The paper contains description of the main properties of the galactic dark matter (DM) particles, available approaches for detection of DM, main features of direct DM detection, ways to estimate prospects for the DM detection, the first collider search for a DM candidate within an Effective Field Theory, complete review of ATLAS results of the DM candidate search with LHC RUN I, and less complete review of exotic dark particle searches with other accelerators and not only. From these considerations it follows that one is unable to prove, especially model-independently,a discovery of a DM particle with an accelerator, or collider. One can only obtain evidence on existence of a weakly interacting neutral particle, which could be, or could not be the DM candidate. The current LHC DM search program uses only the missing transverse energy signature. Non-observation of any excess above Standard Model expectations forces the LHC experiments to enter into the same fighting for the best exclusion curve, in which (almost) all direct and indirect DM search experiments permanently take place. But this fighting has very little (almost nothing) to do with a real possibility of discovering a DM particle. The true DM particles possess an exclusive galactic signature --- annual modulation of a signal, which is accessible today only for direct DM detection experiments. There is no way for it with a collider, or accelerator. Therefore to prove the DM nature of a collider-discovered candidate one must find the candidate in a direct DM experiment and demonstrate the galactic signature for the candidate. Furthermore, being observed, the DM particle must be implemented into a modern theoretical framework. The best candidate is the supersymmetry, which looks today inevitable for coherent interpretation of all available DM data.
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