*Article* **Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium**

#### **Alexander Andrianov 1,2,\*,†, Vladimir Andrianov 1,† and Domenec Espriu 2,†**


Received: 12 December 2019; Accepted: 4 January 2020; Published: 8 January 2020

**Abstract:** We compare the chiral perturbation theory (ChPT) and the linear sigma model (LSM) as realizations of low energy quantum chromodynamics (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 *π*-meson in the medium and for the mass of the *a*0. In the large *Nc* count taken from QCD the correspondence of ChPT and LSM is remarkably good and provides a solid ground for the search of chiral imbalance manifestations in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with local parity breaking) is outlined in the charged pion decays inside the fireball.

**Keywords:** chiral imbalance; chiral perturbation theory; linear sigma model; charged pion decay in chiral medium; local parity breaking
