NMSSM neutralino dark matter for $W$-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 anomalous magnetic moment ($g$-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, B-physics,
dark matter relic density and direct detection experiments, we find that a
neutralino in the mass range of $\sim 160-270$ GeV is a viable solution.
Moreover, the favored parameter region can be effectively probed by the ongoing
direct detection experiments like LZ, PandaX-4T and XENON-nT. The velocity
averaged annihilation cross section of the dark matter particles, however, is
suppressed.
