Search for neutral MSSM Higgs bosons decaying to μ+μ- in pp collisions at √s=7 and 8 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Search for neutral MSSM Higgs bosons decaying to μ ⁺ μ ⁻ in pp collisions at √

s = 7 and 8 TeV

.CMS Collaboration

^

CERN,Switzerland

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

Articlehistory:

Received6August2015

Receivedinrevisedform2November2015 Accepted10November2015

Availableonline23November2015 Editor:M.Doser

Keywords:

CMS Physics Higgs MSSM Dimuons

A searchfor neutralHiggs bosonspredicted inthe minimalsupersymmetricstandard model (MSSM) forμ⁺μ⁻decaychannelsispresented.Theanalysisusesdata collectedbytheCMSexperimentatthe LHCinproton–protoncollisionsatcentre-of-massenergiesof7and8 TeV,correspondingtointegrated luminositiesof5.1and19.3 fb⁻¹,respectively.ThesearchissensitivetoHiggsbosonsproducedeither throughthegluonfusionprocessorinassociationwithabb quarkpair.Nostatisticallysignificantexcess isobservedintheμ⁺μ⁻massspectrum.Resultsareinterpretedintheframeworkofseveralbenchmark scenarios,andthedataareusedtosetanupperlimitontheMSSMparametertanβasafunctionofthe massofthepseudoscalarAbosonintherangefrom115to300 GeV.Modelindependentupperlimitsare givenfortheproductofthecrosssectionandbranchingfractionforgluonfusionandbquarkassociated productionat√

s=^{8 TeV.Theyarethemoststringentlimitsobtainedtodateinthischannel.}

©^{2015CERNforthebenefitoftheCMS}Collaboration.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The predictions of the standard model (SM) [1–7] of funda- mental interactions have been confirmed by a large number of experimentalmeasurements.Theobservationofanewbosonwith amassof125 GeVandpropertiescompatiblewiththoseoftheSM Higgs boson [8–10] confirms the mechanism of the electroweak symmetrybreaking (EWSB).Despitethe successofthistheory in describingthe phenomenology of particlephysics atpresentcol- lider energies, the mass of the Higgs boson in the SM is not protectedagainstquadraticallydivergentquantum-loopcorrections athighenergy. Supersymmetry(SUSY) [11,12]is one exampleof alternativemodelsthataddressthisproblem.InSUSY,suchdiver- gences are cancelledby introducing a symmetry betweenfunda- mentalbosonsandfermions.

Theminimal supersymmetricextensionofthe standardmodel (MSSM)[13,14]predictstheexistenceoftwoHiggsdoubletfields.

Onedoublet couples to up-typeandone to down-typefermions.

AfterEWSB, fivephysical Higgsbosons remain: a CP-oddneutral scalarA,two chargedscalarsH^±,andtwoCP-evenneutralscalar particlesh and H.Theneutralbosons h,A,andH,willbe gener- icallyreferredto asφcollectivelyinthispaper,unlessdifferently specified.

 E-mailaddress:[email protected].

Atlowestorderinperturbationtheory,theHiggssectorinthe MSSMcanbedescribed intermsoftwofreeparameters:m_A,the massoftheneutralpseudoscalarA,andtanβ,theratioofthevac- uum expectationvaluesofthetwoHiggsdoublets.Themassesof the other fourHiggs bosons can be expressed in terms of these twoparametersandothermeasuredquantities,suchasthemasses mW and mZ of the W and Z bosons, respectively. In particular, themassesoftheneutralMSSMscalarHiggsbosonsH andh are given[13]by

m_H,h

=



1 2



m²_A

+

^m2Z

± 

m²_A

+

^m2Z



2

−

^4m2_A^m2_Z^cos22

β 

1/2



^1/2

.

(1)

The Aand H bosonsare degenerate inmass above140 GeV and forsmall cosβ (large tanβ) values.Thisexpression alsoprovides an upperbound onthemassofthelightscalarHiggsboson,cor- responding to m_h≤^mZ|^{cos 2}β|^{. The value can become as large} as mh≈135 GeV once radiative corrections are taken into ac- count[15].

The main production mechanisms for the three neutral φ bosons at theLHC are the associated productionwith bb quarks (AP), given atthe leading order by the Feynman diagram shown inFig. 1(top),andthegluon fusion(GF)process,showninFig. 1 (bottom)[16–18].TheGFprocesswithvirtualtorbquarksinthe http://dx.doi.org/10.1016/j.physletb.2015.11.042

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

Fig. 1. Leading-orderdiagramsforthemainproductionprocessesofMSSMHiggs bosonsattheLHC(top)inassociationwith bb productionand(bottom)through gluonfusion.

loop isdominantatsmallandmoderatevalues oftanβ. Atlarge tanβ thecouplingofφ todown-typequarksisenhancedrelative to theSM [19] andtheAP process becomes dominant. Similarly, thecouplingoftheφbosontochargedleptonsisalsoenhancedat largetanβ.

This paper reports on a search for the MSSM neutral Higgs bosons produced eitherby the APorGFmechanisms, wherethe Higgs bosons decay via φ→

μ

⁺

μ

⁻. The analysis is sensitive to allthe threebosons, h,H,andAinthe massrangebetween115 and300 GeV. The search is performedby theCMS collaboration usingdatarecordedin ppcollisions attheLHC,corresponding to anintegratedluminosityof5.1 fb⁻¹at√

s=^{7 TeV and19.3 fb−1at}

√s=^{8 TeV.The common}experimental signatureofthetwo pro- cessesisapairofoppositelychargedmuonswithhightransverse momentum(p_T)andasmallimbalanceofp_T intheevent.TheAP processischaracterizedbythepresenceofadditionaljetsoriginat- ingfrombquarks(bjets),whereastheeventswithonlyjetsfrom light quarksorgluonsare sensitive tothe GFproductionmecha- nism.Thepresenceofasignalwouldbecharacterizedbyanexcess ofeventsoverthebackgroundinthe dimuoninvariantmass cor- respondingtotheφmassvalue.

