  Associated production of a dark particle and a photon, represented as a
mono-$\gamma$ event, is a promising channel to probe particle contents and
dynamics in the dark sector. In this paper we study properties of the
mono-$\gamma$ production of a vector dark matter at future $e^+e^-$ colliders.
The photon-like and Pauli operators, as well as triple gauge bosons
interactions involving the dark matter, are considered in the framework of
Effective Field Theory. We show that, comparing to the Pauli operator, the
triple gauge bosons couplings are much more interesting at high energy
collider. Beam polarization effects are also analyzed, and we show that the
experimental sensitivities can not be enhanced significantly because of the
smaller luminosity.
