Columbia plot based on symmetry-improved CJT formalism in linear sigma model

TL;DR

This paper investigates the chiral phase transition in a three-flavor linear sigma model using an improved CJT formalism, revealing a tricritical point and critical masses that are less sensitive to model parameters.

Contribution

It applies the symmetry-improved CJT formalism to accurately study the Columbia plot, overcoming issues of artificial chiral breaking in conventional approaches.

Findings

Identification of a tricritical point at $m_s^{ m tri}/m_s^{ m phys.} = 0.175$

Critical pion mass around 52.4 MeV in the symmetric limit

Critical temperature approximately 51.7 MeV

Abstract

We study the Columbia plot for the chiral phase transition in the framework of a three-flavor linear sigma model based on the Cornwall-Jackiw-Tomboulis (CJT) formalism. The conventional CJT approach with the Hartree truncation suffers from artificial chiral breaking, leading to the violation of the Nambu-Goldstone theorem and the (anomalous) chiral Ward-Takahashi identities. We apply the symmetry-improved CJT formalism to resolve this issue. We observe a first-order phase transition and a tricritical point in the light-quark mass regime, which is fairly insensitive to the size of the sigma meson, in contrast to the conventional CJT approach. The tricritical point, found on the $m_s$ axis, is at $m_s^{\rm tri}/m_s^{\rm phys.} = 0.175$ with $m_s^{\rm phys.}$ being the physical strange quark mass in real-life QCD. The critical pion mass in the three-flavor symmetric limit, on the second-order boundary, is measured at $m_\pi \sim 52.4$ MeV, with the critical temperature $T_c \sim 51.7$ MeV.