  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.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory