMLagrangian isaugmented withthe dimension sixCP-evenoperators oftheStronglyInteracting Light Higgs formulation [6] and corresponding CP-odd operators. The H→γ γ differential cross sections are mainly sensitive to the http://dx.doi.org/10.1016/j.physletb.2015.11.071

0370-2693/©^{2015CERNforthebenefitoftheATLAS}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

operators that affect the Higgs boson’s interactions with gauge bosons andtherelevantterms intheeffective Lagrangiancan be specifiedby

Leff= ¯^cγOγ+ ¯^cgOg+ ¯^cHWOHW+ ¯^cHBOHB

+ ˜^cγ_O˜_γ+ ˜^cg_O˜_g+ ˜^cHW_O˜_HW+ ˜^cHB_O˜_HB,

where c¯i and c˜i are ‘Wilson coefficients’ specifying the strength ofthenewCP-evenandCP-oddinteractions,respectively,andthe dimension-six operators Oi are those described in Refs. [8,10].

In the SM, all of the Wilson coefficients are equal to zero. The Oγ and O˜γ operators introduce new interactions between the Higgs boson and two photons. The Og and O˜g operators intro- duce new interactions betweenthe Higgs boson andtwo gluons andtheanalysispresentedin thisLetteris sensitiveto theseop- eratorsthroughthegluonfusionproductionmechanism.TheOHW andO˜HW operators introduce new HWW,HZZ and HZγ interac- tions.TheHZZ andHZγ interactionsarealsoimpactedbyOHBand O˜HBand,toalesserextent,Oγ andO˜γ .Theanalysispresentedin thisLetter issensitivetotheOHW,O˜HW,OHB andO˜HB operators throughvector-bosonfusionandassociatedproduction.

Other operators inthe fulleffective Lagrangianof Ref.[8]can alsomodifyHiggsbosoninteractions.Combinationsofsomeofthe CP-evenoperators havebeen constrained usingglobal fits to ex- perimentaldatafromLEPandtheLHC[8,11,12].

3. Statisticalcorrelationsbetweendifferentialdistributions

ATLAS [13] is a multipurpose particle physics detector with cylindricalgeometryandnearly 4π coverage insolid angle.¹ The analysis is performed using proton–proton collision data at a centre-of-massenergy√

s=^{8 TeV andanintegratedluminosityof} 20.3 fb⁻¹.

The object and event selections used to define the differen- tialdistributions aredescribed indetail inRef. [9].The statistical correlations between the measured cross sections as a function of different distributions are obtained using a random sampling withreplacement method onthe detector-level data.This proce- dureisoftenreferredtoas‘bootstrapping’[14].Bootstrappedevent samplesare constructedfromthe databy assigning eacheventa weightpulledfromaPoissondistributionwithunitmean.Thefive differentialdistributionsarethenreconstructedusingtheweighted events,andthesignalyields ineachbinofadifferential distribu- tionaredeterminedusinganunbinnedmaximum-likelihoodfitof the diphoton invariant mass spectrum (full details of the fit can befoundinRef.[9]).Theprocedureisrepeated10 000timeswith statisticallyindependentweightsandthecorrelationbetweentwo binsofdifferentdistributionsisdeterminedfromthescattergraph ofthecorrespondingextractedcrosssections.Theobservedcorre- lationsbetweenbinsofthemeasured pγ γ

T andN_jetscrosssections areshowninFig. 1.

Thestatisticaluncertaintiesonthecorrelationduetothefinite numberofbootstrap samples rangesfrom0.5% to 1%.The statis- ticaluncertainty on the correlationsdue tothe finite number of eventsin dataisdetermined to be lessthan2% using thestatis- tical overlap and variance of signal andbackground events in a masswindow around the Higgsboson mass.In orderto validate thisapproach,asetofpseudo-experimentswascreatedfrominput

1 ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominalin- teractionpoint(IP)atthecentreofthedetectorandthez-axisalongthebeampipe.

Thex-axispointsfromtheIPtothecentreoftheLHCring,andthey-axispoints upward.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φbeingthe azimuthalanglearoundthebeampipe.

Fig. 1. Statisticalcorrelationsbetweenthemeasuredcrosssectionsinbinsofthe diphotontransversemomentumandjetmultiplicitydistributions.Thequotedun- certainties refer tothe total statisticaluncertainty due tothe finite number of bootstrappedsamplesandthefinitenumberofdataevents.

conditions(withknowncorrelations)chosentobesimilartothose in data in termsof purity, kinematics and sample size. Foreach pseudo-experiment,avalueforthecorrelationisdeterminedusing 10 000 bootstrapped samples andcomparedto the input correla- tions. No biasduetothebootstrappingisobserved inthecentral valueobtainedfrom500pseudo-experiments.

