Recipes and Ingredients for Neutrino Mass at Loop Level

The large hierarchy between the neutrino mass scale and that of the other fermions seems to be unnatural from a theoretical point of view. Various strategies have been devised in order to generate naturally small values of neutrino masses. One of these techniques is neutrino mass generation at the loop level which requires a mechanism, e.g., a symmetry, to forbid the lower order contributions. Here, we study in detail the conditions on this type of symmetries. We put special emphasis on the discrete Z_n symmetries as a simple example but our results can be also extended to more general groups. We find that regardless of the details of the symmetry, in certain cases the existence of a lower order contribution to neutrino masses can be determined by the topology of the diagrams with a given number of loops. We discuss the lepton flavor violating rare decays as well as (g-2)_\mu in this class of models, which generically appear at the one loop level. Typically the imposed symmetry has important implications for dark matter, with the possibility of stabilizing one or even multiple dark matter candidates.