Proton decay and cosmology strongly constrain the minimal SU(5) supergravity model

We present the results of an extensive exploration of the five-dimensional parameter space of the minimal SU(5) supergravity model, including the constraints of a long enough proton lifetime (τₚ>1×10³² yr) and a small enough neutralino cosmological relic density (Ω_χh₀²≤1). We find that the combined effect of these two constraints is quite severe, although still leaving a small region of parameter space with m_ ̃ \~g, ̃ \~q<1 TeV. The allowed values of the proton lifetime extend up to τₚ≈1×10³³ yr and should be fully explored by the SuperKamiokande experiment. The proton lifetime cut also entails the following mass correlations and bounds: mₕ110 GeV, m_χ≈1/2m_χ₂⁰≈0.15m_ ̃ \~g, m_χ₂⁰≈m_χ₁⁺, and m_χ<85(115) GeV, m_χ₂⁰,χ₁⁺<165 (225) GeV for α₃=0.113 (0.120). Finally, the combined proton decay and cosmology constraints predict that if mₕ75(80) GeV then m_χ₁⁺90(110) GeV for α₃=0.113(0.120). Thus, if this model is correct, at least one of these particles will likely be observed at the CERN e⁺e^- collider LEP II.