Although the product of the cross section and the branching fractionforthe

μ

⁺

μ

⁻channelisafactor10³ smallerthanforthe corresponding

τ

⁺

τ

⁻finalstate,themuonpaircanbefullyrecon- structed,andtheinvariantmasspreciselymeasuredby exploiting the excellent muon momentum resolution of the CMS detector.

SearchesfortheMSSMHiggsbosonshavebeenperformedatLHC bytheLHCbexperimentinthe

τ

⁺

τ

⁻finalstateatlargepseudora- pidityvalues[20],theATLAS experimentinthe

μ

⁺

μ

⁻ and

τ

⁺

τ

⁻

channels [21,22], andby the CMSexperiment in the

τ

⁺

τ

⁻ [23]

andbb[24,25]finalstates.LimitsontheexistenceofMSSMHiggs bosonswerealsodeterminedatTevatron[26–29]andatLEP[30].

Traditionally,searchesforMSSMHiggsbosonsarepresentedin the context ofbenchmark scenarios that describe the mass rela- tion among the three neutral MSSM Higgs bosons, their widths, andcrosssections.Eachscenarioassignswelldefinedvaluestothe relevantparametersoftheMSSM,exceptmA andtanβ,whichare left free to vary. The m^max_h benchmark scenario [19,31] provides m_h valuesaslarge as135 GeV, andtheweakestboundsontanβ forfixedvaluesofthetopquarkmass.Forthisreason,ithasbeen usedinmostofthepreviouslyquotedanalyses topresentthere- sultsfromMSSMHiggsbosonsearches.However,withintheMSSM thenewly discoveredstate withamassof125 GeVcanbe inter- pretedasthelightCP-evenHiggsboson,h[32].Inthiscase,alarge

partofthemA– tanβ parameterspaceisexcludedwithinthem^max_h scenario,andnewbenchmarkswerethereforeproposed inwhich theMSSMparametersareadjustedtohavemhintheinterval122 to 128 GeV,but withawider range oftanβ andmA values[19, 31,32]. To do this, the m^max_h scenario was reformulated in two versions,m^mod_h ⁺ andm^mod_h ⁻, corresponding todifferent valuesof thetopsquarkmixingparameter.Otherrecentlyproposedscenar- ios[31] arethelight topsquark(lightstop)model,whichresults inamodifiedGFrate,andthelighttauslepton(lightstau)model, which yields a modified h→

γ γ

branching fraction. Such mod- elsareexpectedmainlytoaffecttheHiggsbosonproductioncross sectionandnotthekinematicpropertiesoftheevents.A listofthe parametersofthevariousscenarioscanbefoundinRef. [23].The results presentedin thispaperare obtainedin theframework of theMSSMm^mod_h ⁺scenario.Comparisonsarealsomadewithother benchmarks.

2. TheCMSdetectorandeventreconstruction

The central feature of the CMS apparatus is a superconduct- ing solenoidof6 m internal diameter,providing amagneticfield of3.8 T.Withinthe solenoidvolumeare asiliconpixel andstrip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrassandscintillatorhadron calorimeter(HCAL),eachcom- prised ofa barrelandtwo endcapsections.Muonsaremeasured ingas-ionizationdetectorsembeddedinthesteelflux-returnyoke outside the solenoid. Forward calorimetry extends the coverage providedby thebarrelandendcapdetectorsuptopseudorapidity

|

η

_|<5.AdetaileddescriptionoftheCMSdetector,togetherwitha definitionofthecoordinatesystemandkinematicvariables,canbe found inRef.[33].TheCMSofflineeventreconstruction createsa globaleventdescriptionusingtheparticleflow(PF)technique[34].

The PF eventreconstruction attemptsto reconstruct andidentify eachparticlewithanoptimizedcombinationofallsubdetectorin- formation. The missing pT vector is definedasthe projection on the planeperpendicular tothebeams ofthenegative vectorsum ofthemomentaofallreconstructedparticlesinanevent.Itsmag- nitudeisreferredtoasE^miss_T .

An average of 9 and 21 pp collisions take place in any LHC bunch crossing, respectivelyat7 and8 TeV, becauseofthe large luminosity ofthemachineandthesizeofthetotalinelasticcross section. These overlapping events (pileup) are characterized by small-p_T tracks, compared to the particles produced in a φ→

μ

⁺

μ

⁻event,andtheirpresencecandegradethedetectorcapabil- itytoreconstructtheobjectsrelevantforthisanalysis.Theprimary vertexischosen fromall reconstructedinteractionverticesasthe one withthe largestsumin thesquaresof the pT of theassoci- atedtracks.Thechargedtracksoriginatingfromanothervertexare thenremoved.

Offline jet reconstruction is performedusing the anti-kT clus- teringalgorithm [35,36]witha distanceparameterof0.5.The jet momentum isdefinedby thevectorialsumofallthe PFparticles momenta in thejet, andfound in simulation tobe within 5% to 10%ofthetruehadron-levelmomentum,withsome p_T and

η

de- pendence.Extraenergycomingfrompileupinteractionsaffectsthe momentummeasurement.Correctionstothemeasuredjetenergy arethereforeapplied.Theyarederivedfromeventsimulation,and confirmedwithin-situmeasurementsusingenergybalanceindijet andZ/photon+^{jetevents[37].}

Muonsaremeasuredinthepseudorapidityrange|

η

|<2.4,us- ingdetectionplanesbasedonthreetechnologies:drifttubes,cath- odestripchambers,andresistive-platechambers.Matchingmuons totracksmeasuredinthesilicontrackerprovidesrelativepT reso- lutionsformuonswith20<p_T<100 GeV of1.3–2.0%inthebarrel

Table 1

ThemAandtanβvaluesusedtogeneratesignalsamples.

mA(GeV) mAstep (GeV) tanβ tanβstep

115–200 5 5–55 5

200–300 25 5–55 5

300–500 50 5–55 5

andbetterthan6%intheendcaps.The pT resolutioninthebarrel isbetterthan10%formuonswithpT upto1 TeV[38].

