Measurement of angular parameters from the decay B0  → K*0 μ + μ − in proton–proton collisions at √s=8TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

angular

parameters

from

the

decay

B

0

→

K

∗

0

μ

+

μ

−

in

proton–proton

collisions

at

√

s

=

8 TeV

.

The

CMS

Collaboration



CERN,Switzerland

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received8October2017

Receivedinrevisedform22March2018 Accepted15April2018

Availableonline17April2018 Editor: M.Doser

Keywords:

CMS Physics B0_decays

AngulardistributionsofthedecayB0_→K∗0

_μ

+

_μ

−_{arestudiedusingasampleofproton–protoncollisions}

at√s₌8 TeV collectedwiththeCMSdetectorattheLHC,correspondingtoanintegratedluminosityof 20.5 fb−1. Anangular analysis is performedto determine the P1 and P5 parameters,where the P5

parameterisofparticularinterestbecauseofrecentmeasurementsthatindicateapotentialdiscrepancy withthestandardmodelpredictions.Basedonasampleof1397signalevents,theP1and P5 parameters

aredeterminedasafunctionofthedimuoninvariantmasssquared.Themeasurementsareinagreement withpredictionsbasedonthestandardmodel.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Phenomenabeyondthestandardmodel(SM)ofparticlephysics canbecomemanifestdirectly,viatheproductionofnewparticles, or indirectly, by modifying the production and decay properties ofSMparticles.Analysesofflavor-changingneutral-currentdecays are particularly sensitive to the effects of new physics because thesedecays arehighly suppressedinthe SM.An exampleisthe decayB0

→

K∗0

μ

+

μ

−, whereK∗0 indicates the K∗0

(

892

)

meson, withthecharge-conjugatereactionimplied hereandelsewherein thisLetterunlessotherwisestated.Anangularanalysisofthis de-cayasafunctionofthedimuoninvariantmasssquared

(

q2

)

allows itspropertiestobethoroughlyinvestigated.

Thedifferential decayrateforB0

_→

_K∗0

_μ

+

_μ

− _{canbe written}

in terms of q2 and three angular variables as a combination of spherical harmonics,weighted by q2-dependent angular parame-ters.Theseangularparametersinturndependuponcomplexdecay amplitudes,whicharedescribedbyWilsoncoefficientsinthe rele-vanteffectiveHamiltonian [1].Therecanbedifferentformulations oftheangularparameters.InthisLetterwepresentmeasurements oftheso-called P1 andP₅parameters [2,3].

New physics can modify the valuesof these angular parame-ters [1,2,4–18] relativeto theSM [1,19–25].While previous mea-surementsof some oftheseparameters by theBaBar, Belle,CDF, CMS,andLHCbexperimentswerefoundtobeconsistentwiththe SMpredictions [26–31],the LHCbCollaborationrecentlyreported

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

adiscrepancylargerthan3standarddeviationswithrespecttothe SMpredictionsfortheP₅ parameter [32,33],andtheBelle Collab-orationreportedadiscrepancyalmostaslarge [34].

ThenewmeasurementsoftheP1 andP₅angularparametersin B0

→

K∗0

μ

+

μ

− decayspresentedinthisLetterareperformed us-ing a sample of eventscollected in proton–proton(pp) collisions at a center-of-mass energy of 8 TeV with the CMS detector at the CERN LHC. The data correspond to an integrated luminosity of 20

.

5

±

0

.

5 fb−1 [35]. The K∗0 _{mesonis reconstructedthrough}

its decay to K+

π

−, and the B0 _{meson by fitting to a common}

vertex the tracks from two oppositely charged muon candidates andthe tracks fromthe K∗0 decay.The valuesof P1 and P5 are

measured by fitting the distributions of events as a function of threeangularvariables: theanglebetweenthe

μ

+ andtheB0 in the dimuonrestframe, the anglebetweenthe K+ andthe B0 in the K∗0 _{rest frame, and the angle betweenthe dimuon andthe}

Kπ decayplanesintheB0 _{restframe.Themeasurementsare}

per-formed in the q2 _{range from 1 to 19 GeV}2_{. Data in the ranges}

8

.

68

<

q2

_<

₁₀

_.

_{09 GeV}2 _and12

_.

₉₀

_<

_q2

_<

₁₄

_.

_{18 GeV}2 _correspond

toB0

→

J

/ψ

K∗0 andB0

→ ψ

K∗0decays,respectively,andareused ascontrolsamples,sincetheyhavethesamefinalstateasthe non-resonantdecaysofinterest.Here,

ψ

denotesthe

ψ(

2S

)

meson.

CMS previously exploited the same data set used in this analysis to measure two other angular parameters in the B0

_→

K∗0

_μ

+

_μ

−_{decayasafunctionofq}2_{:theforward–backward}

asym-metry of the muons, AFB, and the K∗0 longitudinal

polariza-tion fraction, FL, as well as the differential branching fraction, d

B/

dq2 [31].Afterasimplificationofthetheoreticaldecayrate

ex-https://doi.org/10.1016/j.physletb.2018.04.030

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

pression,thispreviousmeasurementwasperformedusingtwoout of the three angular variables. The analysiswas performed with a blindedprocedure: thedefinition offit strategy andits valida-tion,aswell asbackgrounddistribution determinationhavebeen performed on simulated samples, control region and signal side bands.The final fit on data hasbeen done at theend of valida-tion.TheanalysispresentedinthisLettershareswiththeprevious analysis,together withthedataset,thecriteriausedforselecting signalevents,whicharereportedinSection3forcompleteness. 2. TheCMSdetector

A detaileddescription ofthe CMS detector, together withthe coordinate system and the standard kinematic variables, can be found in Ref. [36]. The main detector components used in this analysisare the silicontracker and the muon detection systems. The silicontracker, positioned within a superconducting solenoid that provides an axial magnetic field of 3.8 T, consists of three pixel layers and ten strip layers (four of which have a stereo view)inthebarrelregion,accompaniedby similarpixelandstrip detectors in each endcap region, for a total pseudorapidity cov-erageof

|

η

|

<

2

.

5.For trackswithtransverse momenta 1

<

pT

<

10 GeV and

|

η

|

<

1

.

4,theresolutions aretypically1.5%in pT and

25–90(45–150) μminthetransverse(longitudinal)impact param-eter [37]. Muons are measured in the range

|

η

|

<

2

.

4 with de-tectionplanesmadeusingthreetechnologies:drifttubes,cathode strip chambers, andresistive platechambers. The probability for apion,kaon,orprotontobemisidentifiedasamuonislessthan 2

.

5

×

10−3_,0

_.

₅

_×

₁₀−3_,and0

_.

₆

_×

₁₀−3_{,respectively,forp}

T

>

4 GeV

and

|

η

|

<

2

.

4. The muon identification efficiency is greater than 0.80(0.98)forpT

>

3

.

5 GeV and

|

η

|

<

1

.

2 (1

.

2

<

|

η

|

<

2

.

4) [38].In additiontothetrackerandmuondetectors,CMSisequippedwith electromagneticandhadroniccalorimeters.

Events are selectedusing a two-leveltrigger system [39]. The first level consists of specialized hardware processors that use information from the calorimeters and muon systems to select events of interest at a rate of around 90 kHz. A high-level trig-gerprocessor farm further decreases the event rateto lessthan 1 kHzbeforedatastorage.

3. Reconstruction,eventselection,andefficiency

The criteria used to select the candidate events during data taking(trigger) andafter full eventreconstruction (offline) make useoftherelativelylonglifetimeofB0 mesons,whichleadsthem todecay an averageof about1 mmfromtheir productionpoint. Thetriggerusesonlymuoninformationtoselectevents,whilethe offlineselectionincludesthefullreconstructionofalldecay prod-ucts.

