incoherent vector mesons production in pbpb ultraperipheral collisions at the lhc 2017 ya-ping xie资料.pdf

该【incoherent vector mesons production in pbpb ultraperipheral collisions at the lhc 2017 ya-ping xie资料 】是由【薛蝌】上传分享，文档一共【10】页，该文档可以免费在线阅读，需要了解更多关于【incoherent vector mesons production in pbpb ultraperipheral collisions at the lhc 2017 ya-ping xie资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。AvailableonlineatScienceDirectNuclearPhysicsA959(2017)56–65ate/nuclphysaIncoherentvectormesonsproductioninPbPbultraperipheralcollisionsattheLHC?Ya-PingXiea,b,c,XurongChena,aInstituteofModernPhysics,ChineseAcademyofSciences,Lanzhou730000,ChinabSchoolofPhysicalScienceandTechnology,LanzhouUniversity,Lanzhou730000,ChinacUniversityofChineseAcademyofSciences,Beijing100049,ChinaReceived17November2016;accepted21December2016Availableonline29December2016AbstractputedindipolemodelinPbPbultrape-ripheralcollisionsattheCERNLargeHadronCollider(LHC).TheIIMmodel?-,ψ(2s),ρandφincoherentrapidityparedwithexperimentaldataandothertheoreticalpredictionsinthispa-.?:Heavyioncollisions;Vectormeson;(UPCs)atRelativisticHadronIonCollider(RHIC)andtheLHCprovidevariabletoolstoprobestructureofthehadrons[1,2].Inrecentyears,developmentofex-[3–8].*-mailaddresses:******@impcas.(Y.-),******@impcas.().http://dx./.-9474/?.-,(2017)56–[9–18].InUPCs,–nucleuscollisions,,,-PbUPCsInRef.[17].TheincoherentcrosssectionoflightvectormesonρisevaluatedineAcollisionsinRef.[19].Inthispaper,,–nucleusinteractionhasbeenstudiedinDeepInelasticScattering(DIS)-xphysics,photon–essfully,Dipoleampli-tudeandlight--protoninteractionathighenergy,anditissolutionoftheBKevolutionequation[20].Im-pactparameterindependentdipoleamplitudehasbeeninvestigatedbysolvingtheBKevolutionequationintheliteratures[21].Butitisdif??rstlyproposedin1999[22].Butitdoesn’,theBGBKmodelwasproposedin2002[23],,theIIMmodelwasalsoproposedbasedontheBKevolutionequationin2004[24–26].TheimpactparameterdependentBGBK(IP-Sat)andIIM(bCGC)modelswereproposedinRefs.[27–31].Thesephenomenologicalmodelsaremainly?ttedfromprotonstructurefunctionF2orreducedcrosssectionfromtheZEUSandH1collabo-.[32].Then,theIIMmodelis?ttedwithnewparametersinRef.[26].Inthispaper,wewillusenewer?-frontwavefunctionsofphotonandvectormesonarealsoincludedinthedipoleam---,forexample,theBoostedGaussian,Gaus-LCandDGKPmodels[28,29,33–38].Inthispaper,weemploytheIIMmodelandusedifferentmodels√ofwavefunctions√topre-dictrapiditydistributionsofvectormesonsinPbPbUPCsatsNN==√thispaperistopredict√theincoherentrapiditydistributionsofvectormesonsinPbPbUPCsatsNN==-,-.-,(2017)56–,thephotoncanscatteroffthenucleus,andvectormesonareproducedafterphoton–’putedas[1]dσA1A2=nA1(ω)σγA2(ω)+nA2(ω)σγA1(ω).(1)(ω)isthecrosssectionofthephoton–nucleus=MV?(ω)istheequivalentphoton?uxinthenucleus,withωleft2exp(y),and=MVωright2exp(y).–nucleusscattering,theputedasfollows[9]2Z2αξ2n(ω)=emξK(ξ)K(ξ)?[K2(ξ)?K2(ξ)],(2)π10210=whereZischargeofthe√nucleusandξ2ωRA/γL,RAistheradiusofthenuclues,γListhelorentzfactor,withγL=sNN/(x)andK1(x)aremodi?(ω)isobtainedbyintegrating|t|–protonscattering,thedifferentialphoton–protoncrosssectioniscalculatedas[28–31]γp→Vp2+2dσRg(1β)=|A(x,)|2,(3)dt16πTwhereTdenotesthetransverseamplitudes,+[39].Theamplitudeofγp→Vpisgivenby[28–31]1dz??·dσqqˉA(x,)=id2rd2b()(z,r)eib(x,r,b).(4)T4πVγTd2b0?2Here(Vγ)T(z,r)anddσqqˉ(x,r,b)/dbarethetraverseoverlapanddifferentialdipolecrosssectionofdipole-.[24–26]thedipolecrosssectionisimpactparameterindependentσqqˉ(x,r)=σ0N(x,r).Indiffractiveprocess,vectormesonproductiondecreasesexponentiallywith|t|as?B|t|,wecanintroduceaGaussianpro?lefunctionofimpactparameterlikeTp(b)=2exp(?b/2Bp).Afterintegratingtheimpactparameter,weobtainσ0=,wemod-ifyσqqˉ(x,r)asimpactparameterdependentdipolecrosssectionasthesameasRef.