A search for pair production of new light bosons decaying into muons

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Physics Letters B

www.elsevier.com/locate/physletb

A search for pair production of new light bosons decaying into muons

.CMS Collaboration

^

CERN,Switzerland

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

Articlehistory:

Received31May2015

Receivedinrevisedform20October2015 Accepted25October2015

Availableonline3November2015 Editor:M.Doser

Keywords:

LHC CMS Muon NMSSM Hiddensectors Darkmatter

Asearchforthepairproductionofnewlightbosons,eachdecayingintoapairofmuons,isperformed with the CMS experiment at the LHC, using adataset corresponding to an integrated luminosity of 20.7 fb⁻¹ collectedinproton–proton collisions atcenter-of-mass energy of√_s

=^{8 TeV. No excessis} observedinthedatarelativetostandardmodelbackgroundexpectationandamodelindependentup- perlimitontheproductofthecrosssection,branchingfraction,andacceptanceisderived.Theresults are comparedwithtwo benchmarkmodels,thefirstoneinthecontextofthenext-to-minimalsuper- symmetricstandardmodel,andthesecondoneinscenarioscontainingahiddensector,includingthose predictinganonnegligiblelightbosonlifetime.

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

1. Introduction

In July 2012 the ATLAS and CMS Collaborations at the CERN LHC announced thediscovery ofa particle [1–3] with properties consistent with the standard model (SM) Higgs boson [4–7]. Di- rectmeasurements oftheproductionanddecayratesofthe new particle,using SM decaychannels, haveso far played a key role in determining whether or not it is indeed consistent with the SM predictions.However,substantially increasing theprecision of thesemeasurements will requirefurtherdata. Searchesfor Higgs bosonsthrough productionmechanismsnotpredictedby theSM, ordecaymodesinvolvingparticlesnotincludedintheSM,provide acomplementaryapproachandhavetheadvantageofprobingspe- cifictypesofnewphysicsmodelswiththeexistingdata.

This letter presents a search for the pair production of new light bosons (denoted as ‘a’) decaying to pairs of isolated, op- positely charged muons (dimuons). One production mechanism for thesenew bosons is in the decay chain of a Higgs boson h, which can be SM-like or not: h→^2a+^X→⁴

μ

+^{X, where X} denotes possible additional particles from cascade decays of the Higgs boson. A range of new physics scenarios predict this de- caytopology,includingthenext-to-minimalsupersymmetricstan- dard model(NMSSM)[8]and modelswithhidden (ordark) sec- tors[9–11].

 E-mailaddress:[email protected].

The NMSSM is an extension of the minimal supersymmet- ric standard model (MSSM) [12,13] that includes an additional gauge singletfield. It resolves the so-called

μ

problem [14] and significantly reduces the amount of fine tuning required in the MSSM [15]. The NMSSM Higgs sector consists of three CP-even neutralHiggsbosons h1,2,3,twoCP-oddneutralHiggsbosonsa1,2 andapairofchargedHiggsbosonsh^±.Theh1 andh2 candecay via h_1,2→^2a1,where eitherthe h₁ or h₂ can be the bosonob- served at125 GeV.The a1 bosoncanbe light andcoupleweakly to SM particles with a coupling to fermions proportional to the fermion mass.Thereforeit canhavea substantial branchingfrac- tion B(^a1→

μ

⁺

μ

⁻)ifits massis withintherange2mμ<m_a1<

2mτ [16,17](benchmark model1inthisletter).A searchforfinal statescontainingmuonpairsprovidessensitivitytomodelsofthis form.

Supersymmetry (SUSY) models withdark sectors (dark SUSY) offer an explanation for the excess in the ratio of the positron flux tothe combinedflux ofpositronsandelectrons observedby the satellite experiments [18–20] in primary cosmic rays aswell as predict cold dark matter with a scale of O(1 TeV). A simple realizationof thesemodels includesa newU(1)D symmetry (the subscript “D”stands for“Dark”)whichisbrokenandgivesriseto massivedarkphotons(denotedas

γ

D).Kineticmixingofthenew U(1)DwiththeSMhyperchargeU(1)Yprovidesasmallmixingbe- tween

γ

D and the SM photon which allows

γ

D to decay to SM particles[21].Dependingonthevalue

ε

ofthekineticmixing,the

γ

Dmayalsobelong-lived.Thelackofanantiprotontoprotonratio excessofthemagnitudesimilartothepositronexcessinthemea- http://dx.doi.org/10.1016/j.physletb.2015.10.067

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

surementsofthecosmicrayspectrumconstrainsthemassof

γ

Dto belessthantwicethemassoftheproton[22].Ifthehiddensec- tordirectlyor indirectlyinteractswiththe Higgsfield, a number ofpossiblescenariosmayberealized.Onesuchscenario,denoted in thisletter as benchmark model 2, is a model of SUSY where theSM-like Higgsbosoncandecayvia h→²ⁿ1,wheren1 isthe lightestneutralinointhevisible(asopposedtohidden)partofthe SUSYspectrum.Then₁ candecayvian₁→ⁿD+

γ

D,wheren_Disa darkneutralinothatescapesdetection.Assumingthat

γ

Dcanonly decaytoSM particles,thebranching fractionB(

γ

D→

μ

⁺

μ

⁻)can beaslargeas45%,dependingonthemassof

γ

D[11].

