Measurement of the CP-violating phase beta in B-0 -> J/psi pi(+)pi(-) decays and limits on penguin effects

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

CP-violating

phase

β

in

B

0

→

J

/ψ

π

+

π

−

decays

and

limits

on

penguin

effects

.

LHCb

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received6November2014

Receivedinrevisedform23December2014 Accepted7January2015

Availableonline13January2015 Editor:W.-D.Schlatter

Time-dependent CP violationis measured in the (—B)0_{→ J/ψπ}+

_π

− _{channel for each}

_π

+

_π

− _resonant final state using data collected with an integrated luminosity of 3.0 fb−1_{in pp collisions}

_{using the LHCb}

detector. The final state with the largest rate, J/ψρ0_{(770), is used to measure the CP-violating}

_angle

2βeffto be (41.7 ±9.6+₋2₆._.8₃)◦. This result can be used to limit the size of penguin amplitude contributions

to CP violation

measurements in, for example,

(—B)0s→J/ψφdecays. Assuming approximate SU(3) flavour symmetry and neglecting higher order diagrams, the shift in the CP-violating

phase

φs is limited to be within the interval [−1.05◦,+1.18◦] at 95% confidence level. Changes to the limit due to SU(3) symmetry breaking effects are also discussed.

©2015 The Authors. 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

Measurementsof CP violation inneutral B mesondecays are usedeithertosearchforphysicsbeyondtheStandardModel(SM)

[1]orsetlimitsoncombinationsofCabibbo–Kobayashi–Maskawa couplings

(V

i j

)

[2]. Interpretations of the measurement of the CP-violatingphase2

β

viatheinterferenceofmixinganddecaysin the

(—)

B0

→

J/ψK0_S channel,andthe phase

φ

s in

(—)

B0_s

→

J/ψφ and

J/ψπ+

π

−decays,1 _{aremadeassumingthatthedecaysare}

domi-natedbytree-levelprocesses.However,penguinprocessesarealso possible,andthey mayhaveamplitudeslargeenough toinfluence the results. Here we use

(—)

B0

→

J

/ψπ

+

π

− decays to set limits onpossiblechanges dueto penguincontributions.Thismodehas both tree and penguin diagrams, asshown in Fig. 1. Theoretical models, to be discussed later, predict that the ratio of penguin to tree amplitudes is greatly enhanced in this decay relative to

(—)

B0

_→

_J

_/ψK

0

S [3,4].Thus,theeffectsofpenguintopologiescanbe

investigatedbyusingthe J/ψπ+

π

− decayandcomparing

differ-1 _{CP violation measurements in}(—)_B0_{→ J/ψK}0

S determine the sum of 2β≡

2arg(−VcdVcb∗)/(VtdVtb∗) and contributions from higher order diagrams.Similar measurements in the(—)B0

s system determine φs which is the sum of −2βs≡

−2arg(−VtsVtb∗)/(VcsVcb∗)andhigherordercorrections.

Fig. 1. (a) Tree level and (b) penguin diagram for B0_{decays into J/ψπ}+_π−_.

ent measurements of the CP-violating phase 2

β

in J/ψK0

S, and

individualchannelssuchas

(—)

B0

_→

_J/ψρ0

₍

₇₇₀

₎

_.2

Next, we discuss the time-dependent decay rate, taking into accountthatthe

π

+

π

−systemiscomposedoftheresonances pre-viously reportedinRef.[5]. Thisanalysislargely followsthe mea-surementprocedureusedinthestudyofCP violationin(—B)0

s decays into J/ψπ+

π

− [6].The totaldecay amplitudefor

(—)

B0 atadecay time of zerois taken to be the sum over individual

π

+

π

− res-onant transversity amplitudes[7],andpossibly onenon-resonant amplitude,witheachcomponentlabeled as Ai( Ai).Thequantities q and p relatethemasseigenstatestotheflavor eigenstates

[8]

.By introducingtheparameter

λ

i

≡

q_pAAi_i,relatingCP violationinthe in-terference betweenmixinganddecayassociated withthestate i,

theamplitudes

A

and

A

canbeexpressedasthesumsofthe in-dividual

(—)

B0 amplitudes,

A

=



Ai and

A =



q_pAi

=



λ

iAi

=

2 _{Inthefollowingρ}0_{orρreferstotheρ}0_(770)meson.

http://dx.doi.org/10.1016/j.physletb.2015.01.008

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.



η

i

|λ

i

|

e−i2β

eff

i _{Ai. For each transversity state i the CP-violating}

phase 2

β

_ieff

≡ −

arg

(η

i

λ

i

)

with

η

i beingthe CP eigenvalue ofthe state.3_{Thedecayratesare}4

Γ (

t

)

=

N

e−Γdt



|

A

|

2

_{+ |}

_A

_|

2 2

+

|

A

|

2

_{− |}

_A

_|

2 2 cos

(

mdt

)

−

I

m



A

∗

A



sin

(

mdt

)



,

Γ (

t

)

=

N

e−Γdt



|

A

|

2

_{+ |}

_A

_|

2 2

−

|

A

|

2

_{− |}

_A

_|

2 2 cos

(

mdt

)

+

I

m



A

∗

A



sin

(

mdt

)



.

(1)

2. Penguinandtreeamplitudes

Thedecay B0

_→

_J/ψK0

S canbewrittenasthesumofonetree

levelamplitude,similar tothatshownin

Fig. 1

(a),butwherethe virtualW− transformstoacs pair,andthreepenguinamplitudes similar to those shown in Fig. 1(b). Here we neglect higher or-der diagrams. The t-quark mediated penguin amplitude can be expressedintermsoftheother twousingCKMunitarity. The re-sultingdecayamplitudeis

[3]

A

(

B0

→

J

/ψ

K_S0

)

=



1

−

λ

2 2

A

1

+

λ

2 1

−λ

2ae iθ_eiγ



,

(2)

where

λ = |

Vus

|

=

0

.

2252[10],

γ

≡

arg

(

−

VudV_ub∗

/V

cdV_cb∗

)

,

A

de-notesthesumoftree andpenguinstrongamplitudes, anda and

θ

arethemagnitudeandphaseofthestrongpartsoftheeffective penguinamplituderelativetothetreeamplitude.

