Pauli form factor contributions to the inelastic proton bremsstrahlung and dark photon production

We study the production of hypothetical vector particles, dark photons $\gamma^\prime$, with masses in the range 0.4--1.8 GeV via inelastic proton bremsstrahlung. We further develop the approach of arXiv:2409.11089 and refs. [2-3], where for the first time we considered the contributions to the cross section that are associated with the Pauli form factor in $pp\gamma^\prime$ vertex and obtained new splitting functions. We demonstrate numerically the importance of these corrections to full inelastic proton bremsstrahlung cross section and refine the sensitivity of the ongoing and future fixed-target experiments T2K, DUNE and SHiP to the parameters of dark photon model. A dedicated experiment on measurements of the proton electromagnetic form factors in the time-like region below the proton-antiproton threshold, like those suggested in PANDA at FAIR, would help to obtain the robust predictions for the dark photon production by a proton beam at fixed target.