Search for lepton ﬂavour violating decays of the Higgs boson to e τ and e μ in proton–proton collisions at √

(1)

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

s = 8 TeV

.The CMS Collaboration

CERN,Switzerland

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

Articlehistory:

Received13July2016

Receivedinrevisedform21August2016 Accepted14September2016

Availableonline6October2016 Editor:M.Doser

Keywords:

CMS Physics Higgs

Lepton-ﬂavour-violation

AdirectsearchforleptonflavourviolatingdecaysoftheHiggsboson(H)intheH→êτ andH→êμ

channels is described. The data sampleused inthe search was collected inproton–proton collisions at √

s=^{8 TeV with} ^the ^CMS ^detector ât ^the ^LHC ând corresponds to an integrated luminosity of 19.7 fb⁻¹.Noevidence isfound for leptonflavourviolatingdecays ineitherfinal state. Upper limits onthebranchingfractions,B(H→êτ)<0.69% andB(H→êμ)<0.035%,aresetatthe95%confidence level.TheconstraintsetonB(^H→êτ)isanorderofmagnitudemorestringentthantheexistingindirect limits.ThelimitsareusedtoconstrainthecorrespondingflavourviolatingYukawacouplings,absentin thestandardmodel.

©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The discovery of the Higgs boson [1–3] has generated great interest in exploring its properties. In the standard model (SM), lepton ﬂavour violating (LFV)decays of the Higgsboson are for- bidden. Such decays can occur naturally in models with more than one Higgs boson doublet [4]. They also arise in supersym- metric models [5–11], composite Higgs models [12,13], models with ﬂavour symmetries [14], Randall–Sundrum models [15–17], and others [18–26]. The CMS Collaboration has recently published a search in the H→

μτ

channel [27] showing an excess of data with respect to the SM background-only hypothesis at mH=125 GeV witha signiﬁcanceof2.4 standarddeviations (

σ

).

Aconstraintisseton thebranchingfractionB(^H→

μτ

)<1.51%

at95%conﬁdencelevel(CL),whilethebestﬁtbranchingfractionis B(H→

μτ

)=(0.84⁺₋⁰₀^._.³⁹₃₇)%. TheATLASCollaborationﬁnds adevi- ationfromthebackgroundexpectationof1.3

σ

signiﬁcanceinthe H→

μτ

channelandsets an upperlimit ofB(H→

μτ

)<1.85%

at 95% CL with a best ﬁt branching fraction of B(H→

μτ

)= (0.77±⁰.62)% [28]. To date, no dedicated searches have been published forthe H→^e

μ

channel. The ATLAS Collaboration recently reported searches for H→^e

τ

and H→

μτ

, finding no significant excessofeventsover thebackgroundexpectation. The searches in channels with leptonic taudecays are sensitive only to a difference between B(^H→ê

τ

) and B(^H→

μτ

). These are

E-mailaddress:[email protected].

combined with the searches in channels with hadronic tau decays to set limitsof B(H→^e

τ

)<1.04%, B(H→

μτ

)<1.43% at 95% CL [29]. There are alsoindirect constraints. The presence of LFV Higgs boson couplings allows,

μ

→^e,

τ

→

μ

, and

τ

→^e to proceed via a virtual Higgs boson [30,31]. The experimental limits on these decays have been translated into constraints on B(H→^e

μ

), B(H→

μτ

) andB(H→^e

τ

) [32,33].The nullresult for

μ

→^e

γ

[34]stronglyconstrainsB(H→^e

μ

)<O(10⁻⁸).How- ever, the constraintB(H→^e

τ

)<O(10%) ismuch lessstringent.

Thiscomesfromsearchesforrare

τ

decays[35]such as

τ

→e

γ

, andthemeasurementoftheelectronmagneticmoment.Exclusion limitsontheelectricdipolemomentoftheelectron[36]alsopro- videcomplementaryconstraints.

This letterdescribesa search for LFVdecays ofthe Higgsbo- son with mH=^{125 GeV,} ^based ^on proton–proton collision data recorded at√

s=^{8 TeV with}^the ^CMS^detector^at^the^CERN ^LHC, correspondingtoanintegratedluminosityof19.7 fb⁻¹.Thesearch is performed in three decay channels, H→^e

τ

μ, H→^e

τ

h, and H→^e

μ

, where

τ

μ and

τ

h correspond to muonic and hadronic decay channels of tau leptons, respectively. The decay channel, H→^e

τ

e, is not considered due to the large background contri- butionfromZ→^{ee decays.}^Theêxpected^final^state^signaturesâre verysimilartotheSMH→

τ

e

τ

handH→

τ

e

τ

μdecays,studiedby CMS[37,38] andATLAS [39],butwithsome signiﬁcantkinematic differences. The electron in the LFV H→^e

τ

decay is produced promptly, andtends to havea largermomentum than intheSM H→

τ

e

τ

hdecay.IntheH→^e

μ

channel,mHcanbemeasuredwith goodresolutionduetotheabsenceofneutrinos.

http://dx.doi.org/10.1016/j.physletb.2016.09.062

0370-2693/©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

(2)

This letter is organized as follows. After a description of the CMSdetector(Section2) andof thecollision dataandsimulated samplesused intheanalysis(Section3),theeventreconstruction isdescribed in Section 4. The eventselection andtheestimation ofthebackgroundanditscomponentsaredescribedseparatelyfor thetwoHiggsdecaymodesH→^e

τ

andH→^e

μ

inSections5and 6.TheresultsarethenpresentedinSection7.

