Functional dependence of axial anomaly via mesonic fluctuations in the three flavor linear sigma model

TL;DR

This paper investigates how mesonic fluctuations influence the temperature dependence of the $U_A(1)$ anomaly in a three-flavor linear sigma model, revealing conditions under which fluctuations strengthen or weaken the anomaly.

Contribution

It introduces a generalized chiral invariant expansion within the functional renormalization group framework to analyze the anomaly's temperature dependence.

Findings

Mesonic fluctuations can either enhance or suppress the anomaly depending on coupling relationships.

An analytic expression for the anomaly coefficient function is derived.

Numerical evidence supports the fluctuation effects on the anomaly's behavior.

Abstract

Temperature dependence of the $U_A(1)$ anomaly is investigated by taking into account mesonic fluctuations in the $U(3)\times U(3)$ linear sigma model. A field dependent anomaly coefficient function of the effective potential is calculated within the finite temperature functional renormalization group approach. The applied approximation scheme is a generalization of the chiral invariant expansion technique developed in [G. Fejos, Phys. Rev. D 90, 096011 (2014)]. We provide an analytic expression and also numerical evidence that depending on the relationship between the two quartic couplings, mesonic fluctuations can either strengthen of weaken the anomaly as a function of the temperature. The role of the six-point invariant of the $U(3)\times U(3)$ group, and therefore the stability of the chiral expansion is also discussed in detail.