Neutrino oscillations in a predictive SUSY GUT - art. no. 113001

In this paper we present a predictive SO(10) supersymmetric grand unified t heory with the family symmetry U(2) X U(1) which has several nice features. We are able to ht fermion masses and mixing angles, including recent neutr ino data, with nine parameters in the charged fermion sector and four in th e neutrino sector. The family symmetry plays a preeminent role. (i) The mod el 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) X U(1)-->U(1)--> no thing generates the family hierarchy. It also constrains squark and slepton mass matrices, thus ameliorating flavor violation resulting from squark an d 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, i n this paper we assume minimal family symmetry-breaking vacuum expectation values (VEV's). As a result we cannot obtain a three neutrino solution to b oth atmospheric and solar neutrino oscillations. In addition, the solution discussed here cannot fit liquid scintillation neutrino detector (LSND) dat a even though this solution requires a sterile neutrino nu(s). It is import ant to note, however, that with nonminimal family symmetry-breaking VEV's, a three neutrino solution is possible with the small mixing angle MSW solut ion to solar neutrino data and large angle nu(mu) - nu(tau) mixing describi ng atmospheric neutrino oscillation data. In the four neutrino case, nonmin imal family VEV's may also permit a solution for LSND. The results with non minimal family breaking are still under investigation and will be reported in a future paper. [S0556-2821(99)00619-0].