Origin of neutrino masses at the LHC: Delta L = 2 effective operators and their ultraviolet completions

Neutrino masses and mixings can be generated in many different ways, with some of these scenarios featuring new physics at energy scales relevant for Large Hadron Collider searches. A systematic approach to constructing a large class of models for Majorana neutrinos may be founded upon a list of gauge-invariant effective operators – formed from quarks, leptons and the Higgs doublet – that violate lepton-number conservation by two units. By opening up these operators in all possible ways consistent with some minimality assumptions, a complete catalogue of a class of minimal radiative neutrino mass models may be produced. In this paper we present an analysis of Feynman diagram topologies relevant for the ultra-violet completions of these effective operators and collect these into a simple recipe that can be used to generate radiative neutrino mass models. Since high mass-dimension effective operators are suppressed by powers of the scale of new physics, many of the resulting models can be meaningfully tested at the Large Hadron Collider.