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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Search for light pseudoscalar boson pairs produced from decays of the 125 GeV Higgs boson in final states with two muons and two nearby tracks in pp collisions at √

s = 13 TeV

.The CMS Collaboration

CERN,Switzerland

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

Articlehistory:

Received16July2019

Receivedinrevisedform12October2019 Accepted4November2019

Availableonline8November2019 Editor: M.Doser

Keywords:

CMS Physics Higgsboson NMSSM 2HD+1S

A search is presented for pairs of light pseudoscalarbosons, in the mass range from 4 to 15 GeV, producedfromdecaysofthe125 GeVHiggsboson.Thedecaymodesconsideredarefinalstatesthatarise whenoneofthepseudoscalarsdecaystoapairoftauleptons,andtheotheroneeitherintoapairoftau leptonsormuons.Thesearchisbasedonproton-protoncollisionscollectedbytheCMSexperimentin 2016atacenter-of-massenergyof13 TeVthatcorrespondtoanintegratedluminosityof35.9 fb1.The 2μ2τand4τ channelsareusedincombinationtoconstraintheproductoftheHiggsbosonproduction cross sectionand the branchingfraction into 4τ finalstate, σB,exploitingthe lineardependence of the fermioniccouplingstrengthofpseudoscalarbosonsonthe fermionmass. Nosignificantexcessis observedbeyondtheexpectationfromthestandardmodel.Theobservedandexpectedupperlimitsat 95% confidencelevel onσB,relativetothe standardmodel Higgsbosonproductioncrosssection,are setrespectivelybetween0.022and0.23andbetween0.027and0.19inthemassrangeprobedbythe analysis.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

After the discovery of the 125GeV Higgs boson (H) [1,2], searches for additional Higgs bosons, based on predictions be- yond the standard model (SM), constitute an important part of the scientific program at the CERN Large Hadron Collider (LHC).

Thepresentanalysisexaminestheoreticalmodelsthatcontaintwo Higgsdoubletsandanadditionalcomplex singletHiggsfield(de- noted hereafter as 2HD+1S), that does not couple at tree level to fermions or gauge bosons and interacts only with itself and the Higgs doublets [3–10]. In CP conserving models, which are considered in this Letter, the Higgs sector features seven physi- cal states, namely three CP-even, two CP-odd, and two charged bosons,whereoneoftheCP-evenstatescorrespondstotheH.This kindof Higgs sector is realized, forexample, in next-to-minimal supersymmetricmodelsthatsolvetheso-called

μ

problemofthe minimalsupersymmetricextension ofthe SM [11].Alarge setof the2HD+1S models is allowed by measurements andconstraints set by searches for additional Higgs bosons andsupersymmetric particles [12–17].

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

This Letter addresses specific 2HD+1S models in which the lightestpseudoscalarboson(a1) withmass2ma1<125GeV hasa large singletcomponent, andthereforeits couplings toSM parti- clesaresignificantlyreduced.Forthisreason,analysesusingdirect production modes of a1, such as gluon-gluon fusion (ggF) or b quarkassociatedproduction,havelimitedsensitivity.Thea1 boson isnonetheless potentially accessibleinthe H decay totwo pseu- doscalarbosons.Thea1statescanbeidentifiedviatheirdecayinto apairoffermions [18–25].ConstraintsontheH couplingsallowa branching fractionforH decays intonon-SMparticles aslarge as 34% [26],whichcanpotentiallyaccommodatetheH→a1a1 decay ataratesufficientlyhighfordetectionattheLHC.

Several searches for H→a1a1 decays have been performed in the ATLAS andCMS experiments in Run1 (8TeV)and Run 2 (13TeV) ofLHC,exploitingvarious decaymodesofthe a1 boson, andprobing different ranges ofits mass [27–40]. These searches found no significant deviation from the expectation of the SM backgroundandupperlimitswereset ontheproductofthepro- ductioncrosssection andthe branchingfractionforsignal result- inginconstraintsonparametersofthe2HD+1Smodels.

Thisanalysispresentsasearchforlight a1 bosonsinthedecay channels H→a1a14

τ

/2

μ

2

τ

, using data corresponding to an integratedluminosityof35.9fb1,collectedwiththeCMSdetector https://doi.org/10.1016/j.physletb.2019.135087

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

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Fig. 1.Illustrationofthesignaltopology,inwhichtheH decaysintotwoa1bosons, whereonea1bosondecaysintoapairoftauleptons,whiletheotheronedecays intoapairofmuonsorapairoftauleptons.Theanalyzedfinalstateconsistsof onemuonandanoppositelychargedtrackineacha1decay.

in2016atacenter-of-massenergyof13TeV.Theanalysiscovers themass rangefrom 4to 15GeV andemploys a special analysis strategytoselectandidentifyhighlyLorentz-boostedmuonortau leptonpairswithoverlappingdecayproducts.Thestudyupdatesa similaroneperformedbytheCMSCollaborationinRun1 [28],and complementsother recentCMSsearches forthe H→a1a1 decay performedinRun2datainthe2

μ

2

τ

[30],2

τ

2b [31],2

μ

2b [38]

and4

μ

[39] finalstates,coveringrespectivemassrangesof0.25<

ma1<3.40GeV forthe 4

μ

final state and15.0<ma1<62.5GeV forthe2

μ

2

τ

,2

τ

2b,and2

μ

2b finalstates.

Thebranching fractiona1

τ τ

dependson thedetailsofthe model,namelytheparametertanβ,the ratioofvacuumexpecta- tionvaluesofthetwoHiggsdoublets,andonwhichHiggsdoublet couples to either charged leptons, up-type quarks or down-type quarks [41]. InType-II 2HD+1S models,whereone Higgsdoublet couplestoup-typefermionswhiletheothercouplestodown-type fermions, the a1

τ τ

decay rate gets enhanced atlarge values oftanβ.Thebranchingfractionofthisdecayreachesvaluesabove 90% attanβ >3 for 2mτ<ma1<2mb,where is themass of thetauleptonandmb isthemassofthebottomquark.Forhigher valuesofma1 thebranching fractiondecreases to 5–6% sincethe decayintoapairofbottomquarksbecomeskinematicallypossible andoverwhelmsthedecayintoapairoftauleptons.However, in someofthe2HD+1Smodelsthea1

τ τ

decaymaybedominant evenabovethe a1bb decay¯ threshold.Thisisrealized,e.g.,for tanβ >1 intheType-III2HD+1Smodels,whereoneHiggsdoublet couplestochargedleptons, whereas theother doubletcouplesto quarks [41].

