Sphaleron-Like Processes in a Realistic Heat Bath

TL;DR

This study investigates the diffusion rate of Chern-Simons number in a (1+1)-dimensional Abelian Higgs model within a realistic heat bath, revealing the limits of the sphaleron approximation at different temperatures.

Contribution

It provides the first numerical analysis of sphaleron-like processes in a realistic heat bath, demonstrating the temperature-dependent validity of the sphaleron approximation.

Findings

Measured diffusion rate approaches sphaleron prediction at low temperatures.

Diffusion rate significantly drops below sphaleron estimates at higher temperatures.

Sphaleron approximation fails when correlation length approaches sphaleron size.

Abstract

We measure the diffusion rate of Chern-Simons number in the (1+1)-dimensional Abelian Higgs model interacting with a realistic heat bath for temperatures between 1/13 and 2/3 times the sphaleron energy. It is found that the measured rate is close to that predicted by the sphaleron approximation at the lower end of the temperature range considered but falls at least an order of magnitude short of the sphaleron estimate at the upper end of that range. We show numerically that the sphaleron approximation breaks down as soon as the gauge-invariant two-point function yields correlation length close to the sphaleron size.