As any e$^+$e$^-$ scattering process can be accompanied by a hard photon emission from the initial state radiation, the analysis of the energy spectrum and angular distributions of those photons can be used to search for hard processes with an invisible final state. Thus high energy e$^+$e$^-$ colliders offer a unique possibility for the most general search of Dark matter based on the mono-photon signature. We consider production of DM particles via a mediator at the International Linear Collider (ILC) and Compact Linear Collider (CLIC) experiments taking into account detector effects within the DELPHES fast simulation framework. Limits on the light DM production in a generic model are set for a wide range of mediator masses and widths. For mediator masses up to the centre-of-mass energy of the collider, results from the mono-photon analysis are more stringent than the limits expected from direct resonance searches in Standard Model decay channels.
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