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Search for light dark matter in the NA64 experimenta Institute for Nuclear Research, Russian Academy of Sciences, prosp. 60-letiya Oktyabrya 7a, Moscow, 117312, Russian Federation b Joint Institute for Nuclear Research, 6 Joliot-Curie Str., Dubna, Moscow Region, 141980, Russian Federation We review the most important models of light dark matter and discuss the NA64 experiment aimed at searching for hypothetical particles, including dark matter, in the mass range \le O(1)\ GeV with the use of electron and muon beams at the Super Proton Synchrotron (SPS) accelerator at CERN. We consider the methods and results of searches in the NA64 and other accelerator experiments and also discuss their further prospects.
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