A model with isospin doublet $U(1)_D$ gauge symmetry

We propose a model with an extra isospin doublet $U(1)_D$ gauge symmetry, in which we introduce several extra fermions with odd parity under a discrete $Z_2$ symmetry in order to cancel the gauge anomalies out. A remarkable issue is that we impose nonzero $U(1)_D$ charge to the standard model Higgs, and it gives the most stringent constraint to the vacuum expectation value of a scalar field breaking the $U(1)_D$ symmetry that are severer than the LEP bound. We then explore relic density of a Majorana dark matter candidate without conflict of constraints from lepton flavor violating processes. A global analysis is carried out to search for parameters which can accommodate with observed data.