Backreaction of mesonic fluctuations on the axial anomaly at finite temperature

May 16, 2022, 11:30 AM


Prof. András Patkós (Eötvös University)


The impact of mesonic fluctuations on the restoration of the $U_A(1)$ anomaly is investigated non-perturbatively 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 semi-classical 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 $T \sim 200 \MeV$ 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.

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