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 mg̃ (and hence on the lightest neutralino mass mχ10≃mg̃/7 for a large class of gravity mediated supergravity unified models. One finds that for the minimal SU(5) model current data (Kamiokande) restricts mg̃≤400 GeV for a scalar soft breaking mass m0≤1 TeV. Expected future data from Super Kamiokande and ICARUS will be sensitive to the entire range of gluino mass for m0≤1 TeV, and be sensitive to the region mg̃≥500 GeV for m0≤5 TeV. Effects of quark mass textures are studied and one finds that the bound mg̃≤500 GeV holds when the experimental proton lifetime for the p→ν̄K+ mode becomes ≥5×1032 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 103.