Measurement of the CP-violating phase phi(s) from B-s(0) -> J/psi pi(+)pi(-) decays in 13 TeV pp collisions

University of Groningen

Measurement of the CP-violating phase phi(s) from B-s(0) -> J/psi pi(+)pi(-) decays in 13 TeV

pp collisions

Aaij, R.; Adeva, B.; Adinolfi, M.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Dufour, L.;

Mulder, M; Onderwater, C. J. G.

Published in:

Physics Letters B

DOI:

10.1016/j.physletb.2019.07.036

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Citation for published version (APA):

Aaij, R., Adeva, B., Adinolfi, M., Ajaltouni, Z., Akar, S., Albrecht, J., Alessio, F., Dufour, L., Mulder, M.,

Onderwater, C. J. G., Pellegrino, A., Tolk, S., van Veghel, M., & LHCb Collaboration (2019). Measurement

of the CP-violating phase phi(s) from B-s(0) -> J/psi pi(+)pi(-) decays in 13 TeV pp collisions. Physics

Letters B, 797, [UNSP 134789]. https://doi.org/10.1016/j.physletb.2019.07.036

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

CP -violating

phase

φ

_s

from

B

0

_s

→

J

/

ψ

π

+

π

−

decays

in

13 TeV

pp collisions

.

LHCb

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Article history:

Received26April2019

Receivedinrevisedform15July2019 Accepted15July2019

Availableonline18July2019 Editor: M.Doser

Decays of B0s and B0s mesons into J/ψ

π

+

π

− final statesare studiedinadata samplecorresponding to 1.9 fb−1 _{of integrated luminosity collected with the LHCb detector in 13 TeV pp collisions.} A time-dependentamplitudeanalysisisused todeterminethe final-stateresonancecontributions, the CP -violating phase φs= −0.057±0.060±0.011 rad, the decay-width difference between the heavier massB0

s eigenstateandtheB0mesonof−0.050±0.004±0.004 ps−1,andtheCP -violatingparameter |λ| =1.01+₋0₀._.08₀₆±0.03, wherethefirstuncertaintyisstatisticalandthesecondsystematic.Theseresults arecombinedwithpreviousLHCbmeasurementsinthesamedecaychannelusing7 TeVand8 TeVpp collisionsobtainingφs=0.002±0.044±0.012 rad,and|λ|=0.949±0.036±0.019.

©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

MeasurementsofCP violationinfinalstatesthatcanbe popu-latedbothbydirectdecayandviamixingprovideanexcellentway oflookingforphysicsbeyondtheStandardModel(SM)[1].Asyet unobservedheavybosons,light bosonswithextremelysmall cou-plings,orfermionscanbepresentvirtuallyinquantumloops,and thusaffect therelative CP phase. Direct decays into non-flavour-specificfinalstatescaninterferewiththosethatundergo B0

s

−

B0s mixingpriortodecay.ThisinterferencecanresultinCP violation.

In certain B0_s decays one CP -violating phase that can be mea-sured,called

φ

s,canbeexpressedintermsofCabibbo–Kobayashi– Maskawa matrix elements as

−

2arg



−

VtsVtb∗

/

VcsVcb∗



. It is not predictedintheSM,butcanbeinferredwithhighprecision from otherexperimentaldatagivingavalueof

−

36

.

5₋+1₁._.3₂mrad [2].This numberisconsistent withprevious measurements,whichdidnot have enough sensitivity to determine a non-zero value [3–7]. In thispaperwe presenttheresults ofa newanalysisofthe B0

s

→

J

/ψ

π

+

π

− decay using data from 13 TeV pp collisions collected usingthe LHCbdetectorin2015and2016.1 Theexistence ofthis decayanditsuseinCP -violationstudieswassuggestedinRef. [8].

2. Detectorandsimulation

The LHCb detector [9,10] is a single-arm forward spectrome-tercoveringthe pseudorapidity range2

<

η

<

5,designedforthe

1 _{Inthis papermention ofaparticular finalstateimplies useofthe}

charge-conjugatestate,exceptwhendealingwith

CP -violating

processes.

studyofparticles containingb or c quarks.The detectorincludes ahigh-precisiontrackingsystemconsistingofasilicon-stripvertex detector surroundingthe pp interaction region [11], a large-area silicon-stripdetectorlocated upstreamofa dipole magnetwitha bending power of about 4 Tm, andthree stations of silicon-strip detectorsandstrawdrifttubesplaceddownstreamofthemagnet. The tracking systemprovides a measurement of themomentum,

p,ofchargedparticleswitharelativeuncertaintythatvariesfrom 0.5% at low momentum to 1.0% at 200 GeV.2 _{The minimum}

dis-tance of a track to a primary vertex (PV), the impact parameter (IP),ismeasuredwitharesolutionof

(

15

+

29

/

pT

)

μ

m,wherepTis

thecomponentofthemomentumtransversetothebeam,in GeV. Different types ofcharged hadronsare distinguished using infor-mationfromtwo ring-imagingCherenkovdetectors [12]. Photons, electronsandhadronsareidentified byacalorimetersystem con-sistingofscintillating-padandpreshowerdetectors,an electromag-neticandahadroniccalorimeter.Muonsareidentifiedbyasystem composedofalternatinglayersofironandmultiwireproportional chambers [13].The onlineeventselection isperformedby a trig-ger,whichconsistsofahardwarestage,basedoninformationfrom thecalorimeterandmuon systems,followed bya softwarestage, whichappliesafulleventreconstruction.

