Dark matter beams at LBNF

High-intensity neutrino beam facilities may produce a beam of light dark matter when protons strike the target. Searches for such a dark matter beam using its scattering in a nearby detector must overcome the large neutrino background. We characterize the spatial and energy distributions of the dark matter and neutrino beams, focusing on their differences to enhance the sensitivity to dark matter. We find that a dark matter beam produced by a $Z'$ boson in the GeV mass range is both broader and more energetic than the neutrino beam. The reach for dark matter is maximized for a detector sensitive to hard neutral-current scatterings, placed at a sizable angle off the neutrino beam axis. In the case of the Long-Baseline Neutrino Facility (LBNF), a detector placed at roughly 6 degrees off axis and at a distance of about 200 m from the target would be sensitive to $Z'$ couplings as low as 0.05. This search can proceed symbiotically with neutrino measurements. We also show that the MiniBooNE and MicroBooNE detectors, which are on Fermilab's Booster beamline, happen to be at an optimal angle from the NuMI beam and could perform searches with existing data. This illustrates potential synergies between LBNF and the short-baseline neutrino program if the detectors are positioned appropriately.