The signal topology targeted by the present analysis is illus- trated in Fig. 1. Each a1 boson is identified by the presence of a muon and only one additional charged particle, the objective of this approach being the decay channels a1

μμ

and a1

τ

μ

τ

one-prong. The

τ

μ denotes the muonic tau lepton decay, and

τ

one-prong standsforitsleptonic orone-pronghadronicdecay.The three-prong modes are not used because of the very high QCD multijetbackgroundandlowerreconstructionsignalefficiency.

Giventhe large differencein massbetween thea1 andtheH states,thea1 bosonswillbeproducedhighlyLorentz-boosted,and their decay products are highly collimated. This will result in a signature with two muons, each of which is accompanied by a nearby particle of opposite charge. The search focuses primarily on the dominant ggF process, in which the H state is produced withrelativelysmall transversemomentum pT,andthe a1 pseu- doscalarsareemitted nearlyback-to-backinthetransverseplane, witha largeseparation inazimuthφ betweenthe particles orig- inating fromone of the a1 decaysand those of the other a1. In theggF process,theHcanbealsoproducedwitharelativelyhigh Lorentzboostwhenahardgluonisradiatedfromtheinitial-state

gluonsorfromtheheavy-quarkloop.Inthiscase,theseparationin φ isreduced, buttheseparationinpseudorapidity

η

canbelarge.

The analysisthereforesearches forasignal ina sample ofsame- charge (SC)dimuoneventswithlargeangularseparationbetween the muons,where eachmuon isaccompaniedby one nearbyop- positely chargedparticleoriginatingfromthe samea1 decay.The requirement ofhaving SC muons in theevent largely suppresses background fromthe top-quark-pair,Drell–Yan, anddibosonpro- duction.Thisrequirementalsofacilitatesthe implementationofa dedicatedSCdimuontriggerwithrelativelylowthresholdsandac- ceptableratesasdescribedinSection4.

2. CMSdetector

The central feature of the CMS detectoris a superconducting solenoid of 6m internal diameter, providing a magnetic field of 3.8T. Within the solenoid volume are a silicon pixel and strip tracker,aleadtungstatecrystalelectromagneticcalorimeter,anda brass andscintillatorhadroncalorimeter,eachcomposedofabar- rel and two endcap sections.Forward calorimeters extend the

η

coverage providedby thebarrelandendcapdetectors.Muonsare detected ingas-ionization chambers embedded in the steelflux- returnyokeoutsidethesolenoid.

Events ofinterest are selected using a two-tiered trigger sys- tem [42].Thefirstlevel,composedofcustomhardwareprocessors, usesinformationfromthecalorimetersandmuondetectorstose- lect eventsat arateof around 100kHz within atime interval of less than 4μs. The second level, known asthe high-level trigger, consistsofafarmofprocessorsrunningaversionofthefullevent reconstructionsoftwareoptimizedforfastprocessing,andreduces theeventratebelow1kHz beforedatastorage.

AmoredetaileddescriptionoftheCMSdetector,togetherwith a definitionofthecoordinatesystemusedandtherelevantkine- maticvariables,canbefoundinRef. [43].

3. Simulatedsamples

For the simulation of the dominant ggF production process, the MonteCarlo (MC)event generatorspythia (v.8.212) [44] and MadGraph5_amc@nlo (v.2.2.2) [45] are used in order to model the H→a1a14

τ

and H→a1a12

μ

2

τ

signal events, re- spectively. For both decay modes the pT distribution of the H emerging fromggF isreweighted withnext-to-next-to-leadingor- der (NNLO) K factors obtained by the program HqT (v2.0) [46, 47] withNNLONNPDF3.0partondistributionfunctions(PDF) [48], hereby takingintoaccount the moreprecise spectrum calculated to NNLO withresummationtonext-to-next-to-leading-logarithms order.Subdominantcontributionsfromother productionmodesof H, namely vector boson fusion process (VBF),vector bosonasso- ciated production(VH) andtop quark pairassociated production (t¯tH)areestimatedusingthepythia(v.8.212)generator.

The backgroundsfromdibosonproductionandquantum chro- modynamics production ofmultijet (QCD multijet) are simulated with the pythia (v.8.212) generator. Inclusive Z and W boson production processes are generated with MadGraph5_amc@nlo (v.2.2.2).The single-topand t¯t production are generatedatNext- to-LO(NLO)withthepowheg(v.2.0)generator[49–53].Thesetof PDFusedisNLONNPDF3.0forNLOsamples,andLONNPDF3.0for LOsamples [48].

Showering and hadronization are carried out by the pythia (v.8.212)generatorwiththeCUETP8M1underlyingeventtune [54], while a detailedsimulation of the CMSdetectoris based on the Geant4[55] package.

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4. Eventselection

EventsareselectedusingaSC dimuontriggerwith pT thresh- oldsof17(8)GeV fortheleading (subleading)muon.Topassthe high-leveltrigger,thetracksofthetwomuonsareadditionallyre- quiredtohavepoints ofclosestapproachtothebeamaxiswithin 2mm ofeachotheralongthelongitudinaldirection.

Events are reconstructed with the particle-flow (PF) algo- rithm [56] whichaims toidentifyandreconstructindividual par- ticlesasphotons, chargedhadrons, neutralhadrons, electrons, or muons(PFobjects).Theproton-proton(pp)interactionverticesare reconstructedusingaKalmanfilteringtechnique [57,58].Typically morethanonesuchvertexisreconstructedbecauseofmultiplepp collisions within the sameor neighbouring bunch crossings. The meannumberof such interactions per bunch crossingwas 23in 2016.

