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 mχ0 1 ≃ 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 Kamionkande and ICARUS will be sensitive to the entire range of gluino mass for m0 ≤ 1 TeV, and be able to exclude 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 × 10 yr. Implications of these results for a test of these models at the Tevatron and at the LHC are discussed. The effects of nonuniversal 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. Introduction: In this Letter we study the combined constraints of proton stability and supersymmetric dark matter on supergravity unified models with R-parity invariance. We consider models where gravity breaks supersymmetry in a hidden sector at scale ≥ MG (the GUT scale) with gravity as the messenger to the physical sector. Models with R parity invariance eliminate in a natural fashion dimension four operators responsible for rapid proton decay. However, as is well known one can have proton decay proceeding via dimension five operators[1, 2]. Simultaneously, with R parity invariance one finds that the lightest supersymmetric particle (LSP) is absolutely stable and further in supergravity unification[3, 4] the LSP is seen to be the