Thermal properties and evolution of the $U_A(1)$ factor for 2+1 flavors

TL;DR

This paper investigates how the axial anomaly evolves with temperature in a 2+1 flavor linear sigma model, revealing that mesonic fluctuations enhance the anomaly at finite temperature and it persists at the critical point, affecting mesonic spectra.

Contribution

It introduces a detailed analysis of the thermal evolution of the axial anomaly and the effective potential in a 2+1 flavor linear sigma model, highlighting the role of mesonic fluctuations.

Findings

The `t Hooft determinant coefficient increases with temperature.

Mesonic fluctuations strengthen the axial anomaly at finite temperature.

The axial anomaly does not vanish at the critical temperature.

Abstract

Thermal evolution of the axial anomaly is investigated in the system of the linear sigma model for $2+1$ flavors. We explore the functional form of the effective potential and the coefficient of the `t Hooft determinant term. It is found that the latter develops a non-trivial structure as a function of the chiral condensate and grows everywhere with respect to the temperature. This shows that mesonic fluctuations strengthen the axial anomaly at finite temperature and it does not get vanished at the critical point. The phenomenon has been found to have significance in the thermal properties of the mesonic spectra, especially concerning the $\eta-\eta'$ system.