Bottom-up model for maximal $ν_μ - ν_τ$ mixing

Abstract

We construct a model which provides maximal mixing between a pseudo-Dirac $ν_μ/ν_τ$ pair, based on a local $U(1)_{L_μ-L_τ}$ 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 $ν_e \to ν_{μ,τ}$ for the solar problem. The model predicts a new intermediate range force mediated by the light gauge boson of $U(1)_{L_μ-L_τ}$. Through the mixing of $μ$, $τ$ and $e$, this force couples to electrons and thus may be searched for in precision ``gravity'' experiments.