2. TheCMSdetector

AdetaileddescriptionoftheCMSdetector,togetherwithadef- inition ofthecoordinate systemusedandthe relevantkinematic variables,canbe foundinRef.[40].Themomentaofchargedpar- ticlesaremeasuredwithasiliconpixelandstriptrackerthatcov- ersthe pseudorapidity range|

η

|<2.5, in a 3.8 Taxial magnetic ﬁeld. Alead tungstate crystalelectromagnetic calorimeter (ECAL) and a brass and scintillator hadron calorimeter, both consisting of a barrel section and two endcaps, cover the pseudorapidity range|

η

_|<3.0.Asteelandquartz-ﬁbre Cherenkovforwarddetec- torextendsthe calorimetriccoverage to|

η

|<5.0. Theoutermost componentoftheCMSdetectoristhemuonsystem,consistingof gas-ionizationdetectorsplacedinthesteelﬂux-returnyokeofthe magnet to identify the muons traversing the detector. The two- levelCMStriggersystemselects eventsofinterestforpermanent storage.Theﬁrsttriggerlevel,composedofcustomhardwarepro- cessors,uses informationfromthe calorimetersandmuon detec- torsto selectevents inlessthan 3.2 μs. Thesoftware algorithms ofthe high-level trigger, executed ona farm of commercial pro- cessors,reducetheeventratetolessthan1 kHzusinginformation fromalldetectorsubsystems.

3. Collisiondataandsimulatedevents

ThetriggersfortheH→^e

τ

μ andH→^e

μ

analysesrequirean electronanda muoncandidate.The trigger forH→^e

τ

h requires asingleelectron.Moredetailsonthetriggerselectionaregivenin Sections5.1and6.1,fortheH→^e

τ

andH→^e

μ

channelsrespec- tively.Simulatedsamplesofsignalandbackgroundeventsarepro- ducedwith severalevent generators. The CMSdetector response ismodelledusingGeant4[41].TheHiggsbosonsareproducedin proton–protoncollisions predominantlybygluonfusion(GF) [42], butalsobyvectorbosonfusion(VBF)[43]andinassociationwith a W or Z boson [44]. The H→^e

τ

decay sample is produced withpythia8.176[45]usingtheCTEQ6Lpartondistributionfunc- tions (PDF). The H→^e

μ

decaysample is produced with pythia 6.426 [46] usingtheCT10 partondistributionfunctions[47].The SMHiggsbosonsamplesaregeneratedusingpowheg1.0[48–52], withCT10partondistributionfunctions,interfacedtopythia6.426.

TheMadGraph5.1.3.30[53]generatorisusedforZ+^jets,^W+^jets, topanti-topquarkpairproductiontt,anddibosonproduction,and powheg forsingle top quark production.The powheg and Mad- Graphgeneratorsareinterfacedtopythia6.426forpartonshower andhadronization.Thepythiaparametersfortheunderlyingevent descriptionare settothe Z2*tune.The Z2*tuneis derivedfrom theZ1tune [54],which usesthe CTEQ5L partondistributionset, whereasZ2*adoptsCTEQ6L.Duetothehighluminositiesattained during data-taking,manyevents havemultipleproton–protonin- teractionsper bunch crossing (pileup).All simulatedsamples are reweightedtomatchthepileupdistributionobservedindata.

4. Eventreconstruction

Datawerecollectedatanaveragepileupof21interactionsper bunch crossing. The tracking system is able to separate collision

vertices as close as 0.5 mm to each other along the beam direction [55]. The primary vertex, assumed to correspond to the hard-scattering process, is the vertex for which the sum of the squared transverse momentum p²_T of all the associated tracks is thelargest.Thepileupinteractionsalsoaffecttheidentiﬁcationof mostofthephysicsobjects,suchasjets,andvariablessuchaslep- tonisolation.

A particle-ﬂow (PF)algorithm [56–58] combines the information from all CMS subdetectors to identify and reconstruct the individual particles emerging from all interactions in the event:

chargedandneutralhadrons,photons,muons,andelectrons.These particles are then required to be consistent with the primary vertex and used to reconstruct jets, hadronic

τ

decays, quantify the isolation of leptons and photons and reconstruct E^miss_T . The missing transverse energy vector, E^miss_T , is deﬁned as the nega- tive of the vector sum of the pT of all identiﬁed PF objects in theevent[59].Its magnitudeis referredto as E^miss_T .The variable

R=

(

η

)²+(φ)²,where φ is theazimuthal co-ordinate, is usedto measurethe separationbetweenreconstructedobjects in thedetector.

Electron reconstruction requires the matching of an energy clusterintheECALwithatrackinthesilicontracker[60].Electron candidates are accepted in the range |

η

|<2.5, with the excep- tion of the region 1.44<|

η

_|<1.56 where service infrastructure for the detector is located. Electron identiﬁcation uses a multi- variate discriminant that combines observables sensitive to the amount ofbremsstrahlungalong the electron trajectory, thegeo- metricalandmomentummatchingbetweentheelectrontrajectory andassociatedclusters, andshower-shapeobservables.Additional requirementsare imposed toremove electrons produced bypho- tonconversions.The electronenergyiscorrectedforimperfection ofthereconstruction usinga regressionbasedonaboosteddeci- siontree[61].

Muon candidatesare obtainedfromcombinedfitsoftracks in the tracker andmuon detectorseeded by tracksegments in the muon detector alone, including compatibility with small energy depositions in the calorimeters. Identification is based on track qualityandisolation.Themuonmomentumisestimatedwiththe combined fit. Any possible bias in the measured muon momen- tumisdeterminedfromthepositionoftheZ→

μμ

masspeakas a functionofmuonkinematic variables,andasmallcorrection is obtainedusingtheproceduredescribedinRef.[62].

Hadronically decaying

τ

leptons arereconstructed andidenti- ﬁed using an algorithm [63] that selects the decay modes with onechargedhadronanduptotwoneutralpions,orthreecharged hadrons. A photon froma neutral–pion decaycan convertin the tracker material into an electron–positron pair, which can then radiate photons. These particles give rise to severalECAL energy deposits at the same

η

value but separated in φ. They are reconstructed asseveral photons by the PF algorithm. To increase theacceptancefortheseconvertedphotons, theneutralpionsare identiﬁedbyclusteringthereconstructedphotonsinnarrowstrips alongtheφdirection.Thechargeof

τ

hcandidatesisreconstructed by summingthechargesofallparticlesincludedintheconstruc- tionofthecandidate,exceptfortheelectrons containedinstrips.

Dedicateddiscriminatorsvetoagainstelectronsandmuons.

