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

TL;DR

This paper investigates how strong magnetic fields affect the neutral pion mass using the linear sigma model with quarks, showing a monotonic decrease consistent with lattice QCD results.

Contribution

It provides a detailed one-loop analysis of magnetic field effects on the neutral pion mass within the linear sigma model, including coupling and vacuum modifications.

Findings

Neutral pion mass decreases monotonically with increasing magnetic field.

Results align well with recent lattice QCD data.

The model reproduces the trend approaching the physical pion mass.

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 approaches the physical vacuum pion mass from larger values.