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Quark-InterchangeProcessesinEvolutionofMesonicMatterXiao-MingXu1.Meson-mesonscatteringiscrucialtochemicalequilibration,kineticequilibration,hadronflowsandhadronyields.2.Earlierdecoupledmesonsduetosmallcrosssectionscanshowrelativelyclearinformationonquark-gluonplasma.Usemasterrateequationsincludinginelasticmeson-mesonscatteringtodescribemesonicmatter.Weconcernaboutpions,rhosandkaonssinceexperimentaldatashowthat,,Karedominantmesonspeciesinhadronicmatter.PHENIXresults:centralAu-Aucollisions,=200GeV,mid-rapiditySTARresults:peripheralAu-Aucollisions,=200GeV,mid-rapiditymostcentralAu-Aucollisions,=200GeV,mid-rapidityNNs984.0933.0KK171.0K162.0KNNs169.00NNs205.00*KKBRAHMSresults:rapiditydependenceincentralcollisionsconstantnearmidrapidityslowlydecreaseintheotherregionconstantinPHENIXresults:centralitydependenceconstantinthewholecentralityrangeincreasewithcentrality,K33y,KKK,KK,KKinelasticmeson-mesonscattering:resonantprocesses;quark-antiquarkannihilationprocesses;quark-interchangeprocesses.Thecrosssectionforanisospinchannelconsistsofthreeparts:forexample,I=3/2K*Kcres=0canni=0cqi=1I=1/2K*Kcres=1canni=1cqi=1),(),(),(),(qiqiannianniresressIcsIcsIcsIinmasterrateequationstheunpolarizedcrosssectionfori(S1I1)j(S2I2)i(S3I3)j(S4I4)IjiijsIIIIs),()12()12)(12(1)(21''resonantprocessesresonances:f0(1370),(1450),f0(1500),3(1690)forK1(1270),K1(1400),K*(1410),K*2(1430),K*(1680),K*3(1780)forK*Kf0(980),(1020),f2(1270),f0(1370),(1450),f0(1500),f2(1525),3(1690),(1700),f0(1710),f2(1810),f4(2050)forcrosssection:KK4/)()12)(12(12)(22outin2221resRmsBBPSSJsquark-antiquarkannihilationprocessescrosssection:forexample,b=2.7mb,c=0.76forb=0.4mb,c=0.5forb=3.5mb,c=0.38forG.E.Brown,etal.,Phys.Rev.C43,1881(1991)W.Cassing,etal.,Nucl.Phys.A614,415(1997)cssbs0anni1)(KK)(**KKKKKKquark-interchangeprocessesforexample,I=2I=1KKKK*I=1KK*K*KI=3/2KK*I=3/2K*K*I=3/2KK*I=3/2K*KY.-Q.Li,X.-M.Xu,Nucl.Phys.A794(2007)210Priorform:gluonpropagationbeforequarkinterchangePostform:gluonpropagationafterquarkinterchangeI=2I=1KKKK*I=1KK*K*KI=3/2KK*I=3/2K*K*I=3/2KK*I=3/2K*KCrosssectionsforendothermicreactionsareparametrizedasarelistedinTable2ofEur.Phys.J.A47(2011)65)()()()(12212211qqDqqCqqBqqAendo0endo0maxqi1expssasssaa,,endomaxmasterrateequations(nu)=forpions(nu)=forrhos(nKu)=Kforkaons(nK*u)=K*forvectorkaonshydrodynamicequationT=0mesonnumberdensity1)2(/33TkuiiiekdgnKKKKnnnnvvv*22KKKKKKKKKKKKnnnnnnvvv*******2vv2nnnKKKKKKKKKKKKnnnnvvv*22KKKKKKKKKKKKnnnnnnvvv*******2vv2nnnKKKKKKKK2**2*****vvKKKKKKKKKKKKKKKnn*****2******vv21KKKKKKKKKKKKKKKnnnKKKKKKKKnnnvv2122**2******vvKKKKKKKKKKKKKKKnn*****2******vv21KKKKKKKKKKKKKKKnnnKKKKKKKKnnnn****vvino(solidcurves):without,,K,K*iqar(dashedcurves):withtheqi,anniandresprocessesiqi(dottedcurves):withonlythequarkinterchangeprocessesmesonicmatterinlongitudinalexpansiondependsontimeaverageovertimeinitialfugacities:results:Tables6-8inEur.Phys.J.A47(2011)65showthatfor81setsofinitialfugacitiesmostareabove0.2.Thequark-interchangeprocessesareimportantinthecontributionoftheinelastic2-to-2scatteringtotheevolutionofmesonicmatter.iRnoqarnoqiiiiiiRhfzfzhiiRdR2.0,5.0,7.0,7.0*KK27.0,21.0,30.0,53.0*KKRRRRmesonicmatterinlongitudinalexpansionwith21processes21processes:needsneedsKneedsK*needsAbout96%ofhavevalueslargerthan0.5and53%largerthan1.Thequark-interchangeprocessesareimportantinthecontributionoftheinelasticmeson-mesonscatteringtotheevolutionofmesonicmatter.iR*KKKKKKKKnnnnnK***2vv22v21nnKKKKKKnnnK***vKKKKKKnnnK***vmesonicmatterinlongitudinalandtransverseexpansionwith21processesfour-velocityofthelocalreferenceframeTheleft-handsidesofthemasterrateequationsinitialfugacities:results:formostofthe81setsofinitialfugacitiesarelargerthan1.Whilethequark-antiquarkannihilationprocessesandtheresonantprocessesaretakenintoaccount,thequark-interchangeprocessesmustbeincludedonanequalfooting.),0,v,(ztur2v11r)v(1)(riiiirnrrnnun2.0,5.0,7.0,7.0*KK85.0,21.1,78.0,11.1*KKRRRRiRSummary(1)Wehaveestablishedthemasterrateequationswiththequark-interchangeprocesses.(2)Ifthenumberdensityofisincreased(reduced)bythequark-interchangeprocesses,thenumberdensityofisreduced(increased)inthesameamount.ThisrelationalsoholdstrueforKandK*.(3)Quark-interchangeprocessesareshowntobeimportantinthecontributionoftheinelasticmeson-mesonscatteringtotheevolutionofmesonicmatter.Therefore,allmicroscopicmodelsinvolvinghadronicmattermustincludethequark-interch
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