At the hardware trigger stage, events are required to have a muon with high pT or a hadron, photon or electron with high

transverseenergyinthecalorimeters.Thesoftwaretriggeris com-posedof two stages,the firstof whichperforms a partial recon-struction and requires either a pair of well-reconstructed,

oppo-2 _{Weusenaturalunitswhereh¯=c=1.} https://doi.org/10.1016/j.physletb.2019.07.036

0370-2693/©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

sitely chargedmuonshavingan invariant massabove 2

.

7 GeV,or a single well-reconstructed muon with pT

>

1 GeV and have a

large IP significance

χ

2

IP

>

7

.

4. The latter is defined as the

dif-ference in the

χ

2 _{of the vertex fit fora given PVreconstructed}

withand withoutthe considered particles. The second stage ap-pliesafulleventreconstructionandforthisanalysisrequirestwo opposite-sign muons to form a good-quality vertex that is well-separatedfromallofthePVs,andtohaveaninvariantmasswithin

±

120 MeV oftheknown J

/ψ

mass [14].

Simulationisrequiredtomodeltheeffects ofthe detector ac-ceptanceandthe imposed selection requirements.In the simula-tion, pp collisionsaregeneratedusingPythia_{[15] withaspecific} LHCb configuration [16].Decaysofunstableparticlesaredescribed by EvtGen _{[17], in which final-state radiation is generated} us-ing Photos [18]. The interaction of the generated particles with thedetector,anditsresponse,areimplementedusingtheGeant4 toolkit [19] asdescribedinRef. [20].

3. Decayamplitude

TheresonancestructureinB0_s andB_s0

→

J

/ψ

π

+

π

−decayshas beenpreviouslystudiedwithatime-integratedamplitudeanalysis using7and8 TeV pp collisions [21]. Thefinal statewas foundto becompatiblewithbeingentirelyCP -odd,withtheCP -evenstate fractionbelow2

.

3%at95%confidencelevel,whichallowsthe de-terminationofthe decaywidthofthe heavy B0_s masseigenstate,



H.The possible presenceofa CP -evencomponentistakeninto

accountwhendetermining

φ

s[22]. Thetotaldecayamplitude fora

( ) B0

s mesonatdecaytimeequal to zero is assumed to be the sum over individual

π

+

π

− reso-nanttransversityamplitudes[23],andonenonresonantamplitude, witheach transversity componentlabelledas Ai ( Ai). Because of the spin-1 J

/ψ

meson in the final state, the three possible po-larizations of the J

/ψ

generate longitudinal (0), parallel (



) and perpendicular (

⊥

) transversity amplitudes.When the

π

+

π

− pair formsaspin-0statethefinalsystemonlyhasalongitudinal com-ponent,andthusisapure CP eigenstate.Theparameter

λ

i

≡

qp

Ai

Ai,

relates CP violation in the interference between mixingand de-cayassociated withthe polarizationstate i for eachresonance in the final state. Here the quantities q and p relate the mass and flavoureigenstates, p

≡ 

B0

s

|

BL



,andq

≡ 

B0s

|

BL



,where

|

BL



isthe

lightermasseigenstate [1].Thetotalamplitudes

A

and

A

canbe expressedasthesumsoftheindividual

( ) B0_s amplitudes,

A

=



Ai and

A =



q_pAi

=



λ

iAi

=



η

i

|λ

i

|

e−iφ i

s_Ai,with

ηi

_beingtheCP

eigenvalue of the state. For each transversity state i there is a

CP -violating phase

φ

si

≡ −

arg

(

η

i

λ

i

)

[24]. Assuming that CP vio-lationin thedecay isthe same forall amplitudes,then

λ

≡

η

i

λ

i and

φ

s

≡ −

arg

(λ)

.Using

|

p

/

q

|

=

1,thedecayratesforB0s and B0s intothe J

/ψ

π

+

π

−finalstateare3

( )

 (

t

)

∝

e−st



|

A

|

2

_{+ |}

_A

_|

2 2 cosh



st 2

±

|

A

|

2

_{− |}

_A

_|

2 2 cos

(

mst

)

−

R

e

(

A

∗

A

)

sinh



st 2

∓

I

m

(

A

∗

_A

₎

_sin

₍

_m st

)



,

(1)

where the – sign before the cos

(

mst

)

term and

+

signbefore the sin

(

mst

)

term apply to

(

t

)

,



s

≡ 

L

− 

H is the

decay-width difference between the light and the heavy mass eigen-states,

ms

≡

mH

−

mL isthe correspondingmassdifference, and



s

≡ (

L

+ 

H

)/

2 istheaverageB0s mesondecaywidth [26].

3 _{ThelatestLHCbmeasurementdetermined|p}

/q|2₌₁

.0039±0.0033 [25].

For J

/ψ

decays to

μ

+

μ

− final states the Ai amplitudes are themselves functionsoffourvariables:the

π

+

π

− invariant mass

mππ , and three angular variables

≡ (

cos

θ

π π

,

cos

θ

J/ψ

,

χ

)

, de-fined in the helicity basis. These angles are defined as

θ

π π

be-tween the

π

+ directioninthe

π

+

π

− restframe withrespect to the

π

+

π

− directionin the B0

s restframe,

θ

J/ψ betweenthe

μ

+ directioninthe J

/ψ

restframe withrespecttothe J

/ψ

direction in the B0

s rest frame,and

χ

betweenthe J

/ψ

and

π

+

π

− decay planesintheB0

s restframe[22,24].(Thesedefinitionsarethesame for B0_s and B0_s,namely,using

μ

+and

π

+ todefine theanglesfor both B0_s and B0_s decays.)The explicitforms ofthe

|

A(

mππ

,

)

|

2,

|

A(

mππ

,

)

|

2, and

A

∗

(

mππ

,

)A(

mππ

,

)

terms in Eq. (1) are giveninRef. [22].