All eventsused in thisanalysiswere recordedwith the same trigger,requiringtwoidentifiedmuonsofoppositechargetoform avertexthatisdisplacedfromtheppcollisionregion(beamspot). Multiple pp collisions in the same or nearby beam crossings (pileup)causemultipleverticesinthesameevent. Thebeamspot position (the most probablecollision point) and size (the extent ofthe luminousregion covering68% ofthe collisions ineach di-mension) were continuously measured through Gaussian fits to reconstructed pileup vertices as part of the online data quality monitoring.ThetriggerrequiredeachmuontohavepT

>

3

.

5 GeV,

|

η

|

<

2

.

2,andtopass within2 cm ofthebeamaxis.Thedimuon systemwas requiredtohave pT

>

6

.

9 GeV,a vertexfit

χ

2

prob-abilitylarger than10%, anda separationofthe vertexrelativeto the beamspot in the transverse plane of at least3 standard de-viations, wherethecalculationofthe standarddeviationincludes thecalculateduncertaintyinthevertexpositionandthemeasured

size of the beamspot.In addition, the cosineof the anglein the transverse planebetweenthe dimuonmomentumvector andthe vector from the beamspotto the dimuon vertexwas required to begreaterthan0.9.

The offline reconstruction requires at least two oppositely chargedmuonsandatleasttwo oppositely chargedhadrons. The muonsare requiredto matchthose that triggeredthe event. The matching is performed by requiring an offline muon to match a trigger-levelmuonwithin



R

=

√

(

η

)

2

+ (φ)

2

<

0

.

1,where



η

and

φ

are the pseudorapidity and azimuthal angle differences, respectively, between the directions of the trigger-level and of-flinemuons.Offlinemuonsmust,inaddition,satisfygeneralmuon identification requirements. For example, the muon track candi-datefromthesilicontrackermustmatchatracksegmentfromthe muondetector,the

χ

2 _{perdegreeoffreedominaglobalfittothe}

silicontrackerandmuondetectorhitsmustbelessthan1.9,there mustbeatleastsixsilicontrackerhits,includingatleasttwofrom thepixeldetector,andthetransverse(longitudinal)impact param-eter withrespect to the beamspot mustbe lessthan 3 (30) cm. Theseselection criteriaarechosen tooptimizethemuon identifi-cationefficiencyasmeasuredusingJ

/ψ

→

μ

+

μ

− decaysindata. The dimuon system atthe offline level is requiredto satisfy the samerequirementsasspecifiedaboveforthetriggerlevel.

The charged hadron candidates are requiredto fail themuon identificationcriteria,havepT

>

0

.

8 GeV,andanextrapolated dis-tance d of closest approach to the beamspot in the transverse planegreaterthantwicethesuminquadratureoftheuncertainty

ind andthebeamspottransversesize.Foratleastoneofthetwo

possible identity assignments—thatthepositively chargedhadron isakaonandthenegativelychargedhadronapion,orviceversa— the invariant mass of the hadron pair must lie within 90 MeV of the nominal K∗0 mass [40]. To remove contamination from

φ (

1020

)

→

K+K− decays,wetemporarilyassignthekaonmassto bothchargedhadrons,andtheneliminatethecandidateifthe re-sulting invariant massof thehadron pair islessthan 1.035 GeV. The B0 _{candidatesare obtainedbyfittingthe fourchargedtracks}

to acommonvertex,andapplyingavertexconstrainttoimprove the resolution of the track parameters. The B0 candidates must have pT

>

8 GeV,

|

η

|

<

2

.

2, vertexfit

χ

2 probability larger than

10%, vertex transverse separation L from the beamspot greater than 12 times the sum in quadrature of the uncertainty in L

and the beamspot transverse size, and cos

α

xy

>

0

.

9994, where

α

xy istheanglein thetransverseplane betweenthe B0 momen-tum vector andthe line-of-flight between thebeamspot and the B0 _{vertex. The invariant mass m of the B}0 _{candidate must lie}

within 280 MeV of the nominal B0 mass

(

m_B0

)

[40] for either

the K−

π

+

μ

+

μ

− or K+

π

−

μ

+

μ

− possibility. The selection crite-riaareoptimizedusingsignaleventsamplesfromsimulationand backgroundeventsamplesfromsidebanddatainm.Thesideband includes both a low- and a high-mass region and is definedby 3σm

<

|

m

−

mB0

|

<

280 MeV, where

σ

m is theaverage mass res-olution (

≈

45 MeV)obtainedfrom fittinga sum oftwo Gaussian functionswitha commonmean tosimulatedsignal events.After applying theselection criteria,about5% ofthe eventshavemore thanonecandidate.A singlecandidateischosenbasedonthebest B0_vertex

_χ

2 _probability.

For each ofthe selected events, thedimuon invariant mass q

anditsuncertainty

σ

q arecalculated.WedefineB0

→

J

/ψ

K∗0and B0

_{→ ψ}

_K∗0_{controlsamplesthroughtherequirements}

_|

_q

₋

_m

J/ψ

|

<

3σqand

|

q

−

mψ

|

<

3σq,respectively,wheremJ/ψandmψ arethe

nominalmasses [40] oftheindicatedmeson.Theaveragevalueof

σ

qisabout26 MeV.

The remaining eventsample still contains contributions from B0

→

J

/ψ

K∗0 andB0

→ ψ

K∗0 decays,mainlybecauseof unrecon-structed softphotonsinthecharmoniumdecay,i.e., J

/ψ

or

ψ



→

μ

+

μ

−

γ

.Theseeventshavealow value ofq andfalloutsidethe control sample selection described above. They also have a low value of m and can be selectively removed using a combined requirement on q and m. For q

<

mJ/ψ

(

q

>

mJ/ψ

)

, we require

|(

m

−

m_B0

)

−(

q

−

mJ/ψ

)

|

>

160

(

60

)

MeV.Forq

<

mψ

(

q

>

mψ

)

,we

require

|(

m

−

mB0

)

− (

q

−

mψ

)

|

>

60

(

30

)

MeV.UsingMonteCarlo

(MC)simulation,theserequirementsweresetsothatlessthan10% ofthebackgroundeventsoriginatefromthecontrolchannels.

Toavoidbias,theoptimizationoftheselectioncriteria,andthe fit strategy described below in Section 4, are determined before datain the signal region are examined. The selection criteriado not depend on the choice of the primary vertex, andtheir opti-mizationproceduremakesuseofbothMCsimulatedsignalevents generatedwiththe samepileupdistributionasindata,and side-banddata.Afterapplyingtheserequirements,3191eventsremain. Theselected four-track vertexis identified asa B0 orB0 can-didatedepending onwhethertheK+

π

− orK−

π

+ invariantmass isclosesttothenominalK∗0 mass.The fractionofcandidates as-signed to the incorrect state is estimatedfrom simulation to be 12–14%,dependingon q2_.

Theglobalefficiency,



,istheproductoftheacceptanceandthe combinedtrigger, reconstruction, and selection efficiencies, all of whichareobtainedfromMCsimulatedeventsamples.Thepp col-lisionsaresimulatedusingthe pythia [41] eventgenerator,version 6.424,with particledecaysdescribed bythe evtgen [42] genera-tor, version 9.1, in which final-state radiation is generated using photos[43]. Thedefaultmatrixelement in pythia isusedto de-scribetheevents.The simulatedparticlesarepropagated through adetailedmodelofthedetectorbasedon Geant4 [44].The recon-structionandselectionofthegeneratedeventsproceedasforthe data.Separate samples of events are generated for B0 decays to K∗0

μ

+

μ

−,J

/ψ

K∗0,and

ψ

 K∗0,withK∗0

→

K+

π

− andboth J

/ψ

and

ψ

decayingto

μ

+

μ

−.Thedistributionofppcollisionvertices ineachsampleisadjustedtomatchtheobserveddistribution.

Theacceptanceisobtainedfromgenerator-levelevents,i.e., be-forethe particle propagationwith Geant4,and isdefined asthe fractionofeventswithpT

(

B0

_{) >}

_{8 GeV and}

_|

_η

₍

_B0

₎

_|

_<

₂

_.

