strength in the $\omega$ propagator) all of the effects of the momentum dependence of the self-energy can be re-absorbed into momentum dependence of the phenomenological vertex functions. Accordingly, there are no observable physical effects in the NN potential induced by such a momentum dependent self-energy. Moreover, including the short range part of the momentum dependence in the propagator of a meson exchange model violates the bookkeeping arrangement in which all of the short range effects are segregated into phenomenological vertices.

The Charge Symmetry Breaking NN Potential And The Momentum Dependence of $\rho -\omega$ Mixing
==============================================================================================

The preceeding section gives us a paradigm for what happens in the charge symmetry breaking part of the potential. We will show, for any realistic model of the momentum dependence of the mixing amplitude, that all of the effects of the momentum dependence can be absorbed into phenomenological short ranged charge-symmetry-breaking nucleon-vector meson couplings.

Consider the charge-symmetry-breaking potential arising from vector meson exchange. Let us begin by implementing this according to the philosophy of scale separation discussed in the previous two sections. Assuming that only the meson exchanges we need to consider are the $\rho$ and $\omega$, the charge symmetry breaking interaction potential can be 