The analysis proceedsby performing an unbinned maximum-likelihoodfittothe

π

+

π

− massdistribution,thedecaytime,and helicityanglesofB0s candidatesidentifiedasB0s orB0s bya flavour-taggingalgorithm[27].4 _{ThefitprovidestheCP -evenandCP -odd}

components, and since we include the initial flavour tag, the fit also determines the CP -violating parameters

φ

s and

|λ|

, andthe decaywidth.Inordertoproceed,weneedtoselectacleansample of B0_s decays,determineacceptancecorrections,performa calibra-tionofthedecay-timeresolutionineacheventasafunctionofits uncertainty,andcalibratetheflavour-taggingalgorithm.

4. Selectionrequirements

The selection of J

/ψ

π

+

π

− right-sign (RS), and wrong-sign (WS) J

/ψ

π

±

π

± final states, proceedsintwo phases. Initiallywe impose loose requirements and subsequently use a multivariate analysisto furthersuppressthecombinatorial background.In the first phase we requirethat the J

/ψ

decaytracks beidentified as muons, have pT

>

500 MeV, and form a good vertex with

ver-tex fit

χ

2 _{lessthan16.The identifiedpions are requiredtohave}

pT

>

250 MeV,notoriginatefromanyPV,andforma goodvertex

withthemuons.Theresulting B0s candidateisassignedtothePV forwhichithasthesmallest

χ

2

IP.Furthermore,werequirethatthe

smallest

χ

2

IPisnotgreaterthan25.TheB 0

s candidateisrequiredto haveitsmomentumvectoralignedwiththevectorconnectingthe PVtothe B0_s decayvertex,andtohaveadecaytime greaterthan 0.3 ps.Reconstructedtrackssharingthesamehitsarevetoed.

Inaddition,backgroundfromB+

→

J

/ψ

K+ decays,5 _wherethe K+ is misidentified as a

π

+ and combined witha random

π

−, is vetoed by assuming that each detected pion is a kaon, com-puting the J

/ψ

K+ mass, andremoving thosecandidates that are within

±

36 MeV of theknown B+ mass [14]. Backgrounds from

B0

→

J

/ψ

K+

π

− or B0_s

→

J

/ψ

K+K− decays with misidentified kaons result inmasses lower than the B0_s peak andthus do not needtobevetoed.

For the multivariate part of the selection, we use a Boosted DecisionTree,BDT [28,29],withtheuBoostalgorithm [30].The al-gorithmisoptimizedtonotfurtherbiasacceptanceonthevariable

cos

θ

π π .ThevariablesusedtotraintheBDTarethedifference

be-tween themuon andpionidentifications forthemuon identified withlowerquality,the pT oftheB0s candidate,thesumofthe pT

of the two pions,and thenatural logarithms of: the

χ

2 IP of each

ofthepions,the

χ

2 _{ofthe B}0

s vertexanddecaytreefits[31],and the

χ

2

IP oftheB 0

s candidate.Inthefit,the B0s momentumvectoris constrainedtopointtothePV, thetwomuonsareconstrainedto

4 _{Weutilizethesamelikelihoodconstructionthatweusedtodetermineφ}

sand

|λ|in

B

0

s→J/ψK+K−decayswith

K

+K−abovetheφ(1020)massregion [6].

5 _{Whendiscussingflavour-specificdecays,mentionofaparticularmodeimplies}

Fig. 1. Results ofthesimultaneousfittothe J/ψπ π massdistributionsRS(black points)andWS(greypoints)samples.Thesolid(blue)curveshowsthefittothe RSsample,thelongdashed(red)curveshowsthesignal,thedot-dashed(magenta) curveshows

B

0_→J/ψπ+_π−_{decays,thedot-long-dashed(brown)curveshowsthe}

combinatorialbackground,thedotted(black)curveshowsthesumof

B

0

s→J/ψη

andΛ0b background,whilethedot-dot-dashed(green)curveshowsthefittoWS

sample.

the J

/ψ

mass,andallfourtracksareconstrainedtooriginatefrom thesamevertex.

ImplementinguBoostrequiresatrainingprocedure.Data back-groundin the J

/ψ

π

+

π

− massinterval between200to 250MeV abovethe B0

s massandsimulatedsignalare firstused.Then, sep-aratesamples are used to test the BDT performance. We weight thetraining simulationsamplestomatchthetwo-dimensional B0_s

p and pT distributions,andsmearthevertexfit

χ

2,tomatchthe

background-subtractedpreselecteddata.Finally,theminimum re-quirementforBDTpointischosentomaximizesignalsignificance,

S

/

√

S

+

B,whereS

(

B

)

istheexpectedsignal(background)yields inarangecorrespondingto

±

2

.

5 timesthemassresolutionaround theknownB0_s mass [14].

