T-dependence of the axion mass when the U_A(1) and chiral symmetry breaking are tied

Abstract

Modulo the scale of spontaneous breaking of Peccei-Quinn symmetry, the axion mass $m_a(T)$ is given by the QCD topological susceptibility ${\chi}(T)$ at all temperatures $T$. From an approach tying the $U_A(1)$ and chiral symmetry breaking and getting good $T$-dependence of ${\eta}$ and ${\eta}$ mesons, we get ${\chi}(T)$ for an effective Dyson-Schwinger model of nonperturbative QCD. Comparison with lattice results for ${\chi}(T)$, and thus also for $m_a(T)$, shows good agreement for temperatures ranging from zero up to the double of the chiral restoration temperature $T_c$.