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We propose an extension of the Standard Model (SM) for radiative neutrinomass by introducing a dark $U(1)_D$ gauge symmetry. The kinetic mixing betweenthe SM gauges and the dark $U(1)_D$ gauge arises at 1-loop mediated by newinert scalar fields. We show that the tiny neutrino mass and dark mattercandidates are naturally accommodated. Motivated by the recent measurement of$(g-2)_{\mu}$ indicating $4.2~ \sigma$ deviation from the SM prediction, weexamine how the deviation $\Delta a_{\mu}$ can be explained in this model.

Neutrino mass and $(g-2)_{\mu}$ with dark $U(1)_D$ symmetry