The approach to equilibrium of a quarkonium in a quark-gluon plasma

TL;DR

This paper derives equations describing how heavy quarkonium reaches equilibrium in a quark-gluon plasma, accounting for temperature effects and collision dynamics, with implications for understanding quarkonium behavior in high-energy physics.

Contribution

It introduces a new set of equations for the quarkonium density matrix that incorporate temperature effects and collision-induced imaginary potentials, advancing the theoretical modeling of quarkonium in plasma.

Findings

Equations of motion for quarkonium in plasma derived.

Collision effects modeled via energy-dependent imaginary potential.

Analysis of entropy and free energy evolution during equilibration.

Abstract

We derive equations of motion for the reduced density matrix of a heavy quarkonium in contact with a quark-gluon plasma in thermal equilibrium. These equations allow in particular a proper treatment of the regime when the temperature of the plasma is comparable to the binding energy of the quarkonium. These equations are used to study how the quarkonium approaches equilibrium with the plasma, and we discuss the corresponding entropy increase, or free energy decrease, depending on the temperature regime. The effect of collisions can be accounted for by the generalization of the imaginary potential introduced in previous studies, and from which collision rates are derived. An important outcome of the present analysis is that this imaginary potential has a sizeable dependence on the energy of the relevant transitions.