Separation of Equilibration Time-Scales in the Gradient Expansion

TL;DR

This paper investigates the different time-scales of chemical equilibration in a plasma using gradient expansion of the Kadanoff-Baym equations, revealing off-shell effects and their suppression by thermal widths.

Contribution

It demonstrates that chemical equilibration can occur without higher loop corrections and explicitly calculates the distinct damping time-scales for on- and off-shell processes.

Findings

Off-shell equilibration is suppressed by the thermal width.

On-shell and off-shell chemical equilibration occur on different time-scales.

Gradient expansion captures the separation of these time-scales.

Abstract

We study thermalization by applying gradient expansion to the Kadanoff-Baym equations of the 2PI effective action to two-loop in a theory with Dirac fermions coupled to scalars. In addition to those chemical potentials which equilibrate in the on-shell limit, we identify modes which are conserved in this approximation, but which relax when off-shell effects are taken into account. This implies that chemical equilibration does not require higher loop contributions to the effective action and is compatible with the gradient expansion. We explicitly calculate the damping time-scales of both, on- and off-shell, chemical equilibration rates. It is shown that off-shell equilibration is suppressed by the thermal width of the particles in the plasma, which explains the separation of on- and off-shell chemical equilibration time-scales.