Topological susceptibility at high temperature on the lattice

TL;DR

This paper introduces a new lattice QCD method to accurately compute the topological susceptibility at high temperatures, crucial for axion cosmology, and validates it against instanton predictions.

Contribution

A novel lattice QCD approach for high-temperature topological susceptibility calculation, effective at very high temperatures and consistent with instanton models.

Findings

Method works well at very high temperatures

Results agree with dilute instanton gas approximation down to 2 T_c

Feasibility demonstrated on small quenched lattice

Abstract

QCD topological susceptibility at high temperature, $\chi_t(T)$, provides an important input for the estimate of the axion abundance in the present Universe. While the model independent determination of $\chi_t(T)$ should be possible from the first principles using lattice QCD, existing methods fail at high temperature, since not only the probability that non-trivial topological sectors appear in the configuration generation process but also the local topological fluctuations get strongly suppressed. We propose a novel method to calculate the temperature dependence of topological susceptibility at high temperature. A feasibility test is performed on a small lattice in the quenched approximation, and the results are compared with the prediction of the dilute instanton gas approximation. It is found that the method works well especially at very high temperature and the result is consistent with the instanton calculus down to $T\sim 2\, T_c$ within the statistical uncertainty.