Singlet scalar Dark Matter in Dark Two Higgs Doublet Model

We consider the case of the Dark Two Higgs Doublet Model (D2HDM) where a $U(1{)}^{\mathrm{\prime }}$ symmetry group and an extra Higgs doublet are added to the Standard Model. This model leads to a gauge singlet particle as an interesting Dark Matter (DM) candidate. We obtain phenomenological constraints to the parameter space of the model considering the one necessary to produce the correct density of thermal relic dark matter $\mathrm{\Omega }{h}^2$. We find a relation between the masses of the DM matter candidate $m_S$ and $m_{Z^{\mathrm{\prime }}}$ that satisfy the relic density for given values of $\tan \beta$.