Measurement of the CP-violating phase phi s in the B0s at root s=13 TeV s -> J/psi phi(1020) -> & micro; plus & micro;& minus; K plus K & minus; channel in proton-proton collisions at & nbsp;root s=13 Te

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

C P -violating

phase

φ

_s

in

the

B

0

_s

→

J

/

ψ

φ(

1020

)

→ μ

+

μ

−

K

+

K

−

channel

in

proton-proton

collisions

at

√

s

=

13 TeV

.

The

CMS

Collaboration



CERN,Switzerland

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received5July2020

Receivedinrevisedform24February2021 Accepted26February2021

Availableonline3March2021 Editor:M.Doser Keywords: CMS Physics Oscillations Bphysics

The C P -violating

weak phase

φsand the decay width difference sbetween the light and heavy B0s

mass eigenstates are measured with the CMS detector at the LHC in a sample of 48 500 reconstructed B0

s→J/ψ φ(1020)→ μ+μ−K+K−events. The measurement is based on a data sample corresponding

to an integrated luminosity of 96.4 fb−1, collected in proton-proton collisions at √s ₌13 TeV in 2017–2018. To extract the values of φsand s, a time-dependent and flavor-tagged angular analysis

of the μ+μ−K+K− final state is performed. The analysis employs a dedicated tagging trigger and a novel opposite-side muon flavor tagger based on machine learning techniques. The measurement yields

φs= −11 ±50 (stat)±10 (syst) mrad and s=0.114 ±0.014 (stat)±0.007 (syst) ps−1, in agreement with

the standard model predictions. When combined with the previous CMS measurement at √s=8 TeV, the following values are obtained: φs= −21 ±44 (stat)±10 (syst) mrad, s=0.1032 ±0.0095 (stat)±

0.0048 (syst) ps−1, a significant improvement over the 8 TeV result.

©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

1. Introduction

Precision testsof the standard model(SM) of particlephysics havebecome increasingly important,since nodirect evidencefor newphysicshasbeenfoundsofarattheCERNLHC.DecaysofB0 s

mesons presentimportantopportunities toprobethe consistency oftheSM. InthisLetter, anewmeasurementoftheC P -violating weak phase

φ

s andthedecaywidthdifference



s betweenthe

light(BL

s)andheavy(BHs)B0s mesonmasseigenstatesispresented.

Charge-conjugatestatesareimpliedthroughout,unlessstated oth-erwise.

The weak phase

φ

s arises from the interference between

di-rect B0

s meson decays to a C P eigenstate of cc ss and decays

through mixing to the same final state. In the SM,

φ

s is

re-latedto theelements ofthe Cabibbo–Kobayashi–Maskawa matrix via

φ

s

 −

2βs

= −

2arg(

−

VtsV_tb∗

/

VcsV∗_cb

),

neglecting penguin

di-agramcontributions,where

β

s isone oftheanglesoftheunitary

triangles. The current best determination of

−

2βs comes from a

globalfittoexperimental dataonb hadronandkaondecays. As-suming no physics beyond the SM (BSM) in the B0

s mixing and

decays,a

−

2βs valueof

−

36.96+₋00..7284mrad isdetermined [1].New

physicscanmodifythisphaseviathecontributionofBSMparticles

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

to B0_s mixing [2,3].Since the numericalvalue of

φ

s in theSM is

knownveryprecisely,evenasmalldeviationfromthisvaluewould constituteevidenceofBSMphysics.Thedecaywidthdifference be-tweentheBL_s andBH_s eigenstates,ontheother hand,ispredicted less precisely at



s

=

0.091

±

0.013 ps−1 [4]. Its measurement

providesan important test fortheoreticalpredictions andcan be usedtofurtherconstrainnew-physicseffects [4].

The weakphase

φ

s was first measured by the Fermilab

Teva-tronexperiments [5–9],andthen attheLHC by theATLAS, CMS, andLHCbexperiments [10–19],usingB0

s

→

J/

ψ φ(

1020)(referred

toas B0_s

→

J/

ψ φ

inwhat follows),B0_s

→

J/

ψ

f₀

(980),

andB0_s

→

J/

ψ

h+h− decays, where h stands for a kaon or pion. Measure-mentsof

φ

s inB0s decaysto

ψ(

2S)

φ(

1020)andD+sD−s were

per-formedbytheLHCbCollaboration [20,21].

In this Letter, CMS results on the B0_s

→

J/

ψ φ

decay to the

μ

+

μ

−K+K− finalstatearepresented,andpossibleadditional con-tributions tothisfinal state fromthe B_s0

→

J/

ψ

f₀

(980)

and non-resonant B0

s

→

J/

ψ

K+K− decays are taken into account by

in-cluding a termfor an additional S-wave amplitude in the decay model.Comparedtoourpreviousmeasurement [14] at

√

s

=

8TeV, we benefit from the increase in the center-of-mass energy from 8 to 13 TeV that nearly doubles the B0

s production cross section

andanovel opposite-side(OS)muon flavor tagger.The new tag-geremploysmachinelearning techniquesandachievesbetter dis-criminationpowerthanprevious methods.Wealsomakeuseofa

https://doi.org/10.1016/j.physletb.2021.136188

0370-2693/©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Definition ofthethreeanglesθT,ψT,andϕTdescribingthetopologyofthe

B0

s→J/ψ φ→ μ+μ−K+K−decay.

specializedtriggerthatrequiresanadditional(third)muon,which canbeusedforflavortagging,improvingthetaggingefficiencyat thecostofareducednumberofsignalevents.Asaresult,thenew measurement, whilebasedon asimilar numberofB0

s candidates

as the earlierone [14], allows us to double theprecision in the determination of

φ

s, aswell asmeasure some of theparameters

that were constrainedtotheir world-averagevaluesinour previ-ouswork [14].Atthesametime,theprecisiononparametersthat donotbenefitfromthetagginginformation,suchas



s,is

com-parabletothatinthepreviousmeasurement.

Finalstatesthat aremixturesofC P eigenstatesrequirean an-gularanalysistoseparatetheC P -oddandC P -evencomponents.A time-dependent angular analysiscanbe performedby measuring thedecayangles ofthefinal-stateparticles andthe properdecay length of the reconstructed B0_s candidate, which is equal to the properdecaytimet multipliedbythespeedoflight,andreferred toasct inwhatfollows.

Inthismeasurement,weusethetransversitybasis [22] defined bythethreedecayangles

= (θ

T

,

ψ

T

,

ϕ

T

),

asillustrated inFig.1.

The angles

θ

T and

ϕ

T are, respectively, the polar and azimuthal

angles ofthe

μ

+ inthe restframeof theJ/

ψ

meson, wherethe x axisisdefinedbythedirectionofthe

φ

mesonmomentumand the x- y planeis defined by the plane of the

φ

→

K+K− decay. Thehelicityangle

ψ

T istheangleoftheK+mesonmomentumin

the

φ

mesonrestframe withrespect tothe negative J/

ψ

meson momentumdirection.

