Pion Mass Modification in presence of external magnetic field

TL;DR

This paper investigates how external magnetic fields affect the effective masses of neutral and charged pions using one-loop calculations, revealing significant modifications for pseudoscalar couplings and modest increases for pseudovector couplings, relevant for astrophysics and heavy ion physics.

Contribution

It provides the first detailed calculation of pion mass modifications in weak magnetic fields considering both pseudoscalar and pseudovector couplings.

Findings

Effective masses depend explicitly on magnetic field strength.

Significant mass modifications occur for pseudoscalar coupling.

Modest mass increases are observed for pseudovector coupling.

Abstract

In this work, the self energies of $\pi^0$ and $\pi^{\pm}$ up to one loop order have been calculated in the limit of weak external magnetic field. The effective masses are explicitly dependent on the magnetic field which are modified significantly for the pseudoscalar coupling due to weak field approximation of the external field. On the other hand, for the pseudovector coupling, there is a modest increment in the effective masses of the pions. These theoretical developments are relevant for the study of the phenomenological aspect of mesons in the context of neutron stars as well as heavy ion collisions.