$M_W$, Dark Matter and $a_\mu$ in the NMSSM

International audience ; We study regions in the parameter space of the NMSSM which are able to simultaneously explain the current measured values for the $W$ mass $M_W$ and the muon anomalous magnetic moment $a_\mu$, and provide a dark matter relic density consistent with the observations as well as constraints from detection experiments. The corresponding regions feature light charginos, sleptons and staus in the 100-800~GeV range, at least some of them with masses below 150~GeV such that the electroweakly-interacting SUSY particles generate sufficiently large contributions to $M_W$. The LSP is always singlino-like with a mass below 140~GeV, and could possibly remain invisible even at future detection experiments. Decays of electroweak sparticles proceed through cascades via staus and/or sleptons which makes their detection challenging. We propose benchmark points for future searches of such sparticles. The lightest CP-even scalar may have a mass in the 95-98~GeV range with, however, modest signal rates in view of the mild excesses reported in this range at LEP and by CMS at the LHC.