will adopt the Bonn potential [@BONN] strategy of incorporating all short range effects in vertex functions. In such a strategy the scale separation between long and short range is particularly easy to enforce: the phenomenological vertex functions are analytic for $q^2 < \Lambda_s^2$ while the propagators are analytic for $q^2 > \Lambda_s^2$, where $q^2$ is the square of the four momentum.

Momentum-Dependent Self-Energies in Meson-Exchange Potentials \[csc\] 
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It is probably useful to discuss an analogous, and perhaps somewhat simpler problem before discussing charge symmetry breaking. The $\rho-\omega$ mixing matrix element is an off-diagonal mass term. Models which give momentum dependence to this off-diagonal mass can also be expected to give momentum dependence to the analogous diagonal mass terms—[*i.e.*]{} to the vector meson self-energies. It is clearly useful to understand the role of the momentum dependence of the $\rho$ and $\omega$ self energies in the charge symmetry preserving potential before taking on the challenge of understanding the the momentum dependence of the $\rho-\omega$ mixing.

For simplicity we examine the one $\omega$ exchange contribution. First consider the traditional meson exchange model description with the scale separation as outlined above. The potential is given by $$V_{\omega} (q^2) = \frac{( g_\omega^{ \rm
v}(q^2)\gamma^{(1)}_{\mu} 