How many 1-loop neutrino mass models are there?

Abstract

It is well-known that at tree-level the d = 5 Weinberg operator can be generated in exactly three different ways, the famous seesaw models. In this paper we study the related question of how many phenomenologically consistent 1-loop models one can construct at d=5. First, we discuss that there are two possible classes of 1-loop neutrino mass models, that allow avoiding stable charged relics: (i) models with dark matter candidates and (ii) models with “exits”. Here, we define “exits” as particles that can decay into standard model fields. Considering 1-loop models with new scalars and fermions, we find in the dark matter class a total of (115+203) models, while in the exit class we find (38+368) models. Here, 115 is the number of DM models, which require a stabilizing symmetry, while 203 is the number of models which contain a dark matter candidate, which maybe accidentally stable. In the exit class the 38 refers to models, for which one (or two) of the internal particles in the loop is a SM field, while the 368 models contain only fields beyond the SM (BSM) in the neutrino mass diagram. We then study the RGE evolution of the gauge couplings in all our 1-loop models. Many of the models in our list lead to Landau poles in some gauge coupling at rather low energies and there is exactly one model which unifies the gauge couplings at energies above 1015 GeV in a numerically acceptable way.

Three-loop inverse scotogenic seesaw models

“…[1] for a review and refs. [2,3] for comprehensive studies of one-and two-loop radiative neutrino mass models. Two-loop neutrino mass models have been proposed in the literature [4][5][6][7][8][9][10][11][12] to provide a more natural explanation for the tiny active neutrino masses than those based on the one-loop radiative seesaw.…”

Mapping the SMEFT to discoverable models

“…For example, one may want to argue that any interesting BSM extension should maintain the perturbativity of the gauge couplings up to some large energy scale, say for example the grand unification scale, m G or even the Planck scale. See for example [38] for a recent discussion on how this argument limits the number of viable models in the case of the Weinberg operator. In this paper, we do not use such theoretical arguments.…”