Hunting ewinos and a light scalar of $Z_3$-NMSSM with a bino-like dark matter in top squark decays at the LHC

We study the prospects of a simultaneous hunt at the Large Hadron Collider (LHC) of relatively light electroweakinos and a singlet-like scalar of the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model ($Z_3$-NMSSM) in the cascade decays of not so heavy ($\lesssim 1.5$ TeV) top squarks that are produced in pairs at the LHC which characteristically involve the singlet-like states. We work in a scenario where the lightest (next-to-lightest) SUSY particle is bino (singlino)-like with a mass below 100 GeV ($\gtrsim 100$ GeV), whereas a pair of immediately heavier neutralinos and the lighter chargino are higgsino-like with masses in the range $\sim 500$ GeV -- 1 TeV. Further, the singlet-like scalar present in the spectrum provides a funnel for a rapid enough mutual annihilation of the LSP thus making the latter meet the experimental upper bound on its relic abundance. The scenario is motivated by its ability to offer a bino-like dark matter with such a mass unlike what is now disfavored in the MSSM while avoiding the stringent lower bounds from the LHC experiments on the masses of these involved particles and still remaining reasonably `natural'. We find that while a usual cut-based analysis (CBA) on LHC data worth 300 $\text{fb}^{-1}$ would be unable to discover such excitations, a multivariate analysis (MVA) can be reasonably sensitive to higgsino-like electroweakinos having masses $\gtrsim 650$ GeV when the lighter top squark has a mass $\gtrsim 1$ TeV. On the other hand, with 3000 $\text{fb}^{-1}$ of data these masses become accessible in a CBA while even an MVA on such a data set is unlikely to find these electroweakinos with masses around 1 TeV when the mass of the lighter top squark hits $\sim 1.5$ TeV.