Jetsmisidentiﬁedaselectrons,muonsortausaresuppressedby imposingisolationrequirements,summingtheneutralandcharged particle contributions in cones of R aboutthe lepton. The en- ergydepositedwithintheisolationconeiscontaminatedbyenergy frompileup andthe underlyingevent. The effectofpileup is re- ducedby requiring thetracks considered inthe isolation sum to be compatiblewithoriginatingfromtheproductionvertexofthe lepton.The contributionto theisolation frompileupandtheun- derlyingeventissubtractedonanevent-by-eventbasis.Inthecase

(3)

ofelectrons,thiscontributionisestimatedfromtheproductofthe measured energy density

ρ

for the event, determined using the

ρ

medianestimatorimplementedinFastJet[64],andan effective areacorrespondingtotheisolationcone.Inthecaseofmuonsand hadronicallydecaying

τ

leptons,itisestimatedonastatisticalba- sisthroughthemodiﬁedβ correctiondescribedinRef.[63].

Jetsarereconstructedfromalltheparticlesusingtheanti-k_Tjet clusteringalgorithm [65]implementedinFastJet,witha distance parameterofR=⁰.5.Thejetenergiesarecorrectedbysubtract- ingthecontributionofparticlescreatedinpileupinteractionsand in the underlying event[66]. Particlesfrom different pileup vertices can be clusteredintoa pileup jet,or signiﬁcantly overlapa jet fromthe primary vertex belowthe selected jet pT threshold.

Thesejetsareidentiﬁedandremoved[67].

5. H→^e

τ

analysis 5.1. Eventselection

The H→^e

τ

h selection begins by requiring an eventrecorded withasingle electrontrigger(p^e_T>27 GeV, |

η

^e_|<2.5).The H→ e

τ

_μchannelrequiresamuon–electrontrigger(p^e_T>17 GeV,|

η

^e_|<

2.5, pμ

T >8 GeV,|

η

^μ|<2.4). Thetriggersalsoapplylooseidenti- ﬁcationandisolationrequirementstotheleptons.

A loose selection is then made for both channels. Electron, muon andhadronic tauleptoncandidates arerequired tobe iso- latedand tolie inthe pseudorapidity ranges where they can be well reconstructed; |

η

^e_|<1.44 or 1.57<|

η

^e_|<2.30, |

η

^μ_|<2.1 and|

η

^τ^h_|<2.3,respectively.Leptonsarealsorequiredtobecom- patiblewiththeprimaryvertexandto beseparatedbyR>0.4 fromanyjetin theeventwith pT>30 GeV.The H→^e

τ

_μ channel then requires an electron (p^e_T>40 GeV) and an oppositely charged muon (pμ

T >10 GeV) separated by R>0.1. Events in this channel with additional muons (pT>7 GeV) or electrons (pT >7 GeV) are also rejected. The H→^e

τ

h channel requires an electron (p^e_T>30 GeV) and an oppositely charged hadronic taulepton(pτh

T >30 GeV). Events inthischannel withadditional muons(pT>5 GeV),electrons(pT>10 GeV),orhadronictaulep- tons(pT>20 GeV)arerejected.

Theeventsarethendividedintocategorieswithineachchannel accordingtothenumberofjetsintheevent. Jetsarerequiredto passidentiﬁcationcriteria,havepT>30 GeV,andlieintheregion

|

η

|<4.7. The 0-jet and1-jet categoriescontain events primarily producedbyGF.The2-jetcategoryisdeﬁnedtoenrichthecontri- butionfromeventsproducedviatheVBFprocess.

The main observable used to discriminate betweenthe signal and the background is the collinear mass, M_col, which provides an estimate of MH usingthe observed decayproducts. It is con- structedusing thecollinearapproximation basedonthe observa- tionthat,sincem_H^Mτ,the

τ

decayproductsarehighlyLorentz boostedinthedirectionofthe

τ

[68].Theneutrinomomentacan be approximated to havethe same directionasthe other visible decayproductsofthe

τ

(

τ

^vis) andthecomponentofthe E^miss_T in the directionofthe visible

τ

decay products isused to estimate the transverse component of the neutrino momentum (pν,est

T ).

The collinear mass can then be derived from the visible mass ofthe

τ

–e system (M_vis) as M_col=^Mvis/

x^visτ , where x^visτ isthe fractionof energycarriedby the visible decayproducts ofthe

τ

(x^visτ =^p^τ_T^vis/(pτ^vis

T +^p^ν_T^,^est)).

Fig. 1showstheobservedMcoldistributionandestimatedback- groundsfor each category andchannel, after the looseselection.

ThesimulatedsignalforB(H→^e

τ

)=^{100% is}^shown. ^The^princi- palbackgroundsareestimatedwithcollisiondatausingtechniques described in Section 5.2. There is good agreement between the

observed distributionsandthecorresponding backgroundestima- tions. The agreement is similar in all of the kinematic variables that are subsequently used to suppress backgrounds. The analysis is subsequentlyperformed blinded by using a ﬁxed selection andcheckingtheagreement betweenrelevant observedandsim- ulateddistributionsoutsidethesensitiveregion100 GeV<M_col<

150 GeV.

Next, a set of kinematic variables is deﬁned, and the event selection criteria are set to maximise the signiﬁcance S/√

S+^B, whereSandBaretheexpectedsignalandbackgroundeventyields inthemasswindow100 GeV<M_col<150 GeV.Thesignalevent yield corresponds to the SM Higgs boson production cross sec- tionatmH=125 GeV withB(H→^e

τ

)=^1%.^The^selection^criteria foreach categoryandchannel are giveninTable 1.The variables usedare:theleptontransversemomentap_Twith=^e,

μ

,

τ

_h;azimuthal angles between the leptons φ

p_T¹−p_T²; azimuthal angle betweentheleptonandtheE^miss_T vectorφ_p

T−^E^missT ;thetransverse massM_T=

2p_TE_T^miss(1−^cosφ_p T−^E^missT ).

Events inwhichatleastone ofthejetsisidentiﬁed asarising from a b quark decayare vetoed using the combined secondary vertex (CSV) b-tagging algorithm [69]. To enhance the VBF contribution in the 2-jet category further requirements are applied.

In the H→^e

τ

h channel, events in this category are additionally required to have two jets separated by |

η

|>2.3 and a dijet invariant mass M_{j j}>400 GeV. In the H→^e

τ

μ channel, the requirementsare|

η

_|>3 andMj j>200 GeV.

