The LHC sensitivity to weak gauginos in light of the latest muon $g-2$ and dark matter results

Among the electroweakinos, the weak gauginos have the largest production rate at the LHC and should therefore be the primary focus of searches. In this work, we examine the LHC sensitivity to weak gauginos in light of the latest constraints from the muon $g-2$ anomaly and dark matter (DM) observations. To simultaneously account for the observed $5\sigma$ deviation in muon $g-2$ and the correct DM relic abundance, the DM candidate in the MSSM must be bino-like: wino- or higgsino-like neutralinos require TeV-scale masses to avoid underabundance, rendering the electroweakino spectrum too heavy to yield a sizable $g-2$ contribution. Moreover, tight direct detection limits disfavor light higgsinos, which can induce sizable DM-nucleon scattering via bino-higgsino mixing. We thus focus on scenarios with a bino-like LSP and relatively heavy higgsinos. Two classes of wino spectra are considered: a light-wino scenario (LWo) with $m_{\tilde{W}} \lesssim 1$~TeV, and a heavy-wino scenario (HWo) with $m_{\tilde{W}} \gtrsim 1$~TeV. For each, we delineate the viable parameter space under current constraints and assess the discovery potential at future LHC stages. We find that while the high-luminosity LHC (HL-LHC) can probe a portion of the parameter space, the high-energy 27~TeV LHC (HE-LHC) is capable of covering most of it.