A Closer Look at Dark Vector Splitting Functions in Proton Bremsstrahlung

High luminosity colliders and fixed target facilities using proton beams are sensitive to new weakly coupled degrees of freedom across a broad mass range. Among the various production modes, bremsstrahlung is particularly important for dark sector degrees of freedom with masses between 0.5 and 2.0 GeV, due to mixing with hadronic resonances. In this paper, we revisit the calculation of dark vector production via initial state radiation in non-single diffractive scattering, using an improved treatment of the splitting functions and timelike electromagnetic form-factors. The approach is benchmarked by applying an analogous calculation to model inclusive $\rho$-meson production, indicating consistency with data from NA27 in the relevant kinematic range.