Todeterminethesignal andbackgroundyields wefitthe can-didate B0

s mass distribution. Backgrounds include combinatorics, whoseshape is estimatedusing WS J

/ψ

π

±

π

± candidates mod-elled by an exponential function, B0_s

→

J

/ψ

η



(

→

ρ

0

_γ

₎

_decays

withthe

γ

ignored,and

Λ

0_b

→

J

/ψ

p K− decayswithbothhadrons misidentified as pions. The latter backgrounds are modelled us-ingsimulation.The B0_s signalshapeisparameterizedbyaHypatia function [32], wherethesignalradiative tailparametersare fixed to values obtained from simulation. The same shape parameters are used for the B0

→

J

/ψ

π

+

π

− decays, with the mean value shiftedby theknown B0

s and B0 mesonmassdifference [14]. Fi-nally,we fitsimultaneouslybothRSandWScandidates,usingthe simulatedshapefor B0_s

→

J

/ψ

η



(

→

ρ

0

_γ

₎

_{whoseyieldis allowed}

tofloat,andfixingboththesizeandshapeofthe

Λ

0_b

→

J

/ψ

p K−

component. The results of the fit are shown in Fig. 1. We find 33530

±

220 signalB0_s within

±

20 MeV oftheB0_s masspeak,with apurityof84%.Thesedecaysareusedforfurtheranalysis.Multiple candidatesinthe sameeventhavea rateof0.20%ina

±

20 MeV intervalaroundthe B0_s masspeak,andareretained.

Tosubtract thebackground inthe signal region inthe ampli-tude fit we add negatively weighted events from the WS sam-pleto the RSsample, also accountingforthe differing

π π

mass anddecay-timedistributions.Theweightsaredeterminedby com-paring the RS and WS mass distributions in the upper mass sideband (5420

−

5550 MeV). In addition, a small component of

B0_s

→

J

/ψ

η



(

η



→

ρ

0

_γ

₎

_{decaysisalsosubtracted,sinceitisabsent}

intheWSsample.

5. Detectorefficiencyandresolution

The correlated efficiencies in mππ and angular variables

are determined fromsimulation. Weweight the simulatedsignal eventstoreproducethe B0

s meson pT and

η

distributionsaswell

as the track multiplicity of the events. The latter may influence theefficienciesofthetrackingandparticleidentification.The cal-culatedefficienciesareshowninFig.2alongwiththedetermined efficiency function. The four-dimensional efficiency is parameter-ized by a combination of Legendre and spherical harmonic mo-ments[33],as

ε(

mπ π

,

cos

θ

π π

,

cos

θ

J/ψ

,χ

)

=



a,b,c,d



abcdPa

(

cos

θ

π π

)

Ybc

(θ

J/ψ

,χ

)

Pd



2mπ π

−

m min π π mmax_{π π}

−

mmin π π

−

1

,

(2)

where Pa andPd areLegendrepolynomials,Ybc arespherical har-monics,mmin_{π π}

=

_2mπ+ andmmax_{π π}

=

m_B0

s

−

mJ/ψ, and



abcd _are ef-ficiencycoefficientsdeterminedfromweightedaveragesofdecays generateduniformlyoverphasespace [6].

The model gives an excellent representation of the simulated data.Theefficiencyisuniformwithin about

±

4%forcos

θ

J/ψ and about 10% for

χ

variables; however the mππ and cos

θ

π π

vari-ablesshowlargeefficiencyvariationsandcorrelations(seeFig.3), due to the

χ

2

IP

>

4 requirements on the hadrons. The loss of

efficiencyinthelowermππ regioncanbe interpretedasthe pro-jectionof the effectsof cutson

χ

2

IP. Events atcos

θ

π π

= ±

1 and mππ

0

.

6

−

0

.

8 GeV areatthekinematicboundaryofm2

J/ψπ+.One

ofthepionsisalmostatrestin B0s restframe,andthus thepion points to the PV, resultingin a very small

χ

2

IP forthispion.The

χ

2

IP variableisthemostusefultool tosuppresslarge pion

combi-natorialbackgroundfromthePV.

The reconstruction efficiency is not constant as a function of

B0

s decay time due to displacement requirements applied to the hadronsintheofflineselectionsandon J

/ψ

candidatesinthe trig-ger.Itisdeterminedusingthecontrolchannel B0

_→

_J

_/ψ

_K∗

₍

₈₉₂

₎

0_,

with K∗

(

892

)

0

→

K+

π

−, which is known to have a lifetime of

τ

_B0

=

1

.

520

±

0

.

004 ps [14].ThesimulatedB0eventsareweighted

toreproducethedistributions inthedatafor pT and

η

ofthe B0

meson,andtheinvariantmassandhelicityangleofK+

π

−system, aswellasthetrackmultiplicityoftheevents.Thesignalefficiency iscalculatedas

ε

B0s data

(

t

)

=

ε

B0 data

(

t

)

·

ε

B0 s sim

(

t

)/

ε

B0 sim

(

t

)

,where

ε

B0 data

(

t

)

is

the efficiency of the control channel asmeasured by comparing data with the known lifetimedistribution, and

ε

B0s

sim

(

t

)/

ε

B

0

sim

(

t

)

is

theratio ofefficienciesofthe simulatedsignal andcontrolmode after the full triggerand selection chain havebeen applied. This correctionaccountsforthesmalldifferencesinthekinematics be-tweenthesignalandcontrolmodes.Thedetailsofthemethodare explainedinRef. [4].

The acceptance is checked by measuring the decay width of

B+

→

J

/ψ

K+ decays. The fitted decay-width difference between the B+ and B0 mesons is



B+

− 

B0

= −

0

.