Forthecaseof

(—)

B0

→

J/ψπ+

π

− decays,the

π

+

π

− pairs are inspin statesrangingfromzeroto two. Sincethey are ina final statewithaspin-1 J/ψresonance,theamplitudesinthedifferent transversitystates f need tobe distinguished forall spinsabove zero.Forexample,theamplitudeforeach J/ψρ0

₍

₇₇₀

₎

_transversity

stateis

−

√

2 A



B0

→ (

J

/ψ

ρ

)

f



=λ

A





1

−

a_feiθf_eiγ

_,

₍₃₎

wheretheprimed quantitiesaredefinedinanalogy withthe un-primed ones in Eq. (2). For B0 decays only the sign in front of iγ changes. We are only concerned here with the relative size of the tree and penguin amplitudes. For J/ψK_S0 the pen-guin is suppressedrelative tothe tree by an additional factorof

≡λ

2

_/(

₁

_−λ

2

₎

₌

₀

_.

_{0534.Thus, comparingevena relativelypoor}

measurementof 2

β

eff measured in J/ψρ0 _with2

_β

_{measured in}

J

/ψK

_S0 allows us to set stringent limits on the penguin contri-bution.Using approximateSU(3) flavor symmetry the size ofthe penguin contribution in(—B)0

_→

_J/ψρ0 _{can be related to that in} (—)

B0

s

→

J/ψφ decaysaspointedoutinRefs.[4,11].

Wenow turn to theexpressions forCP violation in the pres-enceofbothtreeandpenguinamplitudes.Thecomplex-valuedCP

parameter

λ

f isgivenby

λ

f

≡

q p A

(

B0

→ (

J

/ψ

ρ

)

f

)

A

(

B0

_{→ (}

_J

_/ψ

_ρ

₎

f

)

=

η

f 1

−

a_feiθf_e−iγ 1

−

a_feiθf_eiγ e −2iβ

_,

₍₄₎

where

β

isthephaseinducedbymixing.Thusthemeasuredphase

β

eff_f isrelatedto

β

by

3 _{Notethatwhileq/p andA}

i/Aiarephaseconventiondependent,λiisnot.

4 _Weassume

Γd=0 and

|

p/q| =1.Theaveragesofcurrentmeasurementsare Γd/Γd=0.001±0.010 and

|

p/q| =1.0005±0.0011[9].

η

f

λ

f

≡ |λ

f

|

e−i2β eff f

=

1

−

a  fe iθ_f e−iγ 1

−

a_feiθf_eiγ e−i2β

,

(5)

separatingrealandimaginarypartsgives

|λ

f

| =





1

−

afe iθ_f e−iγ 1

−

a_feiθf_eiγ



,

and

2

β

f

≡

2

β

efff

−

2

β

= −

arg



₁

₋

_a fe iθ_f e−iγ 1

−

a_feiθf_eiγ

.

(6) Forthe J/ψK0

S modewereplaceaf and

θ

f inEq.(6)by

−

a

f and

θ

f,respectively.Inaddition,wetakea

=

a and

θ



= θ

.The re-lationship betweenthepenguin influence onthe mixinginduced

CP violation phase in favored decays and the measurements in

(—) B0

→ (

J/ψρ0

₎

f isthengivenby

δ

P

= −

arg



_(λ

 fe 2iγ

₋

₁

₎

₊

_(λ

 f

−

1

)

(λ

_fe2iγ

₋

₁

₎

₊

_(λ

 f

−

1

)

e2iγ

where

λ

_f

≡ |λ

f

|

e−i2βf

.

(7) We will show that the penguinshift hasa weak dependence on

|λ

f

|

,resultingin

δ

P

≈ −

2

β

f.Sincetheuncertaintyonthe cur-rentmeasurementof2

β

is

(

₋+1_1..6₅

)

◦,ameasurementof

2

β

f,even withanuncertaintytentimeslarger,couldlimitpenguin contribu-tionstobewellbelowthecurrentstatisticaluncertainty,whichis themainaimofthisanalysis.

3. Detectorsoftwareandeventselection

The LHCb detector [12] is a single-armforward spectrometer covering the pseudorapidity range 2

<

η

<

5, designed for the studyofparticles containingb or c quarks.The detectorincludes ahigh-precisiontrackingsystemconsistingofasilicon-stripvertex detector surroundingthe pp interaction region [13], a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 T m, and three stations of silicon-strip detectors and straw drift tubes [14] placed downstream of themagnet. Thetracking systemprovides ameasurement of mo-mentum,5 p, with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of

(

15

+

29

/

pT

)

μm, where pT is

the component of p transverse to the beam, in GeV. Different typesofchargedhadronsaredistinguishedusinginformationfrom two ring-imaging Cherenkovdetectors [15].Photon, electron and hadroncandidatesareidentifiedbyacalorimetersystemconsisting of scintillating-pad and preshower detectors, an electromagnetic calorimeterandahadroniccalorimeter.Muonsareidentifiedby a systemcomposedofalternating layersofironandmultiwire pro-portionalchambers[16].

The trigger [17] consistsof a hardware stage, based on infor-mation from the calorimeter and muon systems, followed by a softwarestagethatappliesafulleventreconstruction[17].Events selectedforthisanalysisare triggeredby a J/ψ

→

μ

+

μ

− decay, wherethe J/ψ mesonisrequiredatthesoftware leveltobe con-sistentwithcomingfromthedecayofa

(—)

B0_{mesonbyuseofeither}

ofIPrequirementsordetachmentofthe J/ψmesondecayvertex

fromtheprimaryvertex.Inthesimulation,pp collisionsare gener-atedusing Pythia[18]withaspecificLHCb configuration[19]. De-caysofhadronicparticlesare describedby EvtGen[20],inwhich final state radiationis generated using Photos [21].The interac-tionofthegeneratedparticleswiththedetectoranditsresponse are implemented using the Geant4 toolkit [22] as described in Ref.[23].

