# $\rho^0-\omega$ mixing in the presence of a weak magnetic field

## TL;DR

This paper investigates how a weak magnetic field affects the $
ho^0- ext{omega}$ meson mixing amplitude and the resulting charge symmetry violating nucleon-nucleon potential, with implications for magnetized astrophysical objects.

## Contribution

It provides a detailed calculation of the magnetic field's impact on meson mixing and nucleon-nucleon interactions, highlighting significant effects in astrophysical environments.

## Key findings

- Magnetic field significantly alters the mixing amplitude.
- The mixing amplitude remains non-zero even with equal proton and neutron masses.
- Magnetic field influences the charge symmetry violating nucleon-nucleon potential.

## Abstract

We calculate the momentum dependence of the $\rho^0-\omega$ mixing amplitude in vacuum with vector nucleon-nucleon interaction in presence of a constant homogeneous weak magnetic field background. The mixing amplitude is generated by the nucleon-nucleon ($NN$) interaction and thus driven by the neutron-proton mass difference along with a constant magnetic field. We find a significant effect of magnetic field on the mixing amplitude. We also calculate the Charge symmetry violating (CSV) $NN$ potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the $NN$ potential substantially which can have important consequences in highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to positive contribute to the CSV potential if the proton and neutron masses are taken to be equal.