0475

±

0

.

0013 ps−1,

where the uncertainty is statistical only, in agreement with the knownvalueof

−

0

.

0474

±

0

.

0023 ps−1_[14].

From the measured B0

s candidate momentum and decay dis-tance, the decay time and its event-by-event uncertainty

δ

t are calculated. The calculated uncertainty is imbedded into the res-olution function, which is modelled by the sum of three Gaus-sian functionswithcommonmeansandwidthsproportional toa quadraticfunctionof

δ

t.Theparametersoftheresolutionfunction are determined witha sample of putative prompt J

/ψ

→

μ

+

μ

−

Fig. 2. Overall efficiencynormalizedtounityfor(a)

m

π π,(b)cosθπ π,(c)cosθJ/ψ and(d)χobservables.Thepointswitherrorbarsarefromthe

B

0s→J/ψπ+π−simulation,

whilethecurvesshowtheprojectionoftheefficiencyfunction.

Fig. 3. Overall efficiencyfor(a)

m

π πvscosθπ πand(b)

m

2J/ψπ+vs

m

2

π π.Theinefficiencyisatthekinematicboundaryof

m

2J/ψπ+wherethepionisalmostatrestinthe

B

0

s

frame.

decays combinedwith two pions ofopposite charge. Taking into account the decay-timeuncertainty distributionof the B0_s signal, theaverageeffectiveresolutionisfoundtobe41.5 fs.Themethod isvalidatedusingsimulation;weestimatetheaccuracyofthe res-olutiondeterminationtobe

±

3%.

6. Flavourtagging

Knowledge of the

( )

B0_s flavour at production is necessary. We use informationfrom decaysof the other b hadron in the event (opposite-side,OS)andfragmentsofthejetthatproducedthe

( ) B0s mesonthat contain a charged kaon,called same-sidekaon (SSK) [27].TheOStaggerinferstheflavouroftheotherb hadroninthe event from the charges of muons, electrons, kaons, and the net chargeoftheparticlesthatformreconstructedsecondaryvertices. The flavour tag,

q

, takes values of

+

1,

−

1 or 0 if the signal mesonistaggedasB0_s,B0_soruntagged,respectively.Thewrong-tag probability,

y

,isestimatedevent-by-eventbasedontheoutputofa

neuralnetwork.Itissubsequentlycalibratedwithdatainorderto relateittothetruewrong-tag probabilityoftheeventbyalinear relationas

ω(y)

=

p0

+

p0 2

+

p1

+

p1 2



· (y − y);

ω(y)

=

p0

−

p0 2

+

p1

−

p1 2



· (y − y),

(3)

where p0, p1,

p0 and

p1 arecalibrationparameters,and

ω

(y)

and

ω

(y)

are the calibratedprobabilities for a wrong-tag assign-ment for B0

s and B0s mesons, respectively. The calibration is per-formed separately for the OS and the SSK taggers using B+

→

J

/ψ

K+ and B0_s

→

D−_s

π

+ decays, respectively. When events are tagged by both the OS and the SSK algorithms, a combined tag decisionisformed.Theresultingefficiencyandtaggingpowersare listedinTable1.

Table 1

Taggingefficiency,εtag,andtaggingpowergivenasthe

efficiency timesdilution squared, εtagD2, where D =

(1−2ω) for each categoryand the total. The uncer-taintiesonεtagarestatisticalonly,andthoseforεtagD2

containbothstatisticalandsystematiccomponents. Category εtag(%) εtagD2(%)

OS only 11.0±0.6 0.86±0.05 SSK only 42.6±0.6 1.54±0.33 OS and SSK 24.9±0.6 2.66±0.19 Total 78.5±0.7 5.06±0.38 Table 2 Resonanceparameters.

Resonance Mass (MeV) Width (MeV) Source

f0(500) 471±21 534±53 LHCb[38] f0(980) Varied in fits f2(1270) 1275.5±0.8 186.7+₋22..25 PDG [14] f0(1500) Varied in fits f₂(1525) 1522.2±1.7 78.0±4.8 LHCb [6] f0(1710) 1723+₋65 139±8 PDG [14] f0(1790) 1790+₋4030 270+ 60 −30 BES [37]

7.Descriptionofthe

π

+

π

−massspectrum

Wefittheentire

π

+

π

−massspectrumincludingtheresonance contributions listed in Table 2, and a nonresonant (NR) compo-nent.We use an isobarmodel [21]. All resonances are described by Breit–Wigner amplitudes, exceptfor the f0

(

980

)

state, which

ismodelledbya Flattéfunction [34].The nonresonantamplitude istreatedasbeingconstantinmππ .Other theoreticallymotivated amplitude models are also proposed to describe this decay [35, 36]. Theprevious publication [21] usedan unconfirmed f0

(

1790

)

resonance,reported by theBES collaboration [37], instead ofthe

f0

(

1710

)

state.Wetestwhichonegivesabetterfit.

The amplitude AR

(

mππ

)

, generally represented by a Breit– WignerfunctionoraFlattéfunction,isusedtodescribethemass lineshapeofresonanceR.TodescribetheresonancefromtheB0_s

decays,theamplitudeiscombinedwiththe B0_s andresonance de-caypropertiestoformthefollowingexpression

A

R

(

mπ π

)

=



2 JR

+

1



PRPBF(_BLB)F_R(LR)AR

(

mπ π

)

×

PB mB

L

B

_P R m0

L

R

.

