Sphaleron Transition Rate in Presence of Dynamical Fermions

TL;DR

This study examines how dynamical fermions influence the sphaleron transition rate in a 1D Abelian Higgs model, revealing that massless fermions do not significantly alter the rate and that the transition rate's dependence on fermion mass is weak.

Contribution

The paper introduces a numerical approach using bosonization to include dynamical fermions in the analysis of sphaleron transitions in a simplified model.

Findings

Massless fermions do not affect the transition rate within measurement accuracy.

The transition rate shows a very weak dependence on fermion mass.

The exponential dependence of sphaleron energy on Yukawa coupling is not reflected in the transition rate.

Abstract

We investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.