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

Chiral perturbation theory in the environment with chiral imbalance