_{2 that}

sat-isfythesingle-muonrequirements pT

(

μ

) >

3

.

3 GeV and

|

η

(

μ

)

|

<

2

.

3.Thesecriteriaarelessrestrictivethanthefinalselection crite-riainordertoaccountforfinitedetectorresolution,sincetheyare appliedtogenerator-levelquantities.Onlyeventssatisfyingthe ac-ceptancecriteriaareprocessedthroughthe Geant4simulation,the triggersimulation,andthereconstructionsoftware.

The combined trigger, reconstruction, and selection efficiency is given by the ratio of the number of events that satisfy the trigger and selection requirements and have a reconstructed B0

candidatecompatiblewith agenerated B0 meson, relativeto the numberof eventsthat satisfy the acceptance criteria. The gener-atedandreconstructedB0 _{are consideredto becompatibleifthe}

reconstructedK+ candidate appears withina distance



R ofthe generated K+ meson, andanalogously forthe

π

−,

μ

+, and

μ

−, where



R

=

0

.

3 for thehadronsand



R

=

0

.

004 forthe muons. Requiringallfourparticles intheB0 _{decayto bematchedresults}

inan efficiency of99.6% (0.4% ofthe eventshave a correctly re-constructed B0 _{candidate that is not matched to a generated B}0

meson)andapurityof99.5%(0.5%ofthematchedcandidatesdo notcorrespondtoacorrectlyreconstructedB0candidate). Efficien-ciesare determinedfor bothcorrectlytagged (the K and

π

have the correctcharge) andmistagged (the K and

π

charges are re-versed)candidates.

3.1.Backgroundstudies

Using simulation, we search for possible backgrounds that might peak in the B0 _{mass region. The event selection is}

ap-plied to inclusive MC samples of B0_{, B}

s, B+, and

b decays to

J

/ψ

X and

ψ

 X, where X denotes all of the exclusive decay channels found in the PDG [40], and with the J

/ψ

and

ψ

 de-caying to

μ

+

μ

−. No evidence for a peaking structure near the B0 massisfound.The distributions ofthefeweventsthat satisfy the selection criteria are similar to the shape of the combinato-rial background.Asan additionalcheck, we generateeventswith Bs

→

K∗0

(

K+

π

−

)

μ

+

μ

−decays.Assumingthattheratioof

branch-ing fractions

B(

Bs

→

J

/ψ

K∗0

)/

B(

B0

→

J

/ψ

K∗0

)

≈

10−2 [40], less

thanoneeventpassesourselectioncriteria.

Possiblebackgroundsfromeventswithtwohadrons misidenti-fiedasmuons,inparticularfromthehadronicfullyreconstructable B0

_→

_{DX decays, are suppressed by the misidentification}

prob-ability (10−3

_×

₁₀−3_{), and are thus considered negligible. Also,}

events from B0

_→

_J

_/ψ

_K∗0 _{decays, where a muon and a hadron}

are swapped, are suppressedby the hadron-to-muon misidentifi-cation probability (10−3) and by the muon-to-hadron identifica-tioninefficiency(10−1).Infact,giventheamountofreconstructed B0

→

J

/ψ

K∗0 events(165 k),weexpect

≈

16 eventsdistributedin thetwoadjacentq2 _{binsclosetotheJ}

_/ψ

_{controlregion.}

Backgrounds from semileptonic decays such as B0

_→

_D−

_π

+_,

B0

_→

_D−_K+_{,and B}0

_→

_D−

_μ

+

_ν

μ, where D− decays to K∗0

μ

−

ν

μ

andK∗0 _toK+

_π

−_{,arealsostudiedusingsimulation.Weestimate}

indatalessthanoneeventforeachofthethreedecayspopulating thelow-mass sideband.All thesepotential sources ofbackground are evaluated in the whole q2 range, excluding the J

/ψ

and

ψ



controlregions,andarefoundtobenegligible.

TheimpactofotherpartiallyreconstructedmultibodyB decays thatmightaffectthelow-masssidebandisaddressedinSection5. Backgrounds fromeventsinwhich aB+

→

K+

μ

+

μ

− decayis combined with a random pion, and from events with a

b

→

0

μ

+

μ

− decay, where

0 decays to p K, in which the proton is assigned the pion mass, are found to be negligible. In fact, both processes are flavor-changing neutral-current decays, there-foretheyhaveacomparablebranchingfractiontooursignal pro-cess. The former decayhas atheoretical lower bound on the in-variant mass that lies at

≈

5

.

41 GeV. We search in data for an invariantmasspeakaroundtheB+world-averagemassafter com-putingtheinvariantmassforbothK+

μ

+

μ

− andK−

μ

+

μ

− possi-bilities ineventswith 5

.

41

−

σ

m

<

m

<

mB0

+

0

.

280 GeV, butno

evidence ofsuch apeak is found.Forthe latterdecaywe search indata foran invariant mass peakaround the

b world-average

massafterassigningtheprotonmasstothetrackpreviously iden-tifiedasapion.Alsointhiscase,noevidenceofapeakisfound. Indeed,thesimulationshowsthatlessthanoneeventisexpected topassourselectionrequirements.

4. Analysismethod

ThisanalysismeasurestheP1andP5 valuesinB0

→

K∗0

μ

+

μ

−

decaysasa function ofq2.Fig.1 illustrates theangularvariables neededto describe the decay:

θ

 isthe angle betweenthe

posi-tive(negative)muonmomentumandthedirectionoppositetothe B0



_B0



_{momentuminthedimuonrestframe,}

_θ

K istheangle

be-tween thekaonmomentum andthedirectionopposite to theB0



B0



momentum in the K∗0



K∗0



rest frame, and

ϕ

is the an-gle between the plane containing the two muons andthe plane containing the kaonandthe pioninthe B0 _{restframe. Although}

theK+

π

− invariantmassisrequiredtobeconsistentwiththatof a K∗0 meson, there canbe a contributionfrom spinless(S-wave) K+

π

− combinations [25,45–47]. This is parametrized withthree terms: FS, which is related to the S-wave fraction, and AS and

A5

P-Fig. 1. Illustration of the angular variablesθ(left),θK(middle), andϕ(right) for the decay B0→K∗0(K+π−)μ+μ−.

wavedecays.Includingthesecomponents,theangulardistribution ofB0

_→

_K∗0

_μ

+

_μ

−_{decayscanbewrittenas [25]:}

1 d

/

dq2 d4

_

dq2_dcos

_θ

dcos

θ

Kd

ϕ

=

9 8

π



2 3



(

FS

+

AScos

θ

K

)



1

−

cos2

θ





+

A5_S



1

−

cos2

_θ

K



1

−

cos2

_θ

cos

ϕ

+ (

1

−

FS

)



2 FLcos2

θ

K



1

−

cos2

θ





+

1 2

(

1

−

FL

)



1

−

cos2

θ

K

 

1

+

cos2

θ





+

1 2P1

(

1

−

FL

)

(

1

−

cos2

θ

K

)(

1

−

cos2

θ



)

cos 2

ϕ

+

2 P₅cos

θ

K



FL

(

1

−

FL

)



1

−

cos2

_θ

K



1

−

cos2

_θ

cos

ϕ

,

(1)

whereFLdenotesthelongitudinalpolarizationfractionoftheK∗0.

Thisexpression is an exact simplificationof the full angular dis-tribution,obtainedbyfoldingthe

ϕ

and

θ

 anglesaboutzeroand

π

/

2,respectively.Specifically,if

ϕ

<

0,then

ϕ

→ −

ϕ,

andthenew

ϕ

domainis[0,

π

].If

θ



>

π

/

2,then

θ



→

π

− θ

,andthe new

θ

 domain is [0,

π/

2]. We use thissimplified version of the

ex-pressionbecauseofdifficultiesinthefitconvergencewiththefull angular distribution due to the limited size of the data sample. Thissimplificationexploitstheoddsymmetryoftheangular vari-ableswithrespect to

ϕ

=

0 and

θ



=

π

/

2 in sucha mannerthat

thecancellationaroundtheseangularvaluesisexact.This cancel-lation remains approximately valideven after accounting forthe experimentalacceptancebecausetheefficiencyissymmetricwith respecttothefoldingangles.

