Chern-Simons Diffusion Rate near the Electroweak Phase Transition for $m_H\approx m_W$

Abstract

The rate of $B$-violation in the standard model at finite temperature is closely related to the diffusion rate $\Gamma$ of Chern-Simons number. We compute this rate for $m_H\approx m_W$ in the classical approximation in an effective SU(2)-Higgs model, using Krasnitz's algorithm. The parameters in the effective hamiltonian are determined by comparison with dimensional reduction. In the high temperature phase we find $\Gamma /V({\alpha }_{W}T{)}^4\approx 1$, neglecting a finite renormalization. In the low temperature phase near the transition we find the rate to be much larger than might be expected from previous analytic calculations based on the sphaleron.

23 pages, 8 Postscript figures, uses epsf.sty