The impact of mesonic fluctuations on the restoration of the $U_A(1)$ anomaly is investigated nonperturbatively for three flavors at finite temperature in an effective model setting. Using the functional renormalization group, the dressed, fully field-dependent Kobayashi-Maskawa-’t Hooft (KMT) anomaly coupling is computed. It is found that mesonic fluctuations strengthen this signature of the $U_A(1)$ 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 in consistency with 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 dressed KMT coupling 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 $T\sim 200\mathrm{MeV}$ the $U_A(1)$ 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.

• Received 6 January 2022
• Accepted 15 April 2022

DOI:https://doi.org/10.1103/PhysRevD.105.096007

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Published by the American Physical Society