Explaining the W boson mass anomaly and dark matter with a U(1) dark sector*

The $W$ boson mass recently reported by the CDF collaboration shows a deviation from standard model prediction with an excess at $7\sigma$ level. We investigate two simple extensions of extra $U(1)$ dark sector. One is $U(1)_x$ extension, where gauge field mixes through kinetic terms. other general $U(1)_{\mathbf{A} Y+\mathbf{B} q}$ extension model. Fitting various experimental constraints we find only mixing can enhance for most 10~MeV. While easily generate 77~MeV enhancement and also offer viable matter candidate ranging several hundred GeV to TeV, which may be detected future direct detection experiments improved sensitivities.