  It has been widely known that bino-like dark matter in supersymmetric
theories suffers from over-production. The situation can be improved if the
gluino or wino has a mass of O(10) GeV heavier than the bino, sufficiently
reducing the bino abundance through co-annihilation. In this scenario, the
gluino decays to the bino via squark exchange, and the wino decays to the bino
via higgsino exchange. In split SUSY models favoured after the Higgs discovery,
the intermediate particles in these decays would be much heavier than gauginos,
suppressing the decay of the gluino and wino. This, in addition to the small
mass differences, results in long lifetimes for the gluino and wino. We show
that searches performed at the LHC for long-lived particles with displaced
vertices offer a powerful method to test this scenario.
