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.
I. INTRODUCTIONGrand-Unified-Theories (GUTs) are an attractive extension of the Standard Model (SM) and provide an elegant completion of the SU (3)×SU (2)×U (1) gauge group of the Standard Model (SM). The simplest model for Grand Unification, the original SU (5) 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. Among the most important of these are the inability to account for the observed charged fermion masses, the failure to achieve unification of the gauge couplings, rapid proton decay and the prediction of massless neutrinos. In order to address these issues extensions have been proposed which amend the model in various ways [2][3][4][5][6]. For a classic review of Grand Unified Theories see [7], a more recent overview of GUT phenomenology can be found in [8].One of the simplest extensions is a scalar 45-plet. The 45 contains an additional Standard-Model doublet, the interactions of which lead to additional contributions to the fermion masses and allow for the observed patters of the masses [2]. In addition it has been shown that this model also allows for unification at a scale high enough to suppress the proton decay rate below the observed upper limit from Super-Kamiokande [9]. Nevertheless, the problem that neutrinos are predicted to be massless is not solved in this model.Further extensions of the field content are therefore unavoidable. As is well known from analyses of minimal Standard Model extensions neutrino masses can be generated at tree-level by the type-I, II and III seesaw mechanism [10-16]. The required fields, i.e. complete SM-singlet fermions, scalar or fermionic SU (2) L triplets, can be embedded in SU (5) theories. However, it is also possible that the neutrino masses only arise at loop-level, see for example [17][18][19] for early work in this direction and [20] for a recent review of radiative neutrino mass models. Given that the minimal renormalizable SU (5)