Pion bremsstrahlung in the splitting function formalism and the dark photon production

We study the production of hypothetical vector portal mediators, dark photons ${\gamma }^{\mathrm{\prime }}$, with masses in the range 0.4-3.5 GeV in the negatively charged pion-proton collisions ${\pi }^{-}p\to {\gamma }^{\mathrm{\prime }}X$ via inelastic pion bremsstrahlung and QCD Drell-Yan-like process. In both cases we estimate the value of total dark photon production cross section and obtain the energy distribution for dark photons that could be produced in the NA64h experiment. We also present the mean energies of dark photons produced in the same way by the secondary pions with momenta typical for T2K, DUNE and SHiP experiments.