The Light, the Heavy and the Superheavy --- a Nonabelian Flavor Symmetry for the Full Hierarchy

We give a preliminary report of a new quark mass matrix model basing on a $SU(5)\otimes SU(5)\otimes Q_{12}$ symmetry embedding into a fully gauged $SU(5)\otimes SU(5)\otimes SU(2)$.~\cite{fk} The two $SU(5)$'s contain the standard SUSY $SU(5)$ as a diagonal subgroup, while the $Q_{12}$ or $SU(2)$ is horizontal. Starting by assuming a judiciously-chosen set of chiral supermultiplets, and a pattern of spontaneous symmetry breaking, we obtain the low-energy chiral fermions together with a spectrum of superheavy fermions at two different scales. The latter mediate Froggatt-Nielsen tree graphs that give rise to a phenomenologically viable effective quark mass matrix texture. The model is the first example of a nontrivial combination of supersymmetry without R-parity, gauged nonabelian horizontal symmetry and unification/anti-unification. It is expected to have some very interesting features in SUSY-GUT phenomenology.