The reconstructed vertex with the largest value of summed physics-object p2T is taken to be the primary interaction vertex (PV). The physics objects are the jets, clustered using the jet- findingalgorithm [59,60] withthetracksassignedtothevertexas inputs,andtheassociatedmissingtransversemomentum,takenas thenegative vectorsumofthe pT ofthosejets.Events mustcon- tain atleasttwo SC muonsreconstructed withthe PFalgorithm, whichhavetofulfilthefollowingrequirements.

Thepseudorapidityoftheleading(higherpT)andthesublead- ing(lower pT)muonsmustbe|

η

|<2.4.

The pT of the leading (subleading) muon must exceed 18 (10)GeV.

The transverse (longitudinal) impact parameters of muons with respectto thePVare required tobe |d0|<0.05(|dz|<

0.1)cm.

The angular separation between the muons is R = (φ)2+(

η

2) >2.

IfmorethanoneSCmuonpairisfoundintheeventtosatisfy theserequirements,thepairwiththelargestscalarsumofmuon pTischosen.

Inthenextstep,theanalysisemploysinformationabouttracks associatedwiththereconstructedchargedPFobjects,excludingthe pairofSCmuons.Selectedmuonsandtracksareusedtobuildand isolate candidates for the a1

τ

μ

τ

one-prong or a1

μμ

decays (referredtoasa1candidatesthroughouttheLetter).Threetypesof tracksareconsideredintheanalysis.

•“Isolation”tracksareusedtodefineisolationrequirementsim- posedon a1 candidatesandhavetofulfilthefollowingcrite- ria: pT>1GeV,|

η

|<2.4,|d0|<1cm,|dz|<1cm.

“Signal” tracks are selectedamong “isolation”tracks to build a1candidates.ThesetracksmusthavepT>2.5GeV,|

η

|<2.4,

|d0|<0.02cm,|dz|<0.04cm.

“Soft” tracks are also a subset of “isolation” tracks.They are utilized to define one of the sideband regions, used for the construction of the background model, as described in Sec- tion 5.2. “Soft” tracks must satisfy the requirements: 1.0<

pT<2.5GeV,|

η

|<2.4,|d0|<1cm,|dz|<1cm.

Atrackisregardedasbeingnearbyamuoniftheangularsep- arationR betweenthem issmaller than 0.5.Each muon ofthe SCpairisrequiredtohaveonenearby“signal”trackwithacharge opposite toits charge. This muon-tracksystemis acceptedas an a1candidateifnoadditional“isolation”tracksarefoundintheR coneof 0.5around themuon momentum direction. The eventis selectedinthe final sample ifitcontains two a1 candidates.The

Table 1

Thesignalacceptanceandthenumberofexpectedsignaleventsafterselectionin theSR.Thenumberofexpectedsignaleventsiscomputedforabenchmarkvalue ofbranchingfraction,B(Ha1a1)B2(a1τ τ)=0.2 andassumingthatthe H productioncrosssectionistheonepredictedintheSM.Thequoteduncertainties forpredictionsfromsimulationincludeonlystatisticalones.

ma1[GeV] Acceptance×104 Number of events

4τ 2μ2τ 4τ 2μ2τ

4 3.29±0.16 89.3±1.4 129.9±6.2 54.7±0.9 7 2.50±0.14 69.0±1.4 98.8±5.5 22.5±0.5 10 1.46±0.11 47.1±1.2 57.8±4.2 14.2±0.4 15 0.21±0.04 3.5±0.3 8.5±1.1 1.0±0.1 setofselectionrequirementsoutlinedabovedefinesthesignalre- gion(SR).

Theexpectedsignalacceptanceandsignalyieldforafew rep- resentativevaluesofma1 arereportedinTable1.Thesignalyields are computed for a benchmark value of the branching fraction, B(Ha1a1)B2(a1

τ τ

)=0.2 and assumingthattheH produc- tion cross section is the one predicted in the SM. Contributions from the ggF, VBF, VH and t¯tH processes are summed up. The yield ofthe 2

μ

2

τ

signal is estimatedunderthe assumptionthat thepartialwidthsofthea1

μμ

anda1

τ τ

decayssatisfythe relation [23]

(

a1

→ μμ )

(

a1

→ τ τ ) =

m

2μ

m2τ

1

2mτ

/

ma1

2

.

(1)

The ratioofbranchingfractionsofthe a1a12

μ

2

τ

anda1a1→ 4

τ

decays is computed through the ratio of the partial widths (a1

μμ

)and (a1

τ τ

)as

B

(

a1a1

2

μ

2

τ )

B

(

a1a1

4

τ ) =

2B

(

a1

→ μμ )

B

(

a1

→ τ τ ) =

2

(

a1

→ μμ )

(

a1

→ τ τ ) .

(2) The factor of 2 in Eq. (2) arises from two possible decays, a(11)a(12)2

μ

2

τ

anda(11)a(12)2

τ

2

μ

,thatproducethefinalstate withtwo muonsandtwo tauleptons. TheratioinEq. (2) ranges fromabout0.0073atma1=15GeV to0.0155atma1=4GeV.

The contributionfromtheH→a1a14

μ

decayisestimated takinginto account Eq. (1). It ranges between0.4 and2% of the totalsignalyieldinthe2

μ

2

τ

and4

τ

finalstates,dependingonthe probed massofthea1 boson.Thiscontributionis notconsidered inthepresentanalysis.

The number of observed events selected in the SR amounts to 2035. A simulation-based study shows that the QCD multijet eventsdominatethesampleofeventsselectedintheSR.Contribu- tionfromotherbackgroundsourcesconstitutesabout1% ofevents selectedintheSR.

