The flavor problem and discrete symmetries

In this letter we propose a multi-Higgs extension of the standard model with Abelian and non-Abelian discrete symmetries in which the mass matrices of the charged fermions obtained from renormalizable interactions are diagonal. Corrections induced by non-renormalizable interactions deviate these matrices from the diagonal form. Active neutrinos acquire mass only from non-renormalizable interactions. The main entries of the neutrino mass matrix arise only through dimension five operators, while the diagonal entries arise only from dimension six operators.