Neutrinos in the Family Replicated Gauge Group Model

Abstract

We present a discussion of the neutrino mass problem in the anti-grand unification theory based on three family replicated copies of the Standard Model gauge group (SMG). We consider two versions of the theory, with and without right-handed neutrinos, and present order of magnitude fits to the 17 measured quark-lepton mass and mixing angle variables. In the model without right-handed neutrinos, based on the gauge group $SMG^3\times U(1)_f$ and an isotriplet Higgs, we obtain a good 4 parameter fit, but with a vacuum oscillation solution to the solar neutrino problem. In the second model, based on the gauge group $(SMG\times U(1)_{B-L})^3$, we obtain a good 5 parameter fit using the usual right-handed neutrino see-saw mechanism to generate an LMA-MSW solution to the solar neutrino problem. The CHOOZ mixing angle bound is easily satisfied in the first model and is close to the predicted value in the second model.