Limits on photino and squark masses from proton lifetime in supergravity models

It is shown that the current experimental lower limit on the proton lifetime via p→ν¯$K^{+}$ puts severe constraints on the photino and squark masses in supersymmetric unification. For Higgs-triplet masses ≲${10}^{16}$ GeV (as required to maintain the gauge hierarchy in supergravity models) the Kamioka data imply that squarks would be so heavy as not to be observable at the Fermilab Tevatron (and probably not observable even at the Superconducting Super Collider) for photinos heavier than ∼10 GeV. (W-ino and gluino signals would then still be possible signals of supersymmetry.) For very light photinos, a region of squark mass accessible to the Tevatron is still possible, due to an ‘‘accidental’’ cancellation of the low-lying and high-lying W-ino contribution to the decay amplitude.