The two-dimensional(2D) distributionoftheinvariant masses ofthe muon-tracksystems,constituting a1 candidates, isusedto discriminatebetweensignalandthedominantQCDmultijetback- groundin the signal extractionprocedure. The 2D distribution is filledwithapairofthemuon-trackinvariantmasses(m1,m2),or- deredbytheirvalue,m2>m1.Thebinning ofthe2D distribution adopted inthe analysisis illustrated in Fig. 2. As m2 is required to exceedm1, only(i,j)bins with ji arefilled inthe 2D dis- tribution,yielding intotal6(6+1)/2=21 independentbins.Bins (i,6) withi=1,5 containall eventswithm2>6GeV.Bin (6,6) containsalleventswithm1,2>6GeV.

5. Modelingbackground

Asimulation-based studyrevealsthat thesample ofSC muon pairsselectedasdescribedinSection4,butwithoutrequiringthe

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Table 2

Controlregionsusedtoconstructandvalidatethebackgroundmodel.ThesymbolsNsig,NisoandNsoftdenote thenumberof“signal”,“isolation”(whichareasubsetof“signal”tracks)and“soft”tracks,respectively,withina coneofR=0.5 aroundthemuonmomentumdirection.ThelastrowdefinestheSR.

Control region Firstμ Secondμ Purpose Observed events

N23 Niso=1,Nsig=1 Niso=2,3 Determination off1D(i) 62 438 Niso,2=1 Niso>1,Nsig1 Niso=1,Nsig=1 Validation off1D(i) 472 570 Niso,2=2,3 Niso>1,Nsig1 Niso=2,3 Validation off1D(i) 17 667 900 N45 Niso=1,Nsig=1 Niso=4,5 Assessment of

systematics inf1D(i) 52 437 Both muons

Loose-Iso Nsig=1,Nsoft=1,2 Determination ofC(i,j) 35 824

Signal region Nsig=1,Niso=1 Signal extraction 2 035

Fig. 2.Binning of the 2D (m1,m2) distribution.

presence of a1 candidates, is dominatedby QCD multijet events, whereabout85% ofall selectedevents containbottom quarksin thefinalstate.TheSCmuonpairsintheseeventsoriginatemainly fromthefollowingsources:

muonicdecayofabottomhadroninonebottomquarkjetand cascadedecayofabottom hadron intoa charmhadron with asubsequentmuonicdecayofthecharmhadronintheother bottomquarkjet;

muonicdecayofabottomhadroninonebottomquarkjetand decayofaquarkoniumstateintoapairofmuonsintheother jet;

muonicdecayofabottomhadroninonebottomquarkjetand muonicdecay ofa B0 mesonin the other bottom quark jet.

TheSCmuonpairinthiscasemayappearasaresultofB0B0 oscillations.

The normalized 2D (m1,m2) distribution for the muon-track pairs with m2>m1 is represented in the sample of background eventsbyabinned templateconstructedusingthefollowingrela- tion

f2D

(

i

,

j

) =

C

(

i

,

j

)(

f1D

(

i

)

f1D

(

j

))

sym

, (

f1D

(

i

)

f1D

(

i

))

sym

=

f1D

(

i

)

f1D

(

i

),

(

f1D

(

i

)

f1D

(

j

))

sym

=

f1D

(

i

)

f1D

(

j

) +

f1D

(

j

)

f1D

(

i

)

=

2f1D

(

i

)

f1D

(

j

),

ifj

>

i

,

(3)

where

f2D(i,j)isthecontent ofthebin(i,j) inthenormalized2D (m1,m2)distribution;

f1D(i) is the content of bin i in the normalizedone-dimen- sional(1D)distributionofthemuon-trackinvariantmass;

C(i,j)isasymmetricmatrix,accountingforpossiblecorrela- tion betweenm1 andm2, the elements of thematrix C(i,j) arereferredtoas“correlationfactors”inthefollowing.

The condition C(i,j)=1 for all bins (i,j) would indicate an absenceofcorrelation betweenm1 andm2.Wesumthecontents of the nondiagonal bins (i,j) and(j,i) in the Cartesian product f1D(i)f1D(j)toaccountforthefactthateachevententersthe2D (m1,m2) distribution with ordered values of the muon-track in- variantmasses.

Byconstructionthebackgroundmodelestimatesthedominant QCDmultijetproductionaswellassmallcontributionsfromother processes.

Multiplecontrolregions(CRs)areintroducedinordertoderive and validate the modeling of f1D(i) and C(i,j). The CRs are de- finedonthebasisofamodifiedisolationcriteriaappliedtooneor both muon-track pairs.The isolation criteriaare specified by the multiplicity of“isolation” tracks inthe cone of R=0.5 around the muon momentumdirection. The summary ofall CRsused to derive andvalidate themodelingofbackgroundshapeisgivenin Table2.

5.1. Modelingof f1D(i)

The f1D(i) distribution is modeled using the N23 CR. Events in thisCRpass theSC dimuonselection andcontainonly one a1 candidatecomposedoftheisolated“signal”trackandmuon(first muon). Theinvariant massofthefirstmuonandassociatedtrack entersthe f1D(i)distribution.Anothermuon(secondmuon)isre- quiredtobeaccompaniedbyeithertwoorthreenearby“isolation”

tracks. The simulation shows that more than 95% of events se- lectedintheCRN23areQCDmultijetevents,whiletheremaining 5% is comingfrom t¯t, Drell-Yanand other electroweakprocesses.

The modeling ofthe f1D(i) template is based on the hypothesis that thekinematic distributionsforthe muon-tracksystem,mak- ing up an a1 candidate(the first muonandassociatedtrack), are weaklyaffectedbytheisolation requirementimposed onthesec- ond muon; therefore the f1D(i) distribution of the muon-track system forming an a1 candidate is expectedto be similar in the SRandtheN23CR.

Thishypothesisisverifiedincontrolregionslabelled Niso,2=1 and Niso,2=2,3. Events are selected in these CR if one of the muons(firstmuon)hasmorethanone“isolation”track(Niso>1).

