  Within the Exceptional Supersymmetric Standard Model (E6SSM), we investigate
striking signatures at the Large Hadron Collider (LHC) for a long-lived charged
inert higgsino, which is degenerate with the inert neutralino at tree level and
a mass splitting of order O(0.3) GeV is generated at the loop level, resulting
in a lifetime of order O(0.02) nanoseconds. We focus on the most sensitive
search for long-lived charged inert higgsino decays to the lightest neutral
inert higgsino Dark Matter (DM) and very soft charged leptons, which are
eventually stopped in the detector resulting in a disappearing-track signal.
Furthermore, we study the displaced vertex signature of the inert chargino in
the case where it is produced via the Z' portal. We illustrate how difficult it
is to construct displaced vertices in this class of models, though some
evidence of these could be gained at the High Luminosity LHC. Finally, we
compare the spin independent and spin dependent cross sections of the lightest
inert higgsino DM to those of current direct detection experiments, proving
that it is possible to gain sensitivity to the active DM component of this
scenario in the near future. The combination of these signatures with the one
emerging from Z' production and decay via Drell-Yan, which can be characterised
as belonging to the E6SSM via both the cross section and Forward-Backward
Asymmetry, could point uniquely to this non-minimal realisation of
supersymmetry. In fact, we remark that these evidences of the E6SSM can also be
correlated to the features of standard SUSY cascades in terms of the amount of
missing transverse energy present therein.
