Spontaneous breaking of flavor symmetry and naturalness of nearly degenerate neutrino masses and bi-maximal mixing

The gauge model with S0(3)(F) flavor symmetry and three Higgs triplets is studied. We show how the intriguing nearly degenerate neutrino mass and bi-maximal mixing scenario comes out naturally after spontaneous breaking of the symmetry. The hierarchy between the neutrino mass-squared differences, which is needed for reconciling both solar and atmospheric neutrino data, naturally results from an approximate permutation symmetry. The model can also lead to interesting phenomena on lepton-flavor violations via the 50(3)(F) gauge interactions.