Fermion masses and mixings in a renormalizable SO(10)×Z2 GUT

We investigate a scenario in a supersymmetric SO(10) Grand Unified Theory in which the fermion mass matrices are generated by renormalizable Yukawa couplings of the 10⊕120⊕126¯ representation of scalars. We reduce the number of parameters by assuming spontaneous CP violation and a Z2 family symmetry, leading to nine real Yukawa coupling constants for three families. Since in the “minimal SUSY SO(10) GUT” an intermediate seesaw scale is ruled out and our scenario lives in the natural extension of this theory by the 120, we identify the vacuum expectation value (VEV) wR of (10,1,3)∈126¯ with the GUT scale of 2×1016GeV. In order to obtain sufficiently large neutrino masses, the coupling matrix of the scalar 126¯ is necessarily small and we neglect type II seesaw contributions to the light-neutrino mass matrix. We perform a numerical analysis of this 21-parameter scenario and find an excellent fit to experimentally known fermion masses and mixings. We discuss the properties of our numerical solution, including a consistency check for the VEVs of the Higgs-doublet components in the SO(10) scalar multiplets.