Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case

TL;DR

This paper investigates how a weak magnetic field influences the neutral pion mass within the linear sigma model coupled to quarks, revealing a decreasing trend when magnetic corrections are considered.

Contribution

It provides the first weak field approximation calculation of neutral pion mass dependence on magnetic fields within this model, including boson self-coupling effects.

Findings

Neutral pion mass decreases with magnetic field strength.

Magnetic field corrections to boson self-coupling are significant.

Results set a trend for pion mass behavior in magnetic fields.

Abstract

We compute the neutral pion mass dependence on a magnetic field in the weak field approximation at one-loop order. The calculation is carried out within the linear sigma model coupled to quarks and using Schwinger's proper-time representation for the charged particle propagators. We find that the neutral pion mass decreases with the field strength provided the boson self-coupling magnetic field corrections are also included. The calculation should be regarded as the setting of the trend for the neutral pion mass as the magnetic field is turned on.