After the full selection, a binned likelihood is used to ﬁt the distributions of M_col forthe signalandthe backgroundcontribu- tions. The modiﬁed-frequentistCLs method[70,71] isusedto set upperboundsonthesignal strength

μ

,ordetermineasignalsig- niﬁcance.

5.2. Backgroundprocesses

The contributions from the dominant background processes are estimatedusingcollision datawhilethe lesssigniﬁcant backgrounds are estimated usingsimulation. The largest backgrounds arefromZ→

τ τ

decaysandfromW+^{jets and}^QCD^multijet^production.Inthelatter,PFobjects(predominantlyjets),aremisiden- tiﬁedasleptons.

5.2.1. Z→

τ τ

background

TheZ→

τ τ

backgroundcontributionisestimatedusinganem- bedding technique [38,72]. First, a sample of Z→

μμ

events is selected from collision data using the loosemuon selection. The muons are then replaced with simulated

τ

decays reconstructed withthe PFalgorithm.Thus, thekey features oftheeventtopol- ogysuchasjetmultiplicity,instrumentalsourcesof E^miss_T ,andthe underlying event are takendirectly fromcollision data.Only the

τ

leptondecaysaresimulated.Thenormalizationofthesampleis obtainedfromsimulation.Thetechniqueisvalidatedbycomparing thecollinearmassdistributionsobtainedfromtheZ→

τ τ

simulation andtheembedding techniqueapplied toasimulatedsample ofZ→

μμ

events.Ashiftof2%inthemasspeakoftheembedded sample relativetosimulationisobserved.Thisshiftreflectsabias in theembedding technique,which doesnot take thedifferences between muonsand taus in final-state radiationof photons into account, andis corrected for. Identification and isolation corrections obtainedfromthecomparisonareappliedtotheembedded sample.

5.2.2. Misidentiﬁedleptonbackground

Themisidentiﬁedleptonbackgroundisestimatedfromcollision data by deﬁning a sample with the same selection as the sig-

(4)

Fig. 1.Comparisonoftheobservedcollinearmassdistributionswiththebackgroundexpectationsafterthelooseselectionrequirements.Theshadedgreybandsindicatethe totalbackgrounduncertainty.TheopenhistogramscorrespondtotheexpectedsignaldistributionsforB(H→eτ)=100%.TheleftcolumnisH→eτμandtherightcolumn isH→eτh;theupper,middleandlowerrowsarethe0-jet,1-jetand2-jetcategories,respectively.

(5)

Table 1

Eventselectioncriteriaforthe kinematicvariables afterapplyinglooseselection requirements.

Variable [GeV]

H→eτμ H→eτh

0-jet 1-jet 2-jet 0-jet 1-jet 2-jet

p^e_T >50 >40 >40 >45 >35 >35

p^μ_T >15 >15 >15 – – –

p^τ_T^h – – – >30 >40 >30

M_T^μ – <30 <40 – – –

M_T^τ^h – – – <70 – <50

[radians]

φp_T_,_e−p_T,τ_h – – – >2.3 – –

φ_p

T,μ−E^miss_T <0.8 <0.8 – – – –

φp_T_,_e−p_T_,μ – >0.5 – – – –

Table 2

Definitionofthesamplesusedtoestimatethemisiden- tifiedlepton ()background.They are definedby the chargeofthetwoleptonsandbytheisolationrequire- mentsoneach.Thedefinitionofnot-isolateddiffersbe- tweenthetwochannels.

Region I Region II

^±₁ (isolated) ^±₁ (isolated)

^∓₂ (isolated) ^±₂ (isolated)

Region III Region IV

^±₁ (isolated) ^±₁ (isolated) ^∓₂ (not-isolated) ^±₂ (not-isolated)

nalsample,butinvertingtheisolationrequirementsononeofthe leptons,toenrichthecontributionfromW+^{jets and}^QCD ^multi- jets.TheprobabilityforPFobjectstobemisidentifiedasleptonsis measuredusing anindependent collisiondataset,definedbelow, andthisprobabilityisappliedtothebackgroundenrichedsample tocomputethemisidentifiedleptonbackgroundinthesignalsam- ple.ThetechniqueisshownschematicallyinTable 2inwhichfour regionsaredefinedincludingthesignal (I)andbackground (III)en- richedregionsandtwocontrolRegions (II & IV), definedwiththe sameselectionsasRegions I & IIIrespectively,exceptwithleptons ofthesamecharge.

ThemisidentiﬁedelectronbackgroundisnegligibleintheH→ e

τ

_μ channel duetothehigh pT electronthreshold.The misiden- tifiedmuonbackgroundisestimatedwithRegion Idefinedasthe signalselectionwithanisolatedelectronandanisolatedmuonof oppositecharge.Region IIIisdefinedasthesignalselectionexcept themuonisrequirednottobeisolated.Smallbackgroundsources ofpromptleptonsare subtractedusingsimulation.The misidenti- fiedmuonbackgroundinRegion Iisthenestimatedbymultiplying theeventyieldinRegion IIIbyafactor fμ,where fμistheratioof isolated tononisolatedmuons.It iscomputedonan independent collisiondatasampleofZ→

μμ

+X events,whereXisanobject identiﬁedasamuon,inbinsofmuon p_T and

η

.Intheestimation of fμ,backgroundsourcesofthreepromptleptons,predominantly WZ and ZZ, are subtracted from the Z→

μμ

+^X ^sample ûsing simulation. The technique is validated usinglike-sign lepton collision datainRegions II andIV.In Fig. 2(left) the eventyieldin Region II iscompared tothe estimatefromscaling theRegion IV samplebythemeasuredmisidentificationrate.TheRegion IIsam- ple isdominatedby misidentifiedleptons butalsoincludessmall contributionsoftrueleptonsarisingfromvectorbosondecays,es- timatedwithsimulatedsamples.

