The $SU(2{)}_D$ lepton portals for muon $g-2$, $W$ boson mass and dark matter

We propose a novel model which extends the Standard Model (SM) by introducing a $SU(2{)}_D$ gauge symmetry. In this model, a dark $SU(2{)}_D$ Higgs doublet and a Higgs bi-doublet can contribute to the muon $g-2$ anomaly and the $W$ boson mass, remaining in tune with the recent experimental results. At the same time, the isospin charged gauge boson of $SU(2{)}_D$ becomes a plausible candidate for Dark Matter(DM). We find that the resulting parameter space can fit the muon $g-2$, the $W$ boson mass and the DM constraints simultaneously.