  When dark matter candidate and its parent particles are nearly degenerate, it
would be difficult to probe them at the Large Hadron Collider directly. We
propose to explore their quantum loop effects at the CEPC through the golden
channel process $e^+e^-\to \mu^+\mu^-$. We use a renormalizable toy model
consisting of a new scalar and a fermion to describe new physics beyond the
Standard Model. The new scalar and fermion are general multiplets of the
$SU(2)_L\times U(1)_Y$ symmetry, and couple to the muon lepton through Yukawa
interaction. We calculate their loop contributions to anomalous
$\gamma\mu^+\mu^-$ and $Z\mu^+\mu^-$ couplings which can be applied to many new
physics models. The prospects of their effects at the CEPC are also examined
assuming a 0.002 accuracy in the cross section measurement.
