Equilibration of the chiral asymmetry due to finite electron mass in electron-positron plasma

TL;DR

This paper calculates the rapid decay rate of chiral asymmetry in an electron-positron plasma, revealing it occurs faster than previously estimated due to first-order processes, impacting early Universe physics.

Contribution

It provides the first-order in alpha calculation of the chirality flipping rate, showing it is much larger than earlier estimates and identifying key channels responsible for this rapid relaxation.

Findings

Chirality flipping rate is of order alpha, not alpha squared.

Collinear photon emission and Compton scattering dominate the relaxation.

Infrared divergence regularized by thermal effects enhances the rate.

Abstract

We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant $\alpha$ and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the $\mathcal{O}(\alpha)$ result because of the infrared divergence in its cross section, which is regularized on the soft scale $\sim eT$ due to the thermal corrections. Our results are important for the description of the early Universe processes (such as leptogenesis or magnetogenesis) that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter.