A combined approach to the analysis of space and ground experimental data within a simplified E${}_6$SSM

Within the Exceptional Supersymmetric Standard Model (E${}_6$SSM), we investigate 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 small mass splitting is generated at the loop level, resulting in a lifetime $O$(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 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${}^{\prime }$ portal. We illustrate how difficult it is to construct displaced vertices in this class of models, though some evidence 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${}^{\prime }$ production and decay via Drell-Yan, which can be characterised as belonging to the E${}_6$SSM via both the cross section and Forward-Backward Asymmetry, could point uniquely to this non-minimal realisation of Supersymmetry.