Measurement of the CP-violating phase β in B0→J/ψπ+π− decays and limits on penguin effects

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Measurement of the CP-violating phase β in B0 → J/ψπ+π– decays and limits on penguin effects

R. Aaij, Y. Amhis, S. Barsuk, M. Borsato, O. Kochebina, J. Lefrançois, F.

Machefert, A. Martin Sanchez, Marie Nicol, P. Robbe, et al.

To cite this version:

R. Aaij, Y. Amhis, S. Barsuk, M. Borsato, O. Kochebina, et al.. Measurement of the CP-violating

phase β in B0 → J/ψπ+π– decays and limits on penguin effects. Physics Letters B, Elsevier, 2015, 742,

pp.38-49. �10.1016/j.physletb.2015.01.008�. �in2p3-01081128�

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 ra c t

Articlehistory:

Received6November2014

Receivedinrevisedform23December2014 Accepted7January2015

Availableonline13January2015 Editor:W.-D.Schlatter

Time-dependent CP violationis measuredin the

(—⁾

B⁰→ ^J/ψπ⁺π⁻ channel foreach π⁺π⁻ resonant finalstateusingdatacollectedwithanintegratedluminosityof3.0 fb⁻¹inppcollisionsusingtheLHCb detector. Thefinal statewiththelargest rate, J/ψρ⁰(770),isused tomeasure the CP-violatingangle 2β^efftobe(41.7±⁹.6⁺₋²₆^._.⁸₃)^◦. Thisresultcanbeusedtolimitthesizeofpenguinamplitudecontributions toCPviolationmeasurementsin,forexample,

(—)

B⁰_s→^J/ψφdecays.AssumingapproximateSU(3)flavour symmetryandneglectinghigherorderdiagrams,theshiftintheCP-violatingphaseφs islimitedtobe withintheinterval[−¹.05^◦,+¹.18^◦]at95%confidencelevel.ChangestothelimitduetoSU(3)symmetry breakingeffectsarealsodiscussed.

©^{2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Measurementsof CP violation inneutral B mesondecays are usedeithertosearchforphysicsbeyondtheStandardModel(SM) [1]orsetlimitsoncombinationsofCabibbo–Kobayashi–Maskawa couplings (Vi j) [2]. Interpretations of the measurement of the CP-violatingphase2β viatheinterferenceofmixinganddecaysin the

(—)

B⁰→ ^J/ψK⁰_S channel,andthe phaseφs in

(—)

B⁰_s →^J/ψφ and J/ψπ⁺π⁻decays,¹ aremadeassumingthatthedecaysaredomi- 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_S⁰ [3,4].Thus,theeffectsofpenguintopologiescanbe investigatedbyusingthe J/ψπ⁺π⁻ decayandcomparingdiffer-

1 CP violation measurements in⁽—)

B⁰→ J/ψK⁰_S determine the sum of 2β≡ 2arg(−VcdV_cb^∗)/(VtdV_tb^∗) and contributions from higher order diagrams.Similar measurements in the⁽—)

B⁰s system determine φs which is the sum of −2βs≡

−2arg(−VtsV_tb^∗)/(VcsV_cb^∗)andhigherordercorrections.

Fig. 1.(a) Tree level and (b) penguin diagram forB⁰decays into J/ψπ⁺π⁻.

ent measurements of the CP-violating phase 2β in J/ψK_S⁰, and individualchannelssuchas

(—)

B⁰→^J/ψρ⁰(770).²

Next, we discuss the time-dependent decay rate, taking into accountthatthe π⁺π⁻systemiscomposedoftheresonancespre- viously reportedinRef.[5]. Thisanalysislargely followsthemea- surementprocedureusedinthestudyofCPviolationin^(—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 A_i(A_i).Thequantities qandprelatethemasseigenstatestotheflavor eigenstates[8].By introducingtheparameterλi≡^q_p^A_Aⁱ_i^{,relatingCPviolationinthein-} terference betweenmixinganddecayassociated withthestate i, theamplitudesA^andA^{canbeexpressedasthesumsofthein-} dividual

