Fermion Masses and Mixings in a Minimal SO(10)X A_4 SUSY GUT

A SUSY SO(10) $\times A_4$ GUT model is constructed for fermion masses and mixing by introducing a minimal set of low dimensional Higgs representations needed to break the guage symmetry down to $SU(3{)}_c\times U(1{)}_{em}$. The hierarchy of fermion masses can be understood in the framework of $A_4$ symmetry. From the $A_4$-invariant superpotential, the “double lopsided” mass matrices for the charged leptons and the down quarks are obtained. It is shown that this structure leads to bi-large neutrino mixings simultaneously with small CKM mixing angles. An excellent fit to the masses and mixings of the quarks and leptons as well as to CP violation parameter is obtained. Moreover, the model predicts the neutrino mixing angle $\sin {\theta }_{13}\approx 0.15$.