Preprint Article Version 1 This version is not peer-reviewed

# Chiral Perturbation Theory vs. Linear Sigma Model in A Chiral Imbalance Medium

Version 1 : Received: 15 December 2019 / Approved: 17 December 2019 / Online: 17 December 2019 (07:39:13 CET)

A peer-reviewed article of this Preprint also exists.

Andrianov, A.; Andrianov, V.; Espriu, D. Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium. Particles 2020, 3, 15-22. Andrianov, A.; Andrianov, V.; Espriu, D. Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium. Particles 2020, 3, 15-22.

Journal reference: Particles 2020, 3, 2
DOI: 10.3390/particles3010002

## Abstract

We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM) as realizations of low energy 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 $\pi$-meson in the medium and for the mass of the $a_0$. In the large $N_c$ count taken from QCD the correspondence of ChPT and LSM is remarkably good and give a solid ground for search of chiral imbalance manifestation 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.

## Subject Areas

chiral imbalance; Chiral Perturbation Theory; Linear Sigma Model; charged pion decay in chiral medium; local parity breaking

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