Thermal behavior of effective UA(1) anomaly couplings in reflection of higher topological sectors

Abstract

Thermal behavior of effective, chiral condensate-dependent UA(1) anomaly couplings is investigated using the functional renormalization group approach in the Nf=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, ], we find that for increasing temperatures, the anomalous breaking of chiral symmetry tends to strengthen toward the pseudocritical temperature (TC) of chiral symmetry breaking. It is revealed that below TC, around ∼10% of the UA(1) breaking arises from the |Q|=2 topological sector. Correspondingly, a detailed analysis on the thermal behavior of the mass spectrum is also presented. Published by the American Physical Society 2024