Detecting Dark Matter with Far-Forward Emulsion and Liquid Argon Detectors at the LHC

New light particles may be produced in large numbers in the far-forward region at the LHC and then decay to dark matter, which can be detected through its scattering in far-forward experiments. We consider the example of invisibly-decaying dark photons, which decay to dark matter through $A' \to \chi \chi$. The dark matter may then be detected through its scattering off electrons $\chi e^- \to \chi e^-$. We consider the discovery potential of detectors placed on the beam collision axis 480 m from the ATLAS interaction point, including an emulsion detector (FASER$\nu$2) and, for the first time, a Forward Liquid Argon Experiment (FLArE). For each of these detector technologies, we devise cuts that effectively separate the single $e^-$ signal from the leading neutrino- and muon-induced backgrounds. We find that 10- to 100-tonne detectors may detect hundreds to thousands of dark matter events in the HL-LHC era and will sensitively probe the thermal relic region of parameter space. These results motivate the construction of far-forward emulsion and liquid argon detectors at the LHC, as well as a suitable location to accommodate them, such as the proposed Forward Physics Facility.