Previoussearches forpairproduction ofnewlight bosons de- cayingintodimuonswereperformedattheTevatron[23]andthe LHC [24,25]. Searches for associated production of the light CP- oddscalarbosons havebeenperformedat e⁺e⁻ colliders[26,27]

andthe Tevatron [28]. Direct a₁ productionhas been studied at theLHC[29],butthisisheavily suppressedby thetypically very weakcouplingsofthenewbosonstoSMparticles.Theconstraints onthe allowed NMSSM parameter spaceare driven by the mea- surements of relic density by WMAP [30] and more recently by PLANCK[31],whilespecificallyfortheHiggssectorthemostrele- vantmeasurementscomefromLEP[32–37],LHCmeasurementsof theSM-likeHiggsproperties,anddirectsearchesforh→^{aa [25].}

In the framework of dark SUSY, experimental searches for dark photonshavefocused ontheir productionattheendofSUSYcas- cadesattheTevatron[38–40] andtheLHC[41,42]. Searchesata rangeoflowenergye⁺e⁻colliders(KLOE[43],BaBar[44]),heavy- ioncolliders (PHENIX [45]), fixed-target experiments (APEX [46], A1atMAMI[47],HADES[48]), aswell ascosmologicalmeasure- ments[49–51]andothers[52–56]provideconstraintsoncomple- mentaryregionsoftheavailableparameterspace.

Results are presented in this Letter in the context of the twobenchmark scenarios discussedearlier, one inthecontext of NMSSMandanotheroneintheframeworkofdarkSUSYscenarios.

However,the searchhasbeen designedtobe independentofthe detailsofthesetwo specificmodels,andtheresultscanbeinter- pretedinthecontextofothermodelspredictingtheproductionof thesamefinal states.Comparedtothe previous version[25],the presentanalysishasbeenredesignedtobesensitivetosignatures withthe intermediate bosons traversing a nonnegligible distance beforedecayingintoapairofmuons.Suchsignaturescanbereal- izedindarkSUSYmodelsifthemixingofthedarkphotonwithits SMcounterpartissufficientlyweak.Inaddition,thepresentanaly- sisusesadatasetfourtimeslargerthanthepreviousanalysis,and atahighercenter-of-massenergy,furtherextendingthereachfor signatureswithpromptmuons.

2. TheCMSdetector

This search is based on a data sample corresponding to an integratedluminosity of 20.7 fb⁻¹ ofproton–proton collisions at a center-of-mass energy √

s=^{8 TeV, recorded by the CMS de-} tector in 2012. The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magneticfield of 3.8 T.Withinthe solenoidvolume area silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter,anda brass andscintillator hadron calorimeter, each composed ofa barrel andtwo endcap sections.Muonsare mea- suredingas-ionizationdetectorsembeddedinthesteelflux-return yokeoutsidethesolenoid. Extensiveforwardcalorimetry comple- mentsthe coverage providedby thebarrelandendcapdetectors.

Muonsare measured in thepseudorapidity range |

η

_|<2.4, with detectionplanesmadeusingthreetechnologies:drift tubes,cath- odestripchambers, andresistiveplatechambers. Matchingmuon candidatesto tracksmeasured inthe silicontrackerresultsinan accurate measurement of the transverse momentum (p_T). As an

example, formuonswith pT<10 GeV the relative pT resolution isfound tobe 0.8%–3.0% (dependingon|

η

_|) andformuonswith 20<pT<100 GeV itis1.3–2.0%inthebarrelandbetterthan6%

in theendcaps [57]. Amore detaileddescription ofthe CMSde- tector,togetherwithdefinitionsofthecoordinatesystemusedand therelevantkinematicvariables,canbefoundin[58].

3. Dataselection

Thedatawere collectedwithanonlinetriggerselectingevents containing atleast two muon candidates, one with p_T>17 GeV andanother with pT>8 GeV. In thisanalysisoffline muon can- didates are definedas particle-flow (PF) muons [57]. The PF re- construction algorithm combines information from all CMS sub- detectors to identifyandreconstruct individual particles, such as electrons,photons,hadronsormuons.

