An SO(10) model with adjoint fermions for double seesaw neutrino masses

An SO(10) model where the 10H and 120H representations are used for generating fermion masses is quite predictive, though due to the absence of SU(2)L,R triplet/singlet fields it cannot give rise to neutrino masses through the usual type-I or type-II seesaw mechanisms. In this Letter, for neutrino masses, we propose an extension of such an SO(10) model by adding fermions in the adjoint representation (45F) and a symmetry breaking scalar 16¯H. The 16¯H couples the adjoint fermions to the standard fermions in 16F and induces neutrino masses through the 'double seesaw' mechanism. In addition, we impose (i) a parity symmetry leading to hermitian Yukawa Matrices and (ii) a μ-τ flavor symmetry on the Yukawa matrices for 10H and 16¯H whereas for the 120H it is assumed to be antisymmetric. Thus we consider the model SO(10)⊗Z2(μ−τ)⊗Z2P. We discuss the conditions that the mass matrices must obey so that the model can reproduce the tri-bimaximal mixing pattern.