[40]22dσqqˉ(x,r,b)/db=exp(?b/2Bp)N(x,r).TheamplitudeN(x,r)intheIIMmodeliswrittenas[24,25]+N(rQs)2(γs(1/κλY)ln(2/rQs)),rQ≤2,N=02s(x,r)2(5)1?exp?aln(brQs),rQs>=ln(1/x),N0==(leadingorderBFKLprediction),andQs(x)=λ/2(x0/x)–nucleusscattering,coherentdifferentialcrosssectionisobtainedbysquaringthe2averageofamplitude|A(x,)N|.Thesumofcoherentandincoherentdifferentialcross2sectionisobtainedbyaveragingthesquareofamplitudeA(x,),theincoher-2entdifferentialcrosssectioncanbeobtainedfromthevarianceofamplitudeA(x,)N?Y.-,(2017)56–65592|A(x,)N|.Sincethesquareofaverageamplitudeisverysmallatlarge.Thus,theincoher-2entdifferentialcrosssectioncanbeobtainedbyaveragingthesquareofamplitudeA(x,)Natlarge.Thecoherentdifferentialcrosssectioniscoh2+2dσRg(1β)=|A(x,)|2,(6)dt16πNwheretheaverageamplitudeiscalculatedas[17,18,27]1dz??·A(x,)=id2rd2b()(z,r)eibN4πVγT0×2(1?exp(?2πBpATA(b)N(x,r)).(7)whereTA(b)isthepro?,theincoherentdifferentialcrosssectionofγA→VXinphoton–+2dσRg(1β)=|A(x,)|2,(8)dt16πNwheretheaverageofthesquareamplitudeiscalculatedas[17–19]2A(xp,)N11dzdz??=16πBAd2bd2rd2r[](z,r)[](z,r)p4π4πVγTVγT00?2?[N+N]πBpN(x,r)N(x,r)TA(b)×Bp2πBpATA(b)(x,r)(x,r)ee1?2πBpTA(b)[N(x,r)+N(x,r)]11dzdz??≈16π2B2d2bd2rd2r[](z,r)[](z,r)p4π4πVγTVγT002?Bp?2π(A?1)BpTA(b)[N(x,r)+N(x,r)]×eN(x,r)N(x,r)ATA(b)e.(9)AsimilarexpressionoftheincoherentdifferentialcrosssectioncanbefoundinRefs.[42–44].InUPCs,,[28]?(Vγ)T(r,z)N=eec{m2K(r)φ(r,z)?(z2+(1?z)2)K(r)?φ(r,z)},(10)fπz(1?z)f0T1rT√=whereNcisthenumberofcolors,e4παem,-=?2+2hargeofquarks,andwithz(1z)Qmf,inthefollowingcalculations,wesetQ=0GeV,(r,z)oftheGaus-roundstateofvectormesonisgivenby[28]60Y.-,(2017)56–65Table1ParametersoftheIIMmodel[26].2mu,d,smcσ0Bpγsλx0χ/??×106554/520=(r,z)=N(z(?z))2(?).TT1exp2(11)2RTTheBoostedGaussianmodelisaphenomenologicalmodel,whichisoriginatedfromNNPZmodel[33,36].roundstateofvectormesonisgivenby2R222R2mf2z(1?z)rmfφ1s(r,z)=Nz(1?z)exp?1s?+1s.(12)TT?R28z(1z)1s2TheBoostedGaussianscalarfunctionforψ(2s)isgivenby[41]2R222R2mf2z(1?z)rmfφ2s(r,z)=Nz(1?z)exp?2s?+2sTT8z(1?z)R222s2R22mf4z(1?z)r×1+α2+2s??m2R2.(13)2s?R2f2s8z(1z)2sWithhelpofaboveformulas,putethedifferentialcrosssectionofphoton–,afterintegrating|t|,weobtainthetotalcrosssectionofphoton–nucleusscatter-.(8)isnotvalidatsmall|t|with|t|mininEq.(8)beingthevalueof|t|,,wepresentthenumericalresultsoftheincoherentrapidity√distributionsof=J/ψ√,ψ(2s),=|tmin|ofintegrationofEq.(8)is|t|min=-grationof|t|.=,weusetheBoostedGaussianandGaus--,whichis?ttedfrominclusivecrosssectionofphoton–.[29,31],thelightquarkmassismu,d,s=?t,thelightquarkmassismu,d,s=?rst,wecalculatethecoherentandincoherentdifferentialcrosssectionasafunctionof|t|atmid-rapidityy=√containdifferential=crosssectionofψ(2s)andφ√=|t|,|t|isnotsmall,.[19].Y.-,(2017)56–6561Table2ParametersoftheBoostedGaussianwavefunctionforvectormesons[28,41].22MesonefMass(GeV)fV(GeV)mf(GeV)NTR(GeV)α2sJ/ψ2/(2s)2/?/√.-LCwavefunctionforvectormesons[28].22MesonefMass(GeV)fV(GeV)mf(GeV)NTRT(GeV)J/ψ2//√..(Coloronline.)DifferentialcrosssectionforthecoherentandincoherentproductionofJ/ψ(left√panel)andψ(2s)||==(rightpanel)mesons√(blacklines)andsNN=(bluelines)..(Coloronline.)Differentialcrosssectionforthecoherentandincoherentproduction√ofρ(leftpanel)andφ(right||==panel)√(blacklines)andsNN=(bluelines)..-,(2017)56–.(Coloronline.)Predictions√fortheincoherentrapiditydistributions√ofJ/ψ(leftpanels)calculatedusingtheIIMmodelinPbPbUPCsatsNN=(toppanels)andsNN=(bottompanels)usingtheBoostedGaussian(blacksolidlines)andGaus-LC(bluedashedlines)(blacksolidlines)andinco-herent(bluedashedlines)rapiditydistributionsofψ(2s)(rightpanels)calculatedusingtheIIMmodelwiththeBoostedGaussianwave