Events are further selected by requiring at least four offline muoncandidateswithp_T>8 GeV and|

η

|<2.4 thatformtwoop- positelychargedpairs.Atleastoneofthesemuonsmustaddition- allysatisfy the requirementof pT>17 GeV and |

η

_|<0.9, which ensures that the trigger efficiency is high and independent of theeventtopology,includingeffectsrelatedtooverlapsofnearby muontrajectories.Tracksassociatedwithapairofopposite-charge muon candidatesarefitforacommonvertexusingaKalman fil- teralgorithm [59]. Ifthe vertexis reconstructed, a muon pair is combined into a dimuon system if its invariant mass measured at the common vertex mμ⁺μ⁻<5 GeV and the vertex fit prob- ability P_v(

μ

⁺

μ

⁻)>1%. Muon pairs failing these requirements are still retained for the analysis if at the point of closest ap- proach of the two trajectories they are within R(

μ

⁺,

μ

⁻)=



(

η

_μ+−

η

_μ−)²+ (φμ⁺− φμ⁻)² <0.01, where φ_μ± are the az- imuthal anglesinradians. Thisrecoverystep isdesignedtocom- pensate for the reduced efficiency of the vertex selection for dimuonsinwhichthetwomuontracksarenearlyparalleltoeach other,thereforeagoodefficiencyismaintainedfordimuonmasses down to the2mμ threshold (0.2114 GeV). Fordimuons in which this is the casethe point of closest approach is selected as the vertexposition,withtheadditionalselectionrequirementthatthe distancebetweenthe tracksbe≤⁰.5 mm.The dimuonkinematic variablesaremeasuredatthedimuonvertexposition.Thereisno restriction on the number of ungrouped additional muons. Both dimuonsare requiredtohaveatleastone hitinthefirstlayer of thebarrelorendcapsofthepixeldetector,andthisdefinesanef- fective“fiducial”region.Thisrequirement,alongwiththemuon pT and |

η

| ^{criteria, ensures hightrigger (}>96%), reconstruction, and selection efficiencies, with a greatly reduced dependence on the pT,

η

,oropeninganglebetweenthemuons.

Theprojectedz coordinateofthedimuonsystematthepointof theclosestapproachtothebeamline(zμμ)isreconstructedusing thedimuonmomentum.Therequirement|^z1μμ−^z2μμ|<1 mm is imposedtoensurethatbothdimuonsareconsistentwiththesame pp interaction; no explicitrequirements are madeon theimpact parameterorthe z coordinateatthe pointofclosestapproach to the beamlineof theindividual reconstructed muonsto preserve sensitivitytosignatureswithdisplacedmuons.

To suppress background eventsin which the muons are pro- ducedinthedecayofheavyquarks(andthusappearinjets),the dimuonsarerequiredtobeisolatedfromothereventactivityusing thecriterion Isum<2 GeV.TheisolationparameterIsumisdefined asthescalar sumofthe pT ofcharged trackswith pT>0.5 GeV withinaconeofsizeR=⁰.4 centeredonthemomentumvector ofthe dimuon system, excluding thetracks corresponding to the two muon candidates. The tracks used inthe calculation of Isum mustalsohavea z coordinateatthe pointofclosestapproachto the beam line that lies within 1 mm of zμμ. The I_sum selection

Table 1

Eventselectionefficiencies sim(mh1,ma₁)and sim(mγD,cτγD),asobtainedfromsimulation,thegeometricandkinematicacceptancesαgen(mh1,ma₁)andαgen(mγD,cτγD), calculatedusingonlygenerator-levelinformation,andtheirratios(withstatisticaluncertainties),forafewrepresentativeNMSSManddarkSUSYbenchmarksamples.The experimentaldata-to-simulationscalefactor( data/ sim,describedlater)isnotapplied.

mh₁[GeV] 90 125 125

ma₁ [GeV] 2 0.5 3.55

sim[^%] ^11.0±^{0.1 21.1}±^{0.1 17.3}±^0.1

αgen[^%] ^15.9±^{0.1 32.0}±^{0.1 26.3}±^0.1

sim/αgen 0.69±^{0.01 0.66}±^{0.01 0.66}±^0.01

mγD[^GeV] ^{0.25 1.0}

cτγD[^mm] ^{0 0}.5 2 0 0.5 2

sim[^%] ^8.85±^{0.12 1.76}±^{0.05 0.23}±^{0.03 6.13}±^{0.23 4.73}±^{0.07 1.15}±^0.04

αgen[^%] ^14.32±^{0.14 2.7}±^{0.06 0.31}±^{0.03 8.89}±^{0.28 6.98}±^{0.09 1.68}±^0.05

sim/αgen 0.62±^{0.01 0.65}±^{0.02 0.74}±^{0.13 0.69}±^{0.03 0.68}±^{0.01 0.68}±^0.03

suppressesthecontaminationfrombb productionbyaboutafac- tor of40, asestimatedusing a bb enriched control sample with onedimuonrecoilingoffajetcontaininganunpairedmuon,while rejectinglessthan20%ofeventswiththesignaltopology.

The invariant mass m₁μμ always refers to the dimuon con- taininga muonwith pT>17 GeV and |

η

|<0.9. Foreventswith bothdimuon systemscontainingsuch amuon, theassignment of m1μμ andm2μμ israndomforcompatibilitywiththebackground modelingschemadescribed inSection 5.The invariant massesof bothreconstructeddimuons arerequiredtobecompatiblewithin the detectorresolution, specifically |^m1μμ−^m2μμ|<0.13 GeV+ 0.065(m1μμ+^m2μμ)/2,whichdefinesadiagonalsignal regionin theplaneoftheinvariantmassesofthetwodimuons.Thenumeri- calparametersintherequirementcorrespondtoatleastfivetimes thesizeofthecoreresolutioninthedimuonmass.

