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

We explore hypothetical vector particles, dark photons ${\gamma }^{\mathrm{\prime }}$, which mix with the Standard Model photons and thus mediate interactions with charged particles into the hidden sector. We study the elastic proton bremsstrahlung of dark photons with masses 0.4-1.8 GeV, relevant for direct searches with proton accelerators. A key feature of our calculation is that it explicitly considers the non-zero momentum transfer between protons in the process $pp\to pp{\gamma }^{\mathrm{\prime }}$. We compare the obtained differential and full bremsstrahlung cross sections with the results of other authors. Our calculation agrees well (up to 3-9 % corrections) with the Weizsacker-Williams approximation that confirms its applicability for proton beams. Then we refine predictions for the dark photon production with proton beams of energy 30 GeV, 70 GeV, 120 GeV and 400 GeV relevant for past, present and future experiments considered in literature.