Fitting direct interaction pieces into neutrino puzzles

We develop a framework and unified, compact notation to include neutrino direct interaction effects with neutrino oscillations for a wide class of low-energy, effective four-Fermi interactions. Modest flavor-violating interaction strengths can make significant changes in the boundaries in $\Delta M^2 \leftrightarrow sin^2 2\theta$ and in $tan^2 \theta_{13} \leftrightarrow tan^2 \theta_{23} parameter space. We draw examples from the L-R symmetric and $MSSM + \slash R$ models and find the recently reported decay-at-rest $\mu \leftrightarrow e$ transition probability can be described without oscillations in L-R symmetric models.