Foreachq2 bin,theobservablesofinterest areextractedfrom an unbinned extended maximum-likelihood fit to four variables: theK+

π

−

μ

+

μ

−invariantmassm andthethreeangularvariables

θ

,

θ

K,and

ϕ

.Theunnormalizedprobabilitydensityfunction(pdf)

ineachq2binhasthefollowingform:

pdf

(

m

, θ

K

, θ



,

ϕ

)

=

Y_SC



SC

(

m

)

Sa

(θ

K

, θ



,

ϕ

)



C

(θ

K

, θ



,

ϕ

)

+

fM 1

−

fM S M

₍

_m

₎

_Sa

₍

_−θ

K

,

−θ



,

ϕ

)



M

(θ

K

, θ



,

ϕ

)



+

YBBm

(

m

)

BθK

(θ

K

)

Bθ

(θ



)

Bϕ

(

ϕ

),

(2)

where the three terms on the righthand side correspond to cor-rectly tagged signal events, mistagged signal events, and back-ground events.The parameters YC_S and YB are the yields of cor-rectly tagged signal events and background events, respectively, and are determined in the fit.The parameter fM is the fraction of signal eventsthat are mistaggedandis determined from sim-ulation.Its valuerangesfrom0.124to0.137depending ontheq2

bin.

The signal mass probability functions SC

₍

_m

₎

_{and S}M

₍

_m

₎

_are each the sum of two Gaussian functions, with a common mean for all four Gaussian functions, and describe the mass distribu-tionforcorrectlytaggedandmistaggedsignalevents,respectively. In the fit,the mean,the four Gaussian function’s width parame-ters, andthetwo fractions specifyingthe relative contributionof the two Gaussian functionsin SC

₍

_m

₎

_{and S}M

₍

_m

₎

_{are determined} fromsimulation.Thefunction Sa

_(θ

K

,

θ



, ϕ)

describesthesignalin

thethree-dimensional(3D)spaceoftheangularvariablesand cor-responds toEq. (1). Thecombination Bm

₍

_m

₎

_BθK

_(θ

K

)

Bθ

(θ



)

Bϕ

(

ϕ

)

is obtained from the B0 sideband data in m and describes the background inthespace of

(

m

,

θ

K

,

θ



, ϕ)

,where Bm

(

m

)

isan

ex-ponentialfunction,BθK

_(θ

K

)

andBθ

(θ



)

aresecond- tofourth-order

polynomials, depending on theq2 bin,and Bϕ

(

ϕ

)

isa first-order polynomial.Thefactorizationassumptionofthebackgroundpdfin Eq. (2) isvalidatedbydividingtherangeofanangularvariableinto two atitscenter pointandcomparingthedistributions ofevents fromthetwohalvesintheotherangularvariables.

Thefunctions



C

_(θ

K

,

θ



, ϕ)

and



M

(θ

K

,

θ



, ϕ)

aretheefficiencies

inthe 3Dspaceof

|

cos

θ

K

|

≤

1, 0

≤

cos

θ



≤

1,and0

≤

ϕ

≤

π

for

correctlytaggedandmistaggedsignalevents,respectively.The nu-meratoranddenominatoroftheefficiencyareseparatelydescribed withanonparametrictechnique,whichisimplementedwitha ker-neldensityestimator [48,49].Thefinalefficiencydistributionsused in the fit are obtained from the ratio of 3D histograms derived fromthesamplingofthekerneldensityestimators.Thehistograms have 40bins ineach dimension.A consistency checkof the pro-cedure used todeterminethe efficiencyisperformedby dividing thesimulateddatasample intotwoindependentsubsets,and ex-tracting the angular parameters from the first subset using the efficiency computed from the second subset. The efficiencies for both correctly tagged and mistagged events peak at cos

θ



≈

0,

aroundwhichtheyarerathersymmetricforq2

_<

_{10 GeV}2_,andare

approximatelyflatin

ϕ

.Theefficiencyforcorrectlytaggedevents becomesrelativelyflatincos

θ

forlargervaluesofq2,whileithas

amonotonicdecreaseforincreasingcos

θ

Kvaluesforq2

<

14 GeV2.

Forlargervaluesofq2 adecreaseintheefficiencyisalsoseennear cos

θ

K

= −

1.Theefficiencyformistaggedeventshasaminimumat

cos

θ



≈

0 forq2

>

10 GeV2,whileitismaximalnearcos

θ

K

=

0 for q2

_<

_{10 GeV}2_{.Forlargevaluesofq}2 _{amildmaximumalsoappears}

Thefitisperformedintwosteps.Theinitialfitdoesnotinclude asignalcomponentandusesthesidebanddatainm toobtainthe

Bm

(

m

)

,BθK

_(θ

K

)

,Bθ

(θ



)

,andBϕ

(

ϕ

)

distributions.Thedistributions

obtainedin thisstep arethen fixedforthesecond step,whichis afittothedataoverthefullmassrange.Thefittedparametersin thesecond step are the angularparameters P1, P₅,and A5_S, and theyields Y_SC and YB. Toavoiddifficulties inthe convergenceof thefitrelatedtothelimitednumberofevents,theangular param-etersFL, FS,andASarefixedtopreviousmeasurements [31].

The expression describing the angular distribution of B0

→

K∗0

μ

+

μ

− decays, Eq. (1), and also its more general form in Ref. [25], can become negative for certain values of the angular parameters.Inparticular, thepdf inEq. (2) isonly guaranteedto bepositiveforaparticularsubsetofthe P1, P₅,andA5_Sparameter space. The presence of such a boundary greatly complicates the numericalmaximization process ofthe likelihoodby minuit [50] andespecially the error determination by minos [50], in partic-ularnearthe boundarybetweenphysicalandunphysical regions. Therefore,thesecondfitstepisperformedby discretizingthe P1,

P₅ two-dimensionalspaceandbymaximizing thelikelihoodasa functionofthenuisanceparametersYC_S,YB,andA5_Satfixedvalues ofP1 andP₅.Finally,thedistributionofthelikelihoodvaluesisfit witha bivariate Gaussian distribution. The position of the maxi-mum of thisdistribution inside the physicalregion provides the measurementsof P1andP₅.

The interference terms AS and A5_S must vanish if either of thetwointerfering componentsvanish.Theseconstraintsare im-plemented by requiring

|

AS

|

<

√

12FS

(

1

−

FS

)

FLf and

|

A5_S

|

<

√

3FS

(

1

−

FS

)(

1

−

FL

)(

1

+

P1

)

f , where f is aratiorelatedtothe

S- andP-wavelineshapes,calculatedtobe0.89neartheK∗0

me-sonmass [25].Theconstrainton ASisnaturallysatisfiedsince FS,

FL,andAS aretakenfrompreviousmeasurements [31].

Toensurecorrectcoverage fortheuncertainties, theFeldman– Cousinsmethod [51] isusedwithnuisanceparameters.Twomain setsofpseudo-experimentalsamplesaregenerated.Thefirst (sec-ond)set,usedto computethe coverage for P1 ( P₅), isgenerated byassigningvaluestotheotherparameters asobtainedby profil-ingthebivariateGaussiandistributiondescriptionofthelikelihood determined from data at fixed P1 ( P5) values. When fitting the

pseudo-experimental samples, the same fit procedure as applied tothedataisused.

The fit formalism and results are validated through fits to pseudo-experimentalsamples,MCsimulationsamples,andcontrol channels. Additional details, including the size of the systematic uncertainties assignedonthe basis ofthesefits,are described in Section5.

5. Systematicuncertainties

The systematic uncertainty studies are described below and summarizedinTable1inthesameorder.

