Singlet fermionic dark matter with dark Z

We present a fermionic dark matter model mediated by the hidden gauge boson. We assume the QED-like hidden sector which consists of a Dirac fermion and U(1)X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_X$$\end{document} gauge symmetry, and introduce an additional scalar electroweak doublet field with the U(1)X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_X$$\end{document} charge as a mediator. The hidden U(1)X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_X$$\end{document} symmetry is spontaneously broken by the electroweak symmetry breaking and there exists a massive extra neutral gauge boson in this model which is the mediator between the hidden and visible sectors. Due to the U(1)X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_X$$\end{document} charge, the additional scalar doublet does not couple to the Standard Model fermions, which leads to the Higgs sector of type I two Higgs doublet model. The new gauge boson couples to the Standard Model fermions with couplings proportional to those of the ordinary Z boson but very suppressed, thus we call it the dark Z boson. We study the phenomenology of the dark Z boson and the Higgs sector, and show the hidden fermion can be the dark matter candidate.