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

Abstract

Based on a few basic assumptions, a predictive supersymmetric grand unification $G_U=SO(10)\times {\Delta }_{48}(SU(3))\times U(1)$ 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.

Comments: 9 pages, REVTeX, no figures, two tables i), The superpotentials in eqs. (2) and (3) are simplified and the corresponding notations are redefined below eq. (3); ii), one sentence in the paragraph below eq.(3) is extended to : `Once ..., the resulting Yukawa coupling matrices at the GUT scale will be automatically forced, due to the special features of ${\Delta }_{48}(SU(3))$, to an interesting texture structure with four non-zero textures `33', `32', `22' and `12' ...'. iii) "All other results and conclusions as well as predictions are unchanged!!!"