The adequacy of the fit function and the procedure to deter-minetheparametersofinterestarevalidatedinthreeways.First, alarge, statisticallyprecise MC signal samplewithapproximately 400timesthenumberofeventsasthedataisusedtoverifythat the fitting procedure produces results consistent with the input values to the simulation. The difference between the input and output valuesin thischeck isassigned asa simulation mismod-elingsystematicuncertainty.Itisalsoverifiedthatfittingasample withonly either correctly taggedor mistagged events yields the correct results. Second, 200 subsamples are extracted randomly fromthelarge MCsignal sample andcombinedwithbackground eventsobtainedfromthepdfinEq. (2) tomimicindependentdata sets ofsimilar size to the data.These are used to estimate a fit

Table 1

Systematic uncertaintiesinP1 and P5. Foreachsource, therangeindicatesthe

variationoverthebinsinq2_.

Source P1(×10−3) P5(×10−3)

Simulation mismodeling 1–33 10–23

Fit bias 5–78 10–120

Finite size of simulated samples 29–73 31–110

Efficiency 17–100 5–65 Kπmistagging 8–110 6–66 Background distribution 12–70 10–51 Mass distribution 12 19 Feed-through background 4–12 3–24 FL, FS, ASuncertainty propagation 0–210 0–210 Angular resolution 2–68 0.1–12 Total 100–230 70–250

bias by comparing the average values of the results obtainedby fittingthe 200samplesto theresultsobtained usingthefull MC signalsample. Muchoftheobservedbiasisaconsequenceofthe fittedparameterslyingclosetotheboundariesofthephysical re-gion.Third,200pseudo-experiments, eachwiththesamenumber ofevents asthedatasample, are generatedineach q2 binusing the pdf in Eq. (2), with parameters obtained fromthe fitto the data.Fits to these200samples donot reveal anyadditional sys-tematicuncertainty.

Because the efficiency functions are estimated from a finite number of simulated events, there is a corresponding statistical uncertaintyinthe efficiency.Alternativesto thedefaultefficiency functionareobtainedbygenerating100newdistributionsforthe numerator andthe denominator of the efficiency ratiobased on thedefaultkerneldensityestimators aspdfs, andrederivingnew kerneldensityestimatorsforeachtrial.Theeffectofthese differ-entefficiencyfunctionsonthefinal resultisusedtoestimate the systematicuncertainty.

Theefficiencydeterminationischeckedbycomparing efficien-cy-corrected resultsobtained fromthe control channelswith the corresponding world-average values. The B0

→

J

/ψ

K∗0 control sample contains165 000events,comparedwith11 000eventsfor the B0

_{→ ψ}

_K∗0 _{sample. Because of its greater statistical}

preci-sion, we rely on the B0

_→

_J

_/ψ

_K∗0 _{sample to perform the check}

of the efficiency determination for the angular variables. We do thisby measuringthe longitudinalpolarization fraction FLin the B0

→

J

/ψ

K∗0 decays.Wefind FL

=

0

.

537

±

0

.

002

(

stat

)

,compared with the world-average value 0

.

571

±

0

.

007

(

stat

+

syst

)

[40]. The difference of 0

.

034 is propagated to P1 and P5 by

tak-ing the root-mean-square (RMS) of the respective distributions resulting from refitting the data 200 times, varying FL within a Gaussian distribution with a standard deviation of 0.034. As a cross-check that the overall efficiency is not affected by a

q2_{-dependent offset, we measure the ratio of branching}

frac-tions

B(

B0

_{→ ψ}

_K∗0

_)/B(

_B0

_→

_J

_/ψ

_K∗0

₎

₌

₀

_.

₄₈₀

_±

₀

_.

₀₀₈

₍

_stat

₎

_±

0

.

055

(

Rμμ_ψ

)

, by means of efficiency-corrected yields including bothcorrectlyandwrongly taggedevents(thesamecentralvalue is obtainedalsoseparately forthetwo subsets ofevents), where Rμμ_ψ refers to the ratio

B(

J

/ψ

→

μ

+

μ

−

)/

B(ψ



→

μ

+

μ

−

)

of branching fractions. Thisis compared tothe world-average value 0

.

484

±

0

.

018

(

stat

)

±

0

.

011

(

syst

)

±

0

.

012

(

Ree_ψ

)

[40],where Ree_ψ refers to the corresponding ratioof branching fractions to e+e−. Thetworesultsareseentoagreewithintheuncertainties.

Toevaluatetheuncertaintyinthemistagfraction fM,weallow thisfractiontovaryinafittotheeventsintheB0

→

J

/ψ

K∗0 con-trolsample. We find fM

= (

14

.

5

±

0

.

5

)

%, compared to theresult fromsimulation

(

13

.

7

±

0

.

1

)

%.Thedifferenceof0.8ispropagated to P1 and P5 bydetermining theRMSofthe respective

distribu-Fig. 2. InvariantmassandangulardistributionsofK+π−μ+μ−eventsfor(uppertworows)2<q2_{<4.3 GeV}2

and(lowertworows)4.3<q2_{<6 GeV}2

.Theprojectionof theresultsfromthetotalfit,aswellasforcorrectlytaggedsignalevents,mistaggedsignalevents,andbackgroundevents,arealsoshown.Theverticalbarsindicatethe statisticaluncertainties.

tionsobtainedfromrefittingthedata10times,varying fM within aGaussiandistributionwithastandarddeviationof 0.8.

Thesystematicuncertainty associatedwiththefunctionsused to model the angular distribution of the background is obtained fromthestatisticaluncertaintyinthebackgroundshape,asthese shapes are fixed in the final fit. This uncertainty is determined byfittingthe data200times,varying thebackgroundparameters withintheirGaussianuncertainties,andtakingtheRMSofthe an-gular parameter values as the systematic uncertainty. Moreover, for the q2 binreported in Fig. 2, upper two rows, which shows anexcessaround cos

θ



≈

0

.

7 thatisalsopresentinthesideband

distribution(notshowninthefigure), werefitthedatausing

dif-ferent descriptionsofthe backgroundasafunction ofcos

θ

.The

differencesinthemeasurementof P1 and P5 arewithin the

sys-tematicuncertaintyquotedforthebackgrounddistribution. The low-mass sideband might contain partially reconstructed multibody B0 _{decays.Wetestthispossibilitybyrefittingthedata}

with a restricted range for the low-mass sideband, i.e., starting from

≈

5

.

1 insteadof

≈

5 GeV.Nosignificantdifferencesareseen inthemeasurementofP1andP5,andthereforenosystematic

un-certaintyisassigned.

Toevaluatethesystematicuncertaintyassociatedwiththe sig-nal mass pdfs SC

(

m

)

and SM

(

m

)

, we fit the B0

→

J

/ψ

K∗0 and B0

_{→ ψ}

_K∗0 _{control samplesallowing two ofthe widthvaluesin}

Table 2

Themeasured signalyields,whichincludebothcorrectlytaggedandmistaggedevents,the P1 and P5 values,andthecorrelationcoefficients,inbinsofq2,forB0→

K∗0_μ+_μ−_{decays.Thefirstuncertaintyisstatisticalandthesecondissystematic.Thebinrangesareselectedtoallowcomparisonwithpreviousmeasurements.}

q2_(GeV2_{) Signal yield P}

1 P5 Correlations 1.00–2.00 80±12 +0.12+0.46 −0.47±0.10 +0.10+ 0.32 −0.31±0.07 −0.0526 2.00–4.30 145±16 −0.69+0.58 −0.27±0.23 −0.57+ 0.34 −0.31±0.18 −0.0452 4.30–6.00 119±14 +0.53₋+00..2433±0.19 −0.96+ 0.22 −0.21±0.25 +0.4715 6.00–8.68 247±21 −0.47₋+00..2723±0.15 −0.64+ 0.15 −0.19±0.13 +0.0761 10.09–12.86 354±23 −0.53₋+00..2014±0.15 −0.69+ 0.11 −0.14±0.13 +0.6077 14.18–16.00 213±17 −0.33+0.24 −0.23±0.20 −0.66+ 0.13 −0.20±0.18 +0.4188 16.00–19.00 239±19 −0.53±0.19±0.16 −0.56±0.12±0.07 +0.4621

Fig. 3. CMSmeasurementsofthe(left)P1and(right)P5angularparametersversusq2forB0→K∗0μ+μ−decays,incomparisontoresultsfromtheLHCb [33] andBelle [34]

Collaborations.Thestatisticaluncertaintiesareshownbytheinnerverticalbars,whiletheouterverticalbarsgivethetotaluncertainties.Thehorizontalbarsshowthebin widths.TheverticalshadedregionscorrespondtotheJ/ψandψresonances.ThehatchedregionshowsthepredictionfromSMcalculationsdescribedinthetext,averaged overeachq2_bin.

thefourGaussian termstovary atatime. Themaximumchange inP1andP₅foreitherofthetwocontrolchannelsistakenasthe

systematicuncertaintyforallq2 bins.

