Implications of anomalous isospin violation for the low energy nucleon-nucleon interaction

Quark mass differences are used to derive an anomalous (i.e., due to the strong interactions) isospin violating potential. The potential includes the effects of pseudoscalar ($\pi -\eta -{\eta }^{\prime }$) and vector meson ($\rho -\omega$) mixing. The finite $\rho$ width is included. Low energy $\mathrm{nn}$, $\mathrm{pp}$, and $\mathrm{np}$ phase shift differences are calculated in terms of the fundamental coupling constants. Despite considerable uncertainty in the coupling constants, it is possible to understand the very small $\mathrm{nn}$ and $\mathrm{pp}$ scattering length differences. Furthermore, it appears that effects in the $l>\mathrm{}0\mathrm{}$ partial waves at finite energies are large enough to be observable in the next few years. Estimates of effects in bound nuclei are presented. These include calculations of the contributions to mirror nuclei binding energy differences and to isospin mixing for a few characteristic cases. In most of those cases the anomalous isospin breaking contributions are of roughly the same size as observed discrepancies. However, inclusion of short range correlations substantially reduces the calculated effects in these cases.