# Effect of in-medium $\pi$ and $\eta$ propagators to charge symmetry breaking interaction

## TL;DR

This paper investigates how in-medium modifications of pion and eta meson propagators influence charge symmetry breaking in nucleon-nucleon interactions, highlighting significant effects for pseudoscalar interactions.

## Contribution

It introduces a detailed analysis of in-medium meson propagators' impact on charge symmetry breaking using an one boson exchange model, including nucleon mass modifications.

## Key findings

- Large contribution of in-medium meson propagators to CSB potential for PS interaction
- Medium effects significantly alter $
ho$-meson mediated CSB interactions
- Off-shell $ ext{π}$-$ ext{η}$ mixing amplitude plays a crucial role

## Abstract

We revisit the charge symmetry breaking $(CSB)$ in nucleon-nucleon $(NN)$ interaction caused by $\pi$-$\eta$ mixing in nuclear matter $(NM)$ employing one boson exchange $(OBE)$ model. The medium effect on $CSB$ is incorporated through the in-medium $\pi$ and $\eta$ propagators. In addition, the medium modification to the nucleon mass is also taken into account to construct the $CSB$ class $III$ potential considering off-shell $\pi$-$\eta$ mixing amplitude and large contribution of in-medium meson propagators to $CSB$ potential is found for the pseudoscalar $(PS)$ interaction compared to that of pseudovector $(PV)$ interaction.