Backreaction of mesonic fluctuations on the axial anomaly at finite temperature

Abstract

The impact of mesonic fluctuations on the restoration of the UA(1) anomaly is investigated nonperturbatively for three flavors at finite temperature in an effective model setting. Using the functional renormalization group, the fluctuation corrected, fully field dependent Kobayashi-Maskawa-'t Hooft anomaly coupling is computed. It is found that mesonic fluctuations strengthen the UA(1) breaking as the temperature increases. On the other hand, when instanton effects are included by parametrizing the explicit temperature dependence of the bare anomaly parameter via the semiclassical result for the tunneling amplitude, a natural tendency appears diminishing the anomaly at high temperatures. As a result of the two competing effects, the UA(1) breaking shows a well defined intermediate strengthening behavior around the chiral (pseudo)transition temperature before the axial anomaly gets fully suppressed at high temperature. As a consequence, we conclude that below T ∼ 200 MeV the UA(1) anomaly is unlikely to be effectively restored. Robustness of the conclusions against different assumptions for the temperature dependence of the bare anomaly coefficient is investigated in detail.