Rare Decays of psi and Upsilon

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

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991 naJ 1 1v2021089/hp-pe:hviXraRareDecaysofψandΥ

K.K.SharmaandR.C.Verma

CentreforAdvancedStudyinPhysics,DepartmentofPhysics,

PanjabUniversity,Chandigarh-160014,India.

DepartmentofPhysics,PunjabiUniversity,Patiala-147002,India.

Abstract

Westudytwo-bodyweakhadronicdecaysofψandΥemployingthefactorizationscheme.Branchingratiosforψ→PP/PVandΥ→PP/PVdecaysintheCabibbo-angle-enhancedandCabibbo-angle-suppressedmodesarepredicted.

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

1Introduction

Awealthofexperimentaldataonmasses,lifetimesanddecayratesofcharmandbottommesonshasbeencollected[1].Modelsbasedonfactorizationscheme[2,3],successfullyusedtodescribeweakdecaysofnaked avormesons,canalsobeusedtostudyweakdecaysofhidden avormesons.Lowlyingstatesofquarkoniasystemsusuallydecaythroughintermediatephotonsorgluonsproducedbytheparentcc¯andb¯bquarkpairannihilation.Forinstance,charmoniumstateψ(1S)decayspredominantlytohadronicstates(87.7%),whereasitsleptonicmodesareobservedtobearound6%.ThesametrendfollowsforthebottomoniumstatesΥ(1S)also.TheseOZIviolatingbut avorconservingdecaysleadtonarrowwidthstoψandΥstates.

IntheStandardModelframework,the avorchangingdecaysofthesestatesarealsopossiblethoughtheseareexpectedtohaveratherlowbranchingratios.Atpresent,experimentshavecrossedovertomanymillionψ-eventsandtheprospectusaregoodfora100-foldincreaseintheseeventsinthehighenergyelectron-positroncollider.Itisexpectedthatsomeofitsraredecaymodesmayalsobecomedetectableinfuture.Withthispossibilityinmind,westudytwo-bodyweakdecaysofψinCabibbo-angle-enhancedandCabibbo-angle-suppressedmodes.Employingthefactorizationscheme,wepredictbranchingratiosforψ→PP/PVdecays(wherePandVrepresentpseudoscalarmesonandvectormesonrespectively)andextendthisanalysistoΥ→PP/PVdecaysinvolvingb→ctransitions.

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

2Two-bodyWeakDecaysofψ

Thestructureofthegeneralweakcurrent currentHamiltonianis

HW

GF =VudVcs{a1(¯sc)H(¯ud)H+a2(¯sd)H(¯uc)H}+h.c.,

2

(1)

forCabibbo-angle-enhancedmode( C= S= 1),and

HW=

GF ¯)H (¯VudVcd[a1{(¯ud)H(dcus)H(¯sc)H}2

(2)

¯)H (¯+a2{(¯uc)H(dduc)H(¯ss)H}]+h.c.,

forCabibbo-angle-suppressedmode( C= 1, S=0).q¯¯1q2≡q1γµ(1 γ5)q2representsthecolorsingletV-AcurrentandVijdenoteCabibbo-Kobayashi-Maskawa(CKM)mixingmatrixelements.ThesubscriptHimpliesthat(

′

q¯1q2)istobetreatedasahadron eldoperator.asarethetwoundetermined

coe cientsassignedtothee ectivechargecurrent,a1,andthee ectiveneutralcurrent,a2,partsoftheweakHamiltonian.TheseparameterscanberelatedtotheQCDcoe cientsc1,2as

a1,2=c1,2+ζc2,1,

(3)

whereζisusuallytreatedasafreeparameter,tobe xedbytheexperiment.Wetake

a1=1.26,

onthebasisofD→Kπdecays[4].

a2=

0.51,

(4)

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

2.1ψ→PPDecays

Thedecayrateformulaforψ→PPdecaysisgivenby

Γ(ψ→PP)=

p3c

√

mψ+mP

ι

ψ·q

µρσ22

µνρσ νψ(Pψ+PP)qV(q) ι(mψ+mP) ψA1(q)

q2

ι

ψ·q

(2mψ)qµA3(q2)

2mψ

A1(q2)+

(mψ mP)

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

+

IntheCabibbo-angle-enhancedmode,ψcandecaytoDsπorD0K0.Toillus-+ tratetheprocedure,weconsiderthecolorenhanceddecayψ→Dsπwhose

decayamplitudecanbeexpressedas

+

A(ψ→Dsπ)=

GF +

VudVcsa1 π |Jµ|0 Ds|Jµ|ψ ,2

(10)

whichgetssimpli edto

+

A(ψ→Dsπ)=

GF s

VudVcsa1(2mψ)fπ( ψ·q)AψD(m20π).2

(11)

Similarly,thefactorizationamplitudeofthedecayψ→D0K0andCabibbo-angle-suppresseddecaysofψareobtained.Wetakethefollowingvaluesforthedecayconstants(inGeV)[6]:

fπ=0.132,fη=0.131,

Fortheformfactorsatq2=0,weuse

ψDs

AψD(0)=0.66,0(0)=0.61,A0

fK=0.161,fη′=0.118.

(12)

(13)

obtainedintheearlierwork[5]usingtheBSWmodelwavefunctions[7]atω=0.5GeV.Theoscillatorparameterωisthemeasureoftheaveragetransversemomentumofthequarkinthemeson[7].Weusethefollowingbasisforη η′mixing:

η=η′=

1¯)sinφp (ss(uu¯+dd¯)cosφp,

2

1¯)cosφp+(ss(uu¯+dd¯)sinφp,2

(14)(15)

We study two-body weak hadronic decays of \psi and Upsilon employing the factorization scheme. Branching ratios for \psi -> PP/PV and \Upsilon -> PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

whereφp=θideal θhttp://www.77cn.com.cningthedecayrateformula(5),wecomputebranchingratiosofvariousψ→PPdecayswhicharelistedinTable-1.AmongtheCabibbo-angle-enhanceddecays,we ndthatthedominantdecayisψ→