ThedifferentialdecayrateofB0

s

→

J/

ψ φ

→ μ

+

μ

−K+K−is

de-scribedbyafunction

F(,

ct

,

α

),

asinRef. [23]: d4





B0_s



d

d

(

ct

)

=

F

(,

ct

,

α)

∝

10



i=1 Oi

(

ct

,α)

gi

(),

(1)

where Oi are time-dependentfunctions, gi are angularfunctions,

and

α

isasetofphysicsparameters. ThefunctionsOi

(

ct

,

α

)

are:

Oi

(

ct

,

α)

=

Nie−st



aicosh





st 2



+

bisinh





st 2



+

cicos

(

mst

)

+

disin

(

mst

)



,

(2)

where



ms (s) isthe absolute mass (decay width)difference

between the BL

s and BHs masseigenstates, and



s is the average

decaywidth, definedasthe arithmetic averageofthe BL s andBHs

decay widths.The functions gi

()

andtheparameters Ni,ai,bi,

ci,anddiaredefinedinTable1.

ThecoefficientsC , S,andD containtheinformationaboutC P violation,andaredefinedas:

C

=

1

− |λ|

2 1

+ |λ|

2

,

S

= −

2

|λ|

sin

φ

s 1

+ |λ|

2

,

D

= −

2

|λ|

cos

φ

s 1

+ |λ|

2

,

using the same sign convention as that in the LHCb measure-ment [16]. The amount of C P violation in the B0_s-B0_s system is givenbythecomplexparameter

λ,

definedas

λ

= (

q

/

p

)(

Af

/

Af

),

where Af ( Af

)

is thedecay amplitudeof the B0s (B 0

s) mesonto

thefinal state f ,andtheparameters p andq relatethemassand flavor eigenstates through BH_s

=

p

|

B0_s



−

q

|

B0_s



and BL_s

=

p

|

B0s

+

q

|

B0_s



[24].Theparameters

|

A_⊥

|

2,

|

A0

|

2,and

|

A

|

2 arethe magni-tudes of theperpendicular, longitudinal,and parallel transversity amplitudes of the B0

s

→

J/

ψ φ

decay, respectively;

|

AS

|

2 is the

magnitudeof the S-wave amplitude from B0_s

→

J/

ψ

f₀

(980)

and nonresonant B0

s

→

J/

ψ

K+K− decays,and the parameters

δ

⊥,

δ

0,

δ

,and

δ

S aretherespectivestrongphases.

Equation (1) represents the model for the B0_s meson decay, while the model for the B0_s meson decay is obtained by chang-ingthesignoftheciandditermsinEq. (2).

2. TheCMSdetector

The central feature of the CMS apparatus is a superconduct-ing solenoidof 6 m internal diameter,providing a magnetic field of3.8 T. Withinthe solenoidvolumeare a siliconpixel andstrip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrelandtwo endcapsections.Forward calorimetersextendthe pseudorapidity(

η

)coverageprovidedbythebarrelandendcap de-tectors.Muonsaredetectedingas-ionizationchambersembedded inthesteelflux-returnyokeoutsidethesolenoid.

Thesilicontrackermeasureschargedparticleswithintherange

|

η

|

<

2.5.During theLHC running periodwhen thedata usedin thisLetterwererecorded,thesilicontrackerconsistedof1856 sil-iconpixeland15 148siliconstripdetectormodules.

Muons are measured in the range

|

η

|

<

2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. The efficiency to recon-struct and identify muons is greater than 96%. Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum (pT) resolution, formuons with pT up to

100 GeV,of1%inthebarreland3%intheendcaps [25].

Events of interest are selected using a two-tieredtrigger sys-tem [26].The firstlevel (L1),composed ofcustom hardware pro-cessors, usesinformationfromthe calorimetersandmuon detec-tors to select events at a rate of around 100 kHz within a fixed time interval of less than 4

μ

s. The second level, known as the high-leveltrigger(HLT),consistsofafarmofprocessorsrunninga versionofthefulleventreconstructionsoftwareoptimizedforfast processing,andreducestheeventratetoaround1 kHz beforedata storage.

AmoredetaileddescriptionoftheCMSdetector,togetherwith adefinitionofthecoordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef. [27].

3. Eventselectionandsimulatedsamples

Theanalysisisperformedusingdatacollectedinproton-proton (pp) collisions at

√

s

=

13TeV during 2017–2018, corresponding to an integrated luminosity of 96.4 fb−1. A trigger optimized for the detection of b hadrons decaying to J/

ψ

mesons, along with anadditionalmuonpotentiallyusableforflavortagging,isusedto collectthedatasamplefortheanalysis.AtL1,thetriggerrequires three muons, withthe minimum pT requirement on the highest pT (leading,

μ

1) and second-highest pT (subleading,

μ

2) muons

of pT

>

5 and3 GeV,respectively, andthe dimuoninvariantmass mμ1μ2

<

9GeV. There is no pT requirement on the third muon

Table 1

Angularandtime-dependenttermsofthesignalmodel.

i gi(θT, ψT,ϕT) Ni ai bi ci di

1 2 cos2

ψT(1−sin2θTcos2ϕT) |A0(0)|2 1 D C −S

2 sin2ψT(1−sin2θTsin2ϕT) |A (0)|2 _{1 D C −S}

3 sin2_ψ

Tsin2θT |A⊥(0)|2 _{1 −D C S}

4 −sin2ψTsin 2θTsinϕT |A (0)||A⊥(0)| C sin(δ⊥− δ ) S cos(δ⊥− δ ) sin(δ⊥− δ ) D cos(δ⊥− δ )

5 _√1

2sin 2ψTsin 2_θ

Tsin 2ϕT |A0(0)||A (0)| cos(δ − δ0) D cos(δ − δ0) C cos(δ − δ0) −S cos(δ − δ0)

6 _√1

2sin 2ψTsin 2θTcosϕT |A0(0)||A⊥(0)| C sin(δ⊥− δ0) S cos(δ⊥− δ0) sin(δ⊥− δ0) D cos(δ⊥− δ0)

7 23(1−sin 2 θTcos2ϕT) |AS(0)|2 1 −D C S 8 1 3 √

6 sinψTsin2θTsin 2ϕT |AS(0)||A (0)| C cos(δ − δS) S sin(δ − δS) cos(δ − δS) D sin(δ − δS)

9 1

3

√

6 sinψTsin 2θTcosϕT |AS(0)||A⊥(0)| sin(δ⊥− δS) −D sin(δ⊥− δS) C sin(δ⊥− δS) S sin(δ⊥− δS)

10 43

√

3 cosψT(1−sin2θTcos2ϕT) |AS(0)||A0(0)| C cos(δ0− δS) S sin(δ0− δS) cos(δ0− δS) D sin(δ0− δS)

CMSgeometrical acceptance

|

η

|

<

2.5;two of thesemuonsmust be oppositelycharged,each have pT

>

3.5GeV,formaJ/

ψ

candi-datewithaninvariantmassintherange2.95–3.25 GeV,andhave aprobability tooriginatefromacommonvertexlargerthan0.5%. The third muon is requiredto have pT

>

2GeV and can be used

to infer the flavor of the B0

s meson at production (i.e.,its

parti-cle/antiparticlestate),exploitingsemileptonicb

→ μ

−

+

X decays, asdiscussedfurtherinSection4.

