Chemical nonequilibrium for interacting bosons: applications to the pion gas

TL;DR

This paper develops a diagrammatic thermal field theory approach to describe an interacting pion gas with approximate particle number conservation, exploring thermodynamics, chiral symmetry, and Bose-Einstein condensation.

Contribution

It introduces a novel method incorporating a nonzero pion chemical potential into thermal field theory, extending existing relations and enabling phenomenological applications.

Findings

Derived generalized Luscher and Gell-Mann-Oakes-Renner relations for nonzero pion chemical potential.

Compared field theory results with kinetic theory in dilute regimes for consistency.

Discussed implications for chiral symmetry restoration, freeze-out, and Bose-Einstein condensation.

Abstract

We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $\mu_\pi$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $\mu_\pi\neq 0$ generalization of Luscher and Gell-Mann-Oakes-Renner type relations. We pay special attention to the comparison with the conventional kinetic theory approach in the dilute regime, which allows for a check of consistency of our approach. Several phenomenological applications are discussed, concerning chiral symmetry restoration, freeze-out conditions and Bose-Einstein pion condensation.