A(—B)0

_→

_J/ψπ+

_π

− _{candidateisreconstructedby combininga}

J/ψ

→

μ

+

μ

− candidatewithtwo pions ofopposite charge. The like-signcombinations J/ψπ±

π

±arealsoreconstructedfor back-ground studies. The event selection is described in detail in the time-integratedamplitudeanalysis[5].Theonlydifferencehereis thatwereject K0

S

→

π

+

π

− candidatesbyexcludingtheeventsin

theregionwithin

±

20 MeVoftheK0

S masspeak.

Onlycandidateswithdimuoninvariantmassbetween

−

48 MeV and

+

43 MeVrelativetotheobserved J/ψmasspeakareselected, corresponding a window of about

±

3

σ

. The two muons subse-quently are kinematically constrained to the known J/ψ mass. OtherrequirementsareimposedtoisolateB0_{candidateswithhigh}

signal yield and minimum background. This is accomplished by combiningthe J/ψ

→

μ

+

μ

−candidatewithapairofpion candi-datesofoppositecharge,andthentestingifallfourtracksforma commondecayvertex. Pion candidatesare each requiredto have

pTgreaterthan250 MeV,andthescalarsumofthetwotransverse

momenta,pT

(π

+

)

+

pT

(π

−

)

,mustbelargerthan900 MeV.Totest

for inconsistency with production at the PV, the IP

χ

2 _is

com-puted asthe difference betweenthe

χ

2 _{of the PVreconstructed}

withandwithouttheconsideredtrack.EachpionmusthaveanIP

χ

2 _{greaterthan 9.Pionandkaoncandidatesarepositively}

identi-fiedusingtheRICHsystem.Thefour-trackB0 _{candidatemusthave}

a flight distanceof morethan 1.5 mm, wherethe average decay length resolution is 0.17 mm. The angle between the combined momentum vector ofthe decayproducts and the vector formed fromthepositionsofthePVandthedecayvertex(pointingangle) isrequiredtobelessthan2

.

5◦.Eventssatisfyingthispreselection arethen furtherfilteredusinga multivariateanalyzer basedona Boosted Decision Tree (BDT) technique [24]. The BDT uses eight variablesthatarechosentoprovideseparationbetweensignaland background.ThesearetheminimumofDLL(

μ

−

π

)ofthe

μ

+and

μ

−,pT

(π

+

)

+

pT

(π

−

)

,theminimumofIP

χ

2 ofthe

π

+and

π

−,

andtheB0 _{propertiesofvertex}

_χ

2_{,pointingangle,flightdistance,}

pT andIP

χ

2,whereDLL(

μ

−

π

) isa logarithmofthelikelihood

ratiobetween

μ

and

π

hypothesesforthemuoncandidates. TheBDTistrainedonasimulatedsampleoftwomillion B0

→

J/ψπ+

π

−signaleventsgenerateduniformlyinphasespacewith unpolarized J/ψ

→

μ

+

μ

− decays,andabackgrounddatasample fromthesideband5566

<

m(J/ψπ+

π

−

)

<

5616 MeV.Then sepa-ratesamplesareusedtotrainandtesttheBDT.

The invariant mass of the selected J/ψπ+

π

− combinations, where the dimuon pairis constrained to have the J/ψ mass,is shown in Fig. 2. There is a large peak at the B0_s mass and a smaller one atthe B0 _{masson top of thebackground. A double}

Crystal Ball function with common means models the radiative tails and is used to fit each of the signals [25]. Other compo-nentsinthefitmodeltakeintoaccountbackgroundcontributions from B−

→

J/ψK− and B−

→

J/ψπ− decays combined witha random

π

+, B0s

→

J/ψη(

)

with

η

(



)

→

π

+

π

−

γ

, B0s

→

J/ψφ with

φ

→

π

+

π

−

π

0_{, B}0

_→

_J/ψK−

_π

+ _and

_Λ

0

b

→

J/ψK−p reflec-tions,andcombinatorialbackgrounds.Theexponential combinato-rial background shape is takenfrom like-signcombinations, that are thesum of

π

+

π

+ and

π

−

π

− candidates. The shapesofthe other components are takenfrom the simulationwith their nor-malizationsallowedtovary.Onlythecandidateswithin

±

20 MeV ofthe B0 _{masspeak areretainedforCPviolationmeasurements;}

Fig. 2. InvariantmassofJ/ψπ+π−combinationswithK0

Sveto.Thedatahavebeen

fittedwithdouble-Crystalballsignalandseveralbackgroundfunctions.The(purple) solidlineshowsthe B0 _{signal,the (brown)dottedlineshowsthe combinatorial}

background, the(green) short-dashedshowsthe B− background, the (red)

dot-dashedisB0

s→J/ψπ+π−,the(lightblue)long-dashedisthesumofB0s→J/ψη,

B0

s→J/ψφwhenφ→π+π−π0backgroundsandtheΛ0b→J/ψK−p reflection, the(black)dot-longdashedistheB0_→J/ψK−_π+_{reflectionandthe(blue)solid} lineisthetotal.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

thefitgives17650

±

200 signaland9840

±

160 background can-didates.

4. Thesignallikelihood

We fittheentire

π

+

π

− mass spectrum,byincludingthe res-onance contributionsfoundintheamplitudeanalysis

[5]

,inorder tomeasuretheCP-violating parametersofallthestates,themost important being

(—)

B0

→

J/ψρ0 _{as it has the largest fit fraction}

of approximately 65%. The same likelihood construction as was usedtodeterminetheCP-violatingquantities

φ

s and

|λ|

in

(—)

B0

s

→

J/ψπ+

π

− decays [6] is employed. Here the value of

Γ

d

≈

0 simplifies some terms, andthe smaller value of

m

d makes the decaytimeresolutionfunctionlessimportant.Inaddition,a differ-entsame-signflavor taggingalgorithmisused.

The determination of the CP violation parameters relies upon the formalism developed in Ref. [26]. For J/ψ decays to

μ

+

μ

−

final states theamplitudes arethemselves functionsoffour vari-ables: the

π

+

π

− invariant massmhh

=

m(π+

π

−

)

,andthree an-gles

Ω

, defined in the helicity basis. These consist of:

θ

J/ψ, the

angle betweenthe

μ

+ direction in the J/ψ restframe with re-spect to the J/ψ directionin the

(—)

B0 _{rest frame;}

_θ

hh, the angle betweentheh+ direction in theh+h− restframewithrespectto theh+h−directioninthe(B—)0_{restframe; and}

_χ

_{,theanglebetween}

the J/ψandh+h−decayplanesinthe

(—)

B0_restframe

_[26,27]

_.

