Unification of Gauge Couplings in Radiative Neutrino Mass Models

TL;DR

This paper explores whether various radiative neutrino mass models can achieve gauge coupling unification, analyzing different classes of models through renormalization group calculations and identifying conditions and scales for unification.

Contribution

It systematically studies gauge coupling unification prospects in multiple radiative neutrino mass models, including dark matter extensions, using analytical and numerical RG analysis.

Findings

Gauge couplings unify in some models of class (I) especially with dark matter.

About 25% of models in class (II) admit unification.

Models in class (III) do not lead to unification.

Abstract

We investigate the possibility of gauge coupling unification in various radiative neutrino mass models, which generate neutrino masses at one- and/or two-loop level. Renormalization group running of gauge couplings is performed analytically and numerically at one- and two-loop order, respectively. We study three different classes of neutrino mass models: (I) minimal ultraviolet completions of the dimension-7 $\Delta L=2$ operators which generate neutrino masses at one- and/or two-loop level without and with dark matter candidates, (II) models with dark matter which lead to neutrino masses at one-loop level and (III) models with particles in the adjoint representation of $\mathrm{SU}(3)$. In class (I), gauge couplings unify in a few models and adding dark matter amplifies the chances for unification. In class (II), about a quarter of the models admit gauge coupling unification. In class (III), none of the models leads to gauge coupling unification. Regarding the scale of unification, we find values between $10^{14}$ GeV and $10^{16}$ GeV for models belonging to class (I) without dark matter, whereas models in class (I) with dark matter as well as models of class (II) prefer values in the range $5 \cdot 10^{10}-5 \cdot 10^{14}$ GeV.