More about vacuum structure of Linear Sigma Model

TL;DR

This paper investigates the vacuum structure and phase transition behavior of the U(2)×U(2) linear sigma model, focusing on the effects of U_A(1) symmetry breaking and decoupling of heavy modes near the O(4) fixed point.

Contribution

It provides a detailed analysis of the renormalization group flow and decoupling phenomena in the linear sigma model with U_A(1) symmetry violation using epsilon expansion.

Findings

Flow into O(4) LSM depends on U_A(1) breaking strength

Decoupling of heavy degrees of freedom occurs near the O(4) fixed point

U_A(1) symmetry restoration influences critical behavior

Abstract

In the study of critical phenomena of QCD, a linear sigma model (LSM) is often analyzed as it shares many properties with QCD. Motivated by recent arguments on effective restoration of the U_A(1) symmetry around the critical temperature, the renormalization group flow of U(2)$\otimes$U(2) LSM with a small violation of the U_A(1) symmetry is examined in the traditional epsilon expansion in threedimensions. With a mass-dependent renormalization scheme, we investigate the attractive basin flowing into the O(4) LSM in the parameter space and its dependence on the size of the U_A(1) breaking. Special emphasis is put on how the decoupling of the heavier degrees of freedom occur as approaching the O(4) LSM.