3. Simulatedsamples

Simulatedsamplesareused tomodel thesignal andtodeter- minetheefficiencyofthesignalselection.Backgroundsamplesare alsosimulatedtooptimizetheselectioncriteria.Thenormalization anddistributionofthebackgroundeventsaremeasuredfromdata.

Thesignal samples aregenerated usingthe MonteCarlo(MC) eventgenerator pythia 6.424[39]forawiderangeofmAandtanβ values,aslistedinTable 1,fortheAPandtheGFproductionmech- anisms.The φ production cross sectionsandtheir corresponding uncertaintiesareprovidedbytheLHCHiggsCrossSectionWorking Group[16–18].ThecrosssectionsfortheGFprocessinthem^max_h scenario are obtained using the HIGLU program [40,41], based on next-to-leadingorder (NLO) quantum chromodynamics (QCD) calculations.The sushi program[42] isusedfortheother bench- marks.FortheAPprocess,thefour-flavorNLOQCDcalculation[43, 44]andthefive-flavor next-to-next-to-leadingorder(NNLO) QCD calculationareimplementedin bbh@nnlo[45]andcombinedus- ingthe Santandermatchingscheme[46].TheHiggsYukawa cou- plings computed with the feynhiggs program [47] are used in the calculations. The decay branching fractions to muons in the different benchmark scenarios are obtained with feynhiggs and hdecay[48].Furtherdetailson signalgeneration canbe foundin Refs.[16–18].

Thevalues ofm_h predicted by feynhiggs differtypically by a few GeV from those computed with pythia. The invariant mass spectrumof the h boson istherefore shifted tomatch the feyn- higgsprediction.The smalldifference between pythia and feyn- higgs in assessing the width of the h boson is of the order of 100 MeV, and therefore neglected, since the experimental mass resolution is at least one order of magnitude larger. The pythia parametersusedtosimulatethesignalarethoseforthem^max_h sce- nario.SinceforagivensetofmA andtanβ values,thekinematic propertiesofthefinalstate arethesameforallthescenarios,the simulatedsamplesbasedonthem^max_h benchmarkarealsousedto checkthevalidityoftheothermodels.Furtherdetailsonthispro- cedure and the related systematic uncertainties are discussed in Section7.

Themain source ofbackground forthe φ production andde- cay to

μ

⁺

μ

⁻ isDrell–Yan muon-pairproduction, q^q¯→^Z/

γ

^∗→

μ

⁺

μ

⁻.Anotherbackgroundisfromoppositelychargedmuonpairs produced indecays of top quarks in t¯t production. Theseevents aresimulatedusingthe MadGraph 5.1[49]generator.Otherback- groundprocessessuchasW^±W^∓,W^±Z,andZZ aregeneratedwith pythia. The MC samples also includesimulated pileup events to reproducetheoverlappingppinteractions presentinthedata.All generated events are processed through a detailedsimulation of theCMSdetectorbasedon Geant4[50]andarereconstructedwith thesamealgorithmsusedfordata.

4. Eventselection

The experimental signature of the MSSM Higgs bosons decay consideredin thisanalysisisa pairofoppositely chargedmuons

Table 2

Eventselection:thecriterialistedintheupperpartofthetablearecommontothe C1andC2categories,thatarethenmutuallyexclusive.

Common selection

Single muon trigger pT>24 GeV+isolation+ |η| <2.1 Event primary vertex |zPV| <24 cm

Muon selection 2 opposite-charged muons,

pT>24 GeV,|η| <².1, track quality cuts,

|^dxy| <⁰.02 cm,|^dz| <⁰.1 cm, angular matching with trigger, isolation

E^miss_T E^miss_T <35 GeV

Category C1

b tag 1 or 2 b-tagged jets,

p^jet_T >20 GeV,|η^jet| <2.4 Category C2

No b tag Events with no b-tagged jets

with high pT. The invariant mass of the paircorresponds to the massoftheφbosonwithintheexperimentalresolution.Moreover, theprocessischaracterizedbyasmallE^miss_T intheevent.Iftheφ bosonisproducedinassociationwithabb pair,thepresenceofat leastonebquarkjetisexpected.

Thedetailsoftheeventselectionarelistedbelow,andsumma- rizedinTable 2.Theeventsareselectedusingasingle-muontrig- ger,whichrequiresatleastone isolated muonwith pT>24 GeV inthepseudorapidityrange|

η

|<2.1.Thedistanceoftheprimary vertex along the z axisfrom the nominalcentre of the detector must be |^zPV|<24 cm. Muon candidates are reconstructed and identifiedusingboththeinner trackerandthemuondetectorin- formation.Theselectedeventsmusthaveatleasttwooppositely- chargedmuoncandidates,each withpT>25 GeV.Ineventswith more than two muon candidates, the two withopposite charges andthe highest pT are retained.The

η

of both muoncandidates ischosen tomatchthetriggeracceptance.Eachmuontrackmust haveatleastonehitinthepixeldetector,morethanfiveoreight layers with hits inthe tracker, respectively, for the 8 and7 TeV data and a directional matching to hits in at leasttwo different muondetectorplanes.Inadditiontheglobalfittothehitsofthe muon candidate must include at least one hit in the muon de- tector. The

