$\rho$-$\omega$ mixing and spin dependent CSV potential

TL;DR

This paper develops a detailed charge symmetry violating nucleon-nucleon potential based on $ ho^0$-$7$ mixing, highlighting the significant role of tensor interactions and form factors in accurate modeling.

Contribution

It provides an analytical expression for the two-body CSV potential including central and non-central interactions, emphasizing the impact of tensor forces and form factors.

Findings

Tensor interactions significantly enhance CSV potential.

Form factors remove divergences in the potential.

The scattering length difference depends on short-range treatment.

Abstract

We construct the charge symmetry violating (CSV) nucleon-nucleon potential induced by the $\rho^0$-$\o$ mixing due to the neutron-proton mass difference driven by the $NN$ loop. Analytical expression for for the two-body CSV potential is presented containing both the central and non- central $NN$ interaction. We show that the $\rho$$NN$ tensor interaction can significantly enhance the charge symmetry violating $NN$ interaction even if momentum dependent off-shell $\rho^0$-$\omega$ mixing amplitude is considered. It is also shown that the inclusion of form factors removes the divergence arising out of the contact interaction. Consequently, we see that the precise size of the computed scattering length difference depends on how the short range aspects of the CSV potential are treated.