Additional selection criteriaare applied to eventspassing the HLTrequirements.Thenumericalvaluesoftheselectioncutshave beenoptimizedwiththehelp ofthe tmva package [28,29],using a geneticalgorithm,tomaximizethesignal purity.First,J/

ψ

me-soncandidatesareconstructedusingpairsofopposite-signmuons with pT

>

3.5GeV and

|

η

|

<

2.4,andcompatiblewithoriginating

from a common vertex, obtained from a Kalman fit [30]. Candi-dates areacceptedonly iftheirinvariant massis within 150MeV oftheworld-averageJ/

ψ

mesonmass [31].Next,pairsof opposite-signtracks satisfyingthehigh-purityrequirement [32] with pT

>

1.2GeV and

|

η

|

<

2.5,notassociatedwiththemuonsthatformthe J/

ψ

candidate,are usedto form

φ

candidates. The

φ

candidates are selectedifthe trackpairhasan invariantmass,assuming the kaonmassforbothparticles,within 10MeV ofthe world-average

φ

meson mass [31].Finally, the J/

ψ

and

φ

candidatesare com-bined to form B0_s candidates: a common vertex (“B0_s vertex”) is obtainedfroma fitwiththefour tracks,twoformuonsandtwo forkaons.TheinvariantmassoftheB0

s candidateisobtainedfrom

akinematicfit,wheretheinvariantmassofthetwomuonsis con-strainedto theworld-average J/

ψ

mesonmass [31].The massof the

φ

candidateisnotconstrainedsinceitsnaturalwidthexceeds themassresolution.

Duetothehighinstantaneousluminosityofproton-proton col-lisionsattheLHC,severalprimaryvertices(PVs)arereconstructed ineachevent.ThevertexthatminimizestheanglebetweentheB0 s

candidate momentum vector and the line connectingthis vertex withthe B0_s decayvertexis chosen astheproductionvertexand isusedto determinethecharacteristicsoftheB0_s candidate,such asproperdecaylength.WeusedsimulationstostudyifthePV se-lectionprocedureintroducesanybiasinthemeasurement.Itwas foundthat inabout97%oftheevents,theselectedPVisalsothe closest onetothepointoforiginoftheB0_s meson. Theimpactof choosingadifferentvertexintheremainingcasesonthefinal re-sultsisfoundtobe negligiblewithrespecttothetotalsystematic uncertainties discussed in Section 6. The proper decay length is measured asct

=

cmPDG B0 s Lxy

/

pT,wheremPDG_B0 s isthe world-average B0

s mass [31] andLxyisthereconstructedtransversedecaylength,

whichisdefinedasthe distanceinthetransverseplane fromthe productionvertextotheB0_s vertex.Additionalselectioncriteriaare appliedtoB0

s candidates,requiringpT

>

11GeV,thefour-track

ver-texfit

χ

2_probability

_>

_{2%,aninvariantmassinthe5.24–5.49 GeV}

range,andaproperdecaylengthct

>

70

μ

m,withanuncertainty

σ

ct

<

50

μ

m. Theproper decaylength uncertaintyis obtainedby

propagatingtheuncertaintiesinthedecaydistanceandthe pT of

theB0

s candidatetoct.Inabout2%oftheeventsmorethanoneB0s

candidateisselected.Inthesecases,thecandidatewiththe high-est vertexfit probability is chosen. The impact of thischoice on themeasurement hasbeenevaluated byredoing the analysis us-ingthecandidatewiththelowestvertexfitprobability.Nosizable bias has been observed withrespect to the total systematic un-certainties discussed in Section 6.A total of 65500 B0_s

→

J/

ψ φ

candidatesareselected.

Simulatedeventsamplesareusedtomeasuretheselection ef-ficiency and the flavor tagging performance. These samples are produced usingthe pythia 8.230Monte Carlo(MC) event gener-ator [33] withtheunderlyingeventtuneCP5 [34] andtheparton distributionfunction setNNPDF3.1 [35]. Theb hadron decaysare modeled with the evtgen 1.6.0 package [36]. Final-state photon radiationis accounted forin the evtgen simulation with photos 215.5 [37,38].TheresponseoftheCMSdetectorissimulatedusing the Geant4 package [39]. The effect ofmultiple collisions in the sameorneighboringbunch crossings(pileup)isaccountedforby overlayingsimulatedminimumbiaseventsonthehard-scattering process.Simulatedsamplesarethenreconstructedusingthesame softwareasforcollisiondata.

The simulation is validated via comparison with background-subtracteddatainanumberofcontroldistributions.TheB0

s

candi-dateinvariantmassdistributionafterthesignalselectionisshown inFig.2,whereastheproperdecaylengthanditsuncertainty dis-tributionsareshowninFig.3.

4. Flavortagging

TheflavoroftheB0

s candidateatproductionisdeterminedwith

an OSflavor taggingalgorithm.The OSapproach isbased onthe fact that b quarks are predominantly produced inbb pairs, and thereforeonecaninfertheinitialB0_s mesonflavorbydetermining theflavoroftheother(“OS”)b quarkintheevent.

In thisanalysis, the flavor ofthe OS b hadron is deduced by exploitingthe semileptonic b

→ μ

−

+

X decay, wherethe muon sign

ξ

isused asthe taggingvariable(ξ

= −

1 forB0_s). This tech-niqueworksonaprobabilistic basis.IfnoOSmuon isfound,the event is considered as untagged (ξ

=

0). The tagging efficiency

ε

tag isdefinedasthefractionofcandidateeventsthataretagged.

When a muon is found, the tag is defined to be correct (“right tag”)if the flavor predicted usingthe muon signand the actual B0

s mesonflavor at productioncoincide. The correlation between

themuonsignandthesignalB0

s mesonflavorisdilutedbywrong

tags (mistags)originating fromcascadeb

→

c

→ μ

+

+

X decays, oscillationoftheOSB0 orB0_s meson,andmuonsoriginatingfrom othersources,suchasJ/

ψ

mesonandchargedpionandkaon de-cays.Themistagfraction

ω

tag isdefinedastheratiobetweenthe

Fig. 2. The invariantmassdistributionoftheB0

s→J/ψ φ→ μ+μ−K+K−

candi-datesindata.Theverticalbarsonthepointsrepresentthestatisticaluncertainties. Thesolidlinerepresentsaprojectionofthefittodata(asdiscussedinSection5, solidmarkers),thedashedlinecorrespondstothe signal,the dottedlinetothe combinatorial background, andthe long-dashed linetothe peakingbackground fromB0_{→J/ψK(892)}0_{→ μ}+_μ−_K+_π−_{,asobtainedfromthefit.Thedistribution}

ofthedifferencesbetweenthedataandthefit,dividedbythecombined uncer-taintyinthedataandthebestfitfunctionforeachbin(pulls)isdisplayedinthe lowerpanel.

Fig. 3. The ct distribution (upper) and its uncertainty (lower) for the B0s →

J/ψ φ→ μ+μ−K+K−candidatesindata.ThenotationsareasinFig.2.

numberofwrongly taggedeventsandthetotalnumberoftagged events.Itisusedtocomputethedilution

D ≡

1

−

2

ω

tag,whichisa

measureoftheperformancedegradationduetomistaggedevents. Thetaggingpower Ptag

≡

ε

tag

D

2 istheeffectivetaggingefficiency,

which takes into account the dilutionandis used as a figure of meritinmaximizingthealgorithmperformance.