4. Signalmodeling

The resultsfromthisanalysisare designedto be modelinde- pendent,butare alsopresentedinthecontextofthetwo bench- mark models introduced earlier. NMSSM simulation samples for benchmark model 1 are generated with pythia 6.4.26 [60], us- ingMSSMHiggsbosonproductionviagluon fusiongg→^H0MSSM, withtheHiggsbosonsdecayingviaH⁰_MSSM→^2A0_MSSM^.Themasses of the MSSM bosons H⁰_MSSM and A⁰_MSSM are set to the desired values for the h1 mass and a1 mass of the NMSSM bosons, re- spectively.ThemassofH⁰MSSM isintherange90–150 GeV (mass below90 GeV isexcluded byLEP [37]) andthemassofA⁰_MSSM is in range 0.25–3.55 GeV. Both A⁰_MSSM bosons are forcedto decay promptly to a pair of muons. Dark SUSY simulation samples for benchmarkmodel2are generatedwith MadGraph 4.5.2[61] us- ing SM Higgsboson production via gluon fusiongg→^hSM, with m_hSM=^{125 GeV.} The Bridge program [62] is used to force the Higgs bosons to undergo a non-SM decay to a pair of neutrali- nos,eachofwhichdecaysvian1→ⁿD+

γ

D,wheremn1=^{10 GeV,} m_nD=^{1 GeV, whichis}representative ofthe type ofmodels con- sidered[42]. Dark photonsare generated withmγD in the range 0.25–2.0 GeV and a decaylength c

τ

_γD in the rangeof0–20 mm.

Each ofthe two darkphotons is forced to decay to two muons, while both dark neutralinosescape detection. The narrow-width approximationisimposed by settingthewidthsofthedarkpho- tonstoasmallvalue(10⁻³GeV).

All benchmark samplesare generatedusing the leading-order CTEQ6.6 [63] set of parton distribution functions (PDF), and are interfacedwith pythia usingtheZ2*tune[64] forthe underlying eventactivityattheLHCandtosimulatejetfragmentation.

Thesignalsamplesareprocessedthroughadetailedsimulation oftheCMSdetectorbased on Geant4[65] andarereconstructed

withthesamealgorithms usedfordata.Table 1showstheevent selection efficiencies

sim obtained using the simulated bench- marksamples forafew representative choicesof(m_h1,ma1),and (_mγD,c

τ

_γD).Toprovideasimplerecipeforfuturereinterpretations oftheresults inthecontextofother models,thevariable

α

gen is separately definedasthe geometric and kinematicacceptance of this analysis calculated using only generator-level information. It isdefinedbyselectingeventscontaining atleastfourmuonswith pT>8 GeV and|

η

_|<2.4,withatleastoneofthesemuonshaving p_T>17 GeV and|

η

|<0.9.The newlightboson mustalsodecay withtransversedecaylength L_xy<4.4 cm andlongitudinaldecay lengthLz<34.5 cm (bothdefinedinthedetectorreferenceframe), tosatisfy the“fiducial”regionoftheanalysis. Table 1shows

α

gen alongwiththeratio

sim/

α

gen.

5. Backgroundestimation

TheSMbackgroundforthissearchisdominatedbybb produc- tionandhassmallcontributionsfromtheelectroweakproduction offourmuonsanddirectJ/ψpairproduction.Theleading partof thebb contributionisduetob quarkdecaysthatresultinapairof muons,viaeitherthesemileptonicdecaysofboththeb quarkand theresultingc quark,orviaresonances,i.e.

ω

,

ρ

,φ,J/ψ.Asmaller contributioncomes fromeventswithonegenuine dimuoncandi- dateandaseconddimuoncandidatecontainingonemuonfroma semileptonicb quarkdecayandachargedhadronmisidentifiedas anothermuon.

Usingdatacontrolsamples,thebb backgroundismodeledasa two-dimensional (2D) template B_bb(m₁μμ,m₂μμ) inthe plane of theinvariantmassesofthetwodimuons.Thetemplatedescribing the 2D probability densityfunction is constructed asa Cartesian product B17(m1μμ)B8(m2μμ), where the B17 and B8 templates modeltheinvariantmassdistributionsfordimuonswithandwith- out therequirementthat thedimuoncontains atleastonemuon satisfyingpT>17 GeV and|

η

|<0.9 respectively.TheB17shapeis measuredusingadatasampleenrichedwithbb eventscontaining exactlyone dimuonandoneadditionalmuon,undertheassump- tion that the decay of one of the b quarks results in a dimuon paircontainingatleastonemuonwithp_T>17 GeV and|

