Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

Abstract

We use the linear sigma model with quarks to find the magnetic-field-induced modifications to the neutral pion mass at one-loop level. The magnetic field effects are introduced by using charged particle propagators in the presence of a magnetic background in the strong field regime. We show that, when accounting for the effects of the magnetic field on the model couplings, the vacuum sigma field, and the neutral pion self-energy, the neutral pion mass decreases monotonically as a function of the field strength. We find an excellent qualitative and quantitative agreement with recent lattice QCD calculations, reproducing the monotonically decreasing trend with the field strength as well as the decrease when lattice data approach the physical vacuum pion mass from larger values.