IntheH→^e

τ

hchanneleitherleptoncandidatecanarisefroma misidentified PFobject,predominantlyinW+^{jets and} ^QCD^multijet events,but also from Z→êe+^{jets and} tt production. The misidentification rates fτ and f_e are defined as the fraction of looselyisolated

τ

horelectroncandidatesthatalsopassatightiso- lationrequirement. Thisismeasured inZ→^ee+X collision data events,whereXisanobjectidentiﬁedasa

τ

h ore. Themisiden- tiﬁed

τ

h contribution is estimated with Region I deﬁned as the signal selection. Region IIIisthe signal selectionexceptthe

τ

h is requiredtohavelooseandnottightisolation.Themisidentiﬁed

τ

h leptonbackgroundinRegion Iisthenestimatedbymultiplyingthe eventyieldinRegion IIIbyafactor fτ/(1−^fτ).The sameproce- dureisusedtoestimatethemisidentifiedelectronbackgroundby defining Region Iasthesignal selectionandRegion IIIasthesig- nalselectionbutwitha looseandnottightisolatedelectron,and scaling by f_e/(1− ^fe).To avoiddoublecounting, the eventyield in Region III,multiplied bya factor fe/(1− ^fe)× ^fτ/(1− ^fτ),is subtracted fromthe sumofmisidentifiedelectrons andtaus. The procedureisvalidatedwiththelike-signe

τ

samples.Fig. 2(right) shows the collision data in Region II compared to the estimate

Fig. 2.Distributions ofmcolfor Region II. Left: H→^eτμ. Right: H→^eτh.

(6)

Table 3

Thesystematicuncertaintiesintheexpectedeventyieldsinpercentagefortheeτhandeτμchannels.Alluncertaintiesaretreatedascorre- latedbetweenthecategories,exceptwhentwovaluesarequoted,inwhichcasethenumberdenotedbyanasteriskistreatedasuncorrelated betweencategories.

Systematic uncertainty H→eτμ H→eτh

Muon trigger/ID/isolation 2 2 2 – – –

Electron trigger/ID/isolation 3 3 3 1 1 2

Eﬃciency ofτh – – – 6.7 6.7 6.7

Z→τ τ background 3⊕⁵^∗ ³⊕⁵^∗ ³⊕¹⁰^∗ ³⊕⁵^∗ ³⊕⁵^∗ ³⊕¹⁰^∗

Z→μμ,ee background 30 30 30 30 30 30

Misidentiﬁed leptons background 40 40 40 30 30 30

Pileup 2 2 10 4 4 2

WW,WZ,ZZ+jets background 15 15 15 15 15 15

tt background 10 10 10⊕10^∗ 10 10 10⊕33^∗

Single top quark background 25 25 25 25 25 25

b-tagging veto 3 3 3 – – –

Luminosity 2.6 2.6 2.6 2.6 2.6 2.6

Table 4

TheoreticaluncertaintiesinpercentagefortheHiggsbosonproductioncrosssectionforeach productionprocessandcategory.Alluncertaintiesaretreatedasfullycorrelatedbetweencat- egoriesexceptthosedenotedbyanegativesuperscriptwhicharefullyanticorrelateddueto themigrationofevents.

Systematic uncertainty Gluon fusion Vector boson fusion 0-jet 1-jet 2-jet 0-jet 1-jet 2-jet Parton distribution function 9.7 9.7 9.7 3.6 3.6 3.6 Renormalization/factorization scale 8 10 30⁻ 4 1.5 2 Underlying event/parton shower 4 5⁻ 10⁻ 10 <1 1⁻

derived from Region IV. The method assumes that the misiden- tificationrateinZ→êe+^{X events}îs^the^sameâsⁱⁿ^the^W+^jets andQCDprocesses.Tocheckthisassumption,themisidentification ratesare alsomeasured ina collisiondatacontrol sample ofjets comingfromQCDprocessesandfoundtobeconsistent.Thissam- pleisthesameZ→êe+^{X sample}âsâbove^but^withôneôf^the electroncandidatesrequiredtobenotisolatedandthe pT thresh- oldlowered.

5.2.3. Otherbackgrounds

Theleptonic decayof Wbosons fromtt pairs producesoppo- sitesigndileptons and E^miss_T . Thisbackground isestimatedusing simulatedtt events tocompute the Mcol distributionanda colli- siondatacontrolregionfornormalization.Thecontrolregionisthe 2-jetselectiondescribed inSection5.1,includingtheVBFrequire- ments,withtheadditionalrequirementthatatleastoneofthejets isb-taggedinordertoenhancethett contribution.Othersmaller backgrounds enter from SM Higgs boson production (H→

τ τ

), WW,WZ, ZZ+^jets, ^W

γ

^(∗)+jets processes,andsingle top quark production.Eachoftheseisestimatedusingsimulation[38].

5.3.Systematicuncertainties

Systematicuncertainties are implemented asnuisance parameters in the signal and background ﬁt to determine the scale of their effect. Some of these nuisance parameters affect only the backgroundandsignalnormalizations,whileothersalsoaffectthe shapeofthe M_col distributions.

5.3.1. Normalizationuncertainties

Thevaluesofthesystematicuncertaintiesimplementedasnui- sance parameters in the signal and background ﬁt are summa- rizedin Tables 3 and 4. The uncertainties inthe muon, electron and

τ

h selection eﬃciencies (trigger, identiﬁcation, andisolation) are estimated using collision data samples of Z→

μμ

,ee,

τ

_μ

τ

h events[63,72]. The uncertainty in the Z→

τ τ

background yield

comes fromthecross sectionuncertainty measurement(3% [73]) andfrom the uncertaintyin the

τ

identification efficiency when applyingtotheembeddedtechnique(5–10%uncorrelatedbetween categories).Theuncertaintiesintheestimationofthemisidentified leptonratecomefromthedifferenceinratesmeasuredindifferent collisiondatasamples(QCDmultijetandW+^jets).^The^systematic uncertaintyinthepileupmodellingisevaluatedbyvaryingtheto- tal inelastic cross section by ±^5% ^[74]. ^The uncertainties in the production cross sectionsestimated from simulation are also included[38].

Uncertaintiesondibosonandsingletopproductioncorrespond to the uncertainties of the respective cross section measure- ments[75,76].A10%uncertaintyfromthecrosssection measurement[77]isappliedtotheyieldofthett background.Inthe2-jet categoriesanadditionaluncertainty(10%forH→^e

τ

μand33%for H→^e

τ

h)isconsideredcorrespondingtothestatisticaluncertainty ofthett backgroundyield.

