Axial anomaly effects in finite isospin $\chi$PT in a magnetic field

TL;DR

This paper investigates the effects of the axial anomaly in finite isospin chiral perturbation theory under strong magnetic fields, revealing that only neutral pions condense and identifying a new phase transition involving $bc^{0}$ domain walls.

Contribution

It demonstrates that charged pions cannot condense in strong magnetic fields and introduces a new phase transition line to the $bc^{0}$ domain wall state considering the axial anomaly effects.

Findings

Charged pions are suppressed in strong magnetic fields.

A phase transition to $bc^{0}$ domain wall state exists at high baryon chemical potential.

The phase transition persists beyond the Schwinger limit when photon back-reactions are included.

Abstract

In this paper, we consider finite isospin chiral perturbation theory including the effects of the axial anomaly (through the Wess-Zumino-Witten term) in a strong magnetic field. We firstly prove that in a strong external magnetic field ($H_{\rm ext}$) or more precisely the Schwinger limit, where photon back-reactions are suppressed, only neutral pions can condense and the condensation of charged pions is forbidden. Secondly, we find that the $\pi^{0}$ domain wall is an example of a phase that can exist in a strong magnetic field and suggest the existence of a new phase transition line from the normal vacuum state to the $\pi^{0}$ domain wall state. This phase transition exists for non-zero pion masses if the baryon chemical potential exceeds a critical value $16\pi f_{\pi}^{2}m_{\pi}/eH_{\rm ext}$. The phase transition line persists away from the Schwinger limit when the photons can back-react to the external magnetic field.