Lepton specific two-Higgs-doublet model based on a $U(1)_X$ gauge symmetry with dark matter

We discuss a two Higgs doublet model with extra $U(1)_X$ gauge symmetry where lepton specific (type-X) structure for Yukawa interactions is realized by charge assignment of fields under the $U(1)_X$. Extra charged leptons are introduced to cancel gauge anomaly associated with extra gauge symmetry. In addition, we introduce scalar fields as dark matter candidates to which we assign $Z_2$ odd parity for guaranteeing stability of them. We then analyze phenomenology of the model such as scalar potential, muon anomalous magnetic dipole moment, collider physics associated with $Z'$ boson from $U(1)_X$, and dark matter physics. Carrying out numerical analysis we search for phenomenologically viable parameter region.