Low energy SUSY confronted with new measurements of W-boson mass and muon g-2

The new CDF II measurement of $W$-boson mass shows a 7$\sigma$ deviation from the Standard Model (SM) prediction, while the recent FNAL measurement of the muon $g-2$ shows a 4.2$\sigma$ deviation (combined with the BNL result) from the SM. Both of them strongly indicate new physics beyond the SM. In this work we study the implication of both measurements on low energy supersymmetry. With an extensive exploration of the parameter space of the minimal supersymmetric standard model (MSSM), we find that in the parameter space allowed by current experimental constraints from colliders and dark matter detections, the MSSM can simultaneously explain both measurements on the edge of $2\sigma$ level, taking theoretical uncertainties into consideration. The favored parameter space, characterized by a compressed spectrum between bino, wino and stau, with the stop being around 1 TeV, may be covered in the near future LHC searches.