Tomaximize thesensitivityofthismeasurement,we have de-veloped a novel OS muon tagger taking advantage of machine learning techniques.The use of deep neural networks (DNNs) in thenewtaggerleadstoloweringofthemistagprobability

ω

tagand

reducingoftherelatedsystematicuncertainties.Theuseofa ded-icatedtrigger, whichrequiresan OSmuon, dramaticallyincreases thefractionoftaggedcandidatescomparedtoourearlier measure-ment [14]. Taken together,these two improvements increase the muontaggingperformanceby

≈

20%comparedtothatinRef. [14]. Foreach event,we search fora candidateOSmuonconsistent withoriginatingfromthesameproductionvertexasthesignalB0 s

meson.Thistagging muonisrequiredtohavepT

>

2GeV,

|

η

|

<

2.4,

thelongitudinalimpactparameterwithrespecttotheproduction vertexIPz

<

1.0 cm, andthedistance fromtheB0s candidate

mo-mentainthe

(

η

,

φ)

plane



Rη,φ

>

0.4.Tracks thatbelong tothe

reconstructedB0

s

→

J/

ψ φ

→ μ

+

μ

−K+K− decayareexplicitly

ex-cluded fromconsideration. In order toreduce the contamination from light-flavor hadrons misreconstructed as tagging muons, a discriminatorbased onaDNN wasdeveloped usingthe Keras li-brary [40] within the tmva toolkit. Thisdiscriminator, calledthe “DNN against light hadrons” in thefollowing, uses 25 input fea-tures relatedto the muon kinematics andreconstruction quality, andistrainedwith3.5

×

106simulatedmuoncandidatesofwhich 2.5

×

105 _{are misreconstructed hadrons. The following DNN}

hy-perparametersareoptimizedthroughagridscantomaximizethe discrimination power: number of layers, number of neurons for each layer, and the dropout probability. No signs of overtraining are observed at the chosen hyperparameters configuration when comparingthe output distributions fromthe testingand training samples.Tagging muons are requiredto pass a workingpoint of theDNNoutputthathasanefficiencyof

≈

98%forgenuinemuons and

≈

33% formisreconstructed light-flavor hadrons,when evalu-atedusingmuoncandidatesreconstructedwiththeCMS particle-flow (PF)algorithm [41]. In

≈

3% ofthe eventswhere morethan onetagging muoncandidate passesallthe aboveselections, only thehighestpT oneiskept.

Another DNN is used to further discriminate the right- and wrong-tag muons, as well as to predict the mistag probability on a per-event basis. This DNN, referred to as the muon tagger DNN,hasbeendevelopedusingthe Keras librarywithinthe tmva toolkit, based on simulated B0_s

→

J/

ψ φ

→ μ

+

μ

−K+K− events, andcalibratedwithself-taggingB±

→

J/

ψ

K± MC anddata sam-ples,asdescribedbelow.

Theinput features ofthemuon taggerDNN areoftwo kinds: muon variables and cone variables. The muon variables are the muon pT,

η

,transverse andlongitudinal impact parameters with

respecttotheproductionvertex,alongwiththeiruncertainties,the distance



Rη,φ tothesignalB0s candidate,andthediscriminantof

theDNN against light hadrons. The cone variables are relatedto theactivityinaconeofradius



Rη, φ

=

0.4 aroundthemuon

mo-mentum direction and includethe relative PF isolation [41], the scalarpT sumofalladditionaltrackswithinthecone,thesumof

theirchargesweightedbythetrackpT,themuonrelative

momen-tumand



Rη, φ withrespect to thevector sumof themomenta

ofall additional tracks within thecone, andthe ratioof the en-ergyofthemuontothetotalenergyofalladditionaltrackswithin thecone(assumingthepionmassforeachtrack).Themuon tag-ger DNN is trained on 2.8

×

105 _{simulated B}0

s

→

J/

ψ φ

events,

of which about 85000 have a wrong tag. Its structure is opti-mized similarly to that for the DNN against light hadrons. The optimal DNN has three dense layers of 200 neurons, each with a rectifiedlinearunit activation function. Adropout layer witha dropout probability of 40% is placed after each dense layer. The cross-entropylossfunctionandtheAdamoptimizer [42] areused. The DNNis constructed insuch a waythat its output score d is equalto theprobability oftaggingthe eventcorrectly.Therefore, theper-eventmistagprobabilityissimply

ω

evt

=

1

−

d.

Theoutputd ofthetaggeriscalibratedusingaself-taggingdata sampleofB±

→

J/

ψ

K±

→ μ

+

μ

−K±events,wherethecharge of thekaon corresponds tothe charge andflavor of theB± meson.

Fig. 4. Results ofthe calibration ofthe per-event mistagprobability ωevt based

on B±→J/ψK±→ μ+μ−K± decays fromthe2017(upper)and 2018(lower) datasamples.Theverticalbarsrepresentthestatisticaluncertainties.Thesolidline showsalinearfittodata(solidmarkers).Thepulldistributionsbetweenthedata andthefitfunctionineachbinareshowninthelowerpanels.

The same trigger andJ/

ψ

candidate reconstruction requirements as forthe B0_s signal sample are applied. A chargedparticle with pT

>

1.6GeV,assumedto be a kaon,is combinedin a kinematic

fit withthe dimuon pair to form the B± candidate. The calibra-tionisperformedseparatelyforthe2017and2018datasamples, bycomparingthemeasuredmistagfraction(

ω

meas)withthe

ω

evt

predicted by the muon tagger DNN. The B± events are divided into100binsin

ω

evtandtheright- andwrong-tageventsare

sep-arately counted in each bin to extract the corresponding

ω

meas

value. The B± signal in eachbin isdiscriminated fromthe back-ground via a binned likelihood fit to the J/

ψ

K± invariant mass distributioninthe5.10–5.65 GeV range.

The calibration results for the 2017 and 2018 B± data are shown in Fig. 4. The data points are fitted with a linear func-tion a

+

b

ω

evt.The calibration parameters returnedby the fitfor

the 2017 (2018) data samples are a

= −

0.0010

±

0.0040, b

=

1.012

±

0.013 (a

=

0.0031

±

0.0031,b

=

1.011

±

0.010), statisti-callycompatiblewithaunitslopeandzerooffset.

ThecalibrationoftheDNNoutputisalsoverifiedwitha proce-duresimilartothatdescribedaboveusinganindependentsample of simulated B0_s

→

J/

ψ φ

and B±

→

J/

ψ

K± events. The recon-structedB0

s andB±mesonsarematchedtothegeneratedonesin

orderto findtheir trueflavoratproduction.Ingeneral, the mea-suredmistagprobability ispredictedveryaccurately by

ω

evt over

theentiremeasuredrangeforalltheexamined samplesand pro-cesses, with more than 90% of the tagged events falling in the

ω

evt

=

0.1–0.5 range in all cases. Residual differences are well

approximated by linear functionswith slopes close to unity and offsets consistent with zero.The

χ

2 _{per degree of freedom}

val-ues for all fits are below 2.We concludethat the value of

ω

evt

returnedby thetaggingDNNisagoodapproximationofthetrue

Table 2

Calibratedopposite-sidemuontaggerperformanceevaluatedusingB±→J/ψK± eventsinthe2017and2018datasamples.Theuncertaintiesshownarestatistical only.

Data sample εtag(%) ωtag(%) Ptag(%)

2017 45.7±0.1 27.1±0.1 9.6±0.1 2018 50.9±0.1 27.3±0.1 10.5±0.1

mistag probability in data,with minorresidual differences taken intoaccountwithcalibrationfunctions.