As part of this Letter, the correlations computed above are madepubliclyavailableinHEPDATA[15],allowingtheanalysisto be repeated usingalternative effectiveLagrangians, completeEFT frameworks, or other models with non-SM Higgs boson interac- tions.

4. Theoreticalpredictions

The effective Lagrangian has been implemented in FeynRules [10].² Parton-leveleventsamplesareproduced forspecificvalues ofWilsoncoefficientsbyinterfacingtheuniversalfileoutputfrom FeynRules to the Madgraph5 [17] event generator. Higgs boson productionviagluonfusionisproducedwithuptotwoadditional partonsinthefinalstateusingleading-ordermatrixelements.The 0-, 1- and 2-parton events are mergedusing the MLM matching scheme [18] and passed through the Pythia6 generator [19] to create the fully hadronic final state. Event samples containing a Higgs boson produced either in association with a vector boson or via vector-bosonfusion are produced using leading-order ma- trixelementsandpassedthroughthe Pythia6generator.Foreach production mode, the Higgs boson mass is set to 125 GeV [20]

and events are generated using the CTEQ6L1 parton distribution functionandtheAUET2parameterset[21].AllotherHiggsboson productionmodesareassumedtooccuraspredictedbytheSM.

EventsamplesareproducedfordifferentvaluesofagivenWil- son coefficient. The particle-level differential cross sections are produced using Rivet[22].The Professor method[23] isusedto interpolatebetweenthesesamples,foreach binofeach distribu- tion, and provides a parameterisation of the effectiveLagrangian prediction. The parameterisation function is determined using 11 samples when studying a single Wilson coefficient, whereas

2 The implementationin Ref.[10] involvesa redefinitionofthe gauge boson propagatorsthatresultsinunphysicalamplitudesunlesscertainphysicalconstants arealsoredefined.Theoriginalimplementationdidnotincludetheredefinitionof thesephysicalconstants.However,theimpactofredefiningthephysicalconstantsis foundtobelessthan1%onthepredictedcrosssectionsacrosstherangeofWilson coefficientsstudied.TherelativechangeinthepredictedHiggsbosoncrosssections asfunctionsofthedifferentWilsoncoefficientsisalsofoundtoagreewiththat predictedbytheHiggscharacterisationframework[16],withlessthan2%variation acrosstheparameterrangesstudied.

25 samplesareusedwhenstudyingtwoWilsoncoefficientssimul- taneously.As theWilsoncoefficientsentertheeffectiveLagrangian in a linear fashion, second-order polynomials are used to pre- dictthecross sectionsineach bin.Themethod wasvalidated by comparing the differential cross sections obtained with the pa- rameterisationfunctiontothepredictionsobtainedwithdedicated eventsamplesgeneratedatthespecificpointinparameterspace.

The model implemented in FeynRules fixes the Higgs boson width to be that of the SM, H =⁴.07 MeV [3]. The cross sec- tions are scaled by H/(H + )^{, where}  is the change in partial width due to a specific choice of Wilson coefficient. The changeinpartialwidthisdeterminedforeachHiggscouplingus- ingthepartial-widthcalculator in Madgraph5andnormalisedto reproducetheSMpredictionfrom Hdecay[24].

The leading-order predictions obtained from Madgraph5 are reweightedtoaccount forhigher-orderQCD andelectroweakcor- rections to the SM process, assuming that these correctionsfac- torisefromthe newphysics effects.The differentialcross section asafunction ofvariable X foraspecific choice ofWilsoncoeffi- cient,ci isgivenby

dσ

dX =

j

dσ_j

dX

ref

·

dσ_j

dX

MG5 c_i

/

dσ_j

dX

MG5 c_i=⁰,

wherethesummation j isoverthedifferentHiggsbosonproduc- tionmechanisms,‘MG5’labelsthe Madgraph5predictionand‘ref’

labelsareferencesampleforSMHiggsbosonproduction.

