Neutrino oscillations in a predictive SUSY GUT

In this paper we present a predictive SO(10) supersymmetric grand unified theory with the family symmetry U(2)×U(1) which has several nice features. We are able to fit fermion masses and mixing angles, including recent neutrino data, with nine parameters in the charged fermion sector and four in the neutrino sector. The family symmetry plays a preeminent role. (i) The model is “natural”—we include all terms allowed by the symmetry. It restricts the number of arbitrary parameters and enforces many zeros in the effective mass matrices. (ii) Family symmetry breaking from U(2)×U(1)→U(1)→ nothing generates the family hierarchy. It also constrains squark and slepton mass matrices, thus ameliorating flavor violation resulting from squark and slepton loop contributions. (iii) It naturally gives large angle ${\nu }_{\mu }-{\nu }_{\tau }$ mixing describing atmospheric neutrino oscillation data and small angle ${\nu }_e-{\nu }_s$ mixing, consistent with the small mixing angle Mikheyev-Smirnov-Wolfenstein (MSW) solution to solar neutrino data. (iv) Finally, in this paper we assume minimal family symmetry-breaking vacuum expectation values (VEV’s). As a result we cannot obtain a three neutrino solution to both atmospheric and solar neutrino oscillations. In addition, the solution discussed here cannot fit liquid scintillation neutrino detector (LSND) data even though this solution requires a sterile neutrino ${\nu }_s.$ It is important to note, however, that with nonminimal family symmetry-breaking VEV’s, a three neutrino solution is possible with the small mixing angle MSW solution to solar neutrino data and large angle ${\nu }_{\mu }-{\nu }_{\tau }$ mixing describing atmospheric neutrino oscillation data. In the four neutrino case, nonminimal family VEV’s may also permit a solution for LSND. The results with nonminimal family breaking are still under investigation and will be reported in a future paper.