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, M(Dc), in minimal supersymmetric SU(5). The result for M(Dc) 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 M(Dc) and tau(p), within experimental limits on the inputs and a 1 TeV naturalness bound, we derive a strict bound alpha(3) > 0.117. We discuss how this bound will change as experimental limits improve. Measurements of alpha(3) from deep inelastic scattering and the charmonium spectrum are below the bound alpha(3) > 0.117 by more than 3 sigma. We briefly review several ideas of how to resolve the discrepancy between these low values of alpha(3) and the determinations of alpha(3) from LEP event shapes.