
We systematically analyze the d = 5 Weinberg operator at 2loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2loop models for which both, treelevel and 1loop contributions, are guaranteed to be absent. And (ii) finite 2loop diagrams, which correspond to the 1loop generation of some particular vertex appearing in a given 1loop neutrino mass model, thus being effectively 2loop. From the large list of all possible 2loop diagrams, the vast majority are infinite corrections to lower order neutrino mass models and only a moderately small number of diagrams fall into these two interesting classes. Moreover, all diagrams in class (i) are just variations of three basic diagrams, with examples discussed in the literature before. Similarly, we also show that class (ii) diagrams consists of only variations of these three plus two more basic diagrams. Finally, we show how our results can be consistently and readily used in order to construct twoloop neutrino mass models.