We performa simultaneous unbinnedmaximumlikelihood fit to the decaytime t, mhh,and thethree helicity angles

Ω

, along withinformationon theinitialflavor of thedecaying hadron,i.e.

whether it was produced asa B0 ora B0 meson. The probabil-ity density function (PDF) used in the fit consists of signal and background components that include detectorresolution and ac-ceptance effects. The predicted decay time error for each event is used for the decay time resolution model, and similarly the measured per-event misidentification probability is used for de-termining the initial flavor of the neutral B meson. The

π

+

π

−

invariantmassdistributionisshownin

Fig. 3

alongwiththefitted componentsofthedifferentresonancesusingthe“Bestmodel”

[5]

Fig. 3. Fitprojectionofm(π+π−)showingthedifferentresonantcontributionsin the“Bestmodel”[5].The KS0 vetocausesthe absenceofeventsnear500 MeV.

Theshapevariationnear780 MeVisduetointerferencebetweentheρ(770)and

ω(782)states.Thetotalfitisthesumoftheindividualcomponentsplustheir in-terferences.

Knowledge of the

(—)

B0 _{flavor at production, called “tagging”,}

isnecessary to measure CP violation. We useboth opposite-side (OS)[28] andsame-sidepion(SS

π

)tagginginformation;herewe use the same procedure as for same-side kaon tagging used in the

(—)

B0_s

→

J/ψπ+

π

− and J/ψφ analyses [27], but identify the tagfroma pionrather thana kaon.The wrong-tag probability

η

isestimatedbasedon theoutput ofa neuralnetwork trainedon simulateddata.Itiscalibratedwithdata usingflavor-specific de-cay modes in order to predict the true wrong-tag probability of the event(

ω(η)

—) for an initial flavor

(—)

B0 meson, which has a lin-eardependence on

η

.The calibrationis performedseparately for theOSandtheSS

π

taggers.Ifeventsaretagged byboth OSand SS

π

algorithms,acombinedtagdecisionandwrong-tag probabil-ityaregivenbythealgorithmdefinedinRef.[28].Thiscombined algorithmis implemented inthe overall fit.The effectivetagging powerobtainedischaracterizedby

ε

tagD2

= (

3

.

26

±

0

.

17

)

%,where

D

≡ (

1

−

2

ω

avg

)

isthedilution,

ω

avgistheaveragewrong-tag

prob-abilityfor

ω

and

ω

¯

,and

ε

tag

= (

42

.

1

±

0

.

6

)

% isthesignaltagging

efficiency.

Thesignaldecaytimedistributionincludingflavor taggingis R

(ˆ

t

,

mhh

, Ω, q

|

η

)

=

1 1

+ |q|



1

+ q



1

−

2

ω

(

η

)



Γ (ˆ

t

,

mhh

, Ω)

+



1

− q



1

−

2

ω

¯

(

η

)



1

+

AP 1

−

AP

¯

Γ (ˆ

t

,

mhh

, Ω)



,

(8) wheret is

ˆ

thetruedecaytime,

(—)

Γ

isdefinedinEq.(1),and AP

=

−

0

.

0035

±

0

.

0081[29]isthe B0–B0 productionasymmetryinthe LHCb acceptance.The flavor tag parameter

q

takes values of

−

1 or

+

1ifthesignalmesonistaggedas B0_,B0 _{respectively,or0if}

untagged.

Thesignalfunctionisconvolvedwiththedecaytimeresolution andmultipliedbytheacceptance:

Fsig

(

t

,

mhh

, Ω, q

|

η

, δ

t

)

=



R

(ˆ

t

,

mhh

, Ω, q

|

η

)

⊗

T

(

t

− ˆ

t

; δ

t

)

·

E

t

(

t

)

·

ε

(

mhh

, Ω),

(9) where

ε

(m

hh

,

Ω)

istheefficiencyasafunctionoftheh+h−mass andangles,obtainedfromthesimulationasdescribedinRef. [5],

T

(t

− ˆ

t

;

δ

t

)

is the decay time resolution function which depends uponthe estimateddecaytime errorforeachevent

δ

t,and

E

t

(t)

isthe decaytime acceptancefunction. The decaytime resolution function T

(t

− ˆ

t

;

δ

t

)

isdescribedbyasumofthreeGaussian func-tions with a common mean. Studies using simulated data show that J/ψπ+

π

− combinations produced directly in the pp

inter-action (prompt) havenearly identical resolution to signal events. Specifically, thetime resolution isdetermined usingprompt J/ψ

decays into a dimuon pair, using a dedicated trigger for calibra-tionpurposes,plustwooppositelychargedtracksfromtheprimary vertexwiththesimilar selectioncriteriaasfor J

/ψπ

+

π

− andan invariantmasswithin

±

20 MeVoftheB0 mass.Theeffective res-olutionisfoundto beabout40 fsby usingtheweighted average widthsofthethreeGaussians.Thisisnegligiblysmallcomparedto the B0–B0oscillationtime.

Thedecaytimedistributionisinfluencedbyacceptanceeffects that areintroduced by trackreconstruction,triggerandevent se-lection.Thedecaytimeacceptanceisobtainedusing control sam-ples of

(—)

B0

→

J/ψ

(—)

K∗0

(

→

K∓

π

±

)

decays, corrected by the ac-ceptance ratiobetween J/ψK∓

π

± and J/ψπ+

π

− derived from simulation.

