We construct a model which provides maximal mixing between a pseudo-Dirac ${\nu }_{\mu }/{\nu }_{\tau }$ pair, based on a local ${U\left(1\right)\mathrm{}}_{L_{\mu }-L_{\tau }}$ 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 ${U\left(1\right)\mathrm{}}_{L_{\mu }-L_{\tau }}.$ Through the mixing of μ, τ and e, this force couples to electrons and thus may be searched for in precision “gravity” experiments.

• Received 16 August 2000

DOI:https://doi.org/10.1103/PhysRevD.63.013006