  We investigate the sensitivity at current and future hadron colliders to a
heavy electrically-charged particle with a proper decay length below a
centimetre, whose decay products are invisible due to below-threshold energies
and/or small couplings to the Standard Model. A cosmologically-motivated
example of a framework that contains such a particle is the Minimal
Supersymmetric Standard Model in the limit of pure Higgsinos. The current
hadron-collider search strategy has no sensitivity to the upper range of pure
Higgsino masses that are consistent with the thermal relic density, even at a
future collider with 100 TeV centre-of-mass energy. We show that performing a
disappearing track search within the inner 10 cm of detector volume would
improve the reach in lifetime by a factor of 3 at the 14 TeV LHC and a further
factor of 5 at a 100 TeV collider, resulting in around 10 events for 1.1 TeV
thermal Higgsinos. In order to include the particles with the largest boost in
the analysis, we furthermore propose a purely track-based search in both the
central and forward regions, each of which would increase the number of events
by another factor of 5, improving our reach at small lifetimes. This would
allow us to definitively discover or exclude the experimentally-elusive
pure-Higgsino thermal relic at a 100 TeV collider.
