Abstract
We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate strategies to solve numerically the resulting equations in the case of a quark-antiquark pair. One involves Langevin equations with additional random color forces, the other treats the transition between the singlet and octet color configurations as collisions in a Boltzmann equation which can be solved with Monte Carlo techniques.
Highlights
Heavy quarkonia, bound states of charm or bottom quarks, constitute a prominent probe of the quark-gluon plasma produced in ultra-relativistic heavy ion collisions, and are the object of many investigations, both theoretically and experimentally
In this paper we have obtained a set of equations for the time evolution of the reduced density matrix of a collection of quark-antiquark pairs immersed in a quark-gluon plasma in thermal equilibrium
These equations are fairly general, and rely on two major approximations: weak coupling between the heavy quarks and the quark-gluon plasma, small frequency approximation for the plasma response
Summary
Bound states of charm or bottom quarks, constitute a prominent probe of the quark-gluon plasma produced in ultra-relativistic heavy ion collisions, and are the object of many investigations, both theoretically and experimentally. While we can treat the motion of the heavy quarks within a semi-classical approximation, there is no such semi-classical limit for the color dynamics (except perhaps in the large Nc limit) It follows that the derivation of Fokker-Planck or Langevin equations made in the abelian case needs to be reconsidered, which we do in this paper. This equation, whose structure is close to that of a Lindblad equation, is used as a starting point of all later developments.
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