1. 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

2. ---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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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