A class of inert N-tuplet models with radiative neutrino mass and dark matter

We present a class of models with radiative neutrino mass and stable dark-matter candidates. Neutrino mass is generated by a one-loop diagram with the same topography as Ma's 2006 proposal (which used an inert scalar-doublet and singlet fermion). We generalize this approach and determine all variants with new fields no larger than the adjoint representation. When the neutrino mass diagram contains a Majorana mass insertion there are two possibilities, both of which are known. If the mass insertion is of the Dirac type there are seven additional models, two of which are excluded by direct-detection experiments. The other five models are also constrained, such that only scalar dark-matter is viable. There are cases with an inert singlet, an inert doublet, and an inert triplet, providing a natural setting for inert N-tuplet models of dark matter, with the additional feature of achieving radiative neutrino mass. We show that some of the models admit a simple explanation for the (requisite) discrete symmetry, and briefly discuss cases with representations larger than the adjoint, which can admit a connection to the astrophysical gamma-ray signal.