At least one of these“isolation” tracks should also fulfil the cri- teria imposed on the “signal” track. As more than one of these tracks can pass the criteria imposed on “signal”tracks, two sce- narios havebeen investigated,namely usingeither thelowest or thehighestpT “signal”tracks(“softest”and“hardest”)tocalculate themuon-trackinvariantmass.Ifonlyone“signal”trackisfound nearby tothe firstmuon, thetrackis usedboth asthe“hardest”

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Fig. 3.Theobservedinvariantmassdistribution,normalizedtounity,ofthefirst muonandthesoftest(upper)orhardest(lower)accompanying“signal”trackfor differentisolationrequirementsimposedonthesecondmuon:whenthe second muonhasonlyoneaccompanying“isolation”track(Niso,2=1;circles);orwhenit hastwoorthreeaccompanying“isolation”tracks(Niso,2=2,3;squares).

andthe“softest”signaltrack.Forthesecondmuon,two isolation requirementsare considered: whenthe muon isaccompanied by onlyone“signal”trackandthemuon-tracksystemisisolatedasin theSR(CRNiso,2=1),orwhenitisaccompaniedby twoorthree

“isolation”tracks as inthe CR N23 (CR Niso,2=2,3). The invari- antmassdistributionsofthefirstmuonandthesoftestorhardest accompanyingtrackarethencomparedforthetwodifferentisola- tionrequirementsonthesecondmuon,Niso,2=1 andNiso,2=2,3.

The results of this studyare illustrated in Fig. 3. In both cases, theinvariantmassdistributionsdifferineachbinbylessthan6%.

This observation indicates that the invariant mass of the muon- tracksystem, makingup an a1 candidate,weaklydependsonthe isolationrequirementimposedonthesecondmuon,thussupport- ingtheassumptionthatthe f1D(i)distributioncanbedetermined fromtheN23CR.

Fig. 4.Theobservedinvariantmassdistribution,normalizedtounity,ofthemuon- trackinvariantmassincontrolregionsN23(circles)andN45(squares).

The potential dependence of the muon-track invariant mass distribution onthe isolation requirement imposed onthe second muon isverifiedalsoby comparingshapesinthecontrol regions N23 and N45.The latter CR isdefined by requiring the presence of4or5“isolation”tracksnearbytothesecondmuon, whilethe firstmuon-trackpairpassesselectioncriteriaforthea1 candidate.

TheresultsareillustratedinFig.4.Aslightdifferenceisobserved between distributions in these two CRs. This difference is taken asashapeuncertaintyinthenormalizedtemplate f1D(j)entering Eq. (3).

Fig.5presentsthenormalizedinvariantmassdistributionofthe muon-tracksystem fordata selectedin theSR andforthe back- groundmodelderivedfromtheN23 CR.Thedataandbackground distributions are compared to the signal distributions, obtained fromsimulation,forfourrepresentativemasshypotheses,ma1=4, 7, 10,and 15GeV.The invariant mass ofthe muon-track system is found to havehigher discrimination power betweenthe back- groundandthesignalathigherma1.Forlowermasses,thesignal shape becomes morebackgroundlike, resultingina reduction of discriminationpower.

5.2. ModelingofC(i,j)

In order to determine the correlation factors C(i,j), an addi- tional CR (labelled Loose-Iso) is used. It consists of events that containtwoSCmuonspassingtheidentificationandkinematicse- lectioncriteriaoutlinedinSection4.Eachmuonisrequiredtohave twoorthreenearbytracks.Oneofthemshouldbelongtothecate- goryof“signal”tracks,whereasremainingtracksshouldbelongto thecategoryof“soft”tracks.About36kdataeventsareselectedin thisCR.ThesimulationpredictsthattheQCDmultijeteventsdom- inatethisCR,comprisingmorethan99%ofselectedevents.Itwas alsofoundthattheoverallbackground-to-signalratioisenhanced comparedtotheSRbyafactorof30to40,dependingonthemass hypothesis,ma1. Theeventsample inthisregion isused tobuild thenormalizeddistribution f2D(i,j).Finally,thecorrelationfactors C(i,j)areobtainedaccordingtoEq. (3) as

C

(

i

,

j

) =

f2D

(

i

,

j

)

(

f1D

(

i

)

f1D

(

j

))

sym

,

(4)
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Fig. 5.Normalizedinvariantmassdistributionofthemuon-tracksystemforevents passingthesignalselection.Observednumbersofeventsarerepresentedbydata pointswith errorbars.TheQCDmultijetbackgroundmodelisderivedfromthe controlregionN23.Alsoshownarethenormalizeddistributionsfromsignalsim- ulationsforfourmasshypotheses,ma1=4,7,10,and15GeV (dashedhistograms), whereasforhighermassesthe analysishasnosensitivity.Eacheventinthe ob- servedandexpectedsignaldistributionscontributestwoentries,correspondingto thetwomuon-tracksystemsineacheventpassingtheselection.Thesignaldistri- butionsinclude2μ2τand4τcontributions.Thelowerpanelshowstheratioofthe observedtoexpectednumberofbackgroundeventsineachbinofthedistribution.

Thegreyshadedarearepresentsthebackgroundmodeluncertainty.

Fig. 6.The(m1,m2)correlationfactorsC(i,j)withtheirstatisticaluncertainties, derivedfromdataintheCRLoose-Iso.

where f1D(i) is the 1D normalized distribution withtwo entries perevent(m1andm2).ThecorrelationfactorsC(i,j)derivedfrom dataintheLoose-IsoCRarepresentedinFig.6.Toobtainestimates of C(i,j) in the signal region, the correlation factors derived in theLoose-IsoCRhavetobe correctedforthedifference inC(i,j) betweenthesignal regionandLoose-IsoCR. Thisdifferenceisas- sessedbycomparingsamplesofsimulatedbackgroundevents.The correlationfactors estimatedfromsimulationinthesignal region andtheLoose-IsoCRarepresentedinFig.7.

Fig. 7.The(m1,m2)correlationfactorsC(i,j)alongwith theirMCstatisticalun- certainties,derived fromsimulated samplesinthe (upper:signalregion, lower:

Loose-IsoCR).

