Renormalization group flow of linear sigma model with $U_A(1)$ anomaly

TL;DR

This paper investigates how the U_A(1) anomaly affects the chiral phase transition in massless two-flavor QCD using renormalization group flow analysis within the epsilon expansion, revealing dependence on initial conditions and differences from the O(4) model.

Contribution

It provides a detailed RG flow analysis of the linear sigma model with U_A(1) anomaly, highlighting the impact on phase transition nature and universal exponents.

Findings

Phase transition nature depends on initial parameters.

Universal exponent differs from standard O(4) model.

Non-decoupling effect explains the difference.

Abstract

In the presence of finite $U_A(1)$ breaking, chiral phase transition of massless two-flavor QCD is studied by tracing the renormalization group flow of the corresponding effective theory. In the framework of the $\epsilon$ expansion, it is found that the nature of the phase transition depends on the initial condition for the parameters of the effective theory and that, when it undergoes second order phase transition, one of the universal exponents shows a different value from that in the standard $O(4)$ linear sigma model. We discuss that the origin of the difference is attributed to a non-decoupling effect. The present status of the calculation of the effective potential is presented.