Neutrino Mixings and Fermion Masses in Supersymmetric SU(5)

Abstract

We consider neutrino mixings in supersymmetric SU(5) supplemented by a U(1) flavor symmetry. In particular, we show how bi-maximal neutrino mixings can be realized. Two scenarios for implementing the small mixing angle MSW solution, with one involving a sterile state $\nu_s$ and maximal $\nu_{\mu}-\nu_s$ mixing to resolve the atmospheric anomaly, are also discussed. Finally, a new mechanism for eliminating the asymptotic relations $m^{(0)}_{\mu} =m^{(0)}_s$ and $m^{(0)}_e=m^{(0)}_d$, while retaining $m^{(0)}_{\tau}=m^{(0)}_b$, is presented. It employs `matter' multiplets in the $15+\bar{15}$ of SU(5), and is consistent with the various oscillation scenarios, as well as with the unification at $M_{GUT}$ of the three gauge couplings.