Theacceptancefunctionforthecontrolsampleisdefinedas A

(

t

;

a

,

n

,

t0

, β

1

, β

2

)

=

[

a

(

t

−

t0

)

]

n 1

+ [

a

(

t

−

t0

)

]

n

×



1

+ β

1t

+ β

2t2



,

(10) wherea,n,t0,

β

1,

β

2areparametersdeterminedbythefit.The

de-cay timedistributionof

(—) B0

_→

_J/ψK∓

_π

± _{candidatesisdescribed} bythefunction P0

(

t

)

=



f0A

(

t

;

a

,

n

,

t0

, β

1

, β

2

)

e−ˆt/τB0

τ

_B0

N

_B0

+ (

1

−

f0

)

A



t

;

a0_bkg

,

n_bkg0

,

0

,

0

,

0



e −ˆt/τ0 bkg

τ

0 bkg

N

bkg0

⊗

T

(

t

− ˆ

t

; δ

t

),

(11)

where f0 is the signal fraction, and

N

B0 and

N

_bkg0 are

normal-izations necessary to construct PDFs of signal and background, respectively.The backgroundacceptancefunction inEq.(11)uses thesameformasthesignalanditsparametersa0_bkg,n0_bkgand

τ

0

bkg

are obtainedfrommasssidebandregions of5180–5205 MeVand 5400–5425 MeV.Thelifetimeisconstrainedto

τ

B0

=

1

.

519

±

0

.

007

ps[10].

We usetheproduct ofthe acceptance A(a,n,t0

,

β

1

,

β

2

)

deter-mined from

(—)

B0

→

J/ψ

(—)

K∗0 andthe correction ratio found from simulation asthe time acceptancefunction for(B—)0

_→

_J/ψπ+

_π

−

events,

E

t

(

t

;

a

,

n

,

t0

, β

1

, β

2

,

p1

,

p2

)

=

[

a

(

t

−

t0

)

]

n 1

+ [

a

(

t

−

t0

)

]

n

×



1

+ β

1t

+ β

2t2



×



1

−

p2e−p1t



,

(12) withparametervaluesandcorrelationsgivenin

Table 1

.

5. Measurementsof2

β

eff

TheCP-violatingparametersaredeterminedfromafitthatuses theamplitudemodelwithsixfinalstate

π

+

π

−resonances.Inour previous amplitude analysis [5] we used two parameterizations of the f0

(

500

)

resonance, “default” and “alternate”. The default

usedaBreit–Wignerresonanceshape,withrelativelypoorly mea-sured parameters, while the alternate used a function suggested byBugg

[30]

,withmoretheoreticallymotivatedshapeparameters. In this analysis we choose to switch to the shape suggested by Bugg,whiletheBreit–Wignershapeofthepreviousdefault param-eterizationis used to assesssystematic uncertainties. A Gaussian

Table 1

Parametervaluesandcorrelationsfortheacceptancefunctionεt(t)inEq.(12).

P n a β1 β2 t0 p1 p2 Values n 1.000 0.444 0.574 −0.536 −0.862 0.000 0.000 2.082±0.036 a 1.000 0.739 −0.735 −0.050 0.000 0.000 1.981±0.024 ps−1 β1 1.000 −0.899 −0.374 0.000 0.000 0.077±0.009 ps−1 β2 1.000 0.343 0.000 0.000 −0.008±0.001 ps−2 t0 1.000 0.000 0.000 0.104±0.003 ps p1 1.000 −0.885 6.237±1.669 ps−1 p2 1.000 −0.739±0.424 Table 2

Fitresultsfor2βieffandα i CP. Condition 2βeff i (◦) αiCP(×10−3) Fit 1 ρ 41.7±9.6+₋62..83 ρ −32±28+ 9 −7 other−ρ 3.6±3.6+₋00..98 other −1±25+ 7 −14 Fit 2 ρ0 44.1±10.2₋+36..09 ρ0 −47±34+₋1110 ρ−ρ0 −0.8±6.5₋+11..93 ρ −61±60+ 8 −6 ρ⊥−ρ0 −3.6±7.2₋+21..04 ρ⊥ 17±109+ 22 −15 other−ρ0 2.7±3.9₋+01..09 other 6±27+ 9 −14

constraintusing

m

d

=

0

.

510

±

0

.

003 ps−1 [10] isappliedinthe fit. All other parameters, such asthe time resolution, and those describingthetaggingarefixed.InadditiontotheCP-violating pa-rameters,theotherfreeparametersaretheamplitudesandphases oftheresonances.Tominimizecorrelationsinthefittedresults,we chooseasfreeparameterstheCP asymmetry

α

i

CP

=

1−|λi|

1+|λi|,2

β

ieff of thelargestpolarizationcomponent,and

2

β

_ieff oftheother com-ponentswithrespecttothelargestone.

As J/ψρ is the final state with the largest contribution, we treatitspeciallyandperformtwofits.Inbothcasesallresonances other thanthe

ρ

sharea commonCP violationparameter

λ

.For Fit 1the three

ρ

transversity statesshare thesame CP violation

parameter

λ

,whileforFit 2each

ρ

transversitystatehasitsown

CP violation parameter

λ

i.The results areshown inTable 2.The statisticaluncertaintiesarewithin

±

15% oftheprecisionestimated usingtoy MonteCarlosimulation.Todetermine

2

β

f weusethe measuredvalue inb

→

ccs transitionsof

(

42

.

8₋+1₁._.6₅

)

◦ foundin

(—)

B0

decays

[9]

.Ourmeasurementof2

β

effisconsistentwiththisvalue for both Fit 1 andFit 2. The correlation between

α

ρ_CP and 2

β

eff

ρ

is

−

0

.

01 in Fit 1. Table 3 shows the correlation matrix for the

CP-violatingparametersinFit 2.

Table 4 lists the fit fractions and three transversity fractions of contributing resonances from Fit 1, consistent with the re-sults shown in the amplitude analysis [5]. For a P - or D-wave

resonance, we report its total fit fraction by summing all three transversitycomponents.Thistime-dependentanalysisdetermines thephase difference betweentheCP-odd componentof

ρ

(

770

)

⊥

andtheCP-evencomponentof

ρ

(

770

)

0 tobe

(

167

±

11

)

◦ inFit 1.

Table 4

FitandtransversityfractionsofcontributingresonancesfromFit 1.Uncertaintiesare statisticalonly.Theseresultsarepresentedonlyasacross-check.

