The 3-3-1 model with A4 flavor symmetry

We argue that the A4 symmetry as required by three flavors of fermions may well-embed in the SU(3)C x SU(3)L x U(1)X gauge model. The new neutral fermion singlets as introduced in a canonical seesaw mechanism can be combined with the standard model lepton doublets to perform SU(3)L triplets. Various leptoscalar multiplets such as singlets, doublets, and triplets as played in the models of A4 are unified in single SU(3)L antisextets. As a result, naturally light neutrinos with various kinds of mass hierarchies are obtained as a combination of type I and type II seesaw contributions. The observed neutrino mixing pattern in terms of the Harrison-Perkins-Scott proposal is obtained by enforcing the A4 group. The quark masses and Cabibbo-Kobayashi-Maskawa mixing matrix are also discussed. By virtue of very heavy antisextets, the nature of the vacuum alignments of scalar fields can be given.