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Dark matter searches in the mono-$Z$ channel at high energy $e^+e^-$ colliders

We explore the mono-$Z$ signature for dark matter searches at future high energy $e^+e^-$ colliders. In the context of effective field theory, we consider two kinds of contact operators describing dark matter interactions with electroweak gauge bosons and with electron/positron, respectively. For five benchmark models, we propose kinematic cuts to distinguish signals from backgrounds for both charged leptonic and hadronic decay modes of the $Z$ boson. We also present the experimental sensitivity to cutoff scales of effective operators and compare it with that of the Fermi-LAT indirect search and demonstrate the gains in significance for the several configurations of polarized beams.