Chiral perturbation theory in the environment with chiral imbalance

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.