How many 1-loop neutrino mass models are there?

TL;DR

This paper systematically counts and classifies 1-loop neutrino mass models at dimension five, identifying over 700 phenomenologically viable models with different features, and analyzes their gauge coupling evolution.

Contribution

It provides the first comprehensive enumeration of 1-loop neutrino mass models, including dark matter and decay-exit classes, and studies their gauge coupling unification properties.

Findings

Over 700 models identified across two classes.

Many models lead to low-energy Landau poles.

One model achieves gauge coupling unification above 10^{15} GeV.

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 (113+205) models, while in the exit class we find (38+368) models. Here, 113 is the number of DM models, which require a stabilizing symmetry, while 205 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 $10^{15}$ GeV in a numerically acceptable way.