Thermal behavior of effective, chiral condensate-dependent $U_A(1)$ anomaly couplings is investigated using the functional renormalization group approach in the $N_f=3$ flavor meson model. We derive flow equations for anomaly couplings that arise from instantons of higher topological charge, dependent also on the chiral condensate. These flow equations are solved numerically for the $|Q|=1$, 2 topological sectors at finite temperature. Assuming that the anomaly couplings at the ultraviolet scale may also exhibit explicit temperature dependence, we calculate the thermal behavior of the effective potential. In accordance with our earlier study, [G. Fejos and A. Patkos, Phys. Rev. D 105, 096007 (2022)], we find that for increasing temperatures, the anomalous breaking of chiral symmetry tends to strengthen toward the pseudocritical temperature ($T_C$) of chiral symmetry breaking. It is revealed that below $T_C$, around $\sim 10\%$ of the $U_A(1)$ breaking arises from the $|Q|=2$ topological sector. Correspondingly, a detailed analysis on the thermal behavior of the mass spectrum is also presented.

• Received 10 November 2023
• Accepted 2 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.036035

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society