The correlationfactorsinthe signalregionare thencomputed as

C

(

i

,

j

)

SRdata

=

C

(

i

,

j

)

CRdataC

(

i

,

j

)

SRMC

C

(

i

,

j

)

CRMC

,

(5)

where

C(i,j)CRdata are correlation factorsderived fortheLoose-IsoCR indata(Fig.6);

C(i,j)SRMC arecorrelationfactorsderivedfortheSRinthesim- ulatedQCDmultijetsample(Fig.7,upper);

C(i,j)CRMC are correlation factors derived for the Loose-IsoCR inthesimulatedQCDmultijetsample(Fig.7,lower).

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Table 3

SystematicuncertaintiesandtheireffectontheestimatesoftheQCDmultijetbackgroundandsignal.

Source Value Affected sample Type Effect on the total yield

Stat. unc. inC(i,j) 3–60% bkg. bin-by-bin

Extrapolation unc. inC(i,j) bkg. shape

Unc. in f1D(i) bkg. shape

Integrated luminosity 2.5% signal norm. 2.5%

Muon id. and trigger efficiency 2% per muon signal norm. 4%

Track id. efficiency 4–12% per track signal shape 10–18%

MC stat. unc. in signal yields 8–100% signal bin-by-bin 5–20%

Theoretical uncertainties in the signal acceptance

μRandμFvariations signal norm. 0.8–2%

PDF signal norm. 1–2%

Theoretical uncertainties in the signal cross sections

μR,Fvariations (ggF) 5–7% signal norm. 5–7%

μR,Fvariations (other processes) 0.4–9% signal norm. <0.5%

PDF (ggF) 3.1% signal norm. 3.1%

PDF (other processes) 2.1–3.6% signal norm. <0.5%

Fig. 8.Thedistributionofthesignaltemplates f2D(i,j)inonerowformasshy- pothesisma1=4GeV (upper)and 10GeV (lower).TheHa1a12μ2τ (blue histogram)andHa1a14τ(redhistogram)contributionsareshown.Thenota- tionofthebinsfollowsthatofFig.2.

The difference incorrelation factors derived in the SR(Fig. 7, upper)andintheLoose-IsoCR(Fig.7,lower)usingtheQCDmul- tijetsampleistakenintoaccountasanuncertaintyinC(i,j). 6. Modelingsignal

The signal templates are derived fromthe simulated samples oftheH→a1a14

τ

andH→a1a12

μ

2

τ

decays.The study probes the signal strength modifier, defined as the ratio of the product of the measured signal cross section andthe branching

fraction into the 4

τ

final state B(Ha1a1)B2(a1

τ τ

) to the inclusive cross section of the H production predictedin the SM.

The relative contributions from different production modesof H are defined by the corresponding cross sectionspredicted in the SM.ThecontributionoftheH→a1a12

μ

2

τ

decay,iscomputed assumingthatthepartialwidthsofa1

τ τ

anda1

μμ

decays satisfyEq. (1).

The invariant mass distribution of the muon-track system in the a1

μμ

decay channel peaks at the nominal value of the a1 boson mass, while the reconstructed mass of the muon-track system in the a1

τ τ

decay is typically lower, because of the missingneutrinos.ThisiswhytheH→a1a12

μ

2

τ

signalsam- ples have a largely different shape of the (m1,m2) distribution compared totheH→a1a14

τ

signal samples.Fig.8compares the (m1,m2) distributions unrolled in a one row between the H→a1a14

τ

and H→a1a12

μ

2

τ

signal samplesfor mass hypothesesma14GeV and10GeV.Thesignaldistributionsarenor- malized assuming the SM H production rate withthe branching fractionB(Ha1a1)B2(a1

τ τ

)equalto0.2.

7. Systematicuncertainties

Table3liststhesystematicuncertaintiesconsideredintheanal- ysisforbothsignalandbackground.

7.1. Uncertaintiesrelatedtothebackground

TheestimationoftheQCDmultijetbackgroundisbasedonob- served data, therefore it is not affected by imperfections in the simulation,reconstruction,ordetectorresponse.

The shape of the background in the (m1,m2) distribution is modeledaccordingtoEq. (3),whileitsuncertaintyisdominatedby uncertaintiesrelatedtothecorrelationfactorsC(i,j)(asdescribed inSection5.2).Additionally,itisalsoaffectedbytheshapeuncer- taintyinthe1Dtemplate f1D(m)(asdiscussedinSection5.1).The bin-by-binuncertaintiesinmasscorrelationfactorsC(i,j),derived fromEq. (5), are composed of the statisticaluncertainties in ob- serveddataandsimulatedsamples,aspresentedinFigs. 6and7, andrangefrom3to60%.Theseuncertaintiesareaccountedforin thesignalextractionprocedurebyonenuisanceparameterperbin inthe (m1,m2)distribution [61].The systematicuncertainties re- latedtotheextrapolationofC(i,j)fromtheLoose-IsoCRtotheSR are derivedfromthe dedicatedMC studyoutlinedinSection 5.2.

Therelatedshapeuncertaintyisdeterminedbycomparingcorrela- tionfactors derivedinthesimulatedsamples,betweenthesignal regionandtheLoose-IsoCR.

In the case when B(H→a1a1)B2(a1

τ τ

)=0.34, corre- sponding to an upper limit at 95% confidence level (CL) on the
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branching fraction of the H decay into non-SM particles from Ref. [26],theimpactofpossiblesignalcontaminationintheLoose- IsoCRisestimatedonabin-by-binbasis,anditisatmost2.8%in thebin(6,6) whichwas foundto haveanegligible effectonthe finalresults.ForallotherCRs,thesignalcontaminationwasfound tobewellbelow1%.

7.2. Uncertaintiesrelatedtosignal

Anuncertaintyof2.5%isassignedtotheintegratedluminosity estimate [62].

