Embedding A4 into SU(3) x U(1) flavor symmetry: large neutrino mixing and fermion mass hierarchy in the SO(10) GUT

We give an explanation of both the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Starting from an (SU(3) x U(1))(F) flavor symmetry and an SO(10) GUT, the main ingredient of our model is that two different breaking patterns of the flavor symmetry are at work. On the one hand, the dynamical breaking of (SU(3) x U(1))(F) flavor symmetry into (U(2) x Z(3))(F) explains why one family is much heavier than the others. On the other hand, an explicit symmetry breaking of SU( 3) F into a discrete flavor symmetry, A(4), leads to the observed tri-bimaximal mixing for the leptons. Naturalness of the charged fermion mass hierarchy appears as a consequence of the continuous SU(3) F symmetry. Moreover, the same discrete SO(10) x A(4) invariant operators are the root of the large lepton mixing, small Cabibbo angle and neutrino masses.