In the realm of natural supersymmetric models, higgsinos are typically the
lightest electroweakinos. In gauge-mediated supersymmetry breaking models, the
lightest higgsino-dominated particles decay into a Z-boson or a Higgs boson
(h), along with an ultra-light gravitino (G~) serving as the
lightest supersymmetric particle (LSP). This scenario suggests a significant
non-resonant hh production. Basing on the recent global fitting results of
the G~-EWMSSM (MSSM with light electroweakinos and an eV-scale
gravitino as the LSP) performed by the \textsf{GAMBIT} collaboration, which
support a higgsino-dominated electroweakino as light as 140 GeV, we develop two
simplified models to evaluate their detection potential at the high-luminosity
LHC (HL-LHC) with s​=14 TeV and an integrated luminosity of
3000 fb−1. The first model examines the processes where heavier
higgsino-dominated states decay into soft W/Z bosons, while the second
focuses on direct decays of all three higgsino-dominated electroweakinos into
W/Z/h plus a G~. Our study, incorporating both models and their
distinct decay channels, utilizes detailed Monte Carlo simulations for signals
and standard model backgrounds. We find that the HL-LHC can probe higgsinos up
to above 500 GeV, potentially discovering or excluding the natural SUSY
scenario in the context of a gravitino LSP. Further, we reinterpret this
discovery potential using the GAMBIT global fit samples, and find that the
entire parameter space of ∣μ∣≤500 GeV with an electroweak
fine-tuning measure (ΔEW​) under 100 in G~-EWMSSM is
accessible at the HL-LHC.Comment: 31 pages, 12 figures, and 6 table