Perturbative RG analysis of the condensate dependence of the axial anomaly in the three flavor linear sigma model

TL;DR

This paper uses perturbative renormalization group methods within the three flavor linear sigma model to study how the axial anomaly, influenced by mesonic fluctuations, varies with the chiral condensate, especially near phase transitions.

Contribution

It introduces a perturbative RG approach to analyze the condensate dependence of the axial anomaly in the three flavor linear sigma model, highlighting the role of mesonic fluctuations.

Findings

Anomaly increases as the chiral condensate decreases at low temperatures.

Mesonic fluctuations significantly influence the anomaly near phase transitions.

The analysis provides insights into the anomaly behavior at the nuclear liquid-gas transition.

Abstract

Coupling of `t Hooft's determinant term is investigated in the framework of the three flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field dependent correction to the coupling of the conventional U_A(1) breaking determinant term. It is found that at low temperatures mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid-gas transition.