Dirac neutrinos, dark matter stability and flavour predictions from Lepton Quarticity

Abstract

We propose to relate dark matter stability to the possible Dirac nature of neutrinos. The idea is illustrated in a simple scheme where small Dirac neutrino masses arise from a type-I seesaw mechanism as a result of a $Z_4$ discrete lepton number symmetry. The latter implies the existence of a viable WIMP dark matter candidate, whose stability arises from the same symmetry which ensures the Diracness of neutrinos. The symmetry groups $\Delta_{27}$ and $A_4$ are then used to extract a rich variety of flavour predictions.