ThereferencesampleforHiggsbosonproductionviagluonfu- sionissimulatedusingMG5_aMC@NLO[25]withtheCT10parton distribution function [26]. The H+^{n-jets topologies are gener-} ated usingnext-to-leading-order (NLO) matrix elements for each partonmultiplicity (n=^{0, 1or 2) andcombined using the FxFx} mergingscheme[27].Theparton-level eventsarepassed through Pythia8 [28] to produce the hadronic final state using the AU2 parameter set [29]. The sample is normalised to the total cross section predicted by a next-to-next-to-leading-order plus next- to-next-to-leading-logarithm(NNLO+^{NNLL) QCD} calculation with NLOelectroweakcorrectionsapplied[3].Thereferencesample for Higgsbosonproductionviavector-bosonfusion(VBF)isgenerated atNLOaccuracyinQCDusingthe PowhegBox[30].Theeventsare generatedusing the CT10 partondistribution function (PDF) and Pythia8withtheAU2parameterset.TheVBFsampleisnormalised toan approximate-NNLOQCDcrosssectionwithNLOelectroweak correctionsapplied[3].ThereferencesamplesforHiggsbosonpro- duction inassociation witha vector boson (VH, V =^W,Z ) or a top–antitoppair(tt H )¯ are producedatleading-order accuracyus- ing Pythia8withtheCTEQ6L1PDFandthe4Cparameterset[21].

The ZH andWH samples are normalised tocross sections calcu- latedatNNLOinQCDwithNLO electroweakcorrections, whereas thet¯t H sampleisnormalisedtoacrosssectioncalculatedtoNLO inQCD[3].

The ratio of the differential cross sections to the SM predic- tionsforsomerepresentativevaluesoftheWilsoncoefficientsare showninFig. 2.Theimpactofthec¯g andc˜g coefficientsarepre- sentedforthegluonfusion productionchannel andshowa large change in the overall cross section normalisation. The ^c˜g coeffi- cient also changes the shape of the φj j distribution, which is expectedfromconsiderationofthetensorstructureofCP-evenand CP-oddinteractions[31,32].Theimpactofthe¯^cHW and^c˜HW coef- ficientsare presented forthe VBF + ^{VH productionchannel and} showlargeshapechanges inall ofthestudieddistributions.³ The

3 Formfactorsaresometimesusedtoregularisethechangeofthecrosssection aboveamomentumscaleFF.ThiswasinvestigatedbyreweightingtheVBF+^VH

Fig. 2. RatioofdifferentialcrosssectionspredictedbyspecificchoicesofWilson coefficienttothedifferentialcrosssectionspredictedbytheSM.

φj j distribution is known to discriminate between CP-odd and CP-eveninteractionsintheVBFproductionchannel[34].

5. Limit-settingprocedure

Limitson theWilsoncoefficientsare setbyconstructing a χ²

function

χ²=



σdata− σpred

T

C⁻¹



σdata− σpred

,

where σ_data and σ_pred are vectors from the measured and pre- dicted cross sections of the five analysed observables, and C= Cstat+^Cexp+^Cpred isthe total covariancematrix definedby the sum of the statistical, experimental and theoretical covariances.

The predicted cross section σpred and its associated covariance C_pred arecontinuousfunctionsofWilsoncoefficients.Scansofone or two Wilsoncoefficients are carriedout andthe minimum χ²

value, χ_min² ,isdetermined.Theconfidencelevel(CL)ofeachscan pointcanbecalculatedas

1−^CL=ⁿ

∞

χ²(c_i)−χ_min²

dx f(x;^m),

with χ²(c_i)beingthe χ² valueevaluated fora givenWilsonco- efficient ci,and f(x;^m) beingthe χ² distributionfor m degrees offreedomsandn=^{1 or 1}₂ ^{fortwo-sidedorone-sidedlimits.The} coverageofCL andtheeffectivenumberofdegreesoffreedomare determinedusingensemblesofpseudo-experiments.⁴

Theinputdatavector iscomparedinFig. 3totheSM hypoth- esisaswellastwonon-SMhypothesesspecifiedby^c¯g=¹×¹⁰⁻⁴ andc¯HW=⁰.05,respectively.

Thecovariancematrixforexperimentalsystematicuncertainties is constructed fromall uncertainty sources provided by Ref. [9], which include the jet energy scale and resolution uncertainties, photonenergyandresolutionuncertainties, andmodeluncertain- ties. Identical sources are assumed to be fully correlated across

samplesusingform-factorpredictionsfrom VBFNLO[33].Theimpact onthec¯HW and^c˜HWlimitsarenegligibleforFF>1 TeV.

4 For one-dimensional limits on the CP-even (odd) Wilson coefficients, good agreementisfoundbetweentheasymptoticformulaandthepseudo-experiment teststatisticwithm=1 andn=1 (¹₂).Forthetwo-dimensionallimitsonc¯gver- sus ˜cg,and c¯HW versusc˜HW,good agreementbetweenpseudo-experimentsand asymptoticformulaisfoundform=1 andn=1.Forthetwodimensionallimit on^c¯gversus^c¯γ,goodagreementbetweenpseudo-experimentsandasymptoticfor- mulaisfoundform=^{2 andn}=^1.