Unification of gauge couplings in radiative neutrino mass models

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 representative classes of radiative neutrino mass models: (I) minimal ultraviolet completions of the dimension-7 ΔL = 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 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 admits gauge coupling unification. In class (III), none of the models leads to gauge coupling unification. Regarding the scale of unification, we find values between 1014 GeV and 1016 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 5·1010 − 5·1014 GeV.