χ

²/dof of the global fit of the muon track must be smallerthan 10.Theserequirementsensure agoodmeasurement ofthemomentum,andsignificantlyreducetheamountofhadronic punch-through background [38]. Toreject cosmic ray muons, the transverseandlongitudinalimpactparametersofeachmuontrack mustsatisfy the requirements|^dxy|<0.02 cm and |^dz|<0.1 cm, respectively. Both parameters are definedrelative to the primary vertex.Toensurethatthetriggermuoncandidateiswell-matched to the reconstructed muon track, at least one of the two muon tracks isrequiredto matchthe directionofthetrigger candidate within a cone R=⁰.2, where R=√

[^b](

η

)²+ (

ϕ

)² is the distancebetweenthemuontrackandthetriggercandidatedirec- tioninthe

η

–

ϕ

plane,with

ϕ

beingtheazimuthalanglemeasured inradians. Bothreconstructed muoncandidatesmust fulfillisola- tion criteria. A muon isolation variable is constructed using the scalar sum of the pT of all PF particles, except the muon, re- constructed within a cone R=⁰.4 around the muon direction.

Acorrection isapplied to accountforthe possiblecontamination fromneutralparticlesarising frompileup interactions.Amuon is acceptedifthevalueofthecorrectedisolationvariableislessthan 12%ofthemuonpT.

A selection based on E^miss_T provides good separation between signal eventsand t¯t background,in thecaseof leptonic decayof

Fig. 2. TheE_T^missdistributionforeventswithareconstructeddimuoninvariantmass mμ⁺μ⁻>60 GeV indataandinsimulatedeventsat√

s=7 (top)and√ s=8 TeV (bottom).TheexpectedcontributionisalsoshownforasignalatmA=150 GeV and tanβ=^30.

the W boson from top decay. The E^miss_T distributions for events collectedat√

s=^{7 and8 TeVareshowninFig. 2foreventswith} areconstructedmuon pairwithinvariant massmμ⁺μ⁻>60 GeV.

The background contributions from SM processes are superim- posed. For illustration, the expected distribution for signal pro- cesses is also shown formA=150 GeV and tanβ=^{30. Studies} performedusing the simulation show that the E^miss_T distribution forsignal eventsdoesnot vary significantly fordifferentmA and tanβ assumptions,andindicatethat theselection E^miss_T <35 GeV provideshighestsensitivityforsignalatbothcentre-of-massener- gies.

Thereconstructedjetsarerequiredtohavetransversemomenta p^jet_T >20 GeV within the range|

η

_|<2.4. A multivariate analysis techniqueisusedtoremovejetsfrompileupinteractions[51].Tag- gingof bquarks injetsrelieson thecombined secondary-vertex discriminator [52],based on the reconstruction of the secondary vertex from weakly decaying b hadrons. The discriminant b_disc isconstructedfromtracks andsecondary vertexinformation,and helpsto distinguishjets containing b,c,or light-flavourhadrons.

Jetswithanassociatedbdisc>0.679 areconsideredtobebtagged.

Thisvaluerepresentsagoodcompromisebetweenefficiencytotag bjetsinsignaleventsfromAP(≈^{80%)andmistagging}probability forlight-quarkjets(≈^{1%).Fig. 3showsthe}distributionofb_disc in

Fig. 3. Thedistributionofthebtaggingdiscriminant,bdisc,foreventsthatsatisfythe selectionE_T^miss<35 GeV indatacollectedat√

s=^{7 (top)and}√

s=8 TeV (bottom).

Foreachevent,thelargestvalueofbdiscisselected.

eventsthat satisfy theselection E^miss_T <35 GeV,forthedatacol- lected inthetwobeamenergies.Foreachevent,thelargestvalue of bdisc is selected.The distribution ofsignal eventsfrom theAP process for mA=150 GeV and tanβ=^{30 is} superimposed. Jets originated from b quark fragmentation tend to be emitted more forwardinsignaleventsthan fort¯t,thus resultinginalowerob- served b-jetmultiplicity.Forthisreasonthet¯t backgroundisfur- thersuppressedbyrejecting eventswithmorethantwob-tagged jets, withoutsignificantly affectingtheselectionefficiencyforsig- nal.

Theeventsaresplitintotwomutually-exclusivecategories.The first category(C1)contains eventswithatleastonejet identified asoriginatedfromb-quarkfragmentation(btagged),andprovides highest sensitivity to AP production channel. Events that do not containb-taggedjetsare assignedtocategory2(C2),andprovide sensitivityto GFproduction.The dimuoninvariant massdistribu- tions for the C1 and C2 categories are shown in Fig. 4 for data and simulated events for both centre-of-mass energies. The dis- tributions expected forMSSM Higgs bosons with m_A=^{150 GeV} and tanβ=^{30, derived from the mmod}_h ^{+ scenario are also given} forcomparison.Adoublepeakstructurearound125and150 GeV appears intheC2category,duetothehboson andA+^{H bosons,} respectively.The lowerpeakisnot visibleinC1,astheh produc- tionissuppressedintheAPmechanismrelativetotheGFprocess.

Fig. 4. ThedimuoninvariantmassdistributionforeventsthatbelongtoC1(upperleft)andC2category(upperright),fordataandsimulatedeventsat√

s=7 TeV.The correspondingquantitiesareshownfor√

s=8 TeV (lowerleftandlowerright).Theexpectedcontributionstosignalassumingthem^mod_h ⁺scenarioformA=150 GeV and tanβ=^{30 aredisplayedfor}comparison.