(—)

B⁰ amplitudes, A=

Ai and A=q pAi=

λiAi=

2 Inthefollowingρ⁰orρreferstotheρ⁰(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.

ηi|λi|^{e−i2βeffi A}i. For each transversity state i the CP-violating phase 2β_i^eff≡ −^arg(ηiλi)with ηi beingthe CP eigenvalue ofthe state.³Thedecayratesare⁴

Γ (t)=Ne^−Γdt

|A|²+ |A|²

2 +|A|²− |A|²

2 cos(m_dt)

−I^m A^∗A

sin(m_dt)

, Γ (t)=Ne^−Γdt

|A|²+ |A|²

2 −|A|²− |A|²

2 cos(m_dt) +I^m

A^∗A

sin(m_dt)

. (1)

2. Penguinandtreeamplitudes

Thedecay B⁰→ ^J/ψK⁰_S canbewrittenasthesumofonetree levelamplitude,similar tothatshowninFig. 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. There- sultingdecayamplitudeis[3]

A(B⁰→ ^J/ψK_S⁰)=

1−λ²

2 A

1+ λ² 1−λ^2ae

iθe^iγ

, (2)

whereλ= |^Vus|=⁰.2252[10], γ ≡^arg(−^VudV_ub^∗ /VcdV_cb^∗),A ^de- notesthesumoftree andpenguinstrongamplitudes, anda and θarethemagnitudeandphaseofthestrongpartsoftheeffective 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

−√ 2A

B⁰→(J/ψρ)f

=λA

1−^a_f^eiθfeiγ

, (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

≡λ²/(1−λ²)=⁰.0534.Thus, comparingevena relativelypoor measurementof 2β^eff measured in J/ψρ⁰ with2β 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 violationin the pres- enceofbothtreeandpenguinamplitudes.Thecomplex-valuedCP parameterλf isgivenby

λ_f ≡^q p

A(B⁰→(J/ψρ)_f)

A(B⁰→(J/ψρ)f)=η_f^1−a

fe^iθfe^−iγ 1−a_fe^iθfe^iγ

e^−2iβ, (4) whereβisthephaseinducedbymixing.Thusthemeasuredphase β^eff_f isrelatedtoβ by

3 Notethatwhileq/pandAi/Aiarephaseconventiondependent,λiisnot.

4 WeassumeΓd=^{0 and}|^p/q|=^{1.Theaveragesofcurrent}measurementsare Γd/Γd=⁰.001±⁰.010 and|^p/q|=¹.0005±⁰.0011[9].

ηfλf ≡ |λf|^e−i2βefff =¹−a_fe^iθfe^−iγ 1−^a_f^{eiθfeiγ e}

−ⁱ²β, (5) separatingrealandimaginarypartsgives

|λf| =

¹−^a_f^eiθfe−iγ 1−^a_f^eiθfeiγ

, and 2β_f≡2β^eff_f −2β= −arg

₁−^a_f^eiθfe−iγ

1−^a_f^eiθfeiγ . (6) Forthe J/ψK⁰_S modewereplacea_f andθ_f inEq.(6)by−a_f andθf,respectively.Inaddition,wetakea=^aandθ=θ.There- 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_fe^2iγ−¹)+(λ_f −¹)e^2iγ

whereλ_f ≡ |λf|^e−i2βf. (7) We will show that the penguinshift hasa weak dependence on

|λf|^,resultinginδP≈ −2βf.Sincetheuncertaintyonthecur- rentmeasurementof2β is(⁺₋¹₁^._.⁶₅)^◦,ameasurementof2βf,even withanuncertaintytentimeslarger,couldlimitpenguincontribu- 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 orc 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 ofmo- 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 layersofironandmultiwirepro- 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 leveltobecon- sistentwithcomingfromthedecayofa

(—⁾

B⁰mesonbyuseofeither ofIPrequirementsordetachmentofthe J/ψmesondecayvertex

5 Weusenaturalunitswhere^h¯=^c=^1.

fromtheprimaryvertex.Inthesimulation,ppcollisionsaregener- atedusingPythia[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^±arealsoreconstructedforback- ground studies. The event selection is described in detail in the time-integratedamplitudeanalysis[5].Theonlydifferencehereis thatwereject K_S⁰→π⁺π⁻ candidatesbyexcludingtheeventsin theregionwithin±^{20 MeVoftheK0}_S ^masspeak.