Thecalibratedflavortaggerperformance,evaluatedusingB±

→

J/

ψ

K±eventsindata,isshowninTable2.Ataggingefficiencyof

≈

50%andataggingpowerof

≈

10%areachievedinboththe2017 and 2018 data samples. The efficiency is much higher than the semileptonicb hadron branchingfractionduetothe requirement ofanadditionalOSmuonattheHLT,asdescribedinSection3.

Possible differences in the mistag probability calibration be-tween the B0

s and B± samples, as well as the statistical

uncer-taintiesinthecalibrationparametersandpossiblevariations from linearity ofthe calibration function,are considered as systematic uncertaintiesanddescribedinSection6.

5. Maximum-likelihoodfit

An unbinned multidimensional extended maximum-likelihood fitisperformedonthecombineddatasamplesusing8observables asinput:theB0

s candidateinvariantmassmB0

s,thethreedecay

an-gles

ofthereconstructedB0_s candidate,theflavortagdecision

ξ,

themistagfraction

ω

evt,theproperdecaylengthoftheB0s

candi-datect,anditsuncertainty

σ

ct.

From the multidimensional fit, the physics parameters of in-terest

φ

s,



s,



s,



ms,

|λ|

, the squares of amplitudes

|

A⊥

|

2,

|

A0

|

2,

|

AS

|

2, and the strong phases

δ

,

δ

_⊥, and

δ

S⊥ are deter-mined,where

δ

S⊥ isdefinedasthedifference

δ

S

− δ

⊥.The B0_s

→

J/

ψ φ

amplitudes are normalized to unity by constraining

|

A

|

2 to 1

− |

A_⊥

|

2

− |

A0

|

2. The fit model is validated with simulated

pseudo-experimentsandwithsimulatedsampleswithdifferent in-putparametersets.

Thelikelihoodfunction iscomposedof theprobabilitydensity functions(pdfs)describingthesignalandbackgroundcomponents. Thelikelihoodfitalgorithmisimplementedusingthe RooFit pack-age [28,43]. The signal and background pdfs are formed as the product of functions that model the invariant mass distribution and the time-dependent decay rates of the reconstructed candi-dates.Inaddition,thesignal pdfincludestheefficiencyfunctions. Theeventpdf P isdefinedas:

P

=

Nsig Ntot Psig

+

Nbkg Ntot Pbkg

,

(3) where Psig

=

ε(

ct

)

ε()

[

F

(,

ct

,

α)

⊗

G

(

ct

,

σ

ct

)

]

×

Psig

(

mB0 s

)

Psig

(σ

ct

)

Psig

(ξ )

(4) and Pbkg

=

Pbkg

(

cos

θ

T

, φ

T

)

Pbkg

(

cos

ψ

T

)

×

Pbkg

(

ct

)

Pbkg

(

mB0 s

)

Pbkg

(σ

ct

)

Pbkg

(ξ ).

(5)

Thecorrespondingnegativeloglikelihoodis:

−

ln

L

= −

Nevt



i=0

Here, Psig andPbkg arethepdfs thatdescribethe B0s

→

J/

ψ φ

→

μ

+

μ

−K+K− signal and background contributions, respectively. Theyields ofsignalandbackgroundeventsare Nsig andNbkg,

re-spectively, Ntot istheir sum, andNevt

=

65500 is the numberof

candidatesselectedindata.Thepdf

F(,

ct

,

α

)

isthedifferential decayratefunction

F(,

ct

,

α

)

definedinEq. (1), modifiedto in-clude theflavor information

ξ

andthedilutionterm

(1

−

2

ω

evt

),

which are applied asmultiplicative factors to each of the ci and

di termsinEq. (2).Inthe

F

expression,thevalue of

δ

0 isset to

zero,followingageneralconvention [6,8],andthevalueof



s is

constrainedtobe positive,basedonthe LHCbmeasurement [44]. Alltheparametersofthepdfsare allowedtofloatinthefinal fit, unlessexplicitlystatedotherwise.

Thefunctions

ε

(

ct

)

and

ε

()

modelthedependenceofthe sig-nal reconstruction efficiency onthe proper decaylength and the threeanglesofthetransversitybasis,respectively.Theproper de-cay lengthefficiencyisparameterizedwithafourth-order Cheby-shev polynomial multiplied by an exponential function with a negative slope,whiletheangularefficiencyisparameterizedwith spherical harmonics and Legendre polynomials up to order six. Bothparameterizationsareobtainedfromfitstotherespective ef-ficiencyhistogramsinB0_s

→

J/

ψ φ

simulatedevents,andarefixed inthefittodata.

The term G

(

ct

,

σ

ct

)

is a Gaussian resolution function, which

makes use of the per-event decaylength uncertainty

σ

ct,scaled

byacorrectionfactor

κ

introduced toaccount fortheresidual ef-fectswhen the decaylength uncertaintyis usedto modelthe ct resolution. The value of

κ

is estimated using simulated samples andisequalto

≈

1.2forboththe2017and2018datasamples.

The signal mass pdf Psig

(

mB0

s

)

is a Johnson’s SU

distribu-tion [45], whilethe decaylength uncertainty pdf Psig

(

σ

ct

)

is

de-scribed by thesumoftwo Gamma distributions.These pdfs best model each individual variable in one-dimensional fits to simu-latedsamples.

The background pdf contains two terms to model both the combinatorialbackgroundandthepeakingbackground,dominated by B0

→

J/

ψ

K(892)0

→ μ

+

μ

−K+

π

−,wherethepionisassumed to be a kaon candidate.The background from

Λ

0_b

→

J/

ψ

pK−

→

μ

+

μ

−pK−,wheretheprotonisassumedtobeakaoncandidate, is estimated using simulated events to have a negligible effect on the fit results compared to the systematic uncertainties dis-cussedinSection6.Thebackgroundinvariantmasspdf Pbkg

(

mB0

s)

isdescribedbyanexponentialfunctionforthecombinatorial back-ground and a Johnson’s SU distribution for the peaking

back-ground. The background decay length pdf Pbkg

(

ct

)

is described

by the sum of two exponential distributions for the combinato-rialbackground,whileasingleexponentialdistributionisusedfor thepeakingbackground.Theangularpartsofthebackgroundpdfs Pbkg

(cosθ

T

,

ϕ

T

)

andPbkg

(cos

ψ

T

)

aredescribedanalyticallybya

se-riesofLegendre polynomialsforcos

θ

T andcos

ψ

T,andsinusoidal

functionsfor

ϕ

T.Forthecos

θ

Tand

ϕ

Tvariables,atwo-dimensional

pdf is used to take into account a possible correlation between thetwo.Thebackgrounddecaylengthuncertaintypdf Pbkg

(

σ

ct

)

is

described byasumoftwoGammadistributionsforthe combina-torial background, while thepeaking background isfixed to that forthesignal.

The tag pdfs are defined as P

(ξ )

=

1

−

ε

tag forthe untagged

events (ξ

=

0) and P

(ξ )

=

ε

tag

(1

±

Atag

)/2 for

the tagged ones

(ξ

= ±

1),where

ε

tag isthetaggingefficiencyand Atag isthe

tag-ging asymmetry,defined asthe difference between the numbers of positively and negatively tagged events (ξ

= ±

1) divided by the total number. The measured tagging asymmetry is found to becompatiblewithzero.

Thecorrelationbetweenthedifferentfitcomponentshasbeen studiedinbothdataandsimulations,andfoundtobenegligible.