(4)

HerePB isthe J

/ψ

momentumintheB0s restframe, PR isthe mo-mentumofeitherofthetwohadronsinthedihadronrestframe,

mB is the B0s mass, m0 is the mass of resonance R,6 JR is the spin of the resonance R, LB is the orbital angular momentum betweenthe J

/ψ

meson and

π

+

π

− system, and LR the orbital angularmomentuminthe

π

+

π

− system,andthusisthesameas thespin of the

π

+

π

− resonance.The terms F(LB)

B and F (LR)

R are theBlatt–Weisskopfbarrierfactors forthe B0_s mesonand R

reso-nance,respectively [39].Theshapeparametersforthe f0

(

980

)

and

f0

(

1500

)

resonancesareallowedtovary.

6 _{Equation (4) ismodifiedfromthatusedinpreviouspublications [4,21] and}

fol-lowstheconventionsuggestedbythePDG[14].

8. Likelihooddefinition

Thedecay-timedistributionincludingflavourtaggingis

R

(ˆ

t

,

mπ π

,

, q

|y) =

1 1

+ |q|

[1

+ q (

1

−

2

ω(y))

]

(ˆ

t

,

mπ π

,

)

+

[1

− q (

1

−

2

ω(y))

¯

]1

+

AP 1

−

AP

¯(ˆ

t

,

mπ π

,

)



,

(5)

where

ˆ

t isthetruedecaytime,

(–)



isdefinedinEq. (1), and AP is

theproductionasymmetryofB0

s mesons.

Thefitfunction forthesignal ismodifiedto takeintoaccount thedecay-timeresolutionandacceptanceeffectsresultingin

F

(

t

,

mπ π

,, q

|y, δt

)

=



R

(ˆ

t

,

mπ π

,

, q

|y) ⊗

T

(

t

− ˆ

t

|δt

)



ε

B0s

data

(

t

)ε(

mπ π

,),

(6)

where

ε

(

mππ

,

)

istheefficiencyasafunctionofmππ and angu-larvariables, T

(

t

− ˆ

t

|δ

t

)

isthedecay-timeresolutionfunction,and

ε

B0s

data

(

t

)

isthedecay-timeacceptancefunction.Thefreeparameters

inthefitare

φ

s,

|λ|

,



H

− 

B0,themagnitudesandphasesofthe

resonances amplitudes, and the shape parameters of some reso-nances.Theotherparameters,including

ms,and



L,arefixedto

theknownvalues[14] orothermeasurementsmentionedbelow. The signal function is normalized by summing over

q

values andintegratingoverdecaytimet,themassmππ ,andtheangular variables,

,giving

N

(δ

t

)

=

2



[(ˆ

t

,

mπ π

,

)

+

1

+

AP 1

−

AP

¯(ˆ

t

,

mπ π

,

)

]

⊗

T

(

t

− ˆ

t

|δt

)ε

B0s data

(

t

)ε(

mπ π

,)

dmπ πd

dt

.

(7)

Weassume noasymmetries inthetaggingefficiencies,whichare accountedforinthesystematicuncertainties.Theresultingsignal PDFis

P

(

t

,

mπ π

,, q

|y, δt

)

=

1

N

(δ

t

)

F

(

t

,

mπ π

,, q

|y, δt

).

(8)

ThefitterusesatechniquesimilartosPlot [40] tosubtract back-groundfromthelog-likelihoodsum.Eachcandidateisassigneda weight,Wi

= +

1 fortheRSeventsandnegativevaluesfortheWS events.Thelikelihoodfunctionisdefinedas

−

2 ln

L

= −

2 sW



i

Wiln

P

(

t

,

mπ π

,

, q

|y, δt

),

(9)

wheresW

≡



iWi

/



iWi2 isaconstantfactoraccountingforthe effectofthebackgroundsubtractiononthestatisticaluncertainty.

The decay-time acceptance is assumed to be factorized from other variables,butduetothe

χ

2

IP cuton thetwo pions,the

de-caytimeiscorrelatedwiththeangularvariables.Toavoidbiason thedeterminationof



Hfromthedecay-timeacceptance,the

sim-ulated B0s signal isweightedinordertoreproducethemππ reso-nantstructure observedindataby usingthepreferredamplitude modelthatisdeterminedbytheoverallfit.Aniterativeprocedure isperformedtofinalizethedecay-timeacceptance.Thisprocedure converges in three steps beyondwhich



H doesnot vary. When

weapply thismethodtopseudoexperimentsthatincludethe cor-relationmentionedbefore,thefitterreproducestheinputvaluesof

Table 3

Likelihoodsofvariousresonancemodelfits.Positiveornegativeinterferences(Int) amongthecontributingresonancesareindicated.TheSolutionsareindicatedby#.

# Resonance content Int −2 lnL

I f0(980)+f0(1500)+f0(1790)+f2(1270)+f2(1525)+NR − −4850 II f0(980)+f0(1500)+f0(1710)+f2(1270)+f2(1525)+NR + −4834 III f0(980)+f0(1500)+f0(1790)+f2(1270)+f2(1525)+NR + −4830 IV f0(980)+f0(1500)+f0(1790)+f2(1270)+f2(1525) − −4828 V f0(980)+f0(1500)+f0(1710)+f2(1270)+f2(1525) − −4706 Table 4

Fitresultsforthe

CP -violating

parametersforSolutionI.Thefirstuncertaintiesare statistical,andthesecondsystematic.Thelastthreecolumnsshowthestatistical correlationcoefficientsforthethreeparameters.