5. Signalselectionefficiency

WhilethecalculationsfortheMSSMcross sectionsperformed inthenarrow-widthapproximationrefertotheon-shellHiggsbo- son production,at large values of m_A and tanβ the convolution ofthe larger intrinsicsignal widths withthe parton distribution functions(PDF)resultsinanon-negligiblefractionofsignalevents producedsignificantlyoff-shell.Eventswithinvariantmasssignifi- cantlysmallerthanitsnominalvaluehavealower reconstruction efficiency than those produced near the mass peak. For consis- tency, we define signal efficiency as the probability for a signal eventwiththegeneratedinvariantmassclosetoitsnominalvalue to be reconstructed and pass all selection requirements of this analysis.Theclosenessisdefinedusingawindowofsizeequalto 3timesthe intrinsicsignal width(anuncertaintyassociatedwith thisdefinitionis evaluated usinga windowof 5times its width, asdiscussedinSection7).Withthisdefinition,theproductofthe MSSMHiggsbosonproductioncrosssection,luminosityandsignal efficiencyprovidesthenormalizationfortheHiggsbosonproduced near on-shell. The full predicted rate of signal events also con- tains an additional off-shell contribution, which varies with mA andtanβ andislessthan 5% formA<250 GeV and tanβ <15, andcanbeaslargeas15%form_A=300 GeV andtanβ=^30.

Additional corrections are applied to the signal efficiency to takeintoaccount differencesbetweendataandsimulationinthe muon trigger, reconstruction, and isolation efficiencies. A correc-

tionisalsoappliedtoaccountforknowndata-simulationdiscrep- ancies inthe btaggingefficiencyandmistaggingprobability.The correctionsaresummarizedby aweight factor,whichisassigned toeach signal event.The averageoftheweight factorscomputed overalltheeventsisveryclosetoone,reflectingthefactthatthe simulationdescribesthedatawithgoodaccuracy.

Fig. 5 showsthe signal efficiencyat √

s=^{8 TeV for AP (top)} andGF(bottom)processaftercombiningthetwoeventcategories C1andC2.Theefficienciesat√

s=^{7 TeV aresimilar.Thebandin} thefigurerepresentsthevariationoftheefficiencyduetothelim- itedstatistics ofthesamplesused.TherelativeamountofAPand GFevents inthe two eventcategoriesvarieswithm_A and tanβ, since the production crosssections ofthe two processes depend ontheseparameters.Forexample,inthecasemA=150 GeV and tanβ=^{30, more than 90% of the signal events in C1 would be} fromAPproduction,andabout60%inC2.FormA=150 GeV and tanβ=^{5,wherethe GF}contribution becomesmore relevant,the contentofAPeventswouldbe60%inC1andonly15%inC2.

6. Fitprocedure

TheproceduredescribedbelowisappliedseparatelytoC1and C2 events. The event selection criteria are applied to the simu- latedsamples listedin Table 1. Foreach sample, andforeach of the threeφ bosons, theinvariant massdistribution ofthe events thatpasstheeventselectionisapproximatedwithaBreit–Wigner

Fig. 5. SignalefficiencyfortheAPprocessat√

s=8 TeV,shownseparatelyforthethreeφbosontypes,(upperleft)h,(uppercentre)H,and(upperright)A,asafunction ofmA.ThecorrespondingefficiencyfortheGFproductionprocessisshowninthelowerrow.ThecontributionsfromthetwoeventcategoriesC1andC2arecombined.

Theresultsareintegratedovertanβ,sincetheefficiencydoesnotstronglydependonthisquantity.Thebandshowsthechangeinefficiencyduetothelimitednumberof simulatedevents.

functionconvolvedwithaGaussian,thataccountsfordetectorres- olution. This analyticalexpression provides a good description of thesignal shapeforall them_A andtanβ values.The threefunc- tionsaredenotedF_h,FH,andFA,andcontainthemassandwidth oftheBreit–WignerandthewidthoftheGaussianasfreeparam- eters.ThefunctionFsigrepresentstheexpectedsignalyield,andit isalinearcombinationofthethreefunctionsdescribedabove:

Fsig

=

whFh

+

wHFH

+

wAFA

,

(2) wherew_h,wH,andwA,arethenumberofeventscontainingh,H, andAbosons,respectively, calculatedaccordingtotheir expected productioncrosssections.Anexampleofthisprocedureisshown inFig. 6(top)form_A=150 GeV and tanβ=^{30.Thehighestpeak} represents the superposition of the contributions from H and A bosons,thatinthiscasearealmostdegenerateinmass.

Since the Drell–Yan muon pair production is the dominant backgroundprocess,itismodeledbyaBreit–Wignerfunctionplus aphoton-exchangeterm,whichisproportionalto1/m²μ⁺μ⁻.Defin- ingm=mμ⁺μ⁻,thefunctionF_bkg becomes:

F_bkg

=

^eλm

⎡

⎣

^fZ

N₁^norm

1

(

m

−

^mZ

)

²

+

₄^Z2

+ (

1

−

^fZ

)

N^norm₂

1 m²

⎤

⎦ ,

(3)

wheree^λm describestheeffects ofthePDF, andthe N^norm_i terms correspond to the integral ofthe corresponding functionsin the chosenmassrange.Thequantity fZrepresentsthecontributionof theBreit–Wigner termrelativetothe photon-exchangeterm. The quantitiesλand fZ arefreeparametersofthefit.Theparameters Z andm_ZaredeterminedseparatelyfortheC1andtheC2events

from a fitto themμ⁺μ⁻ distributionin the massrange ofthe Z bosonbetween80and120 GeV.Thefitprovidestheeffectiveval- uesofsuchquantities,thatincludedetectorandresolutioneffects for each set of data. Their valuesare used in F_bkg andare kept constantinthefit.

Alinearcombinationofthetwofunctionsfortheexpectedsig- nal andbackgroundisthenused inan unbinnedlikelihoodfit to thedata:

F_fit

= (

¹

−

^fbkg

)

F_sig

+

^fbkgF_bkg

.

(4) The parametersthat describethesignal aredetermined inthe fitofthesimulatedsignaltoEq.(2),foreachpairofmA andtanβ values.Subsequently,theyarefixedinFfit,wherethefreeparame- tersarethequantitiesλ, fZ,and f_bkg.Thefractionofsignalevents is defined as fsig= (¹− ^fbkg). The data are fittedto Ffit in the mass range from 115to 300 GeV for each point in the m_A and tanβ parameterspace. Asanexample,thefittothedataofC2at

√s=^{8 TeV is}illustratedinFig. 6,(bottom),assumingasignalwith mA=150 GeV andtanβ=^30.

7. Systematicuncertainties

Thefollowingsourcesofsystematicuncertaintiesaretakeninto account, and the impact ofone standard deviationchange is re- ported in terms of a variation in the nominal signal efficiency definedinSection5.

The limited number of simulated events introduces an un- certainty in the signal selection efficiency that is at most 2.0%.

The muon trigger, reconstruction, identification, andisolation ef- ficiencies are determined fromdata using a tag-and-probe tech- nique [38].The uncertainty in the triggerefficiency correction is

Fig. 6. InvariantmassdistributionoftheexpectedsignalformA=150 GeV and tanβ=30 (top),andanexampleofthefittothedataat√

s=8 TeV includingthe samesignalassumption(bottom).Thedistributionrepresentstheexpectednumber ofeventsforanintegratedluminosityof19.3 fb⁻¹.Foreachplotthepullofthefit asafunctionofthedimuoninvariantmassisshown.

0.5%,whereas1.0%isassignedtothecombinationofuncertainties inmuonreconstruction andidentification, aswell asonisolation efficiencies.

Asystematicuncertaintyinthepileupmultiplicityisevaluated by changing the total cross section for inelastic pp collisions in simulation.Thecorresponding uncertaintyonthesignalefficiency isatmost0.8%inbothcategories.

Theeventfractionsinthetwocategoriesdependonthebtag- gingefficiencyandthemistaggingprobability.The uncertaintyin thebtaggingefficiencyisestimatedby comparingdataandsim- ulatedeventswithsamples ofenriched b quark contentanddif- ferenttopologies,asdescribedinRef.[52].The uncertaintyinthe efficiencyto detectbjetsisabout3.0%.Similarly,theuncertainty inthemistagging rateisabout10%. Theiroverall contributionto theselection efficiencyis weighted by thefraction ofAPandGF eventsthat are expected in each eventcategory, which depends onmAandtanβ.Thelargestoveralluncertaintyis3.0%forC1,and 0.4%forC2events.

Thejet energyscale uncertaintyis estimatedbysmearing the jetmomentumbya factordependingon pT and

η

ofeachjet, as described in Ref. [37]. The effecton signal selection efficiencyis 4.0% forevents that belong to the C1 and 0.5% for the C2 cate- gories,at√

s=^{8 TeV.For}√

s=^{7 TeV the}correspondingnumbers are3.8% and0.6%.The uncertaintyinthe E^miss_T scaleandresolu- tionisestimatedthrough comparisonsbetweendataandsimula-

Table 3

SourcesofsystematicuncertaintiesforC1andC2eventcategoriesthataffectthe signal efficiencyat √

s=8 TeV.They areexpressed interms ofrelative signal selectionefficiency.Whenthesystematicuncertaintyat√

s=7 TeV differsfrom

√s=^{8 TeV,the}correspondingvalueisquotedinparenthesis.

Source Systematic uncertainty (%)

C1 C2

MC statistics 2.0 2.0

Trigger efficiency 0.5 0.5

Muon efficiency 1.0 1.0

Muon isolation 1.0 1.0

Pileup 0.8 0.8

b tagging 3.0 0.4

Jet energy scale 4.0 (3.8) 0.5 (0.6)

E^miss_T 3.0 (2.0) 3.0 (2.0)

Integrated luminosity 2.6 (2.2) 2.6 (2.2)

PDFs 3.0 3.0

Width correction 1–3 1–5

tion[53,54].Theeffectonthesignalselectionefficiencyis3.0%and 2.0%,thesameforbothcategories,forthesamplewith√

s=^{8 and} 7 TeV,respectively.Theuncertaintyintheintegratedluminosityis 2.6%and2.2%at√

s=^{8 and7 TeV,}respectively[55,56].

UncertaintiesduetothechoiceofPDFsetaffectthesignaleffi- ciency, andare studiedusing thePDF4LHC [57] prescription.The renormalization and factorization scales in the calculations and their changes aresummarized inRefs. [16–18].The effecton the signalselectionefficiencyvariesfrom1.0%to3.0%overthemAand tanβ parameterspace. Thechoiceof3.0%istakenasthesystem- aticuncertainty.

The efficiency is determined for events with generated mass valueswithin awindow ofa factorof3ofthe intrinsicwidthof theHiggsboson,asdescribedinSection5.Thedifferencerelative to the efficiency obtained using a cutoff of a factor of 5 of the intrinsicwidthisassignedasasystematicuncertainty.Theuncer- tainty is between1% to 3% forthe C1 and1% to 5% for the C2 categories.

