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

Abstract: We propose a novel model for lepton flavor and dark matter based on the $SU(2)_D$ gauge symmetry and vector-like leptons in its fundamental representations. We introduce a dark $SU(2)_D$ Higgs doublet and a Higgs bi-doublet for the mass mixing between the vector-like lepton and the lepton. As a result, the seesaw lepton masses are generated and there are sizable one-loop contributions to the muon $g-2$ via the $SU(2)_D$ gauge bosons and the relatively heavy vector-like lepton, as indicated in Fermilab E989. The tree-level mass mixing between the $Z$ boson and the isospin neutral gauge boson of $SU(2)_D$ in our model accounts for the shift in the $W$ boson mass, being consistent with Tevatron CDFII. Finally, we show that the isospin charged gauge boson of $SU(2)_D$ becomes a plausible candidate for dark matter with a small mass splitting tied up to the modified $W$ boson mass, and there is a viable parameter space where the favored corrections to the muon $g-2$ and the $W$ boson mass and the dark matter constraints are simultaneously fulfilled.