The classical sphaleron transition rate exists and is equal to $1.1(\alpha_w T)^4$

Abstract

Results of a large scale numerical simulation show that the high temperature Chern-Simons number diffusion rate in the electroweak theory has a classical limit $\Gamma = \kappa (\alpha_w T)^4$, where $\kappa = 1.09\pm 0.04$ and $\alpha_w$ is the weak fine structure constant.