Table 3lists thesystematicuncertainties thataffectthe deter- minationofsignalefficiency.Theimpactofthesesystematicuncer- taintiesontheexclusionlimitsthatwillbepresentedinSection8 is negligible compared to the statistical uncertainty. All the sys- tematicuncertaintiesinTable 3arecorrelatedforthe√

s=^{7 TeV} and8 TeVdata,withtheexceptionoftheuncertaintiesrelatedto thelimitedMCstatisticsandtheintegratedluminosity.

The uncertainties inthe MSSM cross sections depend onm_A, tanβ,andthescenario,andare providedby theLHCHiggsCross Section Working Group [16–18]. The signal eventsare generated using pythia, assuming the parameters of the m^max_h scenario, as discussed inSection 3.The differentbenchmarksareexpectedto affecttheproductioncrosssection,butnotthekinematicproper- tiesoftheeventsrelatedtoHiggsbosonproductionanddecay.To checkthisassumption,eventsaregeneratedwith pythia usingthe parametersforthem^mod_h ⁺,m^mod_h ⁻,lightstopandlightstaubench- marks, assuming mA=150 GeV and tanβ=^{20. The events are} generatedforboththeGFandtheAPmechanisms,andtheHiggs boson pT andthe E^miss_T of theevents are comparedat generator level for the various benchmark scenarios. No significant differ- encesareobservedinthedistributionsofthesequantities.

Sincethenumberofbackgroundeventsisdeterminedthrough a fittothedata,an additionalsystematicuncertaintyarisesfrom the possibility that the background parametrizationmay not ad- equately describe thedata asa functionof thedimuon invariant mass. Amethod similar to that described inRef. [10] is used to evaluatetheeffect,byestimatingtheuncertaintythroughthebias intermsofthenumberofsignal eventsthat arefound whenfit-

tingthesignal+^{backgroundmodel(asdescribed inSection6)to} pseudo-datagenerated for different alternative backgroundmod- els. Such alternative background parametrizations include Bern- stein polynomials and combinations of Voigtian and exponential functions. Bias estimatesare performed formasspoints between mA=^{115 and300 GeV.Foreachm}Avalue,thelargestbiasamong thetestedfunctionsistakenastheresultinguncertainty.Thebias isimplementedasa floatingadditive contributiontothenumber ofsignalevents,constrainedbyaGaussianprobabilitydensitywith mean of zero and width set to the systematic uncertainty. The width of the Gaussian is the largest systematicuncertainty, and the effectis to increase the expected limit on the presence ofa signalby20%intheregionnearmA=120 GeV andbyabout10%

atlargermassvalues.

Inthe massrangebetween115and300 GeV,that isrelevant forthisanalysis, the mass resolutionis estimatedto be between 1.2and4 GeV.Uncertaintiesinthemuonmomentum determina- tion can affect the invariant mass measurement, and have been carefullystudiedin dataandsimulation[38].The dimuoninvari- antmassresolutionformassesabovethe Zpeakhasbeenprevi- ouslystudied inthesearch fora SMHiggs decayingtoadimuon pair[58].ThemassresolutiondeterminedfromdataattheZmass value is 1 GeV, in excellent agreement withthe prediction from simulation. This value is consistent with the mass resolution of 1.2 GeVthatwe estimatefromsimulationforamassof115 GeV, thatcorresponds tothelower edgeofthe Higgsmassrangecon- sideredinthisanalysis.

Theoverallcapabilityoftheanalysistodetectthepresenceofa signalisverifiedbyintroducingahypotheticalsimulatedsignalin the datausing the shape parametrizationdiscussed inSection 6.

The average measured number of signal events is found to be within1.3% oftheinjectedsignal fortheC1category, andwithin 4.3%fortheC2category.Thesedifferencesareassignedassystem- aticuncertainties.

8. Results

No evidenceofMSSM Higgsbosons productionisobservedin the mass range between 115 and 300 GeV, where the analysis has been performed. Upper limits at 95% confidence level (CL) on theparameter tanβ are computedusingthe CLs method[59, 60], which is a modified frequentist criterion, andare presented as a function of m_A. Systematic uncertainties are incorporated as nuisance parameters andtreated according to the frequentist paradigm [61]. The results are obtained from a combination of botheventcategoriesandcentre-of-massenergies.Foreachvalue ofmA,the value oftanβ atwhichthe CLexceeds 95%is chosen todefinetheexclusionlimitonthatm_A.Thisisperformedforall themA values andthe resultsare shownin Fig. 7.These results areobtainedwithin them^mod_h ⁺scenario.Theobservedupperlim- itsrangefromtanβ ofabout15inthelow-mAregion,toabove40 atmA=^{300 GeV.Forlarger valuesofm}A theuncertaintyonthe tanβ upperlimit becomes large,exceeding tanβ=^{50,for which} theMSSMcross-sectionpredictionsarenotreliable.

Acomparison withtheresults obtainedforthe m^mod_h ⁻,m^max_h , lightstopandlightstauscenariosisalsoperformed.Theexclusion limitscomputedwithintheseotherbenchmarkmodelsareallvery similar. Foranyvalue ofm_A,the quantity tanβ=^tanβ_mmod+

h −

tanβscenario representsthedifferenceofthetanβ valuesatwhich the95% CL limit isdetermined ifan alternative scenariois used.

Fig. 8 showsthequantity tanβ asa function ofmA forallthe testedscenarios. FormostmA values,the 95% CLlimitson tanβ computedwithinagivenscenariodifferbylessthanoneunitfrom theresultsobtainedwithinthem^mod_h ⁺ scenario.

Fig. 7. The95%CLupperlimitontanβasafunctionofmA,aftercombiningthedata fromthetwoeventcategoriesatthetwocentre-of-massenergies(7and8 TeV).The resultsareobtainedintheframeworkofthem^mod_h ⁺benchmarkscenario.

