gamma+gamma -- pi+pi, K+K leading term QCD vs handbag model

《gamma+gamma -- pi+pi, K+K leading term QCD vs handbag model》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、γγ→ππ,KK:leadingtermQCDvshandbagmodelVictorL.Chernyak1BudkerInstituteofNuclearPhysics,630090Novosibirsk,RussiaAbstractThe”handbag”modelwasproposedasanalternative,atthepresentdayenergies,totheleadingtermQCDpredictionsforsomehardexclusiveprocesses.TherecentprecisedatafromtheBelleCollaborat

2、iononthelargeanglecrosssectionsγγ→ππ,KKallowacheckofthesetwoapproachestobeperformed.ItisshownthatthehandbagmodelfailstodescribethedatafromBelle,whiletheleadingtermQCDpredictionsareinreasonableagreementwiththesedata.I.TheleadingtermQCDpredictionsTheleadingcontributionstothehardkernelsfort

3、heseamplitudesatlarges=W2=(q+q)2andfixedc.m.s.angleθwerefirstcalculatedin12[1]forsymmetricmesonwavefunctions,φM(x)=φM(1−x),andlaterin[2](BCinwhatfollows)forarbitrarywavefunctions.TwotypicaldiagramsarXiv:hep-ph/0605072v415Jun2006areshowninfig.1.Themainfeaturesofthesecrosssectionsareasfollows

4、(everywherebelowwefollowmainlythedefinitepredictionsfromBCin[2]).Thehelicityamplitudeslookas:64π2Z1Z1(lead)2Aλ1λ2(s,θ)=ααsfKdxsφK(xs)dysφK(ys)Tλ1λ2(xs,ys,θ).(1)9s00ThehardkernelsTλ1λ2(xs,ys,θ)are:21AT++=T−−=(es−eu)2,(2)sinθD1E-mail:v.l.chernyak@inp.nsk.su1q1M¯M¯q1q2Mq2MFigure1:TwotypicalF

5、eynmandiagramsfortheleadingtermhardcontributionstoγγ→MM,thebrokenlineisthehardgluonexchange."#1(e−e)2AC(e2−e2)susuT+−=T−+=Dsin2θ(1−A)+eseuA2−B2cos2θ+2(ys−xu),where:A=xsyu+xuys,B=xsyu−xuys,C=xsxu+ysyu,D=xuxsyuys,xs+xu=1,eu=2/3,es=ed=−1/3,fMarethecouplings:fπ=130MeV,fK=160MeV,andφK(xs)isth

6、eleadingtwistK-mesonwavefunction.TheaboveexpressionsaregivenforK+K−,othercasesareobtainedbyevidentreplacements.Thepionwavefunctionissymmetric,φπ(xu,xd)=φπ(xd,xu),whileφK(xs,xu)−φK(xu,xs)6=0duetoSU(3)-symmetrybreakingeffects.Besides,eventhepartofφ(xs,xu)symmetricinxu↔xsdiffersfromφπ(xu,xd),

7、forthesamereason.Thecrosssectionis:dσ(γγ→K+K−)11X2=Aλ1λ2.(3)dcosθ32πs4λ1λ2a)Theleadingcontributiontodσ(π+π−)canbewrittenas:s3dσ(γγ→π+π−)

8、Φ(eff)(s,θ)

9、2

10、sF(lead)(s)

11、2ππ2≡=

12、1−υ(θ)

13、,(4)16πα2d

14、cosθ

15、sin4θsin4θwhereF(lead)(s)istheleadingtermofthepionformfactor[3]:π8παZ1dx2(lead)