Angular analysis of the decay B0→K*0μ+μ- from pp collisions at √s=8 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Angular analysis of the decay B

→ ^K

μ

μ

from pp collisions at

√ s = ^{8 TeV}

.CMSCollaboration^

CERN,Switzerland

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

Articlehistory:

Received29July2015

Receivedinrevisedform30November2015 Accepted7December2015

Availableonline11December2015 Editor:M.Doser

Keywords:

CMS Physics B0decays

The angular distributions and the differential branching fraction of the decay B⁰→^K∗(892)⁰μ⁺μ⁻

are studiedusingdatacorresponding toanintegratedluminosity of20.5 fb⁻¹ collectedwiththeCMS detector at the LHCin pp collisions at√

s=^{8 TeV. From1430 signal decays,the} forward–backward asymmetryofthemuons,theK^∗(892)⁰longitudinalpolarizationfraction,andthedifferentialbranching fraction are determined as afunction ofthe dimuoninvariant mass squared.The measurements are amongthemostprecisetodateandareingoodagreementwithstandardmodelpredictions.

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

1. Introduction

Phenomenabeyondthestandardmodel(SM)ofparticlephysics can manifestthemselves directly, via the productionof newpar- ticles,or indirectly, by affectingthe production anddecayof SM particles. Analyses of flavor-changing neutral current (FCNC) de- cays are particularly sensitive to the effectof newphysics, since such decays are highly suppressed in the SM. The FCNC decay, B⁰→^K∗0μ⁺μ⁻(K^∗0indicatestheK^∗(892)⁰,andcharge-conjugate states are implied for all particles unless statedotherwise), pro- videsmanyopportunitiesto search fornewphenomena. Inaddi- tion to the branching fraction, other properties of the decaycan be measured, including theforward–backward asymmetry ofthe muons, AFB,andthelongitudinalpolarization fractionoftheK^∗0, FL.Tobetterunderstandthisdecay,thesequantitiescanbe mea- sured as a function of the dimuon invariant mass squared (q²). Newphysicsmaymodifyanyofthesequantities[1–17]relativeto theirSMvalues[1,18–24].WhilepreviousmeasurementsbyBaBar, Belle, CDF, LHCb, and CMS are consistent with the SM [25–29], theyarestill statisticallylimited, andmoreprecisemeasurements offerthepossibilitytouncoverphysicsbeyondthe SM.

InthisLetter,wepresentmeasurementsofA_FB,F_L,andthedif- ferential branchingfractiondB/^{dq2 fromB0}→^K∗0μ⁺μ⁻ decays, using data collected from pp collisions at the CERN LHC by the CMSexperimentatacenter-of-massenergyof8 TeV.Thedatacor- respondto an integratedluminosity of 20.5±⁰.5 fb⁻¹ [30].The

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

K^∗0 is reconstructed through its decay to K⁺π⁻, and the B⁰ is reconstructed by fitting the two identified muon tracks and the two hadron tracks to a common vertex. The values of A_FB and FL are measured by fitting the distribution of events asa func- tion of two angular variables: the angle between the positively chargedmuonandtheB⁰inthedimuonrestframe,andtheangle between the K⁺ and the B⁰ in the K^∗0 rest frame. All measure- ments are performed inq² bins from1 to 19 GeV².The q² bins 8.68<q²<10.09 GeV² and12.90<q²<14.18 GeV²,correspond- ing tothe B⁰→^J/ψK^∗0 andB⁰→ ψ^{K∗0 decays(}ψ^ refers tothe ψ(2S)), respectively,areused tovalidate theanalysis.The former isalsousedtonormalizethedifferentialbranchingfraction.

2. CMSdetector

AdetaileddescriptionoftheCMSdetector,togetherwithadef- inition ofthecoordinatesystemusedandthestandardkinematic variables,canbefoundinRef.[31].Themaindetectorcomponents used inthisanalysisare thesilicon trackerandthemuon detec- tion systems. The silicon tracker, located in the 3.8 T field of a superconducting solenoid, consists of three pixel layers and ten strip layers (four ofwhich have a stereoview) in the barrel re- gion accompanied by similarendcap pixelandstrip detectors on each side that extendcoverage out to |η_|<2.5. For tracks with transverse momenta 1<pT<10 GeV and |η_|<1.4, the resolu- tionsaretypically1.5%inp_Tand25–90(45–150) μminthetrans- verse(longitudinal)impactparameter[32].Muonsaremeasuredin therange|η_|<2.4,withdetectionplanesmadeusingthreetech- nologies: drift tubes, cathode strip chambers, and resistiveplate http://dx.doi.org/10.1016/j.physletb.2015.12.020

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

estingevents.Ahigh-leveltriggerprocessorfarmfurtherdecreases theeventratefromaround90 kHztoaround400 Hz,beforedata storage.

