A search is performed for a new sub-GeV vector boson (A') mediated production of Dark Matter (χ) in the fixed-target experiment, NA64, at the CERN SPS. The A', called dark photon, could be generated in the reaction e~- Z → e~- ZA' of 100 GeV electrons dumped against an active target which is followed by the prompt invisible decay A' → χχ. The experimental signature of this process would be an event with an isolated electron and large missing energy in the detector. From the analysis of the data sample collected in 2016 corresponding to 4.3 × 10~(10) electrons on target no evidence of such a process has been found. New stringent constraints on the A' mixing strength with photons, 10~(-5) approx.< ∈ approx.< 10~(-2), for the A' mass range m_A' approx.< 1 GeV are derived. The results are obtained by using tree level, exact calculations of the A' production cross-sections, which turn out to be significantly smaller compared to the one obtained in the Weizsacker-Williams approximation for the mass region m_A' approx.> 0.1 GeV.
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