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We explore hypothetical vector particles, dark photons $\gamma'$, which mixwith the Standard Model photons and thus mediate interactions with chargedparticles into the hidden sector. We study the elastic proton bremsstrahlung ofdark photons with masses 0.4-1.8 GeV, relevant for direct searches with protonaccelerators. A key feature of our calculation is that it explicitly considersthe non-zero momentum transfer between protons in the process $pp\rightarrowpp\gamma'$. We compare the obtained differential and full bremsstrahlung crosssections with the results of other authors. Our calculation agrees well (up to3-9 % corrections) with the Weizsacker-Williams approximation that confirms itsapplicability for proton beams. Then we refine predictions for the dark photonproduction with proton beams of energy 30 GeV, 70 GeV, 120 GeV and 400 GeVrelevant for past, present and future experiments considered in literature.

Dark photon production via elastic proton bremsstrahlung with non-zero momentum transfer