η

|<0.9, while the other b quark decays semileptonically resulting in the additionalmuonwithpT>8 GeV.FortheB8shape,asimilarsam- ple and procedure is used but the dimuon is required to have both prongs with p_T>8 GeV, while the additional muon must have p_T>17 GeV and |

η

|<0.9.The two templates are required as the shape of the dimuon invariant mass distribution depends on the pT thresholdsused to selectthe muonsand whetherthe muonsarerestrictedtothecentral(|

η

_|<0.9)regionorcanbein thefullacceptancerange(|

η

|<2.4),asaresultofthedifferences

Fig. 1. Distributionoftheinvariantmassesm1μμvs.m2μμfortheisolateddimuon eventsfollowingthe application ofallconstraintsexceptthe m1μμm2μμ re- quirementofcompatibilitywithinthedetectorresolution.Thecompatiblediagonal signalregion(outlinedwith dashed lines) containsone dataevent (triangle) at m1μμ=⁰.33 GeV andm2μμ=⁰.22 GeV.Therearealsonine dataevents(white circles)whichfailthem1μμ^m2μμcompatibilityrequirement.Thecolorscalein- dicatestheexpectedSMbackgroundinrange2mμ<m1μμ,m2μμ<2mτ.

inthemomentum resolutionofthebarrelandendcapregions of thetracker. The B17 and B8 distributions are fitted witha para- metric analytical function using a sum of Bernstein polynomials andCrystalBallfunctions[66] describingresonances.Theseevent samplesdonotoverlapwiththe samplecontaining two dimuons that is usedfor the main analysisand they havenegligible con- tributions from non-bb backgrounds. Once the B_bb(m1μμ,m2μμ) templateisconstructed,itis usedtoprovidea descriptionofthe bb backgroundshapeinthesignalregion.Thistechniqueassumes thateachb quarkfragmentsindependentlyandthatiftheshapes ofthesedistributionsaremeasuredusingdatasampleswithkine- matics very similar to that of the background events then the effectsofresidualkinematically-inducedcorrelationsaresmall(al- beitweaklyinduced,theshapedependsontheb jetp_Tandthep_T ofthetwob jetsinbackgroundbb eventstendtobesimilar).The backgroundtemplateisvalidatedinaregionwherebothdimuons failthe I_sum<2 GeV requirementandgoodagreementwithdata isobserved.

Thedata eventsthat satisfy all analysisselectionsbutfail the m1μμ^m2μμ requirement are used to normalizethe B_bb(m1μμ, m2μμ) template. This selection yields nine events in the off- diagonal sideband region of the (m₁μμ,m₂μμ) plane, leading in thediagonal signal region to an expectedrate ofbb background eventsof2.0±⁰.7.Thisisessentially(9±√

9)×⁰.18/0.82,where 0.18 and 0.82 correspond to the integral of the areasunder the backgroundtemplateinsideandoutsidethesignaldiagonalregion, respectively.Thesenineeventsintheoff-diagonalsidebandsofthe (m₁μμ,m₂μμ)planeareshownaswhitecirclesinFig. 1.

Thecontribution fromdirectJ/ψ pair productionisestimated usinganotherdatacontrolsample.Eventsareselectedwithatrig- ger that requires at least three muon candidates, two of which haveacommonvertexandaninvariantmassconsistentwiththat oftheJ/ψ particle.Eventsarefurtherrequiredtocontainatleast fourreconstructedmuonswith pT>3.5 GeV,whichformdimuon pairs. This control sample does not specifically require that the dimuonssatisfy the requirement I_sum<2 GeV since I_sum isused toseparate thecontribution of “prompt” and“nonprompt” (from b quark decays) J/ψ in data. Finally, both dimuons are required to have an invariant mass between 2.8 and 3.3 GeV. Following these requirements the data sample consists of events contain- ingpromptandnonpromptJ/ψ.Tosubtractthenonprompt com-

ponent, two independent methods have been studied: the first one divides the control sample based on the values of the iso- lation variable Isum for each of the two dimuons in each event.

Thenumberofeventsinwhichbothdimuons satisfytherequire- ment Isum<2 GeV is extrapolated fromthe regions in which at least one of the dimuons fails thisrequirement. The second ap- proach uses the lifetime of the J/ψ candidate, calculated under the hypothesis of it being produced at the beam line, as a dis- criminatingvariable.Thedatadistributionisfittedintheisolated region using prompt and nonprompt templates from simulation and nonisolated sideband in data, respectively. Both approaches giveconsistentresultswithintheassociateduncertaintiesandthe resultsoftheisolation-basedmethodareusedinthefinalanalysis.

There are two mechanisms forthe production of prompt double J/ψ events: single- and double-parton scattering (SPS and DPS, respectively), corresponding to whether the two J/ψ mesons are produced from one or two independent parton interactions. The number of prompt events in the control region is further sepa- ratedintoSPSandDPScomponentsusingtheJ/ψ rapidity differ- enceasthediscriminatingvariable.Finally,thedata-to-simulation normalizationfactorandthefractionofSPSandDPSeventsareex- trapolatedfromthecontroltothesignalregion,resultinginafinal estimationforthecontributionfrompromptdoubleJ/ψeventsof 0.06±⁰.03 events.

