Realizing tri-bimaximal mixing in minimal seesaw model with S4 family symmetry

In this Letter, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group S4 as the family symmetry. In order to constrain the form of superpotential, a Z3 symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of O(0.01) at NLO. The mechanism to get the particular scalar VEV alignments used is also presented. Phenomenologically, the mass spectrum is of normal hierarchy with m₁=0, and ∑mi and |mee| are about 0.058 eV and 0.003 eV respectively.