Gravitationally violated U(1) symmetry and neutrino anomalies
Abstract
The current searches for neutrino oscillations seem to suggest an approximate Le-L-Lτ flavor symmetry. This symmetry implies a pair of degenerate neutrinos with mass m0 and large leptonic mixing. We explore the possibility that gravitational interactions break this global symmetry. The Planck scale suppressed breaking of the Le-L-Lτ symmetry is shown to lead to the right amount of splitting among the degenerate neutrinos needed in order to solve the solar neutrino problem. The common mass m0 of the pair can be identified with the atmospheric neutrino scale. A concrete model is proposed in which smallness of m0 and hierarchy in the solar and atmospheric neutrino scales get linked to hierarchies in the weak, grand unification and the Planck scales.
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