  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.
