Nanjing University of Sci. & Tech. QPT2017, Xi’an Jiaotong University, Jul.21-23, 2017 Evaluation of the charm and anti-charm quark recombination rate in the quark gluon plasma CHEN Shile Nanjing University of Sci. & Tech. Jul.21,2017

---Recombination of J/ψ in QGP Outline Introduction ---Recombination of J/ψ in QGP c + c bar  g+ J/ψ --- Effective Hamiltonian from QCD multipole expansion --- Cross section of E1 and M1 transition --- Recombinant J/ ψ momentum spectrum Numerical results --- charm quark spectra --- J/ ψ spectrum: Coulomb vs full potential --- J/ ψ spectrum: E1 vs M1 Summary Jul.21,2017

Introduction: c-cbar recombination J/ ψ production from c & cbar recombination in QGP Hard process: initial c quark and J/ψ production Pb/Au Pb/Au T0=400MeV c + c bar  g + J/ψ J/ψ dissociation & recombination g + J/ψ c + c bar QGP Time Tc=170MeV HRG Charm & anti-charm quark distribution Recombination cross section Jul.21,2017

Cross section: c + cbar  g + J/ψ An effective Hamiltonian from QCD multipole expansion Yan 80 Heff = H0 + HI Fermi Golden rule Cross section of this process: E1: M1: Under Coulomb potential approximation, detailed balance entails: Jul.21,2017

J/ψ recombinant cross section: E1 vs M1 This calculation ignores the interaction of the initial state(c cbar)8, so there exists a singular point around gluon zero energy point for M1. E1: from 1.1Tc to 1.3 Tc, cross section declines to ~30% M1: most significant at low energies & temperatures close to Tc Full potential result significantly enhanced over Coulomb approximation Jul.21,2017

In-medium potential: Schrodinger Equation Schrodinger Equation for J/ψ Potential at finite temperature Stationary Schrodinger Equation Full potential magnitude of J/ψ wave function enhanced by 50% than Coulomb potential Wave function curve declines and broadens with temperature Jul.21,2017

Recombinant J/ψ production Recombinant J/ψ spectrum from Boltzmann equation : The relation between invariant amplitude M and <f|H’|i> :  Recombinant J/ψ spectrum fromE1 & M1, respectively E1: M1: Jul.21,2017

Charm quark spectra pp collision: the initial spectrum—power law – very hard Hydro: complete thermalization –exponential –very soft Langevin : partially thermalized (from realistic Langevin simulation, high pT particles are shifted to low pT) Jul.21,2017

Recombinant J/ψ spectra: numerical results The yield of J/ψ much enhanced from Coulomb potential to full potential At low pT Langevin spectrum overtakes pp substantially J/ψ at pT ~ 4GeV, where Langevin simulation & hydro results are very similar, comes from c(c bar) at pT ~ 2GeV Mixed result is 75% of the result of full potential Jul.21,2017

Recombinant J/ψ spectra: E1 vs M1 At low pT M1 contribution is about 15% of the yield of E1 M1 yield is larger at low pT than at high pT, for M1 cross section is most significant at low energies Jul.21,2017

Thanks for your attention ! Summary Using effective Hamiltonian from QCD multipole expansion, cross section derived from quantum mechanical time- dependent perturbation theory Recombinant J / ψ spectrum calculated for both E1 & M1, M1 accounts for 10%-15% at low pT Different charm quark spectra at inputs compared, recombinant J/ψ spectrum from Langevin overtakes pp substantially thermalization helps for c-cbar recombination Recombination put into a more microscopic & solid framework, instead of 2->1 process Thanks for your attention ! Jul.21,2017