Long-lived NLSP in the NMSSM

We analyze the scenario within the next to minimal supersymmetric Standard Model, where the lightest supersymmetric particle is singlinolike neutralino. By systematically considering various possible admixtures in the electroweakino sector, we classify regions of parameter space where the next to lightest supersymmetric particle is a long-lived electroweakino while remaining consistent with constraints from flavor physics, dark matter direct detection, and collider data. We identify viable cascade decay modes featuring the long-lived next to lightest supersymmetric particle for directly produced chargino-neutralino pairs, thus, leading to displaced vertex signatures at the high luminosity LHC (HL-LHC). We construct a track-based analysis in order to uncover such scenarios at the HL-LHC and analyze their discovery potential. We show that through such focused searches for the long-lived particles at the HL-LHC, one can probe regions of the electroweakino parameter space that are otherwise challenging.