Abstract: We propose a “scotogenic” mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two-loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical Diraconthat induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhances sensitivities to spin-independent WIMP dark matter search below m(h)/2.

Abstract: By introducing three Higgs fields that are SU(2) doublets and a flavor permutational symmetry, S(3), in the theory, we extend the concepts of flavor and generations to the Higgs sector and formulate a Minimal S(3)-Invariant Extension of the Standard Model. The mass matrices of the neutrinos and charged leptons are re-parameterized in terms of their eigenvalues, then the neutrino mixing matrix, V(PMNS), is computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of neutrinos and charged leptons are obtained in excellent agreement with the latest experimental data. We also compute the branching ratios of some selected flavor-changing neutral current (FCNC) processes, as well as the contribution of the exchange of neutral flavor-changing scalars to the anomaly of the magnetic moment of the muon, as functions of the masses of charged leptons and the neutral Higgs bosons. We find that the S(3) x Z(2) flavor symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector, well below the present experimental bounds by many orders of magnitude. The contribution of FCNC's to the anomaly of the muon's magnetic moment is small, but not negligible.