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

The temperature (T) dependence of the axion mass is predicted for T's up to ∼2.3 x the chiral restoration temperature of QCD. The axion is related to the UA(1) anomaly. The squared axion mass ma(T)^2 is, modulo the presently undetermined scale of spontaneous breaking of Peccei-Quinn symmetry fa (squared), equal to QCD topological susceptibility χ(T) for all T. We obtain χ(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 UA(1) symmetry breaking and restoration through χ(T). In our previous studies, such χ(T) yields the T-dependence of the UA(1)- anomaly-influenced masses of η′ and η 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