Table 3

Resultsofthefittodata.Statisticaluncertaintiesareobtainedfromtheincreasein

− logLby0.5,whereassystematicuncertaintiesaredescribedbelowand summa-rizedinTable4.

Parameter Fit value Stat. uncer. Syst. uncer.

φs[mrad] −11 ±50 ±10 s[ps−1] 0.114 ±0.014 ±0.007 ms[ps−1] 17.51 ₋+00..1009 ±0.03 |λ| 0.972 ±0.026 ±0.008 s[ps−1] 0.6531 ±0.0042 ±0.0026 |A0|2 0.5350 ±0.0047 ±0.0049 |A⊥|2 0.2337 ±0.0063 ±0.0045 |AS|2 0.022 +₋00..008007 ±0.016 δ [rad] 3.18 ±0.12 ±0.03 δ⊥[rad] 2.77 ±0.16 ±0.05 δS⊥[rad] 0.221 +₋00..083070 ±0.048

Thepeakingbackgroundpartof Pbkg isdeterminedusing

sim-ulatedsamples,whiletheinitialcombinatorialbackgroundpartis foundfromafittotheB0_s invariantmasssidebands5.24–5.28 GeV and5.45–5.49 GeV indata, andthenleft free to floatinthe final fit,startingfromthisinitialpdf. Thesignal andbackground com-ponentsofthedecaylengthuncertaintypdfarefixed totheones obtained froma two-dimensional fit together with the invariant masspdf. The 2017and2018data samplesare fitted simultane-ously. Thejointlikelihoodfunction ofthesimultaneous fitshares thedecayratemodel,the invariantmass pdfs,the peaking back-ground model, and the lifetime and angular components of the combinatorial background model between the two samples. The numberofsignal andbackgroundeventsaremeasured separately in each data sample, as is the tagging efficiency. The efficiency functions, P

(

σ

ct

)

pdfs,tag pdfs,and

κ

factors arealso specificto

eachdatasample.

6. Systematicuncertaintiesandresults

The resultsof thefit withtheir statisticalandsystematic un-certaintiesaregiveninTable3,whereasthestatisticalcorrelations betweenthemeasuredparametersarereportedinthe supplemen-talmaterial [URLwill beinserted bypublisher]. Statistical uncer-taintiesareobtainedfromtheincreasein

−

log

L

by 0.5,whereas systematicuncertainties are described belowand summarizedin Table4.ThemeasurednumberofB0

s

→

J/

ψ φ

→ μ

+

μ

−K+K−

sig-nal events fromthe fit is 48500

±

250.The distributions of the inputobservablesandthecorrespondingfitprojectionsareshown inFigs.2,

3

,and

5

.

Severalsources ofsystematic uncertainties inthe physics pa-rametersare studiedby testingthe variousassumptions madein thefitmodelandthoseassociatedwiththefittingprocedure.

Modelbias: Possiblebiasesinthefittingprocedureareevaluated bygenerating1000pseudo-experiments, each statistically equiva-lentto thedata samples,fromthe fittedmodelin data(referred toas“nominal-modelpseudo-experiments”inwhatfollows).Each of them is fitted with the nominal model, and the pull distri-butions (i.e.,thedifference divided bythe combineduncertainty) betweentheparametersobtainedfromthefitandtheirinput val-uesareproduced. Eachpull distributionisfittedwitha Gaussian function, and the estimated central value is taken as the corre-sponding systematic uncertainty, if different from zero by more thanitserror.Toavoiddouble-countingthisuncertainty,whenever pseudo-experimentsareused toevaluate other systematic uncer-tainties, the modelbias is always subtracted. In thesecases, the corresponding pull distributions are compared to those obtained withthe nominal-model pseudo-experiments.Ifthe mean ofthe pulldistributiondiffersfromthemeanofthenominal-model dis-tributionbymorethantheircombinedRMS,thedifferenceistaken asthecorrespondingsystematicuncertainty.

Fig. 5. The angular distributions cosθT(left), cosψT(middle), andϕT(right) for the B0scandidates and the projections from the fit. The notations are as in Fig.2.

Table 4

Summaryofthesystematicuncertainties.Thedashes(—)meanthatthecorrespondinguncertaintyisnotapplicable.Thetotalsystematicuncertaintyisobtainedasthe quadraticsumoftheindividualcontributions.

φs [mrad] s [ps−1] ms [ps−1] |λ| s [ps−1] |A0|2 |A⊥|2 |AS|2 δ [rad] δ⊥ [rad] δS⊥ [rad] Statistical uncertainty 50 0.014 0.10 0.026 0.0042 0.0047 0.0063 0.0077 0.12 0.16 0.083 Model bias 7.9 0.0019 — 0.0035 0.0005 0.0002 0.0012 0.001 0.020 0.016 0.006 Model assumptions — — — 0.0046 0.0003 — 0.0013 0.001 0.017 0.019 0.011 Angular efficiency 3.8 0.0006 0.007 0.0057 0.0002 0.0008 0.0010 0.002 0.006 0.015 0.015 Proper decay length efficiency 0.3 0.0062 0.001 0.0002 0.0022 0.0014 0.0023 0.001 0.001 0.002 0.002 Proper decay length resolution 3.5 0.0009 0.021 0.0015 0.0006 0.0007 0.0009 0.007 0.006 0.025 0.022 Data/simulation difference 0.6 0.0008 0.004 0.0003 0.0003 0.0044 0.0029 0.007 0.007 0.007 0.028 Flavor tagging 0.5 <10−4 ₀ .006 0.0002 <10−4 ₀ .0003 <10−4 <10−3 ₀ .001 0.007 0.001

Sig./bkg.ωevtdifference 3.0 — — — 0.0005 — 0.0008 — — — 0.006

Peaking background 0.3 0.0008 0.011 <10−4 ₀

.0002 0.0005 0.0002 0.003 0.005 0.007 0.011 S-P wave interference — 0.0010 0.019 — 0.0005 0.0005 — 0.013 — 0.019 0.019 P(σct)uncertainty <10−1 0.0019 0.028 0.0004 0.0008 0.0006 0.0008 0.001 0.001 0.002 0.005 Total systematic uncertainty 10.0 0.0070 0.032 0.0083 0.0026 0.0049 0.0045 0.016 0.028 0.045 0.048

Modelassumptions: Theassumptions madeindefiningthe like-lihoodfunctionsaretestedbygeneratingpseudo-experimentswith different hypotheses and fitting the samples with the nominal model. The following assumptions are tested: signal and back-ground invariant mass models, background proper decay length model,andbackgroundangularmodel.Pulldistributions with re-spectto theinput valuesareused toevaluatethe systematic un-certainty,asdescribedinthe“modelbias”paragraph.

Angularefficiency: Thesystematicuncertaintyrelatedtothe lim-ited MCeventcountusedtoestimate theangularefficiency func-tion is evaluated by regenerating the efficiency histograms 1000 times usingthe referenceone, with the fitrepeated after reesti-matingtheefficiency.Therootmeansquare(RMS)oftheobtained physics parameter distributions istaken asthesystematic uncer-tainty.

