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

Article

Reference

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

ATLAS Collaboration

ANCU, Lucian Stefan (Collab.), et al .

Abstract

The strength and tensor structure of the Higgs boson's interactions are investigated using an effective Lagrangian, which introduces additional CP-even and CP-odd interactions that lead to changes in the kinematic properties of the Higgs boson and associated jet spectra with respect to the Standard Model. 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→γγ decay channel with an integrated luminosity of 20.3 fb −1 at s=8 TeV . In order to perform a simultaneous fit to the five distributions, the statistical correlations between them are determined by re-analysing the H→γγ candidate events in the proton–proton collision data.

No significant deviations from the Standard Model predictions are observed and limits on the effective Lagrangian parameters are derived. The statistical correlations are made publicly available to allow for future analysis of theories with non-Standard Model interactions.

ATLAS Collaboration, ANCU, Lucian Stefan (Collab.), et al . 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. Physics Letters. B , 2016, vol. 753, p. 69-85

DOI : 10.1016/j.physletb.2015.11.071

Available at:

http://archive-ouverte.unige.ch/unige:79084

Disclaimer: layout of this document may differ from the published version.

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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 andHZγ interac- tions.TheHZZandHZγ 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- trixelementsandpassedthroughthePythia6generator.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 usingRivet[22].The Professormethod[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 inMadgraph5andnormalisedto reproducetheSMpredictionfromHdecay[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’labelstheMadgraph5predictionand‘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 atNLOaccuracyinQCDusingthePowhegBox[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- ingPythia8withtheCTEQ6L1PDFandthe4Cparameterset[21].

The ZH andWH samplesare normalised tocross sections calcu- latedatNNLOinQCDwithNLO electroweakcorrections, whereas thet¯t H sample isnormalisedtoacrosssectioncalculatedtoNLO 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} coverageofCLandtheeffectivenumberofdegreesoffreedomare 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-factorpredictionsfromVBFNLO[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.