Component Fit fraction (%) Transversity fractions (%)

0  ⊥ ρ(770) 65.6±1.9 56.7±1.8 23.5±1.5 19.8±1.7 f0(500) 20.1±0.7 1 0 0 f2(1270) 7.8±0.6 64±4 9±5 27±5 ω(782) 0.64₋+00..1913 44±14 53±14 3+ 10 −3 ρ(1450) 9.0±1.8 47±11 39±12 14±8 ρ(1700) 3.1±0.7 29±12 42±15 29±15

Fig. 4. Decaytimedistributionof(—)B0_→J

/ψπ+π−candidates.Thesignal compo-nentisshownwitha(red)dashedline,thebackgroundwitha(black)dottedline, and the(blue)solidlinerepresentsthetotal. Thelowerplotshowsthe normal-izedresidualdistribution.(Forinterpretationofthereferencestocolorinthisfigure legend,thereaderisreferredtothewebversionofthisarticle.)

This quantity is not accessible in the time-integrated amplitude analysis. Fig. 4 shows the decay time distribution superimposed withthefitprojection.

The statisticalsignificances oftheCP measurementsare ascer-tained by fittingthedata requiringthat CP-violating components

Table 3

ThecorrelationmatrixfortheCP-violatingparametersdeterminedusingFit 2,where2βeffi =2β eff i −2β eff ρ0. αother CP α ρ0 CP α ρ⊥ CP α ρ

CP 2βothereff 2βρeff⊥ 2β eff ρ 2β eff ρ0 αother CP 1.00 −0.62 −0.28 −0.13 0.05 −0.42 −0.19 0.05 αρ0CP 1.00 0.03 0.16 0.29 0.22 0.16 −0.11 αρ⊥ CP 1.00 −0.21 −0.19 0.59 −0.07 0.10 αρCP 1.00 0.01 −0.04 −0.25 −0.09 2βeff other 1.00 0.00 0.26 −0.16 2βeff ρ⊥ 1.00 0.39 −0.08 2βeff ρ 1.00 −0.10 2βρ0eff 1.00

Table 5

ResultsallowingfordifferentCP-violatingeffectsforresonancesotherthantheρ

inanextensionofFit 1. 2βeff i (◦) α i CP(×10−3) ρ 41.8±9.6 ρ 2±39 f0(500)−ρ 2.7±3.8 f0(500) −58±46 f2(1270)−ρ 1.8±7.5 f2(1270) 9±63

other spin-1−ρ 3.7±11.1 other spin-1 15±58

arezero. Wefind that fortheentirefinal state, thisrequirement changes

−

2 timesthelogarithmofthelikelihood(

−

2ln

L

)by28.6, correspondingto4.4standard deviationsforfourdegreesof free-dom(ndf),andforthe

ρ

(

770

)

componentonly,thechangeis24.0, correspondingto4.5standarddeviationsfortwondf.Hereweonly considerthestatisticaluncertainties.

We also perform a fit by extending Fit 1 to allow different

CP-violating effects in final states with either the f0

(

500

)

, the

f2

(

1270

)

,orspin-1resonances. Theresultsareshownin

Table 5

.

WefindthatthesefitsallgiveconsistentvaluesoftheCP-violating

parameters.

The systematic uncertainties evaluated for both fit configura-tions are summarizedfor theCP-violating phases inTable 6 and forthemagnitudesoftheasymmetriesin

Table 7

.Theyaresmall comparedtothestatisticalones.Thetwolargestcontributions re-sultfromtheresonancefit modelandthe resonanceparameters. Fit model uncertainties are determined by adding an additional resonancetothedefaultsix-resonancemodel,eitherthe f0

(

980

)

,

the f0

(

1500

)

,the f0

(

1700

)

,ornon-resonant

π

+

π

−,replacingthe

f0

(

500

)

modelbyaBreit–Wignerfunction,andusingthe

alterna-tiveGounaris–Sakuraimodelshapes

[31]

forthevarious

ρ

mesons. Thelargestvariationamongthosechangesisassignedasthe sys-tematicuncertaintyfor modeling.Including anon-resonant com-ponentgivesthelargestnegativechangeon2

β

effforthe

ρ

and

ρ

0

categories.

To evaluate the uncertainties due to the fixed parameters of resonances,we repeattheamplitude fit byvarying themass and widthofalltheresonancesusedinthesix-resonancemodelwithin their errors one at a time, and add the changes in quadrature. To evaluate the systematic uncertainties due to the other fixed parametersincludingthoseinthedecaytimeacceptance,the back-ground decay time PDF, the m(π+

π

−

)

distribution, the angular acceptance,andbackgroundmassPDF, thedatafitisrepeatedby varying the fixed parameters from their nominal values accord-ing to the errormatrix, one hundred timesfor each source. The matrixelementsare determinedusingsimulation,

(—)

B0

_→

_J/ψ(—_K)∗0

data,andlike-sign J

/ψπ

±

π

± data.Ther.m.s. ofthefittedphysics parameterofinterestistakenasitsuncertaintyforeachsource.

Theacceptancemodelforeachofthethreeanglesasafunction ofmhh isdeterminedindependently. Toevaluatethe reliabilityof thismethodweparameterizethemassandangleefficienciesasa combinationofLegendrepolynomialsandsphericalharmonicsthat takesinto account all correlations. The amplitude fit is repeated usingthenewacceptanceparameterizations;changesarefoundto besmallandtakenasthesystematicuncertainty.

Inthenominalfitthe backgroundisdividedintothreesources: background to the

ρ

0 _{component from}(—_B)0

s

→

J/ψη

,

η



→

ρ

0

γ

, reflectionfrom(—B)0

_→

_J/ψ(_K—)∗0 _{whenthe kaonismisidentifiedas}

apion,andtheremaining background.Thelatter includesthe re-flectionsfrom

Λ

(—)0_b

→

J/ψK∓(—p decays,) where both thekaon and proton are misidentified, and combinatorial background.The de-pendence onmhh of thedecay time distributionfor this remain-ingbackgroundismodeled byusingdifferentdecaytimePDFsin differentmhh regions. We also change the background modeling

Fig. 5. ThemagnitudeofthepenguininducedshiftδP ontheCP-violatingphase infavored decays,assumingSU(3)flavor symmetry,showningreyorcolor scalein degrees,asafunctionofthemeasureddifference2βf (x-axis)andαCP=

1−|λf|

1+|λf| ( y-axis).Hereweusefixedvaluesforγ=70◦and =0.0534.Theprojected68% (solid)and95%(dashed)confidencelevelsonδPareshownbytheegg-shaped con-tours.

bydividingtheremainingbackgroundintoseparate combinatorial and

Λ

0_b reflection components.The fit is repeatedwith the new backgroundmodel,andchangesaretakenasthesystematic uncer-tainty.

