Heavy gluino as the lightest supersymmetric particle

We consider the possibility that the lightest supersymmetric particle is a heavy gluino. After discussing models in which this is the case, we demonstrate that the \~{}g-LSP could evade cosmological and other constraints by virtue of having a very small relic density. We then consider how neutral and charged hadrons containing a gluino will behave in a detector, demonstrating that there is generally substantial apparent missing momentum associated with a produced \~{}g-LSP. We next investigate limits on the \~{}g-LSP deriving from CERN, LEP, LEP2 and run I Fermilab Tevatron experimental searches for excess events in the jets plus missing momentum channel and for stable heavily ionizing charged particles. The range of m \~{g} that can be excluded depends upon the path length of the \~{}g in the detector, the amount of energy it deposits in each hadronic collision, and the probability for the \~{}g to fragment to a pseudo-stable charged hadron after a given hadronic collision. We explore how the range of excluded m \~{g} depends upon these ingredients, concluding that for non-extreme cases the range 3GeVm \~{g}130--150GeV can be excluded at 95% C. L. based on currently available OPAL and CDF analyses. We find that run II at the Tevatron can extend the excluded region (or discover the \~{}g) up to m \~{g}160--180GeV. For completeness, we also analyze the case where the \~{}g is the NLSP (as possible in gauge-mediated supersymmetry breaking) decaying via \~{}g+gravitino. We find that the Tevatron run I data exclude m \~{g}<~240GeV. Finally, we discuss application of the procedures developed for the heavy \~{}g-LSP to searches for other stable strongly interacting particles, such as a stable heavy quark.