Nearly Degenerate Mass and Bi-maximal Mixing of Neutrinos in the SO(3) Gauge Model of Leptons

Abstract

A realistic scheme for masses and mixing of leptons is investigated in the model with gauged SO(3) lepton flavor symmetry. Within this scheme, a nearly `bi-maximal' neutrino mixing pattern with maximal CP-violating phase is found to be the only possible solution for reconciling both solar and atmospheric neutrino flux anomalies. Three Majorana neutrino masses are nearly degenerate and allow to be large enough to play a significant cosmological role. Lepton flavor-violating effects via SO(3) gauge interactions can be as large as the present experimental limits. Masses of the SO(3) gauge bosons are bounded to be above 24 TeV when taking the SO(3) gauge boson mixing angle $\theta_{F}$ and coupling constant $g'_{3}$ to be the same as those ($\theta_{W}$ and $g$) in the electroweak theory.