Chiral perturbation theory vs. Linear Sigma Model in a chiral imbalance medium

TL;DR

This paper compares Chiral Perturbation Theory and the Linear Sigma Model in a chirally imbalanced medium, establishing their relations and exploring potential experimental signatures of chiral imbalance in pion physics.

Contribution

It establishes the relations between ChPT and LSM low-energy constants in a chiral imbalance medium and discusses experimental detection of chiral imbalance effects.

Findings

Good correspondence between ChPT and LSM in large N_c limit

Expressions for pion decay constant and a_0 mass in medium derived

Potential experimental signatures in charged pion decays outlined

Abstract

We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM) as realizations of low energy QCD for light mesons in a chirally imbalanced medium. The relations between the low-energy constants of the Chiral Lagrangian and the corresponding constants of the Linear Sigma Model are established as well as the expressions for the decay constant of the $\pi$-meson in the medium and the mass of the $a_0$. In the large $N_c$ count taken from QCD the correspondence of ChPT and LSM is remarkably good and give a solid ground for search of chiral imbalance manifestation in pion physics. A possible experimental detection of chiral imbalance tracks (and therefore a phase with Local Parity Breaking) in the charged pion decays inside the fireball is outlined.