The uncertainty in the muon identification and trigger effi- ciencyisestimatedtobe2%foreachselectedmuonobtainedwith thetag-and-probe technique [63].The trackselection andmuon- trackisolationefficiencyisassessedwitha studyperformedona sampleofZ bosonsdecayingintoa pairoftauleptons.Inthese- lected Z→

τ τ

events,one taulepton isidentified viaits muonic decay,while the other is identified asan isolated trackresulting froma one-prongdecay. The trackisrequired topass the nomi- nal selection criteria usedin the main analysis. From this study, the uncertainty in the track selection and isolation efficiency is evaluated. Therelated uncertaintyaffects theshape ofthe signal estimate, while changingthe overall signal yield by 10–18%. The muon and trackmomentum scale uncertainties are smaller than 0.3%andhaveanegligibleeffectontheanalysis.

Thebin-by-binstatisticaluncertaintiesinthesignal acceptance rangefrom8to100%,whiletheimpactontheoverallsignalnor- malizationvariesbetween5and20%.

Theoretical uncertainties have an impact on the differential kinematic distributions of the produced H, in particular its pT spectrum,therebyaffectingsignalacceptance.Theuncertaintydue tomissinghigher-ordercorrectionstotheggF processisestimated with the HqT program by varying the renormalization (

μ

R) and factorization(

μ

F)scales.TheHpT-dependentK factorsarerecom- puted accordingtothese variations andappliedto thesimulated signalsamples.Theresultingeffectonthesignalacceptanceisesti- matedtovarybetween1.2and1.5%,dependingonma1.Inasimilar way,theuncertaintyinthesignal acceptanceiscomputedforthe VBF, VHandt¯tH productionprocesses.The impacton theaccep- tanceisestimatedtovarybetween0.8and2.0%,dependingonthe processandprobedmassofthea1 boson.

The HqT program is also used to evaluate the effect of the PDF uncertainties. The nominal K factors for the H pT spectrum are computedwiththe NNPDF3.0PDF set [48]. Variations ofthe NNPDF3.0PDFswithintheiruncertaintieschangethesignalaccep- tancebyabout1%,whilstusingtheCTEQ6L1PDFset [64] changes the signal acceptance by about 0.7%. The impact of the PDF un- certaintiesonthe acceptancefortheVBF,VHandt¯tH production processes is estimatedin the same wayand a 2% uncertaintyis consideredtoaccountforthese.

Systematicuncertaintiesintheoreticalpredictionsforthesignal crosssectionsaredrivenbyvariationsofthe

μ

Rand

μ

Fscalesand PDF uncertainties. Uncertainties related to scale variations range from0.4to9%, dependingon theproductionmode.Uncertainties relatedtoPDFvarybetween2.1and3.6%.

8. Results

The signal is extractedwitha binned maximum-likelihoodfit appliedtothe (m1,m2) distribution.Foreach probedmassofthe a1 boson,the(m1,m2)distribution isfittedwiththe sumoftwo templates,corresponding to expectationsforthesignal andback- ground,dominatedbyQCDmultijetevents.

The normalizationof both signal andbackground are allowed to float freely in the fit. The systematic uncertainties affecting

Fig. 9.The(m1,m2)inonerowdistributionusedtoextractthesignal.Observed numbersofeventsarerepresentedbydatapointswitherrorbars.Thebackground withitsuncertaintyisshownasthebluehistogramwiththeshadederrorband.

Theshapeandthenormalizationofthebackgrounddistributionareobtainedby applyingafittotheobserveddataunderthebackground-onlyhypothesis.Signal expectationsforthe4τand2μ2τ finalstatesareshownasdottedhistogramsfor themasshypothesesma1=4,7,10and15GeV.Therelativenormalizationofthe4τ and2μ2τfinalstatesaregivenbyEq. (1) asexplainedinSection6.Thesignalnor- malizationiscomputedassumingthattheH bosonisproducedinpp collisionswith aratepredictedbytheSM,anddecaysintoa1a14τfinalstatewiththebranch- ingfractionof20%.Thelowerplotshowstheratiooftheobserveddataeventsto theexpectedbackgroundyieldineachbinofthe(m1,m2)distribution.

the normalizationofthesignal templates areincorporatedin the fit via nuisance parameters with a log-normal prior probability density function. The shape-altering systematic uncertainties are represented by nuisance parameters whose variations causecon- tinuousmorphingofthesignalorbackgroundtemplateshape,and are assigned a Gaussian prior probability density functions. The bin-by-binstatisticaluncertaintiesareassignedgammapriorprob- abilitydensityfunctions.

Fig.9showsthedistributionof(m1,m2),wherethenotationfor thebinsfollowsthatofFig.2.Theshapeandthenormalizationof the backgrounddistributionare obtainedby applyinga fitto the observeddataunderthebackground-onlyhypothesis.Alsoshown are the expectations for thesignal atma1=4, 7, 10,and 15GeV.

ThesignalnormalizationiscomputedassumingthattheH ispro- ducedinpp collisionswitharatepredictedbythestandardmodel, anddecaysintoa1a14

τ

finalstatewithabranchingfractionof 20%.Nosignificantdeviationsfromthebackgroundexpectationare observedinthe(m1,m2)distribution.

Results of the analysis are used to set upper limits at 95%

CL on the product of the cross section and branching fraction,

σ

(pp→H+ X)B(Ha1a1)B2(a1

τ τ

), relative to the inclu- sive SM cross section of H production. The modified frequentist CLs criterion [65,66], and the asymptotic formulae are used for the test statistic [67], implemented inthe RooStats package [68].

