NMSSM neutralino dark matter for CDF II $W$-boson mass and muon $g-2$ and the promising prospect of direct detection

Two experiments from the Fermilab, E989 and CDF II, have reported two anomalies for muon $g-2$ and $W$-boson mass that may indicate the new physics at the low energy scale. Here we examine the possibility of a common origin of these two anomalies in the Next-to-Minimal Supersymmetric Standard Model. Considering various experimental and astrophysical constraints such as the Higgs mass, collider data, flavor physics, dark matter relic density, and direct detection experiments, we find that lighter electroweakinos and sleptons can generate sufficient contributions to muon $g-2$ and $m_W$. Moreover, the corresponding bino-like neutralino dark matter mass is in the $\sim 180-280$ GeV range. Interestingly, the favored DM mass region can soon be entirely probed by ongoing direct detection experiments like PandaX-4T, XENONnT, LUX-ZEPLIN, and DARWIN.