The contribution from other SM processes (low mass Drell–

Yan production and pp→^Z/

γ

^∗ →⁴

μ

) is estimated with the CalcHEP 3.6.18 generator [67] using the HEPMDB infrastruc- ture [68], and is found to be 0.15±⁰.03 events in the entire signal region.Thecombinedexpectedbackgroundcontribution to thediagonal signalregion is2.2±⁰.7 events.This backgroundis representedbythecolorscaleinFig. 1.

6. Systematicuncertainties

The selection efficiencies for the offline muon reconstruction, trigger,anddimuonisolationrequirementsareobtainedfromsim- ulation,andarecorrectedwithscalefactorsderivedfromcompar- isonbetweendataandsimulationusing Z→

μμ

andJ/ψ→

μμ

samples. The scale factor per event is found to be

data/

sim= 0.93±⁰.07 and it accounts for the differences in the efficiency ofthetrigger,theefficiencyofthemuonreconstructionandiden- tificationforeachofthefourmuoncandidates,andthecombined efficiencyoftheisolation requirementforthetwo dimuoncandi- dates. The estimate accountsfor correlationsassociated withthe presence of multiple muons per event. The main systematicun- certaintyistheofflinemuonreconstruction(4.1%),whichincludes an uncertainty (1% per muon) to cover variations of the scale factorasa functionofthe muon pT and

η

.Other systematicun- certainties include: the uncertainty in dimuon reconstruction ef- fects related to overlaps of muon trajectories in the tracker and in the muon system(3.5%), the trigger efficiency(1.5%), the un- certainty in the efficiency caused by the modeling of the tails in the dimuon invariant mass distribution that arises from the requirement that the two dimuon massesare compatible (1.5%), andthedimuonisolation(negligible).Theuncertaintyintheinte- grated luminosityofthe datasample(2.6%) [69] isalsoincluded.

Alluncertaintiesquotedabovearerelatedtovariationsinthesig- nal efficiencydueto experimental selection andsumup to 6.3%.

The uncertainties related to variations in the signal acceptance due to the model include: the uncertainties related to the PDFs and the knowledge of the strong coupling constant

α

s, which are estimatedbycomparing the PDFsinCTEQ6.6[63] withthose in NNPDF2.0 [70] and MSTW2008 [71], following the PDF4LHC recommendations[72,73]. Usingtheanalysisbenchmark samples, they are found to be 3% for the signal acceptance.The variation

oftherenormalizationandfactorizationscaleshasanegligibleef- fect.In additionare-weighting procedureisapplied totheHiggs boson p_T spectra in the benchmark signal samples to reproduce theNNLO+^{NNLLprediction[74] andaccountforpossiblechanges} to the analysisacceptance.Only a weak sensitivity tothis is ex- pectedandtheresultofthere-weighting procedureislimitedby thestatisticaluncertaintyofthesimulatedsamples(2%),whichis thereforeincludedasaconservativesystematicuncertaintyonthis effect.Thus, the totalsystematic uncertaintyin thesignal accep- tanceandselectionefficiencyis7.3%.

7. Results

Afterthe full analysisselection isapplied to thedata sample, one eventisobserved in thediagonal signal region,asshown in Fig. 1. Thisis consistentwiththe expectedbackground contribu- tionof2.2±⁰.7 events.

Forfuturereinterpretations ofthisanalysis, theresultscan be presentedasa 95% confidencelevel(CL) upperlimit on

σ

(pp→ 2a+ ^X)B²(a →²

μ

)

α

gen = ^N(mμμ)/(L¯^r), where

α

gen is the generator-level kinematic and geometric acceptance defined ear- lier.Thecalculation usesthe integratedluminosityL=²⁰.7 fb⁻¹ andcentral value ¯^{r ofthe ratior}=

data/

α

gen=⁰.63±⁰.07.The ratioincludesascalefactorcorrectingforexperimentaleffectsnot included in the simulation and its uncertainty covers the varia- tion inthe ratio over all the benchmark modelpoints used. The limit is calculated as a function of the dimuon mass using the CLS approach [75,76]. The chosen test statistic is based on the profile likelihood ratio andis used to determine how signal- or background-like the data are. Systematic uncertainties are incor- poratedintheanalysisvianuisanceparameterswithalog-normal probability densityfunction andaretreatedaccordingto thefre- quentistparadigm.Theoverallstatisticalmethodologyusedinthis analysiswas developed by the ATLAS and CMSCollaborations in thecontextoftheLHCHiggsCombinationGroupandisdescribed in[3,77].The obtained limit asa function of dimuonmass mμμ can be conveniently approximated as a constant everywhere ex- ceptthevicinityoftheobservedevent,whereitfollowsaGaussian distribution:

N

(

m_μμ

) ≤

3

.