The systematicuncertaintydueto the taggingparameter cali-bration is givenby the difference in quadrature ofthe statistical uncertainties foreachphysics parameterbetweenthe nominalfit andan alternativefit wherethe taggingparameters areGaussian constrainedbytheirtotaluncertainties.Thesystematicuncertainty duetotheasymmetry of B0

₋

_B0 _{mesonproductionisestimated}

by varying the central value AP

= −

0

.

0035

±

0

.

0081 [29] by its

uncertainty.

6. Discussionofresultsandconclusions

Wecomparethe

ρ

-onlyFit 1resultof2

β

J/ψρ

₌

₂

_β

eff

_{= (}

₄₁

_.

₇

_±

9

.

6₋+2_6..8₃

)

◦ with the Cabibbo-favored B to charmonium result, de-noted J/ψK_S0.Themeasureddifferenceis

2

β

f

=

2

β

J/ψρ

−

2

β

J/ψK 0 S

=



−

₀

_.

₉

±

₉

_.

₇+2.8 −6.3



_◦

.

(13)

Sincetheresultisconsistentwithzerowedeterminelimitson the magnitude of the CP-violating phase shift due to a possible penguin component in b

→

ccs decays,

δ

P. The limit is evalu-ated using pseudo-experiments by generating datasets with dif-ferent values of

α

CP, 2

β

J/ψρ

−

2

β

J/ψK

0

S,and

γ

= (

70

_.

0+7.7 −9.0

)

◦ [9]

accordingtothemeasured uncertainties,includingthecorrelation of

−

0

.

01 between

α

CP and 2

β

J/ψρ . Then

δ

P foreach dataset is calculated using Eq. (7). We find a Gaussian distribution with a 95%confidencelevel(CL)intervalof

[−

1

.

05◦

,

1

.

18◦

]

.Thisresultis consistent withthatobtainedby projecting acontour of

α

CP and 2

β

J/ψρ

₋

₂

_β

J/ψK0

S _{withregionsproportionaltothetotal}

uncertain-tiesofthetwophysicsvariablesasshownin

Fig. 5

. The two reactions

(—)

B0

→

J/ψρ0 _and(—_B)0

s

→

J/ψφ are related by SU(3) symmetry if we also assume that the difference be-tween the

φ

being mostly a singlet state, and the

ρ

0 _{an octet}

statecausesnegligiblebreaking.Takingthemagnitudesofthe pen-guinamplitudesa

=

aandthestrongphases

θ

= θ

tobeequalin

(—)

B0

→

J/ψρ0 _and(—_B)0

s

→

J/ψφ decays,and neglectinghigher or-derdiagrams

[3]

,wefind

δ

P

= (

0

.

05

±

0

.

56

)

◦

=

0

.

9

±

9

.

8 mrad.At

Table 6

SystematicuncertaintiesonCP-violatingphases2βeff

i (◦).Statisticaluncertaintiesarealsoshown. Fit Sources Fit 1 Fit 2 ρ other−ρ ρ0 ρ−ρ0 ρ⊥−ρ0 other−ρ0 Resonance model +1.85 −5.94 + 0.51 −0.33 + 1.99 −6.56 + 1.35 −0.05 + 1.50 −0.59 + 0.68 −0.52 Resonance parameters ±1.21 ±0.43 ±1.35 ±0.68 ±0.57 ±0.60

Mass and angular acceptance ±0.27 ±0.05 ±0.28 ±0.21 ±0.16 ±0.05

Angular acc. correlation ±0.22 ±0.03 ±0.22 ±0.21 ±0.08 ±0.03

Decay time acceptance ±0.05 ±0.02 ±0.06 ±0.04 ±0.04 ±0.03

Bkg. mass and angular PDF ±0.43 ±0.09 ±0.47 ±0.22 ±0.26 ±0.11

Bkg. decay time PDF ±0.14 ±0.05 ±0.12 ±0.06 ±0.08 ±0.07

Bkg. model ±0.49 ±0.23 ±0.15 ±0.97 ±0.38 ±0.13

Flavor Tagging ±1.46 ±0.03 ±1.66 ±0.44 ±0.86 ±0.01

Production asymmetry ±0.17 ±0.50 ±0.28 ±0.09 ±0.49 ±0.42

Total systematic uncertainty +₋26..83 +

0.9 −0.8 + 3.0 −6.9 + 1.9 −1.3 + 2.0 −1.4 + 1.0 −0.9 Statistical uncertainty ±9.6 ±3.6 ±10.2 ±6.5 ±7.2 ±3.9 Table 7

Systematicuncertaintiesforthemagnitudeoftheasymmetriesαi

CP(×10−3).Statisticaluncertaintiesarealsoshown. Fit Sources Fit 1 Fit 2 ρ other−ρ ρ0 ρ ρ⊥ other−ρ0 Resonance model +6.0 −0.0 + 0.0 −11.4 + 3.7 −0.0 + 5.0 −2.7 + 16.4 −0.0 + 0.4 −11.0 Resonance parameters ±5.2 ±6.1 ±7.8 ±3.1 ±9.2 ±7.3

Mass and angular acceptance ±0.6 ±0.5 ±0.8 ±0.8 ±1.6 ±0.7

Angular acc. correlation ±0.2 ±0.9 ±0.2 ±0.9 ±0.6 ±0.9

Decay time acceptance ±0.1 ±0.1 ±0.2 ±0.3 ±1.1 ±0.1

Bkg. mass and angular PDF ±0.9 ±1.5 ±0.8 ±2.5 ±4.6 ±1.2

Bkg. decay time PDF ±0.5 ±0.4 ±0.6 ±0.5 ±1.7 ±0.4

Bkg. model ±2.6 ±2.9 ±5.2 ±3.5 ±0.9 ±4.6

Flavor Tagging ±2.8 ±2.5 ±0.5 ±1.0 ±10.7 ±1.6

Production asymmetry ±3.0 ±0.5 ±2.5 ±1.1 ±0.4 ±0.3

Total systematic uncertainty +₋97 +

7 −14 + 11 −10 + 8 −6 + 22 −15 + 9 −14 Statistical uncertainty ±28 ±25 ±34 ±60 ±109 ±27

95% CL,thepenguin contributionin

(—)

B0

s

→

J/ψφ decayiswithin the interval from

−

1

.