Theq2 _{binjustbelowtheJ}

_/ψ

₍

_ψ

_{) controlregion,andtheq}2

bin just above, may be contaminated with B0

_→

_J

_/ψ

_K∗0 _(B0

_→

ψ

K∗0) “feed-through”events that arenot removed by the selec-tion procedure. A special fit in these two bins is performed, in which an additional background term is added to the pdf. This backgrounddistribution isobtainedfrom simulatedB0

_→

_J

_/ψ

_K∗0

(B0

_{→ ψ}

_K∗0_{)events,withthebackgroundyieldasafitted}

param-eter.The resultingchanges in P1 and P₅ areusedasestimatesof thesystematicuncertaintyassociatedwiththiscontribution.

Toproperlypropagate theuncertaintyassociatedwiththe val-ues of FL, FS, and AS, taking into account possible correlations,

10pseudo-experimentsperq2 _{binaregeneratedusingthepdf}

pa-rametersdetermined fromthe fit todata. The number ofevents in these pseudo-experiments is 100 times that of the data. The pseudo-experimentsare then fittwice, once with the same pro-cedureasfor thedataandonce with P1, P5, A5S, FL, FS,and AS

allowed to vary. The average ratio

ρ

of the statistical uncertain-ties in P1 and P₅ from the first fit to that in the second fit is

usedtocomputethissystematicuncertainty,whichisproportional tothe confidenceinterval determined fromthe Feldman–Cousins methodthrough the coefficient

√

ρ

2

₋

_{1. The stability of}

_ρ

_{as a}

function of the number of events of the pseudo-experiments is alsoverified.Ascross-checksofourprocedureconcerningthefixed value of FL, we fit the two control regions either fixing FL or allowing it to vary, and find that the values of P1 and P5 are

essentially unaffected, obtaining the same value of FL as in our previousstudy [31]. Moreover,we refitallthe q2 binsusingonly theP-wavecontribution forthedecayrateinEq. (1) and leaving

all threeparameters, P1, P5,and FL,free tovary. Thedifferences

in the measured values of P1 and P₅ are within the systematic uncertaintyquotedfortheFL,FS,andASuncertaintypropagation. Theeffectsofangularresolutiononthereconstructedvaluesof

θ

Kand

θ

areestimatedbyperformingtwofitsonthesamesetof

simulatedevents.Onefitusesthetruevaluesoftheangular vari-ablesandtheotherfittheirreconstructedvalues.Thedifferencein thefittedparametersbetweenthetwofitsistakenasanestimate ofthesystematicuncertainty.

The systematic uncertainties are determined for each q2 bin, withthetotalsystematicuncertaintyobtainedbyaddingthe indi-vidualcontributionsinquadrature.

As a note for future possible global fits of our P1 and P₅

data, the systematic uncertainties associated with the efficiency, Kπ mistagging, B0 mass distribution, and angularresolution can beassumedtobefullycorrelatedbin-by-bin,whiletheremaining uncertaintiescanbeassumedtobeuncorrelated.

6. Results

Theeventsarefitinsevenq2 _{binsfrom1to19 GeV}2_,yielding

1397signal and1794backgroundeventsintotal. Asan example, distributions fortwoofthesebins,along withthefitprojections, are shown in Fig. 2. The fitted values of the signal yields, P1,

and P₅ are given in Table 2 for the seven q2 _{bins. The results}

for P1 and P₅ are shown in Fig. 3, along with those from the LHCb [33] andBelle [34] experiments.ThefittedvaluesofA5

S vary

from

−

0

.

052 to

+

0

.

057.

ASM prediction,denoted SM-DHMV,isavailable for compari-sonwiththemeasuredangularparameters.TheSM-DHMVresult, derived fromRefs. [18,25],updatesthecalculationsfromRef. [52]

to accountfor theknown correlation betweenthedifferent form factors [53]. It also combines predictions from light-cone sum rules, which are valid in the low-q2 region, with lattice predic-tionsathighq2 _{[54] toobtainmoreprecisedeterminationsofthe}

formfactorsoverthefullq2 range.Thehadroniccharm-quarkloop contributionisobtainedfromRef. [55]. A reliabletheoretical pre-diction is not available nearthe J

/ψ

and

ψ

 resonances. The SM predictionis shownincomparisonto thedata inFig.3 andit is seen to be in agreement with the CMSresults. Thus, we do not obtainevidenceforphysicsbeyondtheSM.Qualitatively,theCMS measurements are compatible with the LHCb results. The Belle measurementsliesystematicallyaboveboththeCMSandLHCb re-sultsandtheSMprediction.

7. Summary

Usingproton–protoncollisiondatarecordedat

√

s

=

8 TeV with theCMSdetectorattheLHC,correspondingtoanintegrated lumi-nosity of 20

.

5 fb−1, an angular analysishas been performed for thedecayB0

→

K∗0

μ

+

μ

−.Thesignalsampleconsistsof1397 se-lectedevents.Foreachofsevenbinsbetween1to19 GeV2 inthe dimuoninvariantmasssquaredq2_{,unbinnedmaximum-likelihood}

fitsareperformedonthedistributionsoftheK+

π

−

μ

+

μ

− invari-ant mass andthree angular variables to obtain values ofthe P1

andP₅ parameters.Theresultsareamongthemostprecisetodate fortheseparametersandareconsistentwithpredictionsbasedon thestandardmodel.

Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN 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-tionandoperation oftheLHCandthe CMSdetectorprovidedby thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIEN-CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN(Italy); MSIPandNRF(RepublicofKorea);LAS (Lithuania);MOE andUM (Malaysia); BUAP, CINVESTAV,CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland);FCT(Portugal);JINR(Dubna);MON,RosAtom,RAS,RFBR andRAEP(Russia);MESTD (Serbia);SEIDI,CPAN,PCTI andFEDER (Spain);SwissFundingAgencies(Switzerland);MST(Taipei); ThEP-Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).

References

[1] W.Altmannshofer,P.Ball,A.Bharucha,A.J.Buras,D.M.Straub,M.Wick, Sym-metries and asymmetriesof B→K∗μ+μ− decays inthe standard model andbeyond,J.HighEnergyPhys.01(2009)019,https://doi.org/10.1088/1126 -6708/2009/01/019,arXiv:0811.1214.

[2] J. Matias, F.Mescia, M. Ramon, J. Virto, Complete anatomy of Bd→K∗

0 (→Kπ)+−anditsangulardistribution,J.HighEnergyPhys.04(2012)104,

https://doi.org/10.1007/JHEP04(2012)104,arXiv:1202.4266.

[3] S.Descotes-Genon, J.Matias,J.Virto,Global analysisofb→sanomalies, J.HighEnergyPhys.06(2016)092,https://doi.org/10.1007/JHEP06(2016)092, arXiv:1510.04239.

