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

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 ($H_{\mathrm{ext}}$) 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 $16\pi f_{\pi }^2{m}_{\pi }/e{H}_{\mathrm{ext}}$. The phase transition line persists away from the Schwinger limit when the photons can back-react to the external magnetic field.

Comments: 7 pages, 3 figures