The existence of dark sectors, consisting of weakly-coupled particles that do not interact with the known Standard Model forces, is theoretically and phenomenologically motivated. The hidden particles are candidates for Dark Matter and can interact with photon through electric dipole moment (EDM) and magnetic dipole moment (MDM). We investigate the possibility a hidden sectors Dark Matter which is charged under a hidden $U(1)_X$ gauge symmetry can interact with photon at loop level. We evaluate the scattering cross section of hidden Dirac fermion with nuclei and set bounds for dipole moment. Using the results of the XENON1T experiment for direct detection of Dark Matter, we get bounds of electromagnetic dipole moment $(mu_chi)$ for mass $m_chi=100$ GeV : $ 1.93448 times 10^{-8}mu_B leq mu_chi leq 1.9496 times 10^{-8}mu_B$ and electric dipole moment $(d_chi): 3.3204 times 10^{-23}embox{.}cm leq d_chi leq 3.3464 times 10^{-23}embox{.}cm$. Using the condition of the existence of dipole moment we constraint the kinetic mixing parameter $ 3times 10^{-3} leq epsilon leq 10^{-2}$ and the mass of the hidden $U(1)_X$ gauge boson to be in the range of 5 GeV $leq m_X leq$ 9 GeV. Our results complement previous works and are within detection capability of LHC.
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