CP Violation from Flavor Symmetry in a Lepton Quarticity Dark Matter Model

Abstract

We propose a simple $\Delta (27) \otimes Z_4$ model where neutrinos are predicted to be Dirac fermions. The smallness of their masses follows from a type-I seesaw mechanism and the leptonic CP violating phase correlates with the pattern of $\Delta (27)$ flavor symmetry breaking. The scheme naturally harbors a WIMP dark matter candidate associated to the Dirac nature of neutrinos, in that the same $Z_4$ lepton number symmetry also ensures dark matter stability.