The classical sphaleron transition rate exists and is equal to $1.1(α_w T)^4$
arXiv:hep-ph/9508202 · doi:10.1016/0370-2693(95)01157-L
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 $Î= κ(α_w T)^4$, where $κ= 1.09\pm 0.04$ and $α_w$ is the weak fine structure constant.
12 pages, plain LaTeX, figures part of the LaTeX source, minor errors corrected, acknowledgment added, to be published in Phys. Lett. B