3. Reconstruction,eventselection,andefficiency

Thecriteriausedtoselectthecandidateeventsduringdatatak- ing(trigger)andafterfull eventreconstructiontake advantageof thefact that B⁰ mesons have relativelylong lifetimes andthere- foredecay on average about 1 mm from their production point.

Thetriggeronlyusesmuonstoselectevents,whiletheofflinese- lectionincludesthefullreconstructionofalldecayproducts.

Allevents used inthis analysiswere recorded withthe same trigger,requiringtwoidentifiedmuonsofopposite chargetoform avertexthatisdisplacedfromtheppcollisionregion(beamspot).

The beamspot position (most probable collision point) and size (theextent ofthe luminousregion covering68% ofthe collisions in each dimension) were continuously measured through Gaus- sianfitstoreconstructedverticesaspartoftheonlinedataquality monitoring.Thetriggerrequiredeachmuontohavep_T>3.5 GeV,

|η|<2.2,andtopasswithin2 cm ofthebeamaxis.Thedimuon systemwas requiredtohave pT>6.9 GeV,avertexfit χ² proba- bilitylargerthan10%,andaseparationofthevertexrelativetothe beamspotinthetransverseplaneofatleast3σ,where σ includes thecalculateduncertaintyinthevertexpositionandthemeasured sizeof thebeamspot. Inaddition, thecosine oftheangle, inthe transverseplane,betweenthedimuonmomentumvector andthe vector fromthe beamspot tothe dimuon vertexwas requiredto begreaterthan0.9.

The offline reconstruction requires two muons of opposite charge and two oppositely charged hadrons. The muons are re- quiredto matchthosethat triggered the eventreadout,andalso topassgeneralmuonidentificationrequirements.Theseincludea trackmatchedtoatleastonemuonsegment(collectionofhitsin amuon chamber consistent withthepassage ofa chargedparti- cle),atrackfit χ² per degreeoffreedom lessthan1.8, hitsinat leastsixtrackerlayers withat leasttwo fromthe pixeldetector, anda transverse(longitudinal) impactparameter withrespect to thebeamspotlessthan 3 cm(30 cm).The reconstructeddimuon systemmustalsosatisfythesamerequirementsthatwereapplied inthetrigger.

Thehadron tracks arerequired tofail the muonidentification criteria,have p_T>0.8 GeV, andhavean extrapolateddistanceof closestapproach tothe beamspot inthetransverse plane greater thantwicethesuminquadratureofthedistanceuncertaintyand thebeamspot transversesize.The two hadronsmusthavean in- variant mass within 90 MeV of the accepted K^∗0 mass [34] for eitherthe K⁺π⁻ or K⁻π⁺ hypothesis. To remove contamination fromφ (1020)→^{K+K− decays,the invariant mass ofthe hadron} pairmustbegreaterthan1.035 GeV whenthechargedkaonmass isassignedtobothhadrons.TheB⁰ candidatesareobtainedbyfit- tingthefourchargedtracks toa commonvertex, andapplyinga vertexconstraint toimprove the resolution ofthe track parame- ters.The B⁰ candidates must have pT>8 GeV, |η_|<2.2, vertex fit χ² probability larger than 10%, vertex transverse separation fromthebeamspotgreaterthan12timesthesuminquadratureof theseparationuncertaintyandthebeamspot transversesize,and cosαxy>0.9994,where αxy is theangle,inthe transverseplane, betweenthe B⁰ momentum vectorandtheline-of-flightbetween

atleastonecandidateisfoundcontainonaverage1.05candidates.

AsinglecandidateischosenfromeacheventbasedonthebestB⁰ vertexfit χ².

From the selected events, the dimuon invariant mass q and its calculated uncertainty σq are used to distinguish the signal fromthe control samples.The control samples B⁰→^J/ψK^∗0 and B⁰→ ψ^{K∗0 are definedby} |^q−^mJ/ψ|<3σq and|^q−^mψ^|<3σq, respectively, where mJ/ψ and m_ψ are the accepted masses[34].

The average value for σq is about26 MeV. The signal sample is composed oftheevents that arenot assignedto theJ/ψ and ψ^ samples.

The signal sample still contains contributions from the con- trol samples,mainly dueto unreconstructed soft photons inthe charmoniumdecay.Theseeventswillhavealow q valueandfall outsidetheselection describedabove.Theseeventswillalsohave a lowm value andthereforetheycan be selectivelyremovedus- ing a combined selection on q andm. For q<mJ/ψ (q>mJ/ψ), werequire|(^m−^mB⁰)− (^q−^mJ/ψ)|>160(60)MeV. Forq<m_ψ

(q>m_ψ),werequire|(^m−^mB⁰)− (^q−^mψ^)|>60(30)MeV.The requirements are set such that less than 10% of the background eventsoriginatefromthecontrolchannels.

