Searches for long-lived dark photons at proton accelerator experiments

A systematic and unified study of the ability of lifetime frontier experiments to explore the parameter space of hypothetical long-lived particles is one of the main steps in defining their parameter space. Such an analysis has not been conducted for dark photons -- hypothetical massive particles that have kinetic mixing with Standard Model photons. Existing studies have varied in their assumptions about dark photon phenomenology, often using outdated models that do not reflect recent advancements. In this paper, we present a unified calculation of the parameter space for GeV-scale dark photons probed by lifetime frontier experiments, delineating the regions excluded by past experiments and those accessible to future experiments. Our approach incorporates the latest advances in studying dark photon production mechanisms, including proton bremsstrahlung and mixing with neutral mesons, and utilizes the full palette of hadronic decays. Additionally, we explore the impact of uncertainties in proton bremsstrahlung on the dark photon parameter space, and find that they may severely affect the reach of many past and future experiments, including the maximal probed mass. The results are provided in a publicly accessible format, specifically through the implementation of the updated phenomenological models in \texttt{SensCalc} - a unified tool for calculating event rates of new physics particles at lifetime frontier experiments, that has been supplemented by the module \texttt{EventCalc} that samples events similar to traditional Monte Carlo generators.