[4] D. Melikhov, N. Nikitin, S. Simula, Probing right-handed currents in B→ K∗+− transitions, Phys. Lett. B 442 (1998) 381, https://doi.org/10.1016/ S0370-2693(98)01271-4,arXiv:hep-ph/9807464.

[5] A.Ali,P.Ball,L.T.Handoko,G.Hiller,AcomparativestudyofthedecaysB→ (K,K∗)+−inthestandardmodelandsupersymmetrictheories,Phys.Rev.D 61(2000)074024,https://doi.org/10.1103/PhysRevD.61.074024,arXiv:hep-ph/ 9910221.

[6] Q.-S.Yan,C.-S.Huang,W.Liao,S.-H.Zhu,Exclusivesemileptonicraredecays

B→ (K,K∗)+−insupersymmetrictheories,Phys.Rev.D62(2000)094023,

https://doi.org/10.1103/PhysRevD.62.094023,arXiv:hep-ph/0004262. [7] G.Buchalla,G.Hiller,G.Isidori,Phenomenologyofnonstandard Z couplings

inexclusivesemileptonic b→s transitions, Phys.Rev.D63(2000)014015,

https://doi.org/10.1103/PhysRevD.63.014015,arXiv:hep-ph/0006136. [8] T.Feldmann,J. Matias,Forward–backwardand isospinasymmetryfor B→

K∗+− decayinthestandardmodelandinsupersymmetry,J.HighEnergy Phys. 01 (2003) 074, https://doi.org/10.1088/1126-6708/2003/01/074, arXiv: hep-ph/0212158.

[9] G.Hiller,F.Krüger,Moremodel-independentanalysisofb→s processes,Phys. Rev.D69(2004)074020,https://doi.org/10.1103/PhysRevD.69.074020, arXiv: hep-ph/0310219.

[10] F.Krüger,J.Matias,ProbingnewphysicsviathetransverseamplitudesofB0_→

K∗0_(→K−_π+_)+_− _{at largerecoil,Phys.Rev.D71(2005)094009,https://}

doi.org/10.1103/PhysRevD.71.094009,arXiv:hep-ph/0502060.

[11] W.-S. Hou, A. Hovhannisyan, N. Mahajan, B→K∗+− forward–backward asymmetryandnewphysics,Phys.Rev.D77(2008)014016,https://doi.org/ 10.1103/PhysRevD.77.014016,arXiv:hep-ph/0701046.

[12] U. Egede,T.Hurth, J.Matias,M.Ramon, W.Reece,Newobservablesinthe decaymodeBd→K∗

0

+−,J.HighEnergyPhys.11(2008)032,https://doi. org/10.1088/1126-6708/2008/11/032,arXiv:0807.2589.

[13] T.Hurth,G.Isidori,J.F.Kamenik,F.Mescia,ConstraintsonnewphysicsinMFV models:a model-independentanalysisofF=1 processes,Nucl.Phys.B808 (2009)326,https://doi.org/10.1016/j.nuclphysb.2008.09.040,arXiv:0807.5039. [14] A.K. Alok, A. Dighe, D. Ghosh, D. London, J. Matias, M. Nagashima, A.

Szynkman,New-physicscontributionstotheforward–backwardasymmetryin

B→K∗μ+μ−, J.HighEnergy Phys.02(2010)053,https://doi.org/10.1007/ JHEP02(2010)053,arXiv:0912.1382.

[15] A.K.Alok,A.Datta,A.Dighe,M.Duraisamy,D.Ghosh,D.London,Newphysics inb→sμ+μ−:CP-conservingobservables,J.HighEnergyPhys.11(2011)121,

https://doi.org/10.1007/JHEP11(2011)121,arXiv:1008.2367.

[16] Q.Chang,X.-Q.Li,Y.-D.Yang,B→K∗+−, K+− decaysinafamily non-universalZmodel,J.HighEnergyPhys.04(2010)052,https://doi.org/10.1007/ JHEP04(2010)052,arXiv:1002.2758.

[17] S.Descotes-Genon,D.Ghosh,J.Matias,M.Ramon,Exploringnewphysicsin theC7–C7plane,J.HighEnergyPhys.06(2011)099,https://doi.org/10.1007/ JHEP06(2011)099,arXiv:1104.3342.

[18] S.Descotes-Genon,J.Matias,M.Ramon,J.Virto,Implicationsfromclean ob-servablesfor the binnedanalysis of B→K∗μ+μ− at largerecoil,J. High EnergyPhys. 01(2013)048,https://doi.org/10.1007/JHEP01(2013)048,arXiv: 1207.2753.

[19] C.Bobeth,G.Hiller,D.vanDyk,ThebenefitsofB→K∗+−decaysatlow re-coil,J.HighEnergyPhys.07(2010)098,https://doi.org/10.1007/JHEP07(2010) 098,arXiv:1006.5013.

[20] C. Bobeth, G. Hiller, D. van Dyk, C. Wacker, The decay B→K+− at lowhadronicrecoil andmodel-independentB=1 constraints,J.High En-ergyPhys.01(2012)107,https://doi.org/10.1007/JHEP01(2012)107,arXiv:1111. 2558.

[21] C.Bobeth,G.Hiller,D.vanDyk,GeneralanalysisofB→K(∗)_+_− _decaysat

lowrecoil,Phys.Rev.D87(2012)034016,https://doi.org/10.1103/PhysRevD.87. 034016,arXiv:1212.2321.

[22] A.Ali,G.Kramer,G.Zhu, B→K∗+−decayinsoft-collineareffective the-ory,Eur.Phys.J.C47(2006)625,https://doi.org/10.1140/epjc/s2006-02596-4, arXiv:hep-ph/0601034.

[23] W.Altmannshofer,P.Paradisi,D.M.Straub,Model-independentconstraintson newphysicsinb→s transitions,J.HighEnergyPhys.04(2012)008,https:// doi.org/10.1007/JHEP04(2012)008,arXiv:1111.1257.

[24] S.Jäger,J.Martin Camalich,On B→Vat smalldileptoninvariantmass, power corrections, and new physics, J. High Energy Phys. 05 (2013) 043,

https://doi.org/10.1007/JHEP05(2013)043,arXiv:1212.2263.

[25] S.Descotes-Genon,T.Hurth,J.Matias,J.Virto,OptimizingthebasisofB→ K∗+−observablesinthefullkinematicrange,J.HighEnergyPhys.05(2013) 137,https://doi.org/10.1007/JHEP05(2013)137,arXiv:1303.5794.

[26] B.Aubert,etal.,BABAR,AngulardistributionsinthedecayB→K∗+−,Phys. Rev.D79(2009)031102,https://doi.org/10.1103/PhysRevD.79.031102, arXiv: 0804.4412.

[27] J.-T.Wei,etal.,Belle,Measurementofthedifferentialbranchingfractionand forward–backwardasymmetryfor B→K(∗)_+_−_{,Phys.Rev.Lett.103(2009)}

[28] T. Aaltonen, et al., CDF, Measurements of the angular distributions in the decays B→K(∗)_μ+_μ− _{at CDF,Phys. Rev.Lett.108(2012) 081807,https://}

doi.org/10.1103/PhysRevLett.108.081807,arXiv:1108.0695.

[29] LHCbCollaboration,Differentialbranchingfractionandangularanalysisofthe decayB0_→K∗0_μ+_μ−_{,J.HighEnergyPhys.08(2013)131,https://doi.org/10.}

1007/JHEP08(2013)131,arXiv:1304.6325.

[30] CMSCollaboration,Angularanalysisand branchingfractionmeasurementof thedecayB0_→K∗0_μ+_μ−_{,Phys.Lett.B727(2013)77,https://doi.org/10.1016/}

j.physletb.2013.10.017,arXiv:1308.3409.

[31] CMSCollaboration,AngularanalysisofthedecayB0_→K∗0_μ+_μ−_frompp

col-lisionsat√s=8 TeV,Phys.Lett.B753(2016)424,https://doi.org/10.1016/j. physletb.2015.12.020,arXiv:1507.08126.