Fig. 8. Comparisonofthe95%CLexclusionlimitsontanβobtainedwithinMSSM benchmark models, as a function ofmA. The quantity tanβ=^tanβ_mmod+

h −

tanβscenariorepresentsthedifferenceintanβatwhichthe95%CLlimitisobtained foralternativescenarios.

Limits on the productioncross section times decay branching fraction

σ

B(φ →

μ

⁺

μ

⁻) for a generic single neutral boson φ aredetermined.Inthismodelindependentanalysisnoassumption is made on the cross section, mass, andwidth of the φ bosons, which is sought as a single resonance with mass mφ. The anal- ysis isperformed assuming thenarrow widthapproximation, for whichtheintrinsicwidthofthesignalissmallerthantheinvari- ant massresolution.For thispurposethesimulated signal ofthe A boson for the case tanβ =^{10 is used as a template to com-} pute thedetectionefficiencyfora generic φboson decayingto a muonpair.Thesingleφbosonisassumedtobeproducedentirely either via the AP or the GFprocess, and the search for a single resonance with massm_φ is performed. The 95% CL exclusion on

σ

B(φ →

μ

⁺

μ

⁻) is determined as a function of m_φ, separately for the two production mechanisms. The combination of events belonging to C1 andC2 is shown in Fig. 9, assuming the φ bo- son is produced either via the AP or the GF process. Only data collected at√

s=^{8 TeV are used,asthey providea bettersensi-} tivity because of the higher luminosity. In addition, since the φ production cross section depends on the centre-of-mass energy, a combination with the 7 TeV results would introduce a model

Fig. 9. The95%CLlimitontheproductofthecrosssectionandthedecaybranching fractiontotwomuonsasafunctionofmφ, obtainedfromamodelindependent analysisofthedata.Theresultsreferto(top)bquarkassociatedand(bottom)gluon fusionproduction,obtainedusingdatacollectedat√

s=^{8 TeV.}

dependenceinthedescriptionofthecrosssectionevolutionwith energy.

9. Summary

Asearch has beenperformed forneutralMSSM Higgs bosons decayingto

μ

⁺

μ

⁻ frompp collisionscollected withtheCMSex- perimentat√

s=^{7 and8 TeV,}corresponding tointegratedlumi- nositiesof5.1and19.3 fb⁻¹,respectively.Theanalysisissensitive to Higgs boson production via gluon fusion, and via association witha bb quark pair. The results ofthe search, whichhas been performedinthemassrangebetween115and300 GeV,arepre- sentedinthe m^mod_h ⁺ framework of theMSSM.With noevidence forMSSM Higgs boson production, this analysisexcludes at 95%

CL values of tanβ larger than 40 for Higgs boson masses up to 300 GeV.Comparisonswithm^mod_h ⁻,m^max_h ,lightstop,andlightstau scenariosarealsopresented,andofferverysimilarresultsrelative to them^mod_h ⁺ benchmark. Limits are determined on the product ofthecrosssectionandbranchingfraction

σ

B(φ →

μ

⁺

μ

⁻)fora genericneutralboson φat √

s=^{8 TeV, withoutany}assumptions ontheMSSMparameters.Inthiscasethe φbosonisassumedto beproducedeitherinassociationwithabb quarkpairordirectly throughgluonfusion,andsoughtasasingleresonancewithmass mφ.Exclusionlimitsareinthemassregionfrom115to500 GeV.

Form_φ=^{500 GeV,values}

σ

B(φ →

μ

⁺

μ

⁻)>4 fb areexcludedat 95%CLforbothproductionmechanisms.Thesearethemoststrin- gentresultsinthedimuonchanneltodate.

Acknowledgements

WecongratulateourcolleaguesintheCERNacceleratordepart- ments for the excellent performance of the LHC and thank the technicalandadministrative staffsatCERN andatother CMS in- stitutes for their contributions to the success of the CMS effort.

Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses.

Finally, we acknowledge the enduring support for the construc- tion and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria);

F.R.S.- FNRS andFWO(Belgium);CNPq,CAPES,FAPERJ,andFAPESP (Brazil);MES(Bulgaria);CERN;CAS,MOST,andNSFC(China);COL- CIENCIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);MoER, ERC IUT and ERDF (Estonia); Academy ofFinland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India);IPM(Iran); SFI(Ireland);INFN (Italy); NRF andWCU (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia);

CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu- gal);JINR(Dubna);MON,RosAtom,RASandRFBR(Russia);MESTD (Serbia);SEIDIandCPAN(Spain);SwissFundingAgencies(Switzer- land); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thai- land);TUBITAKandTAEK(Turkey);NASUandSFFR(Ukraine);STFC (UnitedKingdom);DOEandNSF(USA).

Individuals have received support from the Marie-Curie pro- gramme and the European Research Council and EPLANET (Eu- ropean Union); the Leventis Foundation; the A. P. Sloan Founda- tion; the Alexander von Humboldt Foundation; the Belgian Fed- eral Science Policy Office; the Fonds pour la Formation à la Recherchedansl’Industrieetdansl’Agriculture(FRIA-Belgium);the AgentschapvoorInnovatiedoorWetenschapenTechnologie(IWT- Belgium); theMinistry ofEducation, YouthandSports (MEYS) of theCzechRepublic;theCouncilofScienceandIndustrialResearch, India; the HOMING PLUS programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund;the CompagniadiSan Paolo(Torino); the Consorzioper la Fisica (Trieste); MIURproject20108T4XTM (Italy);the Thalisand Aristeia programmes cofinanced by EU-ESF andthe Greek NSRF;

the National Priorities Research Program by Qatar National Re- search Fund;theRachadapisekSompot FundforPostdoctoral Fel- lowship,ChulalongkornUniversity(Thailand);andtheWelchFoun- dation.

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