Limits on SUSY particle Spectra from Proton Stability and Dark Matter Constraints

It is shown that the combined constraints on the amount of cold dark matter and of proton stability produce a stringent upper limit on the gluino mass $m_{\tilde g}$ (and hence on the lightest neutralino mass $m_{\chi_1^0}\simeq m_{\tilde g}/7$) for a large class of gravity mediated supergravity unified models. One finds that for the minimal SU(5) model current data (Kamiokande) restricts $m_{\tilde g}\leq 400$ GeV for a scalar soft breaking mass $m_0\leq 1$ TeV. Expected future data from Super Kamionkande and ICARUS will be sensitive to the entire range of gluino mass for $m_0\leq 1$ TeV, and be able to exclude the region $m_{\tilde g}\geq 500$ GeV for $m_0\leq 5$ TeV. Effects of quark mass textures are studied and one finds that the bound $m_{\tilde g}\leq 500$ GeV holds when the experimental proton lifetime for the $p\to \bar \nu K^+$ mode becomes $\geq 5\times 10^{32}$ yr.Implications of these results for a test of these models at the Tevatron and at the LHC are discussed. The effects of non-universal soft breaking in the Higgs and the third generation squark sectors are also examined, and it is found that the proton lifetime is sensitive to these non-universal effects. The current data already eliminates some regions of non-universalities. The constraints of proton stability on the direct detection of dark matter are seen to reduce the maximum event rates by as much as a factor of $10^3$.