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

Abstract

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.

Comments: RevTeX, 14 pages. Expanded discussion of the intermediate range force mediated by the light gauge boson. To appear in Phys. Rev. D