Fermion Masses and Mixing Angles from SU(3) Family Symmetry and Unification

Abstract

We develop a bottom-up approach to constructing a theory of fermion masses and mixing angles based on the gauge group $SU(3)\times G$ where SU(3) is a family symmetry and $G$ contains a unified group such as SO(10) or its Pati-Salam subgroup, together with other discrete symmetries. We construct a realistic model and show that it can provide an excellent description of quark and lepton masses and mixing angles, including almost maximal atmospheric mixing and the LMA MSW solar neutrino solution. We predict a neutrino mixing angle $\theta_{13}$ near the current limit. The model provides the basis for a new solution to the flavour problem with a characteristic soft SUSY breaking mass spectrum.