Mono-$\gamma$ Production of a Vector Dark Matter at Future $e^+e^-$ Collider

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.