夸克模型中的Dsj (2317),Dsj(2460)衰变

用夸克模型结合Ds,Ds*, 讨论窄共振态Dsj*(2317),Dsj(2460). 除η-π0混合角由D*s衰变宽度给出, 所有的参数均取自Godfrey和Isgur的夸克模型. 得到的电磁衰变宽度与实验数据和其他作者的结果相一致. 但是, 与现有的实验结果比较, Dsj*(2317), Dsj(2460)的π介子衰变宽度要小一

第30卷第11期2006年11月

高能物理与核物理

HIGH

ENERGY

PHYSICS

AND

NUCLEAR

PHYSICS

Vol.30,No.11

Nov.,2006

*

DecaysofD sj(2317)andDsj(2460)MesonsintheQuarkModel

WANGFeng-LinCHENXiao-LinLUDa-Hai

ZHUShi-Lin

DENGWei-Zhen1)

(DepartmentofPhysics,PekingUniversity,Beijing100871,China)

AbstractWestudythedecaywidthsofthenarrowresonancesD sj(2317)andDsj(2460)inthechiralquarkmodel,togetherwiththewell-knownD andD smesons.AlltheparametersinourcalculationaretakenfromGodfreyandIsgur’squarkmodelexcepttheπ0-ηmixinganglewhichis xedbytheD sdecaywidths.Thecalculatedelectromagneticdecaywidthsagreewiththosefromothergroupsandtheexperimentaldataavailablequitewell.However,thepionicdecaywidthsofDsj(2317)andDsj(2460)aretoosmallto ttheexperimentaldata.Wesuspectthatthesimplechiralquarkpionaxial-vectorinteractionHamiltonianisnotsuitableforhadronstrongdecaysofDsj(2317)andDsj(2460).

Keywordsquarkmodel,narrowresonance,decaywidth

1Introduction

ThediscoveryofnarrowresonancesD sj(2317)

[1]

mixingfromthechiralperturbationtheoryInapreviouswork

[20]

[18,19]

.

,wehavecalculatedthepi-

)3

onicdecaywidthsoftheD(sjmesonsusingtheP0

andDsj(2460)

[2]

raiseschallengestothequarkmodel.

[3]

strongdecaymodel.Anothersimpledecaymodeltodealpionicdecaysisthechiralquarkmodel

[21]

Massesofthesetwostatesareabout100MeVlowerthanthepredictionsofthepotentialquarkmodel.Furthermore,theisospinconservingdecaychannels

)( )

D(Kareforbiddenbykinematics.Theob-sj→D

)0

breaktheisospinservedpionicdecaysintoD(sπ

.

Inthiswork,wecalculateboththeelectromag- )

netic(EM)decaysandstrongdecaywidthsofD(sj

mesonsinthequarkmodel.Themesonwavefunc-tionsaretakenfromthewell-knownGodfreyandIs-gur’smodel

[3]

symmetry.Several

[4]

whichgivesanimpressinglygoodover-

non-conventional

[9,10]

schemes,suchas

alldescriptionofmesonstates.Thechiralcouplingsoflightquarkswithπ,ηmesonandtheisospinviolat-ingπ0-ηmixingparameteraretakenfromthechiralperturbationtheory

[18,22]

molecules,tetraquarkstatesnersofDsandD s

[5—8]

,orthechiralpart-

etc.,havebeenproposed

(forareview,seeRefs.[11,12]).Buttheconven-tionalc¯sinterpretationisstillattractiveiftheex- )

perimentalmassesofD(canbeaccommodatedinsj

.Sincetherelativemomen-

)

tumisverylargeinthedecaysofD(mesons,thesj

relativistice ectshouldbeimportant.Wedonotmakethenon-relativisticreductionsofthetransitionoperators.InsteadwekeepDiracspinorsinourcal-culation.

Inthenextsection,wepresentourformalism.The

)decaysofD(sjareevaluatedandcomparedwithex-

thequarkmodel

[13—15]

.Intheheavyquarklimit,

Dsj(2317)andDsj(2460)naturallyformaP-wave

1

doubletJP=(0+,1+)withjl=.Couple-channel

2e ectscouldleadtomassshifts

[16,17]

.Theobserved

pionicdecayscanalsobeunderstoodthroughη-π0perimentaldatainSec.3.Wegiveabriefdiscussion

Received13April2006

*SupportedbyNSFC(10375003,10421503)andKeyGrantProjectofChineseMinistryofEducation(305001)1)E-mail:dwz@http://doc.guandang.net

1041—1047

用夸克模型结合Ds,Ds*, 讨论窄共振态Dsj*(2317),Dsj(2460). 除η-π0混合角由D*s衰变宽度给出, 所有的参数均取自Godfrey和Isgur的夸克模型. 得到的电磁衰变宽度与实验数据和其他作者的结果相一致. 但是, 与现有的实验结果比较, Dsj*(2317), Dsj(2460)的π介子衰变宽度要小一

1042高能物理与核物理(HEP&NP)第30卷

andsummaryinSec.4.

2

DecaysofDsjinthequarkmodel

Theelectromagneticinteractionisstandard

¯µΨAµ.Lγ=eΨγ

(1)

( )

withthequarkoperators

3

dk11

φ(k,P,D)b|M,P =sQTMdq¯|0 .3c(2π)2Qq¯

(8)Herewetreatthequarkoperatorsinamatrixform

T bbqQ,↑¯,↑

b d=.(9)Q=q¯

bQ,↓bq¯,↓TheinnerQ¯qstructurematrixTMofDs,D s,D sj(2317)andDsj(2460)mesonsaretakenfromthequarkmodel

[3,23]

Inthechiralquarkmodel,thepionsinteractwiththelightupanddownquarksthroughtheaxial-vectorcoupling

q

gA

¯µγ5τΨ µφπ.Lπq=Ψγ2fπ

.TheyarelistedinTable1.The

(2)spatialwavefunctionsφ(k,P)arenormalizedas

Table1.Theinnertensorstructurematrixof

( )

Dsmesons.

meson

JP0 1 0+1+1+1+

TM1σ· σ·kσ· σ·kk· ik×σ·

AspointedoutinRefs[18,22],thereasonablevalue

qofgArangesfrom0.75to1.

ThepionicdecayofD

( )

sj

cannotoccurfromthe

( )sj

aboveisospinconservinginteractionsinceDhasno

DsD sD sj(2317)Dsj(2460)

1P13P1

u-ord-light avorquarksintheconventionalc¯scon- guration.However,thisisospinbreakingdecaycanoccurthroughπ0-ηmixingduetotheupanddownquarkmassdi erence.Inthechiralperturbationthe-ory,theη-π0mixingamplitudereads

√

md mu

θm= 0.010.(3)

4m du

s

2

FromSUF(3)symmetry,theηcouplingshouldbe

qgA

¯µλ8Ψ µφη.Lηq=Ψγ2fη

[18,19]

d3k

2E=|φ(k,p)|2.3(2π)

(10)

(4)

Intheheavyquarklimit,jl=L+sqisagoodquantumnumberwhenmQ→∞.Thelowest0+and1+exci-tationstatesD sj(2317)andDsj(2460)havejl=1/2.Theyformthe(0+,1+)doubletoftheP-waveorbitalexcitation.Dsj(2460)isanidealmixtureofthe1P1and3P1statesinthislimit 12

|Dsj(2460),P =|Dsj(1P1),P +|Dsj(3P1),P .

33

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