Neutrino oscillations in an SO(10) supersymmetric grand unified theory withU(2)×U(1)nfamily symmetry

In a previous paper we analyzed fermion masses (focusing on neutrino masses and mixing angles) in an SO(10) SUSY GUT with ${\mathrm{U}\left(2\right)\mathrm{}\times \mathrm{U}\left(1\right)\mathrm{}}^n$ family symmetry. The model is “natural” containing all operators in the Lagrangian consistent with the states and their charges. With minimal family symmetry breaking vacuum expectation values (VEVs) the model is also predictive giving a unique solution to atmospheric (with maximal ${\nu }_{\mu }\to {\nu }_{\tau }$ mixing) and solar (with SMA MSW ${\nu }_e\to {\nu }_s$ mixing) neutrino oscillations. In this paper we analyze the case of general family breaking VEVs. We now find several new solutions for three, four, and five neutrinos. For three neutrinos we now obtain SMA MSW, LMA MSW, or vacuum oscillation solutions for solar neutrinos. In all three cases the atmospheric data are described by maximal ${\nu }_{\mu }\to {\nu }_{\tau }$ mixing. In the four and five neutrino cases, in addition to fitting atmospheric and solar data as before, we are now able to fit LSND data. All this is obtained with the additional parameters coming from the family symmetry breaking VEVs, providing only minor changes in the charged fermion fits.