  In this paper we investigate the projected sensitivity to effective dark
matter (DM) - diboson interaction during the high luminosity $Z$-pole and 240
GeV runs at the proposed Circular Electron Positron Collider (CEPC). The
proposed runs at the 91.2 GeV $e^+e^-$ center of mass energy offers an
interesting opportunity to probe effective dark matter couplings to the $Z$
boson, which can be less stringently tested in non-collider searches. We
investigate the prospective sensitivity for dimension 6 and dimension 7
effective diboson operators to scalar and fermion dark matter. These diboson
operators can generate semi-visible $Z$ boson decay, and high missing
transverse momentum mono-photon signals that can be test efficiently at the
CEPC, with a small and controllable Standard Model $\gamma\bar{\nu}\nu$
background. A projected sensitivity for effective $\gamma Z$ coupling efficient
$\kappa_{\gamma Z}< (1030$ GeV$)^{-3}$, $(1970$ GeV$)^{-3}$ for scalar DM,
$\kappa_{\gamma Z}< (360$ GeV$)^{-3}$, $(540$ GeV$)^{-3}$ for fermion DM are
obtain for 25 fb$^{-1}$ and 2.5 ab$^{-1}$ $Z$-pole luminosities assuming the
optimal low dark matter mass range. In comparison the effective DM-diphoton
coupling sensitivity $\kappa_{\gamma \gamma}< (590$ GeV$)^{-3}$ for scalar DM,
$\kappa_{\gamma \gamma}< (360$ GeV$)^{-3}$ for fermion DM are also obtained for
a 5 ab$^{-1}$ 240 GeV Higgs run. We also compare the CEPC sensitivities to
current direct and indirect search limits on these effective DM-diboson
operators.