Fit result Correlation

Parameter H− B0 |λ| φs

H− B0 ( ps−1) −0.050±0.004±0.004 1.000 0.022 0.038

|λ| 1.01₋+00..0806±0.03 0.022 1.000 0.065

φs(rad) −0.057±0.060±0.011 0.038 0.065 1.000

9. Fitresults

Wefirstchoosethe resonancesthatbestfitthemππ

distribu-tion. Table 3 lists the different fit components and the value of

−

2ln

L

.In thesecomparisons,themassandwidthofmost reso-nancesarefixed tothecentralvalueslistedinTable2,exceptfor the f0

(

980

)

and f0

(

1500

)

resonances, whose parameters are

al-lowedtovary.Wefindtwotypesoffitresults,onewithapositive integratedsumofallinterferingcomponentsandonewitha nega-tiveone.ThefirstlistedSolutionIisbetterthanSolutionIIbyfour standard deviations, calculated by taking the square root of the

−

2ln

L

difference. We take Solution I for our measurement and IIforsystematicuncertaintyevaluation.Themodelscorresponding toSolutionsIandIIareverysimilartothosefoundinourprevious analysisofthesamefinalstate [21].

Fig. 5. Data distributionof

m

π πwiththeprojectionoftheSolutionIfitresult

over-laid.Thedataaredescribedbythepoints(black)witherrorbars.Thesolid(blue) curveshowstheoverallfit.

ForthefitweassumethattheCP -violationquantities(

φ

s i,

|λ

i

|

) arethesameforalltheresonances.Wealsofix

mstothecentral value of the world average 17

.

757

±

0

.

021 ps−1 _{[14], and fix}

_

L

tothecentralvalueof0

.

6995

±

0

.

0047 ps−1 _{fromtheLHCb B}0

s

→

J

/ψ

K+K− results [6].

The fit valuesandcorrelations ofthe CP -violating parameters are shown in Table 4 for Solution I. The shape parameters of

f0

(

980

)

and f0

(

1500

)

resonancesare foundtobeconsistentwith

our previous results [21]. The angular anddecay-time fit projec-tionsareshowninFig.4.Themππ fitprojectionisshowninFig.5, wherethecontributionsoftheindividualresonancesarealso dis-played.AllsolutionslistedinTable3giveverysimilarfitvaluesfor

φ

s and



H.Wealsofind thatthe CP -odd fractionisgreater than

97% at95% confidencelevel.The resonantcontent forSolutions I andIIarelistedinTable5.

Table 5

FitresultsoftheresonantstructureforbothSolutionsIandII.Theseresultsdonot supersedethoseinRef. [21] fortheresonantfractionsbecausenosystematic un-certaintiesarequoted.Thesumoffitfractionisnotnecessary100%duetopossible interferencesbetweenresonanceswiththesamespin.

Component Fit fractions (%) Transversity fractions (%)

0  ⊥ Solution I f0(980) 60.09±1.48 100 − − f0(1500) 8.88±0.87 100 − − f0(1790) 1.72±0.29 100 − − f2(1270) 3.24±0.48 13±3 37±9 50±10 f₂(1525) 1.23±0.86 40±13 31±14 29±25 NR 2.64±0.73 100 − − Solution II f0(980) 93.05±1.12 100 − − f0(1500) 6.47±0.41 100 − − f0(1710) 0.74±0.11 100 − − f2(1270) 3.22±0.44 17±4 30±8 53±10 f2(1525) 1.44±0.36 35±8 31±12 34±17 NR 8.13±0.79 100 − − 10. Systematicuncertainties

ThesystematicuncertaintiesfortheCP -violatingparameters,

λ

and

φ

s,aresmallerthanthestatisticalones.Theyaresummarized inTable6alongwiththeuncertaintyon



H

−

B0.Theuncertainty

onthedecay-timeacceptanceisfoundbyvarying theparameters ofthe acceptancefunction within their uncertainties and repeat-ing the fit.The same procedure is followedfor the uncertainties onthe B0 lifetime,

ms,



L,mππ and angularefficiencies, reso-nancemassesandwidths,flavour-taggingcalibration,andallowing fora2%productionasymmetry [41];thisuncertaintyalsoincludes anypossibledifferenceinflavourtaggingbetweenB0_s andB0_s. Sim-ulationisusedtovalidatethemethodforthetime-resolution cali-bration.Theuncertaintiesoftheparametersofthetime-resolution modelareestimatedusingthedifference betweenthesignal sim-ulation andprompt J

/ψ

simulation. These uncertainties are var-ied to obtain the effects on the physics parameters. Resonance modelling uncertainty includes varying the Breit–Wigner barrier factors, changing the default values of LB

=

1 for the D-wave resonances to one or two, the differencesbetween the two best solutions,and replacingthe NR component by the f0

(

500

)

reso-nance.Furthermore,includinganisospin-violating

ρ

(

770

)

0 compo-nentinthefit,resultsinanegligiblecontributionof

(

1

.

1

±

0

.

3

)

%. Thelargest shiftamongthe modellingvariations is takenas sys-tematicuncertainty.Theinclusion of

ρ

componentsresultsinthe largestshiftsofthethreephysicsparameters quoted.The process

B+_c

→

π

+B0

s canaffectthemeasurementof



H

− 

B0.Anestimate

ofthefractionofthesedecaysinoursampleis0.8% [5].Neglecting theB+c contributionleadstoabiasof0.0005 ps−1,whichisadded asasystematicuncertainty.Otherparametersareunchanged.

