Nucleon Decay as a Probe of Flavor Symmetry: The Case of Fake Unification

This paper explores nucleon decay within the framework of a "fake Grand Unified Theory (GUT)" combined with the Froggatt-Nielsen (FN) mechanism. In this fake GUT framework, quarks and leptons may have distinct high-energy origins but fit into complete $\mathrm{SU}(5)$ multiplets at low energies without requiring force unification, setting it apart from conventional GUTs. By introducing flavor symmetry through the FN mechanism, the model addresses the flavor puzzle of quark and lepton mass hierarchies and mixing patterns. Our analysis demonstrates that nucleon decay rates and branching fractions in the fake GUT are sensitive to flavor symmetry, providing a means to distinguish it from conventional GUT predictions. These findings underscore the importance of nucleon decay searches in probing both baryon number violation and the underlying flavor structure.