The four-trackvertexcandidateis identifiedasa B⁰ or B⁰ de- pendingonwhethertheK⁺π⁻ orK⁻π⁺invariantmassisclosest to the acceptedK^∗0 mass.The fraction ofcandidates assignedto the incorrect state is estimated from simulations to be 12–14%, dependingonq².

The global efficiency, , is the product ofthe acceptance and thecombinedtrigger,reconstruction,andselectionefficiency,both ofwhichareobtainedfromMonteCarlo(MC)simulations.Thepp collisions are simulatedusing pythia [35] version 6.424, the un- stableparticlesaredecayedby evtgen[36] version9.1(using the defaultmatrixelementforthesignal),andtheparticlesareprop- agatedthroughadetailedmodelofthedetectorwith Geant4[37].

The reconstructionandselection ofthegeneratedeventsproceed asfordata.ThreesimulatedsampleswerecreatedinwhichtheB⁰ wasforcedtodecaytoK^∗0(K⁺π⁻)μ⁺μ⁻,J/ψ(μ⁺μ⁻)K^∗0(K⁺π⁻), orψ^(μ⁺μ⁻)K^∗0(K⁺π⁻).Thesampleswereconstructedtoensure thatthenumberandspatialdistributionofppcollisionverticesin each eventmatchthedistributions foundindata.The acceptance isobtainedfromgeneratedevents,beforetheparticlepropagation with Geant4, and is calculated as the fraction ofevents passing thesingle-muonrequirementofp_T(μ)>3.3 GeV and|η(μ)|<2.3 relative to all events with pT(B⁰)>8 GeV and |η(B⁰)|<2.2. As theacceptance requirementsare placedon thegeneratedquanti- ties,they arelessrestrictivethanthefinalselectionrequirements, whichare basedonthereconstructed quantities,toallow forthe effectoffiniteresolution.Onlyeventspassingtheacceptancecri- teriaareprocessedthroughthe geant simulation,thetriggersim- ulation,andthereconstructionsoftware.Thecombinedtrigger,re- construction,andselectionefficiencyistheratioofthenumberof eventsthat pass thetrigger andselectionrequirements andhave areconstructedB⁰compatiblewiththegeneratedB⁰ intheevent, relative to the number ofevents that pass the acceptance crite- ria. The compatibility ofgenerated and reconstructed particles is enforced by requiringthe reconstructed K⁺, π⁻, μ⁺, and μ⁻ to have

(η)²+ (ϕ)² lessthan 0.3(0.004)forhadrons(muons), where η andϕ are the differencesin η and ϕ between the reconstructed andgeneratedparticles. Requiringall fourparticles in the B⁰ decay to be matched results in an efficiency of99.6%

Fig. 1. Sketch showing the definition of the angular observablesθl(left),θK(middle), andφ(right) for the decay B⁰→K^∗0(K⁺π⁻)μ⁺μ⁻.

(0.4% of theevents have a correctlyreconstructed B⁰ that is not matched to a generated B⁰) and a purity of 99.5% (0.5% of the matchedcandidatesarenotacorrectlyreconstructedB⁰).Efficien- ciesare determined forboth correctlytagged(the K and π have the correctcharge) and mistagged(the K and π chargesare re- versed)candidates.

4. Analysismethod

Thisanalysismeasures A_FB,F_L,anddB/^{dq2ofthedecayB0}→ K^∗0μ⁺μ⁻ as a function of q². Fig. 1 shows the angular observ- ablesneededtodefinethedecay:θKistheanglebetweenthekaon momentum andthedirectionopposite to the B⁰ 

B⁰

in theK^∗0

K^∗0

rest frame, θl is the angle between the positive (negative) muonmomentumandthedirectionoppositetotheB⁰ 

B⁰ inthe dimuonrestframe,andφistheanglebetweentheplanecontain- ing thetwo muons andtheplane containing thekaon andpion.

