The Sphaleron Rate in the "Symmetric" Electroweak Phase

I calculate the rate of $B+L$ violating processes in the ``symmetric" phase of the Standard Model by means of semiclassical methods, which are based on an appropriately resummed loop expansion within the dimensionally reduced theory. The rate is found to reach its asymptotic form $\Gamma/V=c(\a_W T)^4$ at a temperature about three times the critical temperature of the electroweak phase transition, with a coefficient $c\sim 0.01$ at the one-loop level. The order of magnitude of $c$ is sensitive to higher order corrections to the dynamically generated vector boson mass if these are greater than 20\%. The temperature below which baryon number dissipation is in thermal equilibrium in the early universe is estimated to be $T_*\sim 10^{11} {\rm GeV}$.