Approximate Flavor Symmetries in the Lepton Sector

Abstract

Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the Standard Model. Due to the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the see-saw mechanism, the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several ans\"{a}tze which relate different flavor symmetry breaking parameters and find that the MSW solution to the solar neutrino problem is always easily fit. Further, the $\nu_\mu - \nu_\tau$ oscillation is unlikely to solve the atmospheric neutrino problem and, if we fix the neutrino mass scale by the MSW solution, the neutrino masses are found to be too small to close the Universe.