Horizontal Symmetry for Quark and Squark Masses in Supersymmetric SU(5)

Recent interest in horizontal symmetry model building has been driven mainly by the large top mass and hence strong hierarchy in quark masses, and the possibility of appropriately constrained soft squark mass matrices, in place of an assumed universality condition, for satisfying the relevant FCNC constraints. Here we present the first successful SUSY-$SU(5)$ model that has such a feature. The horizontal symmetry is a gauged $(Q_{12} \times U(1))_H$ ($\subset (SU(2) \times U(1))_H$). All nonrenormalizable terms compatible with the symmetry are allowed in the mass matrices constructions. Charged lepton masses can also be accommodated.