$(g-2)_\mu$ and SUSY Dark Matter: Direct Detection and Collider Search Complementarity

The electroweak (EW) sector of the Minimal Supersymmetric Standard Model (MSSM) can account for variety of experimental data. The EW particles with masses of a few hundred GeV evade the LHC searches owing to their small production cross sections. Such a light EW sector can in particular explain the reinforced $4.2\,\sigma$ discrepancy between the experimental result for the anomalous magnetic moment of the muon, \gmin2, and its Standard Model (SM) prediction. The lightest supersymmetric particle (LSP), assumed to be the lightest neutralino, $\tilde{\chi}_1^0$, as a Dark Matter (DM) candidate is furthermore in agreement with the observed limits on the DM content of the universe. Here the Next-to LSP (NLSP) serves as a coannihilation partner and is naturally close in mass to the LSP. Such scenarios are also to a large extent in agreement with negative results from Direct Detection (DD) experiments. The DM relic density can fully be explained by a nearly pure bino or a mixed bino/wino LSP. Relatively light wino and higgsino DM, on the other hand, remains easily below the DM relic density upper bound. Using the improved limits on $(g-2)_\mu$, we explore the mass ranges of the LSP and the NLSP in their correlation with the DM relic density for bino, bino/wino, wino and higgsino DM. In particular analyze the sensitivity of future DM DD experiments to these DM scenarios. We find that higgsino, wino and one type of bino scenario can be covered by future DD experiments. Mixed bino/wino and another type of bino DM can reach DD cross sections below the neutrino floor. In these cases we analyze the complementarity with the (HL-)LHC and future $e^+e^-$ linear colliders. We find that while the prospects for the HL-LHC are interesting, but not conclusive, an $e^+e^-$ collider with $\sqrt{s} \le 1$ TeV can cover effectively all points of the MSSM that may be missed by DD experiments.