Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

TL;DR

This paper investigates how the strange quark mass affects the tricritical point in a chiral sigma model, revealing complex dependencies and decoupling effects that influence QCD phase transition predictions.

Contribution

It introduces a detailed analysis of the strange quark mass dependence of the tricritical point using a multi-stage sigma model approach with one-loop beta functions and matching conditions.

Findings

The tricritical point's location depends on the strange quark mass and chemical potential.

Decoupling of heavy sectors influences the thermodynamics of the light degrees of freedom.

The model predicts different curvature behaviors of the critical surface near zero chemical potential.

Abstract

We study the strange quark mass dependence of the tricritical point of the U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the \eta-a_0 sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the m_s and \mu_q dependence of the effective model parameters, then the \mu_q^TCP(m_s) function can be determined. Depending on the details, a curve bending upwards or downwards near \mu_q=0 can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with m_s, too.