Pionic dispersion relations in the presence of a weak magnetic field

TL;DR

This paper investigates how weak magnetic fields influence the dispersion relations and effective masses of neutral and charged pions using a phenomenological model, with implications for astrophysics and heavy ion physics.

Contribution

It provides a detailed calculation of pion dispersion relations in weak magnetic fields considering both pseudoscalar and pseudovector couplings, highlighting their different effects on pion masses.

Findings

Effective pion mass depends on magnetic field strength, especially for PS coupling.

Pion dispersion relations are significantly altered by weak magnetic fields.

Results have implications for meson behavior in neutron stars and heavy ion collisions.

Abstract

In this work, dispersion relations of $\pi^0$ and $\pi^{\pm}$ have been studied in vacuum in the limit of weak external magnetic field using a phenomenological pion-nucleon $(\pi N)$ Lagrangian. For our purpose, we have calculated the results up to one loop order in self energy diagrams with the pseudoscalar $(PS)$ and pseudovector $(PV)$ pion-nucleon interactions. By assuming weak external magnetic field it is seen that the effective mass of pion gets explicit magnetic field dependence and it is modified significantly for the case of PS coupling. However, for the PV coupling, only a modest increase in the effective mass is observed. These modified dispersion relations due to the presence of the external field can have substantial influence in the phenomenological aspect of the mesons both in the context of neutron stars as well as relativistic heavy ion collisions.