Gaugino physics of split supersymmetry spectrum at the LHC and future proton colliders

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Discovery of the Higgs boson and lack of discovery of superpartners in the first run at LHC are both predictions of split supersymmetry with thermal dark matter. We discuss what it would take to find gluinos at hadron supercolliders, including the LHC at 14 TeV center of mass energy, and future pp colliders at 100 TeV and 200 TeV. We generalize the discussion by re-expressing the search capacity in terms of gluino to lightest superpartner mass ratio, and apply results to other scenarios, such as gauge mediation and mirage mediation. In those models, distinctive gaugino mass ratios arise at leading order, but can be significantly modified by large logarithmic quantum corrections from split spectrum.