Studying chiral imbalance using Chiral Perturbation Theory

TL;DR

This paper develops a low-energy effective theory incorporating parity-violating effects due to chiral imbalance, analyzing how axial chemical potential influences observables within Chiral Perturbation Theory.

Contribution

It extends Chiral Perturbation Theory to include parity-violating terms parametrized by an axial chemical potential up to order p^4, revealing new terms and constants.

Findings

Derived the most general low-energy Lagrangian with parity violation.

Identified new terms proportional to μ_5^2 and associated low-energy constants.

Studied μ_5 and temperature effects on vacuum energy density.

Abstract

We analize the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential $\mu_5$. This result is obtained following the external source method, up to $\mathcal{O}(p^4)$ order in the chiral expansion for two light flavours. We show that the $\mathcal{O}(p^4)$ lagrangian includes new terms proportional to $\mu_5^2$ and new low-energy constants. Finally, the $\mu_5$ and temperature dependences of several observables related to the vacuum energy density are studied.