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

TL;DR

This paper calculates the Chern-Simons diffusion rate near the electroweak phase transition for a Higgs mass close to the W boson mass using classical simulations, revealing unexpectedly high rates near the transition.

Contribution

It provides a non-perturbative computation of the Chern-Simons diffusion rate in the electroweak theory near the phase transition for specific Higgs mass conditions.

Findings

High diffusion rate in the high temperature phase, approximately equal to (α_W T)^4.

Significantly larger rates near the transition than previous sphaleron-based estimates.

Results obtained using classical lattice simulations with parameters matched to the effective theory.

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.