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

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 ${\eta }^{\prime }$ 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.

Comments: 23 pages, 7 figures, title changed, references added, minor style and language changes, version published in Universe 5 (2019) no.10, 208,