High-temperature behavior of the Chern-Simons diffusion rate in the 1 + 1 dimensional abelian Higgs model

Abstract

We give arguments that in the 1+1 dimensional abelian Higgs model the classical approximation can be good for the leading high temperature behavior of real time processes. The Chern-Simons diffusion rate ('sphaleron rate') is studied numerically in this approximation. New results at high temperature show a T 2/3 behavior of the rate at sufficiently small lattice spacing.

Chern-Simons number asymmetry from CP violation at electroweak tachyonic preheating

“…A typical evolution of this temperature is shown in Figure 10. For a somewhat different value of m H /m W it was shown in [29] that the sphaleron rate in this model is exponentially suppressed by the sphaleron Boltzmann factor when β ′ ≡ µ 3 /(λT ) is larger than ≃ 7. In the case of figure 10 we get β ′ ≈ 10 and so we are deep in the broken phase with a strongly suppressed sphaleron rate.…”

“…We estimate the temperature of the system by monitoring the average canonical momentum of the Chern-Simons degree of freedom [28,29] (this is the only dynamical degree of freedom in the gauge field, as is clear e.g. from the formulation in the Coulomb gauge [29]). A typical evolution of this temperature is shown in Figure 10.…”

Sphaleron transition rate in the presence of dynamical fermions

“…In the absence of fermions v 2 /h is an overall factor in front of the action in path integral. With fermions included, h/v 2 appears explicitly in the Lagrangian (6), in such a way that in the range of validity of the classical approximation the gauge coupling of the σ field is weak.…”

“…There is by now an extensive body of work devoted to numerical study of the sphaleron transition rate in the classical approximation. Over time, the attention has shifted from one-dimensional models [2,3,4,5,6] to realistic aproximations of the electroweak theory in 3+1 dimensions [7,8,9,10]. Nevertheless, the one-dimensional models have not yet exhausted their utility.…”