There areseveral theoreticaluncertainties on theHiggs boson production cross section that depend on the production mech- anism and the analysis category, as reported in Table 4. These uncertainties affect both the LFV Higgs boson andthe SM Higgs bosonbackgroundandarefullycorrelated.Theuncertaintyinthe partondistribution functionis evaluatedby comparing theyields in each category, that span the parameter range of three different PDF sets, CT10 [47], MSTW [78], NNPDF [79] following the PDF4LHC[80] recommendation.Theuncertaintyduetotherenor- malization and factorization scales,

μ

R and

μ

F, is estimated by scaling up and down by a factor of two relative to their nomi- nal values(

μ

R =

μ

F =^MH/2). The uncertaintyin the simulation of the underlying eventand partonshowers is estimated by using two different pythiatunes, AUET2 andZ2*. All uncertainties aretreatedasfullycorrelatedbetweencategoriesexceptthosede- notedby anegativesuperscriptwhicharefullyanticorrelateddue tothemigrationofevents.

(7)

Table 5

Systematicuncertaintiesintheshapeofthesignalandbackgrounddis- tributions,expressedinpercentage.Thesystematicuncertaintyandits implementationaredescribedinthetext.

Systematic uncertainty H→eτμ H→eτh

Z→τ τbias 2 –

Z→^{ee bias} ^– ⁵

Jet energy scale 3–7 3–7

Jet energy resolution 1–10 1–10

Unclustered energy scale 10 10

τhenergy scale – 3

5.3.2. M_colshapeuncertainties

Thesystematicuncertaintiesthatleadtoachangeintheshape ofthe Mcol distributionare summarizedinTable 5. A2% shiftin theM_col distributionoftheembeddedZ→

τ τ

sampleusedtoes- timatethebackgroundisobservedrelativetosimulation.Itoccurs onlyintheH→^e

τ

μchannelastheeffectsofbremsstrahlungfrom themuonareneglectedinthesimulation.The M_col distributionis corrected by 2±^{2% for} ^thisêffect. ^There îs â ^systematic ûncer- taintyof5%inZ→ee backgroundintheH→ê

τ

hchannel,dueto themismeasured energyof theelectron reconstructedasa

τ

h.It causesashiftintheM_col distribution,estimatedbycomparingcol- lisiondatawithsimulationinacontrolregionofZ→^{ee events}ⁱⁿ whichoneofthetwoelectronsthatformtheZpeakisalsoiden- tiﬁedasa

τ

h [63].Correctionsareappliedforthejetenergyscale andresolution[66].Theyaredeterminedwithdijetand

γ

/Z+^jets collisiondataandthemostsigniﬁcantuncertaintyarisesfromthe photonenergyscale.Otheruncertaintiessuchasjetfragmentation modelling, single pion response, and uncertainties in the pileup corrections are also included. The jet energy scale uncertainties (3–7%) are applied asa function of pT and

η

, including all cor- relations,toalljetsintheevent,propagatedtothe E^miss_T ,andthe resultant M_col distribution isusedin theﬁt.There isalsoan additional uncertainty to account for the unclustered energy scale uncertainty.Theunclusteredenergycomesfromjetsbelow10 GeV andPF candidatesnot within jets. It isalso propagated to E_T^miss. TheseeffectscauseashiftoftheMcoldistribution.Theuncertainty inthejetenergyresolutionisusedtosmearthejetsasafunction of pT and

η

andtherecomputed M_col distribution isusedinthe ﬁt.A3% uncertaintyinthe

τ

h energyscaleisestimatedby comparing Z→

τ τ

events in collision data and simulation.Potential uncertaintiesintheshapeofthemisidentiﬁedleptonbackgrounds arealsoconsidered.IntheH→^e

τ

μchannelthemisidentiﬁedlep- tonratesareappliedinbinsofp_T and

η

.IntheH→^e

τ

hchannel, the

τ

h misidentiﬁcation rate is found to be approximately inde- pendentof p_T but todepend on

η

.These ratesare all varied by onestandarddeviationandthedifferencesintheshapesareused

asnuisanceparametersintheﬁt.Finally,thedistributionsusedin theﬁthavestatisticaluncertaintiesineachmassbinwhichisin- cludedasanuncertaintythatisuncorrelatedbetweenthebins.

6. H→^e

μ

analysis 6.1. Eventselection

To select H→^e

μ

events,the trigger requirementis an elec- tronandamuonwithp_Tgreater than17and8 GeVrespectively.

Toenhancethesignal sensitivitythe eventsample isdividedinto nine different categories according to the region of detection of the leptons andthenumberofjets, anda furthertwo categories enriched invector bosonfusionproduction.The resolutionofthe reconstructed mass of the electron muon system, Meμ, depends on whether the leptons are detected in the barrel (|

η

e|<1.48,

|

η

μ|<0.80)orendcap(1.57<|

η

e|<2.50,0.8<|

η

μ|<2.4),while the composition and rate of backgrounds varies with the num- ber ofjets. The deﬁnitionof the categories is shownin Table 6.

Thetwoleptonsarerequiredtobeisolatedinallcategories.Cate- gories0–8,whichareselectedaccordingtotheregionofdetection oftheleptonandnumberofjets,aremutuallyexclusivewithjets requiredto havep_T>20 GeV.Tosuppressbackgroundswithsig- nificant E^miss_T ,suchasWW+^jets,Ê^miss_T îs^required^to^be^less^than 20, 25 or 30 GeV, depending on the category. Jets arising from b quark decays are vetoed using the CSV discriminant to significantly reduce the tt background.In the VBF categories, the two highest pT jets are required to have |

η

_|<4.7 and to be separated by |

η

j1−

η

j2|>3.0. In addition the jets are required to have |

η

^∗_|_{= |}

η

12− ^η^j¹⁺₂^η^j²|<2.5, where =^{e or}

μ

,

η

12 de- notes the pseudorapidity of the dilepton system and j₁,j₂ are the two jets. The φ betweenthe dijetsystemandthe dilepton system isrequiredto be greater than2.6 rad.The VBF tight category selection further requires that both jets have p_T>30 GeV and the dijetinvariant mass be M_j₁_j₂ >500 GeV, while the VBF loosecategoryrelaxesthesecond jetrequirementto pT>20 GeV with Mj1j2>250 GeV andis exclusiveto theVBF tightcategory.

