Systematic classification of two-loop realizations of the Weinberg operator

TL;DR

This paper systematically classifies two-loop realizations of the Weinberg operator, identifying key categories of neutrino mass models and providing a framework for constructing such models.

Contribution

It introduces a comprehensive diagrammatic classification of 2-loop neutrino mass models, highlighting the main classes and their basic diagram variations.

Findings

Most 2-loop diagrams are infinite corrections to lower order models.

Genuine 2-loop models are variations of three basic diagrams.

Finite 2-loop diagrams are variations of five basic diagrams.

Abstract

We systematically analyze the $d=5$ Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop contributions, are guaranteed to be absent. And (ii) finite 2-loop diagrams, which correspond to the 1-loop generation of some particular vertex appearing in a given 1-loop neutrino mass model, thus being effectively 2-loop. From the large list of all possible 2-loop 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 two-loop neutrino mass models.