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We report direct-detection constraints on light dark matter particles interacting with electrons. The results are based on a method that exploits the extremely low levels of leakage current of the DAMIC detector at SNOLAB of 2-610 A cm. We evaluate the charge distribution of pixels that collect for contributions beyond the leakage current that may be attributed to dark matter interactions. Constraints are placed on so-far unexplored parameter space for dark matter masses between 0.6 and 100 MeV. We also present new constraints on hidden-photon dark matter with masses in the range - eV.

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