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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 ($τ_p>1\times10^{32}\y$) and a small enough neutralino cosmological relic density ($Ω_χh^2_0\le1$). We find that the combined effect of these two constraints is quite severe, although still leaving a small region of parameter space with $m_{\tilde g,\tilde q}<1\TeV$. The allowed values of the proton lifetime extend up to $τ_p\approx1\times10^{33}\y$ and should be fully explored by the SuperKamiokande experiment. The proton lifetime cut also entails the following mass correlations and bounds: $m_h\lsim100\GeV$, $m_χ\approx{1\over2}m_{χ^0_2}\approx0.15\gluino$, $m_{χ^0_2}\approx m_{χ^+_1}$, and $m_χ<85\,(115)\GeV$, $m_{χ^0_2,χ^+_1}<165\,(225)\GeV$ for $α_3=0.113\,(0.120)$. Finally, the {\it combined} proton decay and cosmology constraints predict that if $m_h\gsim75\,(80)\GeV$ then $m_{χ^+_1}\lsim90\,(110)\GeV$ for $α_3=0.113\,(0.120)$. Thus, if this model is correct, at least one of these particles will likely be observed at LEPII.