1

+

1

.

2 exp



− (

m_μμ

−

0

.

32

)

² 2

×

⁰

.

03²

 ,

resultingin

σ (

pp

→

^2a

+

^X

)

B²

(

a

→

²

μ ) α

_gen

≤

⁰

.

24

+

⁰

.

09 exp



− (

m_μμ

−

0

.

32

)

² 2

×

⁰

.

03²

 ,

wheremμμ ismeasuredinGeV andthecross-section limitisex- pressedinfemtobarns.Thislimitisapplicabletomodelswithtwo pairsofmuonscomingfromlightbosonsofthesametypewitha massintherange 2mμ<m_a<2mτ ,wherethe newlight bosons are typicallyisolated andspatially separated(so astosatisfy the isolationrequirements).

Theweakmodeldependenceoftheratior allowsforasimple reinterpretationoftheresultsinothermodels.Thisrequirescalcu- lating

α

gen,asdefinedearlier,andthenthefullefficiency

datacan becalculatedbymultiplying

α

gen bytheratior.

There are certain subtleties that must be taken into account whenreinterpreting themodel-independentresults ofthisanaly- sis inthecontext ofother models,particularlywiththe isolation requirement.Aneventshouldbeconsideredtosatisfytheselection requirementsifthereareatleasttwowellisolated

γ

Ddecayingto muon pairs. Experimentally, isolation is based on charged tracks

butitmaybeinsufficienttojustrequiretheabsenceofgenerator- levelchargedparticlesintheisolationcone.Forexampleaneutral piondecayingtoapairofphotons,thatconvertintoelectrons,may resultinthereconstruction ofone ormore tracks.Thiswouldbe particularlyrelevantformodelswithmorethantwodarkphotons producedinthesameevent,someofwhichmaydecaytohadrons or electrons. In this case the safest approach is to require that there are no particleswith pT>0.5 GeV within the

γ

D isolation cone.Thisrestrictionwouldresultinamoreconservativelimitbut itwouldberobustagainsttheseeffects.

Theresultsfromthisanalysisarealsointerpretedinthecontext oftheNMSSMandthedarkSUSYbenchmarkmodels,and95% CL upper limits on the product of the cross section and branching fraction are derived. In these models both the Higgs boson pro- duction crosssectionandthebranching fractionscanvary signif- icantly, depending onthechoiceofparameters. Intheabsenceof broadly acceptedbenchmark scenarios, the production cross sec- tions in theseexamples are normalizedto that of the SM Higgs bosonwithamassof125 GeV[78].

InthecaseoftheNMSSMbenchmarkscenario,theproduction crosssectionsandbranchingfractionsforh1andh2canvarysub- stantiallydependingonthechosenparameters.Anexactinterpre- tationoftheseresultsrequiresevaluatingtheexperimentalaccep- tanceusingthegenerator-levelacceptanceforeachofthetwoh1,2 bosons, andthen using themeasured upperlimit on the sumof twocontributionstoderivelimitsforanychoiceofNMSSMmodel parameters.Topresentresultsinafashionallowingforstraightfor- wardinterpretation,wenotethatifoneofthetwoCP-evenHiggs bosons is the125 GeV state observedatthe LHC,then theother one is either lighter orheavier. In the NMSSM it is typical that oneofthetwohasapproximatelytheSMproductioncrosssection andasmallB(^hi→^2a),whereasthe otherone hasasuppressed productionrateandlarge B(^hi→^2a)duetoitslargesingletfrac- tion. In Fig. 2 (left) the limit at each mass point is calculated taking the CP-evenHiggs boson withthe corresponding mass as theonlysourceofsignalevents;thecurvebelow125 GeV applies to NMSSM models in which m_h1 <m_h2 =^{125 GeV, with h}1 de- caysdominatingtherateof4

μ

events.Thelimitatm_h=^{125 GeV} corresponds tothecasewhere125 GeV=^mh₁<mh₂,withh1 de- cays still responsible for the vast majority of signal-like events.

The points above 125 GeV correspondtomodel points forwhich only h2 (mh2>mh1=^{125 GeV) isallowedtohaveasizeablerate} ofobservable 4

μ

events.Finally,formodelswithmh2>150 GeV, thelimitat150 GeV canbeusedasaconservativeestimateofthe productionratelimit.Ineachofthesescenariositispossiblethat the other Higgs boson also contributes some fraction of the 4

μ

signal events,inwhichcasethelimitshownismoreconservative thanwouldbegivenbyanexactevaluation.

