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We investigate neutrino mass generation scenarios where the lepton numberbreaking new physics couples only to the Standard Model (SM) right-handedcharged lepton chirality. The lowest-order lepton number violating effectiveoperator which describes this framework is a unique dimension nine operatorinvolving SM gauge fields, $\mathcal{O}_9$. We find that there are two possibleclasses of new physics scenarios giving rise to this $\mathcal{O}_9$ operator.In these scenarios neutrino masses are induced radiatively via dark matterinteractions, linking the dark matter to a natural explanation for thesmallness of neutrino masses compared to the electroweak scale. We discuss thephenomenology and existing constraints in the different neutrino mass modelswithin each class. In particular, we analyze the important interplay betweenneutrino mixing and neutrinoless double $\beta$-decay in order to predictcharacteristic signatures and disfavour certain scenarios.

Lepton number violating operators with standard model gauge fields: A survey of neutrino masses from 3-loops and their link to dark matter