The leptons inboth VBFcategoriescan bein eitherthebarrelor endcap. To avoidan eventappearing in more than one category theVBFassignmentismadeﬁrst.Eventswithmorethantwojets arenotconsidered.Theselectioneﬃciency,summedoverallcate- gories,is24%(22%)fortheGF(VBF)productionmechanism.

6.2. Signalandbackgroundmodelling

The signal model is the sum of two Gaussian functions, determined from simulation for each category. The reconstructed

Table 6

TheH→^eμeventselectioncriteriaandbackgroundmodelforeacheventcategory.Thecategoriesareprimarilydeﬁned accordingtowhethertheleptonsaredetectedinthebarrel(B)orendcap(EC),andthenumberofjets(N-jets).Require- mentsarealsomadeon p_T, E_T^missandavetoonjetsarisingfromab-quarkdecay.Thebackgroundmodelfunctionand orderofthatfunctionarealsogiven.

Category Description N-jets p_T

[GeV]

E^miss_T [GeV]

Background model

Function Order

0 eBμB 0 >25 <30 polynomial 4

1 eBμB 1 >22 <30 polynomial 4

2 eBμB 2 >25 <25 power law 1

3 eBμEC 0 >20 <30 polynomial 4

4 eBμEC 1 >22 <20 exponential 1

5 eBμEC 2 >20 <30 exponential 1

6 eECμB or EC 0 >20 <30 polynomial 4

7 eECμB or EC 1 >22 <20 power law 1

8 eECμB or EC 2 >20 <30 polynomial 4

9 VBF Tight 2 >22 <30 exponential 1

10 VBF Loose 2 >22 <25 exponential 1

(8)

massresolutions depend onwhether the leptons are in the barrel(B) orendcap(EC)calorimeterandare:2.0–2.1 GeV foreB

μ

B, 2.4–2.5 GeVforeB

μ

EC,3.2–3.6 GeVforeEC

μ

B or EC categoriesand 2.4(4.0) GeVfortheVBFtight(loose)categories. Thebackground, modelled as either a polynomial function, a sum of exponential functions,orasumofpowerlawfunctionsisgiveninTable 6for each category. The procedureto determine the backgroundfunc- tionfollowsthemethoddescribed in[3].Itisdesignedtochoose amodelwithsuﬃcientparameterstoaccuratelydescribetheback- groundwhile ensuringthat thesignal shapeis notabsorbedinto thebackgroundfunction.Thebackgroundmodelforeachcategory ischosenindependentlyusingthisprocedure.

In a ﬁrst step, referencefunctions are selected for each type offunction(polynomial,sumofexponentials,sumofpowerlaws).

Theorderofthefunctionischosensuchthatthenexthigherorder doesnot give a significantly better fit resultwhen fit to theob- servedM_eμdistributionintherange110 GeV<M_eμ<160 GeV.

Ina second step, an ensemble ofdistributions isdrawn from each ofthethree referencebackground modelscombined witha signalcontributioncorrespondingtoB(^H→^e

μ

)=⁰.1%,andﬁtted forsignal andbackgroundwitheach ofthethreeclassesoffunc- tionsofdifferentorders.

On average, the signal yield extracted from the distributions usingasignalplusbackgroundfitwilldifferfromtheinjectedsig- nal due to the imperfect modelling of the background. The bias is defined as the median deviation of the fit signal event yield fromthegeneratednumberofsignalevents.Thepossiblecombina- tionsofgenerateddistributionswiththefitsignalplusbackground modelsare then reduced by requiringthe bias to be lessthan a thresholdwhichresultsinlessthan 1%uncertaintyinthe fitsig- nalevent yield.The combinationin which thefit modelhas the leastparameters is then selected andthe fit function isused as thebackgroundmodelforthecollisiondata.Ifthereismorethan onemodelwiththesameminimalnumberofparametersthenthe onewiththeleastbiasisselected.

6.3.Systematicuncertainties

The systematic uncertainties are summarized in Table 7. The backgroundisfittotheobservedmassdistributionwithanegligi- blesystematicuncertaintyof<1%inthesignalyieldarisingfrom thechoiceofbackgroundmodelasdescribedabove.Correctionfac- torsare applied tothe leptontrigger, isolation,andidentification efficienciesforeachsimulatedsignalsample toadjustfordiscrep- ancieswiththecollision data.The uncertaintyinthesignal yield fromtheleptonisolationandidentificationcorrectionsis2.0%and is estimated withthe “tag-and-probe”method [72] applied to a collisiondatasampleofZ bosonsdecayingtoleptonpairs[60,62].

Theuncertaintiesintheleptonenergyscaleandthedileptonmass resolutionaretakenfromtheH→ZZ analysis[61].Thesystematic uncertaintyinthepileupmodellingisevaluatedbyvaryingtheto- talinelastic crosssection by ±^5% ^[74].Ît ^variesâccording^to ^the productionprocessandcategorybetween0.7%and2.3%.Thereare systematicuncertainties in the efficiency ofthe b quark jet veto thatalsovarywithproductionprocessandcategoryfrom0.05%to 0.7%.Theuncertaintyontheintegratedluminosityis2.6%[81].The effectsofsystematicuncertaintiesinthejetenergyscaleandres- olution,andthe uncertainties inPDF’sonthe selectionefficiency areestimatedasdescribedinSection5.3.2fortheH→ê

τ

channel.

Thelargest valuesof thesesystematicuncertainties occur dueto themigrationofeventsto,orfrom,acategorywithlowstatistics.

The theoretical uncertainties on the Higgs boson production crosssectionarealsodescribedinSection5.3.2.

Table 7

SystematicuncertaintiesinpercentageontheexpectedyieldforH→^eμ.Ranges aregivenwheretheuncertaintyvarieswithproductionprocessandcategory.All uncertaintiesaretreatedascorrelatedbetweencategories.

