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[References: 36 tit.]

We report the results of a search for a light pseudoscalar particle a that couples to electrons and decays to e+e− performed using the high-energy CERN SPS H4 electron beam. If such light pseudoscalar exists, it could explain the ATOMKI anomaly (an excess of e+e− pairs in the nuclear transitions of 8Be and 4He nuclei at the invariant mass ≃17  MeV observed by the experiment at the 5 MV Van de Graaff accelerator at ATOMKI, Hungary). We used the NA64 data collected in the “visible mode” configuration with a total statistics corresponding to 8.4×1010 electrons on target (EOT) in 2017 and 2018. In order to increase sensitivity to small coupling parameter ε we also used the data collected in 2016-2018 in the “invisible mode” configuration of NA64 with a total statistics corresponding to 2.84×1011 EOT. The background and efficiency estimates for these two configurations were retained from our previous analyses searching for light vector bosons and axionlike particles (ALP) (the latter were assumed to couple predominantly to γ). In this work we recalculate the signal yields, which are different due to different cross section and lifetime of a pseudoscalar particle a, and perform a new statistical analysis. As a result, the region of the two dimensional parameter space ma−ε in the mass range from 1 to 17.1 MeV is excluded. At the mass of the central value of the ATOMKI anomaly (the first result obtained on the beryllium nucleus, 16.7 MeV) the values of ε in the range 2.1×10−4<ε<3.2×10−4 are excluded.