Photoproduction of axion-like particles in the NA64 experiment

Axion-like particles $a$ (ALPs) that couple to the Standard Model (SM) gauge fields could be observed in the high-energy photon scattering $\gamma N\to N a$ off nuclei followed by the $a\to \gamma\gamma$ decay. In the present paper we describe the calculation of the ALP production cross-section and the properties of this production. The cross section formulas are implemented in the program for the simulation of events in the NA64 experiment, the active electron beam dump facility at the CERN SPS. We study the prospects of the NA64 experiment to search for ALP in the $10\, \mbox{MeV} \lesssim m_a\lesssim 100$ MeV mass range for the statistics corresponding to up to $5\times 10^{12}$ electrons on target (EOT).