Damping and reaction rates and wave function renormalization of fermions in hot gauge theories

TL;DR

This paper explores the relationship between damping rates and reaction rates of fermions in hot gauge theories, emphasizing the importance of medium-modified wave functions for accurate rate calculations.

Contribution

It demonstrates the equivalence of damping and reaction rates when using medium wave functions and applies this to compute axion production rates in hot QED.

Findings

Damping rate equals reaction rate when using medium wave functions.

Axion production rate from electron self-energy matches that from axion self-energy.

Medium effects are crucial for accurate rate computations.

Abstract

We examine the relation between the damping rate of a chiral fermion mode propagating in a hot plasma and the rate at which the mode approaches equilibrium. We show how these two quantities, obtained from the imaginary part of the fermion self-energy, are equal when the reaction rate is defined using the appropriate wave function of the mode in the medium. As an application, we compute the production rate of hard axions by Compton-like scattering processes in a hot QED plasma starting from both, the axion self-energy and the electron self-energy. We show that the latter rate coincides with the former only when this is computed using the corresponding medium spinor modes.