Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry

TL;DR

This paper predicts how the axion mass varies with temperature up to about 2.3 times the chiral restoration temperature in QCD, linking it to the topological susceptibility and chiral symmetry restoration.

Contribution

It introduces a method to calculate the temperature dependence of the axion mass using Dyson-Schwinger models of nonperturbative QCD, incorporating chiral symmetry dynamics.

Findings

The axion mass squared is proportional to the QCD topological susceptibility at finite temperature.

The calculated susceptibility matches experimental and lattice results.

The predicted axion mass temperature dependence aligns with previous meson mass studies.

Abstract

The temperature ($T$) dependence of the axion mass is predicted for $T$'s up to $\sim 2.3 \times$ the chiral restoration temperature of QCD. The axion is related to the $U_A(1)$ anomaly. The squared axion mass $m_a(T)^2$ is, modulo the presently undetermined scale of spontaneous breaking of Peccei-Quinn symmetry $f_a$ (squared), equal to QCD topological susceptibility $\chi(T)$ for all $T$. We obtain $\chi(T)$ by using quark condensates calculated in two effective Dyson-Schwinger models of nonperturbative QCD. They exhibit the correct chiral behavior, including the dynamical breaking of chiral symmetry and its restoration at high $T$. This is reflected in the $U_A(1)$ symmetry breaking and restoration through $\chi(T)$. In our previous studies, such $\chi(T)$ yields the $T$-dependence of the $U_A(1)$-anomaly-influenced masses of $\eta'$ and $\eta$ mesons consistent with experiment. This in turn supports our prediction for the $T$-dependence of the axion mass. Another support is a rather good agreement with the pertinent lattice results. This agreement is not spoiled by our varying $u$ and $d$ quark mass parameters out of the isospin limit.