Using gauge coupling unification and proton decay to test minimal supersymmetric SU (5)

We derive a one-loop expression, including all thresholds, for the mass of the proton decay mediating color triplets MDc, in minimal supersymmetric SU (5). The result for MDc does not depend on other heavy thresholds or extra representations with SU (5) invariant masses which might be added to the minimal model. We numerically correct our result to two-loop accuracy. Choosing inputs to maximize MDc and τP, within experimental limits on the inputs and a 1 TeV naturalness bound, we derive a strict bound α3 > 0.117. We discuss how this bound will change as experimental limits improve. Measurements of α3 from deep inelastic scattering and the charmonium spectrum are below the bound α3 > 0.117 by more than 3σ. We briefly review several ideas of how to resolve the discrepancy between these low values of α3 and the determinations of α3 from LEP event shapes.