The exact tree-level calculation of the dark photon production in high-energy electron scattering at the CERN SPS

Dark photon (A′) that couples to the standard model fermions via the kinetic mixing with photons and serves as a mediator of dark matter production could be observed in the high-energy electron scattering e−+Z→e−+Z+A′ off nuclei followed by the bremsstrahlung A′→invisible decay. We cross check the exact tree-level calculations of the A′ production cross sections by other results and implement them in the program for the full simulation of such events in the experiment NA64 at the CERN SPS . Using simulations results, we study the missing energy signature for the A′→invisible decay that allows to probe the γ−A′ mixing strength in a wide, from sub-MeV to sub-GeV, A′ mass range. We refine and expand our earlier studies of this signature by including corrections to the previously used calculations based on the improved Weizsaker-Williams (IWW) approximation, which turn out to be significant. We find that the commonly used IWW approach can lead to substantial overestimation of the sensitivity to A′ in fixed target experiments. The possibility of future searches with high-energy electron beams and their sensitivity to A′ are briefly discussed.