Proposed Tests for Minimal SU(5) Supergravity at Fermilab, Gran Sasso, SuperKamiokande, and LEP

A series of predictions are worked out in order to put the minimal $SU(5)$ supergravity model under experimental test. Using the two-loop gauge coupling renormalization group equations, with the inclusion of supersymmetric threshold corrections, we calculate a new value for the proton decay rate in this model and find that SuperKamiokande and Gran Sasso should see the proton decay mode $p\to\bar\nu K^+$ for most of the allowed parameter space. A set of physically sensible assumptions and the cosmological requirement of a not too young Universe give us a rather restrictive set of allowed points in the parameter space, which characterizes this model. This set implies the existence of interesting correlations among various masses: either the lightest chargino and the next-to-lightest neutralino are below $\approx100\GeV$ (and therefore observable at the Tevatron) or the lightest Higgs boson is below $\approx50\GeV$ (and therefore observable at LEP I-II). These tests are crucial steps towards selecting the correct low-energy effective supergravity model. We also comment on the compatibility of the model with $\sin^2\theta_w(M_Z)$ measurements as a function of $\alpha_3(M_Z)$.