Equilibration, particle production, and self-energy

TL;DR

This paper demonstrates that the relationship between the imaginary part of a self-energy and particle production rates holds at leading order in a linear coupling, considering all orders of other interactions, under certain time scale separation conditions.

Contribution

It extends previous perturbative results to all orders in interactions, establishing the validity of the relations at leading order with a specific time scale separation assumption.

Findings

The imaginary part of self-energy relates to particle production rates.

Relations hold at leading order in linear coupling.

Validity extends to all orders in other plasma interactions.

Abstract

The discontinuity, or imaginary part of a self-energy at finite temperature is proportional to the rate at which the corresponding particles are produced when very few of them are present, and also to the rate at which their phase space density approaches the thermal one. These relations were suggested by Weldon [1], who demonstrated them for low orders in perturbation theory. Here we show that they are valid at leading order in a linear coupling of the produced particles, and to all orders in all other interactions of the hot plasma, if there is a separation of the time scales for the production and for the thermalization of the bulk of the plasma.