In the case of the dark SUSY scenario, a 95% CL limit on the product ofthe Higgsboson productioncross section andthe branching fractions of the Higgsboson (cascade) decay to a pair ofdarkphotonsisdetermined.Thelimit setinthe(_mγD,

ε

)plane fromthisanalysisisshowninFig. 2(right),alongwithlimitsfrom other experimentalsearches,wherethelifetimeisdirectlyrelated to thekineticmixingparameter

ε

andthemassofthedarkpho- tonmγD via

τ

γD(

ε

,_mγD)=

ε

⁻²f(_mγD),where f(_mγD)isafunction that dependsonlyon themass ofthedarkphoton [79].The sig- nificant vertical structures in the limits visible in Fig. 2 (right) arise becausethetotalwidthofthedarkphoton variesrapidlyin thosemassregionsduetoresonantdecaystohadrons.Thissearch constrains alarge,previously unconstrainedarea oftheparameter space. Unlike theother results inthe figure, theCMSand ATLAS limitsare model-dependentandonlyvalidunderthe assumption that B(^h→²ⁿ1→⁴

μ

+^X)=^{0. The recent ATLAS analysis[42]}

Fig. 2. Leftforbenchmarkmodel1:95% CLupperlimitsfromthissearchfortheNMSSMscenarioswithma₁=0.25 GeV (dashedcurve),ma₁=2 GeV (dash-dottedcurve) andma₁=3.55 GeV (dottedcurve)onσ(pp→h1/2→2a1)B²(a1→2μ)asafunctionofmh₁ intherange86<mh₁<125 GeV andofmh₂ formh₂>125 GeV.Asan illustration,thelimitsarecomparedtothepredictedrate(solidcurve)obtainedusingasimplifiedscenariowithσ(pp→^hi→^2a1)=⁰.008σSM,whichyieldspredictions fortheratesofdimuonpaireventscomparabletotheobtainedexperimentallimits,andB(^a1→²μ)=⁷.7%.ThechosenB(^a1→²μ)istakenfrom[17]forma1=^{2 GeV} andtanβ=^{20.Rightforbenchmarkmodel2:95%CLupperlimits(blacksolidcurves)fromthissearchon}σ(pp→^h→²γD+^X)B(^h→²γD+^X)(withmn1=^{10 GeV,} mn_D=^{1 GeV)intheplaneoftwooftheparameters(}εandmγD)forthedarkSUSYscenarios,alongwithconstraintsfromotherexperiments[42–56]showingthe90%CL exclusioncontours.ThecoloredcontoursrepresentdifferentvaluesofB(^h→2γD+X)intherange0.1–40%.

focused on highly displaced objects andthesesearches therefore probedifferentregionsoftheavailableparameterspace.

8. Summary

Asearch forpairs ofnew light bosons producedin thedecay ofa Higgs boson, that subsequently decay to pairs of oppositely chargedmuons,is presented.Oneeventisobservedinthe signal region,with2.2±⁰.7 eventsexpectedfromthe SMbackgrounds.

Amodelindependentupperlimitat95%CLontheproductofthe crosssection,branchingfraction, andacceptanceisobtained.This limitisvalidforlightbosonmassesintherange2mμ<ma<_{2mτ .} Theobtainedresultsallowastraightforward interpretationwithin abroadrangeofphysicsmodelsthatpredictthesametypeofsig- nature.Theresults arecompared withtwobenchmark modelsin thecontextoftheNMSSManddarkSUSY,includingscenariospre- dictinganonnegligiblelightbosonlifetime.

Acknowledgments

We would like to thank J. Ruderman for his guidance with thetheoreticallymotivated benchmarksamplesofdarkSUSY. We congratulate ourcolleagues inthe CERN accelerator departments forthe excellent performance of the LHC and thank the techni- calandadministrativestaffs atCERNandatother CMSinstitutes fortheir contributions to the success ofthe CMSeffort. In addi- tion, we gratefully acknowledge the computingcentres andper- sonnel of the Worldwide LHC Computing Grid for delivering so effectivelythecomputinginfrastructure essential toour analyses.

Finally, we acknowledge the enduring support for the construc- tionandoperationofthe LHCandtheCMSdetectorprovided by thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil);

MES(Bulgaria);CERN;CAS,MOST,andNSFC(China);COLCIENCIAS (Colombia);MSESandCSF(Croatia);RPF(Cyprus);MoER,ERCIUT andERDF(Estonia); AcademyofFinland,MEC, andHIP (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); MSIP and NRF (Republic ofKorea); LAS (Lithuania);MOE andUM (Malaysia); CINVESTAV, CONACYT,SEP,andUASLP-FAI(Mexico);MBIE(NewZealand);PAEC

(Pakistan);MSHEandNSC (Poland);FCT(Portugal);JINR(Dubna);

MON,RosAtom,RASandRFBR(Russia);MESTD(Serbia);SEIDIand CPAN(Spain);SwissFundingAgencies(Switzerland);MST(Taipei);

ThEPCenter,IPST, STARandNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNationalScienceFoundation (USA).

Individuals have received support from the Marie-Curie pro- grammeand theEuropean Research CouncilandEPLANET (Euro- peanUnion);theLeventisFoundation;theAlfredP.SloanFounda- 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;theHOMINGPLUSprogrammeoftheFoundation forPolish 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;

andtheNationalPrioritiesResearchProgrambyQatarNationalRe- searchFund.

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