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 (${\tau }_p>1\mathrm{}\times {10}^{32}$ yr) and a small enough neutralino cosmological relic density (${\Omega }_{\chi }{h}_0^2\le 1$). We find that the combined effect of these two constraints is quite severe, although still leaving a small region of parameter space with $m_{\tilde{g},\tilde{q}}<1\mathrm{}$ TeV. The allowed values of the proton lifetime extend up to ${\tau }_p\approx 1\times {10}^{33}$ yr and should be fully explored by the SuperKamiokande experiment. The proton lifetime cut also entails the following mass correlations and bounds: $m_h\lesssim 110$ GeV, $m_{\chi }\approx \frac{1}{2}{m}_{{\chi }_2^0}\approx 0.15m_{\tilde{g}}$, $m_{{\chi }_2^0}\approx m_{{\chi }_1^{+}}$, and $m_{\chi }<85\mathrm{}\left(115\right)\mathrm{}$ GeV, $m_{{\chi }_2^0,{\chi }_1^{+}}<165\mathrm{} \mathrm{}\left(225\right)\mathrm{}$ GeV for ${\alpha }_3=0.113\mathrm{} \mathrm{}\left(0.120\right)\mathrm{}$. Finally, the combined proton decay and cosmology constraints predict that if $m_h\gtrsim 75\mathrm{}\left(80\right)\mathrm{}$ GeV then $m_{{\chi }_1^{+}}\lesssim 90\mathrm{}\left(110\right)\mathrm{}$ GeV for ${\alpha }_3=0.113\mathrm{}\mathrm{}\left(0.120\right)\mathrm{}$. Thus, if this model is correct, at least one of these particles will likely be observed at the CERN $e^{+}{e}^{-}$ collider LEP II.