# Chiral perturbation theory in the environment with chiral imbalance

## TL;DR

This paper explores how chiral imbalance affects pion matter using Chiral Perturbation Theory with a medium-induced chiral chemical potential, comparing models and suggesting experimental detection methods.

## Contribution

It introduces a method to incorporate chiral imbalance into Chiral Perturbation Theory and compares it with sigma model approaches.

## Key findings

- Chiral imbalance influences pion matter properties.
- A relationship between different sigma models is examined.
- Potential experimental detection in charged pion decays is proposed.

## Abstract

We discuss the description of chiral imbalance imprint in pion matter. It is based on the Chiral Perturbation Theory supplemented by medium induced chiral chemical potential in the covariant derivative. Such an implementation of chiral imbalance recently was explored in linear sigma model inspired by QCD. The relationship between two sigma models is examined. A possible experimental detection of chiral imbalance in charged pion decays inside the fireball is pointed out.