Properdecaylengthefficiency: Theproperdecaylengthefficiency is first validated by fittingthe B± proper decay length distribu-tion in thecontrol B±

→

J/

ψ

K± channel, using severaldifferent data-taking periods. Eachfit is performedapplyingthe efficiency function evaluated using simulated B±

→

J/

ψ

K± samples with the same procedure used for the B0_s

→

J/

ψ φ

analysis. We con-sidereightdifferentdata-takingperiods,eachwiththenumberof B± candidates comparable withthe number ofsignal candidates intheB0_s sample usedintheanalysis.Wealsoconsiderthe2017 and2018data-taking periodsastwo additionallarge controldata sets.Theresultsareingoodagreementwiththeworld-averageB± meson lifetime [31], withdifferencesno larger than1.5 standard deviations, showing no bias or instabilities during the data tak-ing. Havingverified thatthe efficiencyparameterizationdoesnot

introduceany noticeablebias,we evaluate therelated systematic uncertaintybyvaryingtheparameters oftheproperdecaylength efficiencyfunction within their statistical uncertainties. The RMS ofthedistributionofeachextractedphysicsparameterofinterest withrespecttothenominalfitvalueistakenasthecorresponding systematicuncertainty.Weassign asystematicuncertaintytothe efficiencymodelbyrepeatingthefitusingtheefficiencyhistogram insteadofa smoothefficiencyfunction, andtakingthe difference fromthenominalresultastheuncertainty.

Properdecaylengthresolution: A systematic uncertainty is as-signed to the proper decay length resolution by varying the

κ

correctionfactorby

±

10%,asestimatedfromadata-to-simulation comparison, repeating the fit, and taking the largest difference fromthenominalresultastheuncertainty.Wealsoevaluatea sys-tematicuncertaintyrelatedto theassumption that

κ

is indepen-dentoftheproperdecaylength,byparametrizing

κ

asafunction ofct usingsimulatedsamples.Asystematicuncertaintyisassigned withthesamemethodologyusedtoevaluatethe“model assump-tion”systematicuncertainties, usingthe

κ

(

ct

)

parametrizationas analternativehypothesis.

Data/simulation difference: The efficiency parametrization is foundtobeverysensitivetothemuonandkaonpT,andB0s meson

rapiditydistributions,henceasystematicuncertaintyisassignedto coverthedifferencesineachofthesevariables,betweendataand simulation. The effect is evaluated by reweighting the simulated distributions in each variable to agree with the data. The same weightsareappliedtothesimulatedsamplesusedtoestimatethe efficiencies,whicharethenrecomputed.Thefitisrepeatedineach

caseandthesuminquadratureofthedifferencesfromthe nomi-nalresultistakenasthesystematicuncertainty.

Flavortagging: Theuncertaintiesassociatedwiththeflavor tag-gingarepropagatedbyvaryingtheparametersofthemistag prob-ability calibrationcurveswithin their statisticaluncertainties. For each variation,newcalibration curvesare producedandthe data arerefitted.TheRMSofeachfittedparameterdistributionisthen taken asthecorresponding systematic uncertainty.We also eval-uate the effect ofthe assumption that the signal and calibration channelshavethesamemistagcalibration.Thedifferencebetween the B0_s andB± calibrations is evaluated usingsimulated samples andis takenasthe systematicuncertainty. The effectofthe cal-ibration function shape is evaluated by repeating the fit usinga third-order polynomial and takingthe difference with respect to the nominal result as the systematic uncertainty. The combined contribution of the three sources to the total systematic uncer-taintyisnegligible.

Different

ω

evtdistributioninsignalandbackground: Asystematic

uncertainty is assigned to the possible differencesin the mistag probabilities betweensignal and background.The separate signal and background

ω

evt distributions in data are first measured by

using the B0_s candidate invariant mass signal and sidebands re-gions.ThesedistributionsareseparatelymodeledusingtheKernel DensityEstimationmethod [46,47] andaddedtothefittingmodel. One thousand pseudo-experimentsare generated and pull distri-butions withrespecttothe inputvaluesare usedtoevaluate the systematicuncertainty,asdescribedinthe“modelbias”paragraph. Peakingbackground: The systematic uncertainty relatedto the fixed yieldofthepeakingbackgroundcomponentisevaluatedby repeating the fit using a different yield obtained from a B0

→

J/

ψ

K(892)0controlsampleindata.Thedifferencewithrespectto the nominalresult istaken asthe systematicuncertainty. A sys-tematic uncertainty is also assigned to the proper decay length modeling of the peaking background by forcing the lifetime to matchthe world-average value [31],repeating the fit,andtaking the difference from the nominal result as the systematic uncer-tainty.

S- P waveinterference: Thefitmodeldoesnottakeintoaccount the difference inthe invariant massdependence betweenthe P -wavefromtheB0_s

→

J/

ψ φ

decayandtheS-wave,whichmodifies their interference by a factor kSP. The corresponding systematic

uncertaintyisestimatedusingpseudo-experiments.ThekSP factor

is computedby integratingthe P - and S-wave interferenceterm inthe

φ

candidatemassrange,assumingthat the P -wave ampli-tudeisdescribedbyarelativisticBreit–Wignerdistributionandthe S-waveamplitudebya constant,andfoundtobe kSP

=

0.54.

Dif-ferent S-wave lineshapesare foundtolead tovery similarvalues ofkSP,withavariationnolargerthan

≈

2%.Onethousand

pseudo-experimentsare generatedapplyingkSP

=

0.54 tothei

=

8,9,10

terms inTable 1 relatedto the S- and P -waveinterference. Pull distributionswithrespecttotheinputvaluesareusedtoevaluate thesystematicuncertainty,asdescribedinthe“modelbias” para-graph. The parameters

|

AS

|

2 and



ms are the only ones whose

totaluncertaintyisaffectedsignificantlybythisapproximation. P

(

σ

ct

)

uncertainty: In the fit to data the proper decay length

uncertainty pdf is fixed to the one obtained from a pre-fit, as described in Section 5. A systematic uncertainty is assigned by sampling this distribution 1000 times, using the parameter un-certainties obtainedfromthe pre-fit. Eachtime the fit todata is repeated andthe standard deviation of the obtainedphysics pa-rameterdistributionsistakenasthesystematicuncertainty.

Asummary ofthesystematicuncertaintiesisgiveninTable4. After addingthe systematicuncertainties inquadrature,we mea-surethefollowingvaluesoftheC P -violatingphaseandthewidth differencebetweenthetwoB0_s masseigenstates:

φ

s

= −

11

±

50 (stat)

±

10 (syst) mrad

,



s

=

0

.

114

±

0

.

014 (stat)

±

0

.

007 (syst) ps−1

.

The

|λ|

parameteris measured to be

|λ|

=

0.972

±

0.026(stat)

±

0.008(syst), consistent with no direct C P violation (

|λ|

=

1). The average of the heavy and light B0_s mass eigenstate de-cay widths is determined to be



s

=

0.6531

±

0.0042(stat)

±

0.0026(syst) ps−1_{, consistent with the world-average value}

_

s

=

0.6624

±

0.0018 ps−1 _{[31].Themassdifferencebetweentheheavy}

and light B0_s meson mass eigenstates is measured to be



ms

=

17.51+₋0₀._.10₀₉(stat)

±

0.03(syst)



ps−1_{, consistent withthe}

theoreti-calprediction



ms

=

18.77

±

0.86



ps−1 [4],andinslighttension

withthe world-average value



ms

=

17.757

±

0.021



ps−1 [31].

