Heavy quark bound states in a quark–gluon plasma: Dissociation and recombination

We present a comprehensive approach to the dynamics of heavy quarks in a quark–gluon plasma, including the possibility of bound state formation and dissociation. In this exploratory paper, we restrict ourselves to the case of an Abelian plasma, but the extension of the techniques used to the non-Abelian case is doable. A chain of well defined approximations leads eventually to a generalized Langevin equation, where the force and the noise terms are determined from a correlation function of the equilibrium plasma, and depend explicitly on the configuration of the heavy quarks. We solve the Langevin equation for various initial conditions, numbers of heavy quark–antiquark pairs and temperatures of the plasma. Results of simulations illustrate several expected phenomena: dissociation of bound states as a result of combined effects of screening of the potential and collisions with the plasma constituent, formation of bound pairs (recombination) that occurs when enough heavy quarks are present in the system.