Astheextractedangularparameters A_FBandF_Ldonotdependon φandtheproductoftheacceptanceandefficiencyisnearly con- stant asa function of φ, the angleφ isintegrated out. Although the K⁺π⁻ invariant mass mustbe consistent withthat ofa K^∗0, therecanbe acontributionfromspinless(S-wave)K⁺π⁻ combi- nations[24,38–40].Thisisparametrizedwithtwoterms:FS,which is related to the S-wave fraction, and A_S, which is the interfer- enceamplitudebetweentheS-waveandP-wavedecays.Including thiscomponent,theangulardistributionofB⁰→^K∗0μ⁺μ⁻canbe writtenas[24]:

1



d³ d cosθKd cosθldq²

= ⁹

16

2 3



FS+AScosθK

 

1−cos²θl

+ (1−FS)



2FLcos²θK



1−cos²θl

+¹

2(1−^FL)



1−^cos2θK



1+^cos2θl

+⁴

3A_FB

1−^cos2θK

cosθl



. (1)

Foreachq² bin,theobservablesofinterest areextractedfrom an unbinnedextendedmaximum-likelihoodfitto threevariables:

theK⁺π⁻μ⁺μ⁻ invariant massm andthe twoangularvariables θK and θl. Foreach q² bin, theunnormalized probability density function(PDF)hasthefollowingexpression:

PDF(m, θK, θl)=^YC_S 

S^C(m)S^a(θK, θl)^C(θK, θl)

+ ^fM

1−f^M S^M(m)S^a(−θK,−θl)^M(θK, θl)  +^YBB^m(m)B^θK(θK)B^θl(θ_l), (2)

where the contributions correspond to correctly tagged signal events, mistagged signal events,and background events.The pa- rametersY_S^C andYB aretheyieldsofcorrectlytaggedsignalevents and background events, respectively, and are free parameters in thefit.Theparameter f^M isthefractionofsignaleventsthat are mistaggedandisdeterminedfromMCsimulation.Thesignalmass probability functions S^C(m) and S^M(m)are each thesumof two Gaussianfunctionsanddescribethemassdistributionforcorrectly tagged andmistaggedsignal events, respectively.In thefit, there isone freeparameterforthemassvalueinbothsignalfunctions, whiletheother parameters(fourGaussian σ parametersandtwo fractions relatingthecontributionof eachGaussian)are obtained from MC simulation, which has been found to accurately repro- duce the data.The function S^a(θK,θl) describes thesignal in the two-dimensional (2D) space of the angular observables and cor- responds to Eq.(1).The combination B^m(m)B^θK(θK)B^θl(θ_l) isob- tainedfromB⁰ sidebanddataanddescribesthebackgroundinthe space of (m,θK,θl), where the mass distribution is an exponen- tialfunctionandtheangulardistributionsarepolynomialsranging from second to fourthdegree, depending on the q² binand the angularvariable.Thefunctions ^C(θK,θl)and ^M(θK,θl)aretheef- ficiencies in the 2D space of−¹≤^cosθK≤¹,−¹≤^cosθ_l≤^{1 for} correctlytaggedandmistaggedsignalevents,respectively.Theef- ficiencyfunctionforcorrectlytaggedeventsisobtainedfromafit tothe2D-binnedefficiencyfromsimulationandisconstrainedto bepositive.Thereare30bins(5incosθKand6incosθl),andthe efficiencyfitfunctionisapolynomialofthirddegreeincosθKand fifthdegreeincosθl (andallcrossterms),foratotalof24freepa- rameters.This proceduredoesnotwork forthemistaggedevents becauseofthemuchsmallernumberofevents(resultinginempty bins)andamorecomplicatedefficiency.Formistaggedevents,the 2D efficiency is calculated in 5×^{5 bins of cos}θK andcosθl, and an interpolation is performed.This interpolation functionis used to generatea newbinned efficiency(in 120×^{120 bins), withall} bincontentsconstrainedtobenonnegative.Theefficiencyfunction usesthisfinelybinnedefficiency,withlinearinterpolationbetween bins. The efficiencies for both correctly tagged and mistagged events peak at cosθl near 0for q²<10 GeV², becoming flat for largervaluesofq².Theefficiencyforcorrectlytaggedeventstends to decreasewith increasing cosθK,andforq²>14 GeV² a small decrease isseen forcosθK near −^{1.The efficiencyformistagged} eventsismaximalnearcosθK=^{0,withan increaseascos}θK ap- proaches+^{1 thatbecomesmorepronouncedasq2 increases.}

The fitis performedintwo steps.The initial fitusesthe data from the sidebands of the B⁰ mass to obtain the B^θK(θK) and B^θl(θl)distributions(thesignalcomponentisabsentfromthisfit).

The sidebandregions are 3σm<|^m−^mB⁰|<5.5σm, where σm is theaveragemassresolution(≈^{45 MeV),obtainedfromfittingthe} MC simulationsignal to asumoftwo Gaussianswithacommon mean.Thedistributionsobtainedinthissteparethenfixedforthe secondstep,whichisafittothedataoverthefullmassrange.The free parameters in thisfit are A_FB, F_L, F_S, A_S,the parameters in