Magnetic field effect on pion superfluid

TL;DR

This paper studies how magnetic fields influence the phase transition to pion superfluidity using a NJL model, revealing that magnetic fields delay the transition and allow superfluidity to persist at higher temperatures and chemical potentials.

Contribution

It introduces a novel approach using Goldstone's theorem to determine the pion superfluid phase boundary under magnetic fields within a NJL model.

Findings

Critical isospin chemical potential equals pion mass in magnetic field at weak fields

Magnetic field delays pion superfluid phase transition

Superfluid phase persists at higher temperature and chemical potential with magnetic field

Abstract

Magnetic field effect on pion superfluid phase transition is investigated in frame of a Pauli-Villars regularized NJL model. Instead of directly dealing with charged pion condensate, we apply the Goldstone's theorem (massless Goldstone boson $\pi^+$) to determine the onset of pion superfluid phase, and obtain the phase diagram in magnetic field, temperature, isospin and baryon chemical potential space. At weak magnetic field, it is analytically proved that the critical isospin chemical potential of pion superfluid phase transition is equal to the mass of $\pi^+$ meson in magnetic field. The pion superfluid phase is retarded to higher isospin chemical potential, and can survive at higher temperature and higher baryon chemical potential under external magnetic field.