Fermion multiplicities at the GUT scale: a statistical study of unification and proton decay

A bstract We study the impact of multiple vector-like fermions in SU(5) grand unified theory (GUT). Threshold effects from extra fermions allow the observed gauge couplings to be consistently matched to a single unified gauge coupling, and typically raise the unification scale to M GUT ≃ 10 15.5 GeV. Because the Standard Model fermions arise as admixtures of several GUT multiplets, the nucleon decay operator coefficients are further suppressed, leading to longer proton lifetimes than in conventional GUTs. We also find that the admixture of multiple GUT multiplets relaxes the rigid Yukawa relations of conventional GUTs and alleviates the bottom-tau unification problem. Overall, our analysis demonstrates that multi-fermion SU(5) GUTs provide a testable framework that simultaneously reconciles gauge coupling unification, realistic flavor structures, and proton stability. Our results highlight the importance of probing multiple proton-decay channels in next-generation experiments such as Hyper-Kamiokande to critically test this scenario.