Experimental uncertainties

Background model <1

Trigger eﬃciency 1.0

Lepton identiﬁcation 2.0

Lepton energy scale 1.0

Dilepton mass resolution 5.0

Pileup 0.7–2.3

b quark jet veto eﬃciency 0.05–0.70

Luminosity 2.6

Jet energy scale (inclusive categories) 0.6–22

Jet energy scale (VBF categories) 0.1–78

Jet energy resolution (inclusive categories) 2.8–12

Jet energy resolution (VBF categories) 0.0–49

Acceptance (PDF variations) 0.8–5.1

Theoretical uncertainties

GF normalization/factorization scale ⁺₋⁷₇^._.²₈ GF parton distribution function ⁺₋⁷₆^._.⁵₉

VBF normalization/factorization scale ±0.2

VBF parton distribution function ⁺₋²₂^._.⁶₈

7. Results 7.1. H→^e

τ

The distributions of the ﬁtted signal and background contributions, afterthe full selection, areshown inFig. 3andthe cor- responding event yields in the mass range 100 GeV< M_col<

150 GeV aregiveninTable 8.Thereisnoevidenceofasignal.Ta- ble 9showstheexpectedandobserved95%CLmeanupperlimits on B(H→^e

τ

) whicharesummarizedin Fig. 4fortheindividual categoriesin thee

τ

_μ ande

τ

h channelsandfor thecombination.

The combined observed (expected)upperlimit on B(H→^e

τ

) is 0.69 (0.75)%at95%CL[70,71,82].

7.2. H→^e

μ

The M_eμ distributionofthecollisiondatasample, afterall se- lectioncriteria,forallcategoriescombinedisshowninFig. 5.Also shownarethecombinationsoftheinclusivejet-taggedcategories (0–8)andtheVBFcategories(9–10).Theexpectedyieldsofsignal (B(^H→^e

μ

)=⁰.1%)andbackgroundeventsfor124 GeV<M_eμ<

126 GeV,afteralltheselection criteria,are giveninTable 10and comparedtothecollisiondataeventyield.Thecontributionstothe background are takenfrom simulationand givenfor information only,they arenotusedintheanalysis. Thedominantbackground contributions are from Drell–Yan production of

τ

lepton pairs andelectroweakdibosonproduction.Thereis nosignal observed.

An exclusion limit on the branching fraction B(^H→^e

μ

) with MH=^{125 GeV is}^derived ^using^the ^CLs asymptoticmodel[83].It isshowninFig. 4fortheinclusivecategoriesgroupedbynumber of jets, the VBF categories, and all categories combined. The expected limitis B(^H→^e

μ

)<0.048% at 95% CLandthe observed limitisB(^H→^e

μ

)<0.035% at95%CL.

7.3. Limitsonleptonﬂavourviolatingcouplings

The constraints on B(^H→^e

τ

) and B(^H→^e

μ

) can be inter- preted in terms of the LFV Yukawa couplings |^Yeτ|^, |^Yτe| ^and

|^Yeμ|^,|^Yμe|respectively[33].TheLFVdecaysH→^e

τ

,e

μ

ariseat treelevelintheLagrangian, LV,fromtheﬂavour-violatingYukawa interactions, Yα^β, where ^α,^β denote the leptons e,

μ

,

τ

, and

(9)

Fig. 3.Comparisonoftheobservedcollinearmassdistributionswiththebackgroundexpectationsafterthefit.Thesimulateddistributionsforthesignalareshownforthe branchingfractionB(^H→êτ)=⁰.69%.TheleftcolumnisH→êτμ andtherightcolumnisH→êτh;theupper,middleandlowerrowsarethe0-jet,1-jetand2-jet categories,respectively.

(10)

Table 8

Eventyieldsinthesignalregion,100 GeV<Mcol<150 GeV,afterﬁttingforsignalandbackgroundfortheH→^eτ channel,normalizedtoanintegratedluminosityof 19.7 fb⁻¹.TheLFVHiggsbosonsignalistheexpectedyieldforB(H→eτ)=0.69% assumingtheSMHiggsbosonproductioncrosssection.

Jet category H→eτμ H→eτh

Misidentiﬁed leptons 85.2±^5.9 ^38.1±^3.9 ^2.1±^0.7 ³³⁶⁶±²⁵ ²²³±¹¹ ^8.7±^2.2

Z→^ee,μμ 2.3±^0.6 ^5.4±^0.5 ^– ⁷¹⁴±³⁰ ⁸⁵±⁴ ^3.2±^0.2

Z→τ τ 84.7±2.1 113.3±4.2 8.5±0.6 270±10 32±3 1.6±0.3

tt,t,t 13.8±0.3 69.4±2.3 12.7±0.8 10±2 13±2 0.5±0.2

ZZ,WZ,WW 83.0±^2.7 ^51.7±^2.0 ^3.6±^0.4 ⁵³±² ⁶±¹ ^0.3±^0.1

Wγ(^∗) 2.2±^1.0 ^1.2±^0.6 ^– ^– ^– ^–

SM H background 2.3±^0.3 ^3.6±^0.4 ^1.1±^0.2 ¹²±¹ ³±¹ ^1.0±^0.1

Sum of background 273.5±^6.1 ^282.0±^6.0 ^28.1±^1.3 ⁴⁴²⁵±²⁸ ³⁶³±¹¹ ^15.3±^2.3

Observed 286 268 33 4438 375 13

LFV H signal 23.1±1.6 16.0±1.2 5.9±1.0 61±4 15±1 2.8±0.5

Fig. 4.95%CLupperlimitsbycategoryfortheLFVdecaysforMH=^{125 GeV.}^Left:^H→^eτ.Right:H→^eμforcategoriescombinedbynumberofjets,theVBFcategories combined,andallcategoriescombined.

Table 9

Theexpectedand observedupper limits at 95%CL,and best ﬁt valuesfor the branchingfractions B(H→eτ)fordifferentjetcategoriesand analysischannels.

Theasymmetriconestandard-deviationuncertaintiesaroundtheexpectedlimits areshowninparentheses.

0-jet 1-jet 2-jet

Expected limits at 95% CL (%) eτμ <1.63

+0.66

−0.44

<1<