Pathways to Naturally Small Neutrino Masses

In the minimal standard electroweak gauge model, there is an effective dimension-five operator which generates neutrino masses, and it has only three tree-level realizations. One is the canonical seesaw mechanism with a right-handed neutrino. Another is having a heavy Higgs triplet as recently proposed. The third is to have a heavy Majorana fermion triplet, an example of which is presented here in the context of supersymmetric $\mathrm{SU}\left(5\right)$ grand unification. The three generic one-loop realizations of this operator are also discussed.