Bottom-up model for maximal $\nu_{\mu} - \nu_{\tau}$ mixing

We construct a model which provides maximal mixing between a pseudo-Dirac $\nu_{\mu}/\nu_{\tau}$ pair, based on a local $U(1)_{L_{\mu}-L_{\tau}}$ symmetry. Its strengths, weaknesses and phenomenological consequences are examined. The mass gap necessitated by the pseudo-Dirac structure is most naturally associated with the LSND anomaly. The solar neutrino problem then requires a light mirror or sterile neutrino. By paying a fine-tuning price to nullify the mass gap, one can also invoke $\nu_e \to \nu_{\mu,\tau}$ for the solar problem. The model predicts a new intermediate range force mediated by the light gauge boson of $U(1)_{L_{\mu}-L_{\tau}}$. Through the mixing of $\mu$, $\tau$ and $e$, this force couples to electrons and thus may be searched for in precision ``gravity'' experiments.