Onlycandidateswithdimuoninvariantmassbetween−^{48 MeV} and+^{43 MeVrelativetotheobserved J}/ψmasspeakareselected, corresponding a window of about ±³σ. The two muons subse- quently are kinematically constrained to the known J/ψ mass.

OtherrequirementsareimposedtoisolateB⁰candidateswithhigh signal yield and minimum background. This is accomplished by combiningthe J/ψ→μ⁺μ⁻candidatewithapairofpioncandi- datesofoppositecharge,andthentestingifallfourtracksforma commondecayvertex. Pion candidatesare each requiredto have pTgreaterthan250 MeV,andthescalarsumofthetwotransverse momenta,p_T(π⁺)+^pT(π⁻),mustbelargerthan900 MeV.Totest for inconsistency with production at the PV, the IP χ² is com- puted asthe difference betweenthe χ² of the PVreconstructed withandwithouttheconsideredtrack.EachpionmusthaveanIP

χ² greaterthan 9.Pionandkaoncandidatesarepositivelyidenti- 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 χ² ofthe π⁺and π⁻, andtheB⁰ propertiesofvertex χ²,pointingangle,flightdistance, p_T andIP χ²,whereDLL(μ −π) isa logarithmofthelikelihood ratiobetween μand π hypothesesforthemuoncandidates.

TheBDTistrainedonasimulatedsampleoftwomillion B⁰→ J/ψπ⁺π⁻signaleventsgenerateduniformlyinphasespacewith unpolarized J/ψ→μ⁺μ⁻ decays,andabackgrounddatasample fromthesideband5566<m(J/ψπ⁺π⁻)<5616 MeV.Thensepa- 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⁺, B⁰_s → ^J/ψη() with η()→π⁺π⁻γ, B⁰_s → ^J/ψφ withφ→π⁺π⁻π⁰, B⁰→ ^J/ψK⁻π⁺ andΛ_b⁰→ ^J/ψK⁻preflec- tions,andcombinatorialbackgrounds.Theexponentialcombinato- rial background shape is takenfrom like-signcombinations, that are thesum ofπ⁺π⁺ andπ⁻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⁻combinationswithK_S⁰veto.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-dashedisthesumofB⁰_s→^J/ψη, B⁰_s→^J/ψφwhenφ→π⁺π⁻π⁰backgroundsandtheΛ⁰_b→^J/ψK⁻preflection, the(black)dot-longdashedistheB⁰→J/ψK⁻π⁺reflectionandthe(blue)solid lineisthetotal.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

thefitgives17650±^{200 signaland9840}±160 backgroundcan- 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-violatingquantitiesφs and|λ|^in(—B)0s→ J/ψπ⁺π⁻ decays [6] is employed. Here the value of Γd≈⁰ simplifies some terms, andthe smaller value of md makes the decaytimeresolutionfunctionlessimportant.Inaddition,adiffer- 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 massm_hh=^m(π⁺π⁻),andthree an- gles Ω, defined in the helicity basis. These consist of: θJ/ψ, the angle betweenthe μ⁺ direction in the J/ψ restframe withre- spect to the J/ψ directionin the

(—⁾

B⁰ rest frame; θhh, the angle betweentheh⁺ direction in theh⁺h⁻ restframewithrespectto theh⁺h⁻directioninthe^(—B⁾⁰restframe; and χ,theanglebetween the J/ψandh⁺h⁻decayplanesinthe

(—⁾

B⁰restframe[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⁻

invariantmassdistributionisshowninFig. 3alongwiththefitted componentsofthedifferentresonancesusingthe“Bestmodel”[5]

forthe π⁺π⁻resonancecontent.