Testing electroweak SUSY for muon $g-2$ and dark matter at the LHC and beyond

Given that the LHC experiment has produced strong constraints on the colored supersymmetric particles (sparticles), testing the electroweak supersymmetry (EWSUSY) will be the next crucial task at the LHC. On the other hand, the light electroweakinos and sleptons in the EWSUSY can also contribute to the dark matter (DM) and low energy lepton observables. The precision measurements of them will provide the indirect evidence of SUSY. In this work, we confront the EWSUSY with the muon $g-2$ anomaly, the DM relic density, the direct detection limits and the latest LHC Run-2 data. We find that the sneutrino DM or the neutralino DM with sizable higgsino component has been excluded by the direct detections. Then two viable scenarios are pinned down: one has the light compressed bino and sleptons but heavy higgsinos, and the other has the light compressed bino, winos and sleptons. In the former case, the LSP and slepton masses have to be smaller than about 350 GeV. While in the latter case, the LSP and slepton masses have to be smaller than about 700 GeV and 800 GeV, respectively. From investigating the observability of these sparticles in both scenarios at future colliders, it turns out that the HE-LHC with a luminosity of 15 ab$^{-1}$ can exclude the whole BHL and most part of BWL scenarios at $2\sigma$ level. The precision measurement of the Higgs couplings at the lepton colliders could play a complementary role of probing the BWL scenario.