Revisiting the sphaleron and axion production rates in QCD at high temperatures

TL;DR

This paper presents new lattice calculations of sphaleron rates in high-temperature QCD, estimates thermalization times after inflation, and computes axion production rates showing significant deviations from perturbative predictions.

Contribution

It provides the first lattice-based sphaleron rate results across a wide temperature range and evaluates axion production with non-perturbative effects.

Findings

Lattice sphaleron rates are obtained for temperatures from 0.6 GeV to 10^15 GeV.

Estimated thermalization times for ultra-soft gluons during reheating.

Axion production rates deviate significantly from perturbative estimates at electroweak scale.

Abstract

We report our new lattice results for the sphaleron rate calculated within a thermal effective field theory of soft SU(N) gluons whose momenta are below the magnetic scale, where $N=2,3$, for a wide range of temperatures spanning from $0.6$-$10^{15}$ GeV at sufficiently large volumes. Comparing these results with sphaleron rates in a non-thermal SU(N) plasma where the infrared gluons are over-occupied, we estimate the typical thermalization time for these ultra-soft soft gluons during the early stages of reheating after inflation. We also calculate the thermal production rate of relativistic axions due to these non-perturbatively interacting soft gluons which shows a significant deviation from its perturbative estimate even at the electroweak scale.