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We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM)as realizations of low energy QCD for light mesons in a chirally imbalancedmedium. The relations between the low-energy constants of the Chiral Lagrangianand the corresponding constants of the Linear Sigma Model are established aswell as the expressions for the decay constant of the $\pi$-meson in the mediumand the mass of the $a_0$. In the large $N_c$ count taken from QCD thecorrespondence of ChPT and LSM is remarkably good and give a solid ground forsearch of chiral imbalance manifestation in pion physics. A possibleexperimental detection of chiral imbalance tracks (and therefore a phase withLocal Parity Breaking) in the charged pion decays inside the fireball isoutlined.

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