Fig. 10showsthe observed andexpectedupperlimitsat 95% CL onthesignalcrosssectiontimesthebranchingfraction,relativeto the totalcross sectionof theH bosonproductionaspredictedin theSM. Theobservedlimit iscompatiblewiththe expectedlimit within one standard deviationinthe entirerangeof ma1 consid- ered,andrangesfrom0.022atma1=9GeV to0.23atma1=4GeV andreaches0.16atma1=15GeV.Theexpectedupperlimitranges from 0.027 at ma1 =9GeV to 0.16 at ma1=4GeV and reaches 0.19 atma1=15GeV.The degradation ofthe analysis sensitivity towardslowervaluesofma1 iscausedbytheincreaseoftheback- groundyield atlow invariant massesofthe muon-tracksystems, asillustratedinFigs.5and9.Withincreasingma1,theaveragean-

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Fig. 10.Theobservedandexpectedupperlimitsat95%confidencelevelsonthe productofsignalcrosssectionandthebranchingfractionσ(ppH+X)B(Ha1a1)B2(a1τ τ),relativetotheinclusiveHiggsbosonproductioncrosssection σSMpredictedintheSM.Thegreenandyellowbandsindicatetheregionsthatcon- tain68%and95%ofthedistributionoflimitsexpectedunderthebackground-only hypothesis.Theshadedareainblueindicatestheexcludedregionof>34%forthe branchingfractionoftheH decayintonon-SMparticlesat95%CL fromRef. [26].

gular separation between the decay products of the a1 boson is increasing.Asaconsequence,theefficiencyofthesignalselection drops down, aswe require the muon and the track, originating fromthea1

τ

μ

τ

one-prongora1

μμ

decay,tobewithinacone ofR=0.5.Thisexplainsthedeteriorationofthesearchsensitiv- ityathighervaluesofma1.The shadedarea inblueindicatesthe excludedregionof>34%forthebranchingfractionoftheH decay intonon-SMparticlesat95%CL [26].

The new limits improve significantly over the previous 8TeV limits [28] by30%(forlowmasses)andupto80%(forintermedi- atemassesof8GeV),while thenewanalysisfurther extendsthe coverageofma1 upto15GeV.

9. Summary

A search is presented for light pseudoscalar a1 bosons, pro- ducedfromdecaysofthe 125GeV Higgsboson (H) ina dataset correspondingto anintegratedluminosity of35.9fb1 ofproton- protoncollisionsatacenter-of-massenergyof13TeV.Theanalysis isbasedontheH inclusiveproductionandtargetstheH→a1a1→ 4

τ

/2

μ

2

τ

decaychannels. Both channelsareusedincombination to constrain the product of the inclusive signal production cross sectionandthebranchingfractionintothe4

τ

finalstate,exploit- ingthelineardependenceofthefermioniccouplingstrengthofa1 onthefermionmass.Withnoevidenceforasignal,theobserved 95% confidencelevel upper limit onthe product of the inclusive signalcrosssectionandthebranchingfraction,relative totheSM H productioncross section, ranges from0.022 atma1=9GeV to 0.23 at ma1=4GeV and reaches 0.16 at ma1 =15GeV. The ex- pected upper limit ranges from0.027 at ma1=9GeV to 0.16at ma1=4GeV andreaches0.19atma1=15GeV.

Acknowledgements

WecongratulateourcolleaguesintheCERNacceleratordepart- ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMSin- stitutes for their contributions to the success of the CMS effort.

Inaddition,wegratefullyacknowledgethecomputingcentersand

personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses.

Finally, we acknowledge the enduring support for the construc- tionandoperation oftheLHC andtheCMSdetectorprovidedby thefollowing fundingagencies:BMBWF andFWF(Austria); FNRS and FWO(Belgium); CNPq,CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China);

COLCIENCIAS (Colombia); MSES andCSF (Croatia); RPF (Cyprus);

SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia);

AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NK- FIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland);

INFN(Italy);MSIPandNRF(RepublicofKorea);MES(Latvia);LAS (Lithuania);MOEandUM(Malaysia);BUAP,CINVESTAV,CONACYT, LNS,SEP,andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu- gal);JINR(Dubna); MON,ROSATOM,RAS, RFBR,andNRCKI (Rus- sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies(Switzerland); MST (Taipei);

ThEPCenter,IPST,STAR,andNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro- gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract Nos. 675440, 752730, and 765710 (European Union);

the Leventis Foundation; the A.P. Sloan Foundation; the Alexan- der von Humboldt Foundation; the Belgian Federal Science Pol- icy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium);

the F.R.S.-FNRSand FWO(Belgium) underthe “Excellence ofSci- ence – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z181100004218003; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sci- ences, the New National Excellence Program ÚNKP, the NKFIA researchgrants123842,123959,124845,124850,125105,128713, 128786, and 129058 (Hungary); the Council of Science and In- dustrial Research,India;theHOMING PLUSprogramoftheFoun- dation for Polish Science, cofinanced from European Union, Re- gional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/

02861,Sonata-bis2012/07/E/ST2/01406;theNationalPrioritiesRe- search Programby QatarNationalResearchFund;the Ministryof Science and Education, grant no. 3.2989.2017 (Russia); the Pro- gramaEstatalde Fomento delaInvestigación CientíficayTécnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis andAristeiaprogramscofinancedbyEU-ESF andtheGreek NSRF;

theRachadapisekSompotFundforPostdoctoralFellowship,Chula- longkornUniversityandtheChulalongkornAcademic intoIts2nd CenturyProjectAdvancementProject(Thailand);TheWelchFoun- dation,contractC-1845;andtheWestonHavensFoundation(USA).

References

[1] ATLASCollaboration,Observationofanewparticleinthesearchforthestan- dardmodelHiggsbosonwiththeATLASdetectorattheLHC,Phys.Lett.B716 (2012)1,https://doi.org/10.1016/j.physletb.2012.08.020,arXiv:1207.7214.

[2] CMSCollaboration,Observationofanewbosonatamassof125GeVwith theCMSexperimentattheLHC,Phys.Lett.B716(2012)30,https://doi.org/10. 1016/j.physletb.2012.08.021,

수치

Fig. 1. Illustration of the signal topology, in which the H decays into two a 1 bosons, where one a 1 boson decays into a pair of tau leptons, while the other one decays into a pair of muons or a pair of tau leptons
Fig. 4. The observed invariant mass distribution, normalized to unity, of the muon- muon-track invariant mass in control regions N 23 (circles) and N 45 (squares).
Fig. 3. The observed invariant mass distribution, normalized to unity, of the first muon and the softest (upper) or hardest (lower) accompanying “signal” track for different isolation requirements imposed on the second muon: when the second muon has only on
Fig. 6. The (m 1 , m 2 ) correlation factors C ( i , j ) with their statistical uncertainties, derived from data in the CR Loose-Iso.
+6

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