Improved $(g-2)_\mu$ Measurements and Supersymmetry : Implications for $e^+e^-$ colliders

The persistent 3-4$\sigma$ discrepancy between the experimental result from BNL for the anomalous magnetic moment of the muon and its Standard Model (SM) prediction, was confirmed recently by the "MUON G-2" result from Fermilab. The combination of the two measurements yields a deviation of 4.2$\sigma$ from the SM value. Here, we review an analysis of the parameter space of the electroweak (EW) sector of the Minimal Supersymmetric Standard Model (MSSM), which can provide a suitable explanation of the anomaly while being in full agreement with other latest experimental data like the direct searches for EW particles at the LHC and dark matter (DM) relic density and direct detection constraints. Taking the lightest supersymmetric particle (LSP) (the lightest neutralino in our case) to be the DM candidate, we discuss the case of a mixed bino/wino LSP, which can account for the full DM relic density of the universe and that of wino and higgsino DM, where we take the relic density only as an upper bound. We observe that an upper limit of ~ 600 GeV can be obtained for the LSP and next-to (N)LSP masses establishing clear search targets for the future HL-LHC EW searches, but in particular for future high-energy $e^+e^-$ colliders, such as the ILC or CLIC.