Effect of in-medium π and η propagators to charge symmetry breaking interaction

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.