A Predictive Superunification $SO(10)\times {\mathrm{\Delta }}_{48}(SU(3))\times U(1)$ Model for Fermion Masses and Mixings

Based on a few basic assumptions, a predictive supersymmetric grand unification $G_U=SO(10)\times {\mathrm{\Delta }}_{48}(SU(3))\times U(1)$ model is proposed. Thus, all the observed 45 chiral fermions with additional 3 right-handed neutrinos are unified into an irreducible triplet 16-dimensional spinor representation of $G_U$. Electroweak symmetry breaking naturally requires two Higgs doublets which belong to a single 10 representation of $SO(10)$. The model provides an unified description for all the Yukawa and gauge couplings. With a given structure of the physical vacuum, the fermion masses and mixings are predicted in terms of two basic parameters.