Correctionsfrompenguinamplitudesareignoredbecausetheir effects are known to be small [42–44] compared to the current experimentalprecision.

11. Conclusions

Using B0_s and B0_s

→

J

/ψ

π

+

π

− decays, we measure the CP

-violatingphase,

φ

s

= −

0

.

057

±

0

.

060

±

0

.

011 rad,thedecay-width difference



H

− 

B0

= −

0

.

050

±

0

.

004

±

0

.

004 ps−1, and the

pa-rameter

|λ| =

1

.

01₋+0_0..08₀₆

±

0

.

03,wherethequoteduncertaintiesare statistical and systematic. These results are more precise than

Table 6

Absolutesystematicuncertaintiesforthephysicsparameters.

Source H− B0 |λ| φs

[ fs−1] [×10−3_{] [mrad]}

Decay-time acceptance 2.0 0.0 0.3

τB0 0.2 0.5 0.0

Efficiency (mπ π,) 0.2 0.1 0.0

Decay-time resolution width 0.0 4.3 4.0 Decay-time resolution mean 0.3 1.2 0.3

Background 3.0 2.7 0.6 Flavour tagging 0.0 2.2 2.3 ms 0.3 4.6 2.5 L 0.3 0.4 0.4 B+c 0.5 – – Resonance parameters 0.6 1.9 0.8 Resonance modelling 0.5 28.9 9.0 Production asymmetry 0.3 0.6 3.4 Total 3.8 29.9 11.0

those obtainedfromthe previous studyofthismodeusing7 TeV and 8 TeV pp collisions (Run 1) [4]. To combine the Run-1 re-sults with these, we reanalyze them by fixing

ms

=

17

.

757

±

0

.

021 ps−1fromRef. [14],and



L

=

0

.

6995

±

0

.

0047 ps−1fromthe

LHCb B0_s

→

J

/ψ

K+K− results [6]. We remove the Gaussian con-strainton



s andlet



Hvary.Insteadoftakingtheuncertainties

offlavourtagginganddecay-timeresolutionintothestatistical un-certainty,weplacethesesourcesinthesystematicuncertaintyand assume100%correlationwithournewresults.Theupdatedresults are:

φ

s

=

0

.

075

±

0

.

065

±

0

.

014 radand

|λ|

=

0

.

898

±

0

.

051

±

0

.

013 with a correlation of 0

.

025. We then use the updated

φ

s and

|λ|

Run-1 results as a constraintinto our new

φ

s fit.7 The com-bined resultsare



H

− 

B0

= −

0

.

050

±

0

.

004

±

0

.

004 ps−1,

|λ|

=

0

.

949

±

0

.

036

±

0

.

019, and

φ

s

=

0

.

002

±

0

.

044

±

0

.

012 rad. The correlation coefficientsamongthe fitparameters are 0.025

(

ρ

12

)

,

−

0

.

001

(

ρ

13

)

,and0.026

(

ρ

23

)

.

OurresultsstillhaveuncertaintiesgreaterthantheSM predic-tion and are slightly more precise than the measurement using

B0_s

→

J

/ψ

K+K− decays,based only on Run-1 data, which hasa precisionof0.049 rad [5].Hencethisisthemostprecise determi-nationof

φ

s todate.

Acknowledgements

We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb in-stitutes. We acknowledge support from CERN and from the na-tional agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MINECO (Spain); SNSF andSER (Switzerland);NASU (Ukraine); STFC (United King-dom);NSF (USA). We acknowledgethe computingresources that are provided by CERN, IN2P3 (France),KIT andDESY (Germany), INFN(Italy),SURF(Netherlands),PIC(Spain),GridPP(United King-dom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open-sourcesoftwarepackagesonwhichwe depend.Individual groups or members have received support from AvH Foundation (Ger-many); EPLANET,MarieSkłodowska-Curie ActionsandERC (Euro-peanUnion);ANR,LabexP2IOandOCEVU, andRégion

Auvergne-7 _{Wedonotincludeanaveragevalueof}

Hsincenosystematicuncertaintywas

Rhône-Alpes (France); KeyResearch Program ofFrontier Sciences ofCAS,CASPIFI,andtheThousandTalentsProgram(China);RFBR, RSFandYandexLLC(Russia);GVA,XuntaGalandGENCAT(Spain); the Royal Society and the Leverhulme Trust (United Kingdom); Laboratory Directed ResearchandDevelopment program of LANL (USA).

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LHCbCollaboration

R. Aaij

29

,

C. Abellán Beteta

46

,

B. Adeva

43

,

M. Adinolfi

50

,

C.A. Aidala

77

,

Z. Ajaltouni

7

,

S. Akar

61

,

P. Albicocco

20

,

J. Albrecht

12

,

F. Alessio

44

,

M. Alexander

55

,

A. Alfonso Albero

42

,

G. Alkhazov

41

,

P. Alvarez Cartelle

57

,

A.A. Alves Jr

43

,

S. Amato

2

,

Y. Amhis

9

,

L. An

19

,

L. Anderlini

19

,

G. Andreassi

45

,

M. Andreotti

18

,

J.E. Andrews

62

,

F. Archilli

29

,

J. Arnau Romeu

8

,

A. Artamonov

40

,

M. Artuso

63

,