Bose-Einstein condensation and chiral phase transition in linear sigma model

TL;DR

This paper investigates the phase diagram of an interacting pion system using the linear sigma model, revealing the conditions for Bose-Einstein condensation and chiral phase transitions, and how these phenomena coexist or exclude each other.

Contribution

It provides a detailed phase diagram including Bose-Einstein condensation and chiral transition regions within the linear sigma model framework.

Findings

The phase diagram has three distinct regions: BEC, chiral symmetry broken, and chiral symmetry restored.

Bose-Einstein condensation can occur from either chiral phase, but not during the onset of the chiral transition.

The chiral phase transition onset is restricted to regions without Bose-Einstein condensation.

Abstract

With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A $\mu-T$ phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can happen either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area where there is no Bose-Einstein condensation.