Combining the recent lattice calculation of $a_0(1450)$ and $\sigma(600)$ mesons with the overlap fermion in the chiral regime with the pion mass less than $300 {\rm MeV}$, the quenched lattice calculation of the scalar glueball, and the phenomenological s

6K.F.Liu

scalarglueballmassat1710(50)(80)MeVinthequenchedapproximation19)whichseemstocoincidewithf0(1700)discoveredinJ/Ψradiativedecays,longsuggestedtobeachannelforcopiousglueballproduction.

§3.MixingandDecays

ToanswersuchquestionsasraisedinSec.

1,therehavebeenanumberofstudiesonthemixingoftheisoscalarmesonsf0(1370),f0(1500),andf0(1710)tosortouttheirglueballand avorcontentofqq¯.20)Inconsideringthemixingmatrix,theusualpremiseistoplacetheunmixed¯√(connectedinsertionwithoutannihilation)ss¯)/～200MeVabovenn¯≡(uu¯+dd

6

state.Amixingmodel,whichtakesthedegeneracyofunmixednn¯andss¯andthequenchedpredictionofscalarglueballmassat～1700MeVintoaccountwithslightSU(3)breaking,isquitesuccessfulindelineatingthedecaysintopseudoscalarpairsoftheisoscalarmesonsaswellasvariousdecaysfromJ/Ψ.Thedetailsofthe tandpredictionsaregiveninapreviouswork.21)Wewanttopointoutseveralsalientandrobustfeaturesintheresultantmixinganddecaypatterns.

f0(1500)isindeedafairlypureoctet(foctet)withverylittlemixingwiththesingletandtheglueball.f0(1710)andf0(1370)aredominatedbytheglueballandtheqq¯singletrespectively,with～10%mixingbetweenthetwo.ThisisconsisentwiththeexperimentalresultΓ(J/ψ→γf0(1710))～5Γ(J/ψ→γf0(1500))2)whichfavorsf0(1710)tohavelargerglueballcomponent.21) TheratioΓ(f0(1500)→K

K)

31+s

pπ,(3.1)

wherephisthec.m.momentumofthehadronh,u/dandsarethecoe cients¯andssfortheuu¯/dd¯componentsofthef0(1500)wavefunction.Iff0(1500)isaglueball(i.e.a avorsinglet)orss¯,theratiowillbe0.84orlargerthenunity.Eitheroneismuchlargerthantheexperimentalvalue.Ontheotherhand,iff0(1500)isfoctet,thentheratiois0.21whichisalreadyclosetotheexperimentalnumber.Thisfurtherdemonstratesthatf0(1500)ismainlyanoctetanditsdecayratiocanbewelldescribedwithasmallSU(3)breaking.21) Becausethenn¯contentismorecopiousthanss¯inf0(1710)inthismixingscheme,thepredictionofΓ(J/ψ→ωf0(1710))/Γ(J/ψ→φf0(1710))=4.1isnaturallylargeandconsistentwiththeobservedvalueof6.6±2.7.Thisratioisnoteasytoaccommodateinapicturewherethef0(1710)isdominatedby