Theuncertaintiesinallthesemeasuredparametersaredominated bythestatisticalcomponent.Thisanalysisrepresentsthefirst mea-surementby CMSofthemassdifference



ms betweentheheavy

andlightB0_s masseigenstatesandofthedirectC P observable

|λ|

.

7. Combinationwith8 TeV results

TheresultspresentedinthisLetter areinagreement withthe earlierCMSresultatacenter-of-massenergyof8 TeV [14].As ex-plained in Section 1, both measurements are performed with a similar numberof events,with the one at

√

s

=

13TeV having a highertaggingefficiency.Thisleadstoanimprovementinthe un-certaintyin quantitiesthat requiretagging,suchas

φ

s,while but

theuncertaintiesinthosethatdonotusetagging,suchas



s,

de-pendontherawnumberofeventsandare notimprovedrelative tothe8TeV result.Thetwosetsofresultsarecombinedusingthe BLUEmethod [48,49] asimplementedinthe root package [50–52] usingthefollowingphysics parameters:

φ

s,



s,



s,

|

A0

|

2,

|

A⊥

|

2,

|

AS

|

2,

δ

,

δ

_⊥,and

δ

S⊥.Thestatisticalcorrelationsbetweenthe pa-rameters obtained in each measurement are taken into account as well as the correlations of the systematic uncertainties dis-cussed inSection 6. Different sources ofsystematic uncertainties areassumedtobeuncorrelated.Thesystematicuncertainty corre-lationbetween the parameters of the 8TeV result is assumedto be zero. This assumption has been found to not impact the re-sultsin a noticeable way.Since the muon tagging, theefficiency evaluation,andpartofthefitmodelaredifferentinthetwo mea-surements,the respective systematicuncertainties are treated as uncorrelatedbetween the two sets of results. The combined re-sultsfor the C P -violating phase and lifetimedifference between thetwomasseigenstatesare:

φ

s

= −

21

±

44 (stat)

±

10 (syst) mrad

,



s

=

0

.

1032

±

0

.

0095 (stat)

±

0

.

0048 (syst) ps−1

,

withacorrelationbetweenthetwo parametersof

+

0.02.Thefull combinationresultsandthecorrelationsbetweenthevarious ex-tractedparametersarereportedinthesupplementalmaterial[URL willbeinsertedbypublisher].

The two-dimensional

φ

s vs.



s likelihood contours at 68%

confidencelevel (CL) for the individual andcombined results, as well asthe SM prediction, are shownin Fig.6. The contours for theindividualresultsareobtainedwithlikelihoodscans,whichare usedto obtain thecombined contour. Thecontours only account forthestatisticaluncertaintyandthecorrelationbetweenthetwo scannedvariables,whiletheresultsfromthecombinationobtained usingthe BLUE methodtake into accountthe statisticaland sys-tematiccorrelationsofa widerrangeofvariables.The resultsare inagreementwitheachotherandwiththeSMpredictions.

Fig. 6. The two-dimensionallikelihoodcontoursat68%CL intheφs-splane,for

theCMS8 TeV (dashedline),13 TeV (dottedline),andcombined(solidline)results. Thecontoursfortheindividualresultsareobtainedwithlikelihoodscans,whichare usedtoobtainthecombinedcontour.Inallcontoursonlystatisticaluncertainties aretakenintoaccount.TheSMpredictionisshownwiththediamondmarker [1,4].

8. Summary

TheC P -violatingphase

φ

sandthedecaywidthdifference



s

betweenthelightandheavy B0_s mesonmasseigenstatesare mea-sured using a total of 48500 B0

s

→

J/

ψ φ(

1020)

→ μ

+

μ

−K+K−

signal events, collected by the CMS experiment at the LHC in proton-protoncollisionsat

√

s

=

13TeV,correspondingtoan inte-gratedluminosity of96.4 fb−1.Eventsare selectedusingatrigger that requiresan additional muon, which can be exploited to in-fertheflavor oftheB0_s mesonatthetimeofproduction.Anovel opposite-side muon tagger based on deep neural networks has beendevelopedtomaximizethesensitivityofthepresentanalysis. Ahightagging powerof

≈

10%is achieved,aided by the require-ment ofanadditionalmuon inthe signalsample imposed atthe triggerlevel.

TheC P -violatingphaseismeasuredtobe

φ

s

= −

11

±

50(stat)

±

10(syst) mrad, consistent both with the SM prediction

φ

s

=

−

36.96+₋0_0..₈₄72mrad [1] and with the absence of C P violation in the mixing-decay interference. The decay width difference be-tween theB0

s masseigenstatesis measuredto be



s

=

0.114

±

0.014(stat)

±

0.007(syst) ps−1_{,consistentwiththetheoretical}

pre-diction



s

=

0.091

±

0.013 ps−1 [4].Inaddition,theC P -violating

parameter

|λ|

andthe averagelifetimeofthe heavy andlight B0_s masseigenstates,aswellastheirmassdifference,havebeen mea-sured.Theuncertainties inallthesemeasurementsaredominated bythestatisticalcomponents.

The results presented in this Letter are further combined with those obtained by CMS at

√

s

=

8TeV [14], yielding

φ

s

=

−

21

±

44(stat)

±

10(syst) mrad and



s

=

0.1032

±

0.0095(stat)

±

0.0048(syst) ps−1.Theseresultsaresignificantlymoreprecisethan those from the previous CMSmeasurement at 8 TeV, andcan be usedtofurtherconstrainpossiblenew-physicseffectsinB0

s meson

decayandmixing.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

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,wegratefullyacknowledgethecomputingcentersand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythecomputing infrastructureessential toour analyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHCandthe CMSdetectorprovidedby thefollowingfundingagencies: BMBWFandFWF(Austria);FNRS andFWO (Belgium); CNPq, CAPES, FAPERJ,FAPERGS, andFAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NK-FIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN(Italy);MSIPandNRF(RepublicofKorea);MES(Latvia);LAS (Lithuania);MOEandUM(Malaysia);BUAP,CINVESTAV,CONACYT, LNS,SEP,andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu-gal);JINR(Dubna);MON,ROSATOM, RAS,RFBR,andNRCKI (Rus-sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter,IPST, STAR,andNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASU (Ukraine); STFC (United Kingdom);DOE andNSF (USA).

Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract Nos. 675440, 752730, and 765710 (European Union); the Leventis Foundation; the A.P. Sloan Foundation; the Alexan-der von Humboldt Foundation; the Belgian Federal Science Pol-icy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); theF.R.S.-FNRS andFWO (Belgium) underthe “Excellenceof Sci-ence – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic;theDeutscheForschungsgemeinschaft(DFG)under Ger-many’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306; the Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the Hungarian Academy of Sci-ences, the New National Excellence Program ÚNKP, the NK-FIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the Council of Science andIndustrialResearch,India; theHOMING PLUSprogramofthe Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-searchProgram byQatar NationalResearchFund;theMinistry of ScienceandHigherEducation,projectno.02.a03.21.0005(Russia); the ProgramaEstatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the ThalisandAristeiaprogramscofinancedby EU-ESFandtheGreek NSRF;theRachadapisekSompotFundforPostdoctoralFellowship, Chulalongkorn University and the Chulalongkorn Academic into Its2ndCenturyProject AdvancementProject(Thailand);theKavli Foundation;the NvidiaCorporation; the SuperMicroCorporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation(USA).