Systematic U (1) B- L extensions of loop-induced neutrino mass models with dark matter

We study the gauged U(1)B-L extensions of the models for neutrino masses and dark matter. In this class of models, tiny neutrino masses are radiatively induced through the loop diagrams, while the origin of the dark matter stability is guaranteed by the remnant of the gauge symmetry. Depending on how the lepton number conservation is violated, these models are systematically classified. We present complete lists for the one-loop Z2 and the two-loop Z3 radiative seesaw models as examples of the classification. The anomaly cancellation conditions in these models are also discussed.