Linear sigma model at finite density in the 1/N expansion to next-to-leading order

TL;DR

This paper investigates relativistic Bose-Einstein condensation within the linear sigma model at finite density and temperature, deriving a renormalized effective potential at next-to-leading order in the 1/N expansion, and analyzing phase transition behavior.

Contribution

It provides a next-to-leading order effective potential in the 1/N expansion for the linear sigma model at finite density, including thermodynamic analysis of the pion gas and phase transition characteristics.

Findings

The effective potential is renormalizable independently of temperature.

The model predicts a second-order chiral phase transition at finite temperature.

Regularization issues prevent extension of analysis to nonzero chemical potential.

Abstract

We study relativistic Bose-Einstein condensation at finite density and temperature using the linear sigma model in the one-particle-irreducible 1/N-expansion. We derive the effective potential to next-to-leading (NLO) order and show that it can be renormalized in a temperature-independent manner. As a particular application, we study the thermodynamics of the pion gas in the chiral limit as well as with explicit symmetry breaking. At nonzero temperature we solve the NLO gap equation and show that the results describe the chiral-symmetry-restoring second-order phase transition in agreement with general universality arguments. However, due to nontrivial regularization issues, we are not able to extend the NLO analysis to nonzero chemical potential.