Paths to proton stability in grand unification

Abstract

We explore scenarios within grand unification in which proton decay can be suppressed and possibly eliminated due to novel embeddings of the Standard Model matter fields into irreducible representations of the grand unified group and residual symmetries. The scenarios are based on an $SU(7)$ gauge group, in which the matter fields are embedded within an anomaly-free set of fields that can be realized as a natural subgroup of the fundamental spinor representation of an $SO(14)$ gauge symmetry. Depending on the embedding, proton decay can either be forbidden at tree level and generated via one-loop diagrams, or the proton can be made stable by forcing it to decay channels that must have an even number of leptons, independently of the bosonic content of the theory. We describe the theoretical and phenomenological implications of such scenarios, including their implications for dark matter and neutrino masses.