Abstract
Minimal $SU(5)$ Grand Unified models predict massless neutrinos and struggle to achieve gauge coupling unification compatible with the observed lower limit on the proton lifetime. Both of these issues can be resolved by embedding minimal radiative neutrino mass models into $SU(5)$. We systematically analyze the possible ways to realize radiative neutrino mass generation in $SU(5)$ and provide a list of the minimal models. We find various models that have not been considered in the literature and demonstrate the compatibility of radiative neutrino masses with gauge coupling unification and proton decay for a new class of models with vector-like fermions.
Highlights
Grand unified theories (GUTs) are an attractive extension of the Standard Model (SM) and provide an elegant completion of the SUð3Þ × SUð2Þ × Uð1Þ gauge group of the SM
The simplest model for grand unification, the original SUð5Þ model proposed by Georgi and Glashow [1], is known to exhibit a number of issues that seem to prevent a successful description of the world we observe
It has been shown [9] that unification at a scale high enough to suppress the proton decay rate below the observed upper limit from Super-Kamiokande [10] is correlated with a light color octet that is excluded by LHC searches [11]
Summary
Grand unified theories (GUTs) are an attractive extension of the Standard Model (SM) and provide an elegant completion of the SUð3Þ × SUð2Þ × Uð1Þ gauge group of the SM. Given that the minimal renormalizable SUð5Þ does not contain the fields required for tree-level neutrino masses there is no preference for extensions that allow for seesaw scenarios over those with radiative mass generation. The embedding of radiative neutrino masses into GUTs in general and minimal renormalizable SUð5Þ [MRSUð5Þ] in particular is not a completely new question; see [24] for an example of a SUð5Þ-symmetric realization of the Zee model or [25] for a two-loop neutrino mass model.
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