05◦ to

+

1

.

18◦. Relaxing these assumptions changes the limitson the possible penguin induced shift. Fig. 6

showshow

δ

P variesasa function of

θ

− θ

,indicating that the 95%CLlimit onpenguinpollution canincreasetoatmost

±

1

.

2◦. The variation in

δ

P isproportional toa/a. Thus, whenchanging a/aover theinterval0.5to1.5, thelimitonthe penguinshiftat 95% CL variesbetween

±

0

.

9◦ to

±

1

.

8◦,even allowing for maxi-malbreakingbetween

θ

and

θ

.Itmay beexpectedthattheeffect of penguin contributions in other decays, such as

(—)

B0

→

J/ψK_S0, shouldbelimitedtosimilarvalues,evenifthereisnostrictflavor symmetryrelatingthemodeto(—B)0

_→

_J/ψρ0_.Ourlimitis

consis-tentwiththeoreticalpredictions

[32]

.

Wealsosetlimitsonthestrongdecayamplitude.

Fig. 7

shows the68% and95% confidencelevels contours forthepenguin am-plitudeparametersofaand

θ

witha

−

2ln

L

changeof2.3and6 units,forndfequals two,includingsystematicuncertainties. They areobtainedby convertingthecorresponding contoursfor

α

_CPJ/ψρ

and

2

β

f usingtheirrelationshipgiveninEq.(5).Theuncertainty ontheangle

γ

= (

70

.

0₋+7₉._.7₀

)

◦onlyintroducesabouta0.2%increase inthe meancontour radius ofa versus

θ

.The one-dimensional 68% confidence level intervals are found by changing

−

2ln

L

by oneunit,givinga

<

0

.

12 and

θ



∈ (

190◦

,

355◦

)

,ora

=

0

.

035+₋0₀._.082₀₃₅ and

θ



= (

285+₋69₉₅

)

◦.

The decay

(—)

B0

→

J/ψπ0 _{proceeds through a similar diagram}

to that shown in Fig. 1, andthus the CP-violating parameters S

andC shouldbesimilar tothosewe findin(—B)0

_→

_J/ψρ0_.These

parametersarerelatedtotheparameter

λ

f viatherelationships

Fig. 6. ThelimitonthepenguininducedphasechangeδP asafunctionofthe dif-ferenceinthepenguinamplitudestrongphasesinb→c¯cs andb→ccd transitions¯ θ− θ,fora=a. Sf

≡

2

I

m

(λ

f

)

1

+ |λ

f

|

2

= −

2

η

f

|λ

f

|

sin 2

β

eff_f 1

+ |λ

f

|

2

,

and Cf

≡

1

− |λ

f

|

2 1

+ |λ

f

|

2

,

(14)

where we set the CP eigenvalue

η

f

=

1 to compare with the CP-evenmode

(—)

B0

→

J/ψπ0_.

Using Sf and Cf as fit parameters, we obtain from Fit 1 SJ/ψρ

= −

0

.

66+₋00..1213+−00..0309 andCJ/ψρ

= −

0

.

063

±

0

.

056+₋00..019014,with

Table 8

ComparisonofSf andCf betweendifferentmeasurements.

f Experiment Sf Cf Correlation (—) B0_→J/ψρ0 _{LHCb −0.66}+0.13+0.09 −0.12−0.03 −0.063±0.056+ 0.019 −0.014 −0.01 (stat) (—) B0_→J/ψπ0 _{Belle[33] −0.65±0.21±0.05 −0.08±0.16±0.05 −0.10 (stat)} (—) B0_→J /ψπ0 _{BaBar[34] −1} .23±0.21±0.04 −0.20±0.19±0.03 0.20 (stat)

Fig. 7. Contourscorrespondingto68%(dashed)and95%(solid)confidencelevelsfor ndfoftwo,respectively,forthepenguinamplitudeparametersaandθ.

fromthismeasurementwiththatobtainedfromtheBelle[33]and BaBar[34] Collaborations. Our measurements are in good agree-mentwiththeBelleresults.

In conclusion, the measured value of the penguin contribu-tionis

δ

P

= (

0

.

05

±

0

.

56

)

◦

=

0

.

9

±

9

.

8 mrad.Takingthemaximum breaking in phase and a range of breaking 0

.

5

<

a/a

<

1

.

5 the uncertaintyon

δ

P becomes

±

18 mrad.The measured valueof

φ

s currentlyhas an uncertainty of about35 mrad, and the value of 2

β

of1.5◦ or26 mrad

[9]

.Thusourlimitissmallerthanthe cur-rentuncertainties, butwill need to become moreprecise asthe

CP-phasemeasurementsimprove.

Acknowledgements

We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC. WethankthetechnicalandadministrativestaffattheLHCb insti-tutes.WeacknowledgesupportfromCERNandfromthenational agencies: CAPES,CNPq, FAPERJ andFINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);INFN(Italy); FOMandNWO (TheNetherlands);MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Rus-sia);MinECo(Spain);SNSFandSER(Switzerland);NASU(Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing cen-tres are supported by IN2P3 (France), KIT andBMBF (Germany), INFN(Italy),NWOandSURF(TheNetherlands),PIC(Spain),GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we de-pend.We are also thankful forthe computingresources andthe accesstosoftwareR&DtoolsprovidedbyYandexLLC(Russia). In-dividualgroupsormembershavereceivedsupportfromEPLANET, MarieSkłodowska-Curie Actions andERC (EuropeanUnion), Con-seilgénéraldeHaute-Savoie,LabexENIGMASSandOCEVU,Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (UnitedKingdom).

References

[1]S. Glashow, Partial symmetries of weak interactions, Nucl. Phys. 22 (1961) 579;

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