---
abstract: 'The role of the off-shell dependence of $\rho-\omega$ mixing in the charge symmetry breaking nucleon-nucleon potential is discussed. It is shown that models describing the off-shell dependence of $\rho-\omega$ mixing are not sufficient to determine the charge symmetry breaking nucleon-nucleon potential.'
address: 'Department of Physics$^a$ FM-15 and Institute For Nuclear Theory$^b$ NK-12, University of Washington, Seattle, Washington 98195, USA'
author:
- 'Thomas D. Cohen$^{a,b}$[^1], and Gerald A. Miller$^a$'
title: 'Rho-Omega Mixing Off Shell and Charge Symmetry Breaking In the N-N Potential '
---

Introduction
============

Charge symmetry breaking has been studied for a long time, see e.g. the reviews[@NS69; @H69; @SHLOMO; @HM79; @MNS90; @NMS92; @MVO94] and especially the references therein. We follow ref. [@MVO94] in summarizing a few main features. Charge independence and charge symmetry breaking is caused by the $d$-$u$ quark mass difference $m_d-m_u >0$, and electromagnetic effects. The general goal of this area of research is to find small but observable effects of the breaking of charge independence and charge symmetry. This provides significant insight into strong interaction dynamics since the underlying origin of the breaking is understood. Over the years there has been substantial experimental and theoretical progress. First, we recall the old idea that 