Systematic classification of two-loop realizations of the Weinberg operator

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.

General parametrization of Majorana neutrino mass models

“…Unsurprisingly, at loop level there are actually more variations with this type of "asymmetric" diagrams, i.e. y 1 = y 2 , than variations with "symmetric" diagrams (where the field coupling to the two neutrinos is necessarily the same) as can be seen, for example, in the tables of [15,18] or the list of diagrams at d=7 1-loop in [53].…”

“…At 2-loop level we mention two different colored versions of the Babu-Zee topology [16,17]. A general decomposition for all 2-loop models was presented in [18]. At three-loop order there are the KNT [19], AKS [20] and cocktail models [21].…”

Two-loop snail diagrams: relating neutrino masses to dark matter

“…2 Comments on two-loop neutrino masses: crab and snail diagrams Two-loop diagrams contributing to neutrino masses have been systematically discussed in [2,4]. Based on the topologies of the two-loop diagrams, they can be classified in two groups: (1) Diagrams with a one-loop sub-diagram that can be considered as a correction to one of the internal lines.…”

“…In recent years, models in which neutrinos acquire their masses at loop level have received considerable attention (see ref. [1][2][3][4] for a model-independent analysis; see also [5][6][7][8][9][10][11][12][13]). Within these models, the smallness of neutrino masses can be understood (at least partially) by loop suppression.…”

Lepton number violating phenomenology of d = 7 neutrino mass models

“…(For a recent review on theoretical aspects of neutrino masses see [6].) This suppression could be due to loop factors [7,8], or neutrino masses could be generated by higher order operators [9,10], or both. In this paper, we will study the phenomenology of a particular class of models, namely d = 7 1-loop models [11].…”