[32] LHCbCollaboration, Measurementofform-factor-independentobservablesin thedecayB0_→K∗0_μ+_μ−_{,Phys.Rev.Lett.111(2013)191801,https://doi.org/}

10.1103/PhysRevLett.111.191801,arXiv:1308.1707.

[33] LHCbCollaboration,AngularanalysisoftheB0_→K∗_μ+_μ−_{decayusing3 fb}−1

ofintegratedluminosity,J.HighEnergyPhys.02(2016)104,https://doi.org/10. 1007/JHEP02(2016)104,arXiv:1512.04442.

[34] A. Abdesselam, et al., Belle, Lepton-flavor-dependent angular analysis of

B→K∗+−, Phys. Rev. Lett. 118 (2017) 111801, https://doi.org/10.1103/ PhysRevLett.118.111801,arXiv:1612.05014.

[35] CMSCollaboration,CMSLuminosityBasedonPixelClusterCounting—Summer 2013 Update, CMS Physics Analysis Summary CMS-PAS-LUM-13-001, 2013,

http://cdsweb.cern.ch/record/1598864.

[36] CMSCollaboration,TheCMSexperimentattheCERNLHC,J.Instrum.3(2008) S08004,https://doi.org/10.1088/1748-0221/3/08/S08004.

[37] CMSCollaboration,Descriptionandperformanceoftrackandprimary-vertex reconstructionwiththeCMStracker,J.Instrum.9(2014)P10009,https://doi. org/10.1088/1748-0221/9/10/P10009,arXiv:1405.6569.

[38] CMSCollaboration,PerformanceofCMSmuonreconstructioninppcollision eventsat √s=7 TeV, J. Instrum.7(2012)P10002, https://doi.org/10.1088/ 1748-0221/7/10/P10002,arXiv:1206.4071.

[39] CMSCollaboration, The CMS trigger system, J. Instrum. 12(2017) P01020,

https://doi.org/10.1088/1748-0221/12/01/P01020,arXiv:1609.02366. [40] ParticleDataGroup,C.Patrignani,etal.,Thereviewofparticlephysics,Chin.

Phys.C40(2016)100001,https://doi.org/10.1088/1674-1137/40/10/100001. [41] T.Sjöstrand, S. Mrenna,P.Skands, PYTHIA6.4 physics andmanual, J.High

Energy Phys.05(2006) 026,https://doi.org/10.1088/1126-6708/2006/05/026, arXiv:hep-ph/0603175.

[42] D.J.Lange,TheEvtGenparticledecaysimulationpackage,Nucl.Instrum. Meth-odsA462(2001)152,https://doi.org/10.1016/S0168-9002(01)00089-4.

[43] E.Barberio,Z.Was,Photos—auniversalMonteCarloforQEDradiative correc-tionsinZandWdecays,Eur.Phys.J.C45(2006)97,https://doi.org/10.1140/ epjc/s2005-02396-4,arXiv:hep-ph/0506026.

[44] S. Agostinelli,et al., GEANT4, GEANT4—a simulation toolkit, Nucl. Instrum. MethodsA506(2003)250,https://doi.org/10.1016/S0168-9002(03)01368-8. [45] D. Beˇcirevi ´c, A. Tayduganov,Impact of B→K∗0_+_− _{on the newphysics}

searchin B→K∗+− decay,Nucl.Phys.B868(2013)368,https://doi.org/ 10.1016/j.nuclphysb.2012.11.016,arXiv:1207.4004.

[46] J.Matias,OntheS-wavepollutionofB→K∗+−observables,Phys.Rev.D86 (2012)094024,https://doi.org/10.1103/PhysRevD.86.094024,arXiv:1209.1525. [47] T.Blake,U.Egede,A.Shires,TheeffectofS-waveinterferenceonthe B0_→

K∗0_+_− _{angularobservables,J.HighEnergyPhys.03(2013)027,https://doi.}

org/10.1007/JHEP03(2013)027,arXiv:1210.5279.

[48] D.W.Scott,MultivariateDensityEstimation:Theory,Practice,andVisualization, Wiley Seriesin Probabilityand MathematicalStatistics: Applied Probability andStatisticsSection,Wiley-Interscience,NewYork,Chichester,Brisbane,1992,

http://opac.inria.fr/record=b1089297.

[49] K.S.Cranmer,Kernel estimationinhigh-energyphysics, Comput.Phys. Com-mun.136(2001)198,https://doi.org/10.1016/S0010-4655(00)00243-5,arXiv: hep-ex/0011057.

[50] F.James,M.Roos,Minuit—asystemforfunctionminimizationandanalysisof theparametererrorsandcorrelations,Comput.Phys.Commun.10(1975)343,

https://doi.org/10.1016/0010-4655(75)90039-9.

[51] G.J.Feldman,R.D.Cousins,Unifiedapproachtotheclassicalstatisticalanalysis ofsmallsignals,Phys.Rev.D57(1998)3873,https://doi.org/10.1103/PhysRevD. 57.3873,arXiv:physics/9711021.

[52] P. Ball,R. Zwicky, Bd,s→ρ,ω,K∗,φ decay form factorsfrom light-cone

sumrulesreexamined,Phys.Rev.D71(2005)014029,https://doi.org/10.1103/ PhysRevD.71.014029,arXiv:hep-ph/0412079.

[53] A.Bharucha,D.M.Straub,R.Zwicky,b→v+−inthestandardmodelfrom light-conesumrules,J.HighEnergyPhys.08(2016)098,https://doi.org/10. 1007/JHEP08(2016)098,arXiv:1503.05534.

[54] R.R.Horgan,Z.Liu,S.Meinel,M.Wingate,LatticeQCDcalculationofform fac-torsdescribingtheraredecaysB→K∗+−andBs→ φ+−,Phys.Rev.D89

(2014)094501,https://doi.org/10.1103/PhysRevD.89.094501,arXiv:1310.3722. [55] A.Khodjamirian,T.Mannel,A.A.Pivovarov,Y.-M.Wang,Charm-loopeffectin

B→K(∗)_+_− _{and b→K}∗ _{γ, J.HighEnergyPhys. 09(2010)089,https://}

doi.org/10.1007/JHEP09(2010)089,arXiv:1006.4945.

TheCMSCollaboration

A.M. Sirunyan,

A. Tumasyan

YerevanPhysicsInstitute,Yerevan,Armenia

W. Adam,

F. Ambrogi,

E. Asilar,

T. Bergauer,

J. Brandstetter, E. Brondolin,

M. Dragicevic,

J. Erö,

M. Flechl,

M. Friedl,

R. Frühwirth

1

,

V.M. Ghete,

J. Grossmann,

J. Hrubec,

M. Jeitler

1

,

A. König, N. Krammer,

I. Krätschmer,

D. Liko, T. Madlener,

I. Mikulec,

E. Pree, N. Rad,

H. Rohringer, J. Schieck

1

, R. Schöfbeck,

M. Spanring, D. Spitzbart,

W. Waltenberger,

J. Wittmann,

C.-E. Wulz

1

, M. Zarucki

InstitutfürHochenergiephysik,Wien,Austria

V. Chekhovsky,

V. Mossolov,

J. Suarez Gonzalez

InstituteforNuclearProblems,Minsk,Belarus

E.A. De Wolf,

D. Di Croce,

X. Janssen, J. Lauwers,

M. Van De Klundert,

H. Van Haevermaet,

P. Van Mechelen,

N. Van Remortel

UniversiteitAntwerpen,Antwerpen,Belgium

S. Abu Zeid,

F. Blekman,

J. D’Hondt,

I. De Bruyn,

J. De Clercq,

K. Deroover,

G. Flouris,

D. Lontkovskyi,

S. Lowette,

S. Moortgat,

L. Moreels, Q. Python, K. Skovpen,

S. Tavernier,

W. Van Doninck,

P. Van Mulders,

I. Van Parijs