Two-loop Z4 Dirac neutrino masses and mixing, with self-interacting dark matter

Abstract

Choosing how gauge U(1)χ breaks in the context of SO(10)→SU(5)×U(1)χ, Z4 lepton number may be obtained which maintains neutrinos as Dirac fermions. Choosing Δ(27) as the family symmetry of leptons, tree-level Dirac neutrino masses may be forbidden. Choosing a specific set of self-interacting dark-matter particles, Dirac neutrino masses and mixing may then be generated in two loops. This framework allows the realization of cobimaximal neutrino mixing, i.e. θ13≠0, θ23=π/4, δCP=±π/2, as well as the desirable feature that the light scalar mediator of dark-matter interactions decays only to neutrinos, thereby not disrupting the cosmic microwave background (CMB).