  Fixed-target experiments using primary electron beams can be powerful
discovery tools for light dark matter in the sub-GeV mass range. The Light Dark
Matter eXperiment (LDMX) is designed to measure missing momentum in high-rate
electron fixed-target reactions with beam energies of 4 GeV to 16 GeV. A
prerequisite for achieving several important sensitivity milestones is the
capability to efficiently reject backgrounds associated with few-GeV
bremsstrahlung, by twelve orders of magnitude, while maintaining high
efficiency for signal. The primary challenge arises from events with
photo-nuclear reactions faking the missing-momentum property of a dark matter
signal. We present a methodology developed for the LDMX detector concept that
is capable of the required rejection. By employing a detailed GEANT4-based
model of the detector response, we demonstrate that the sampling calorimetry
proposed for LDMX can achieve better than $10^{-13}$ rejection of few-GeV
photons. This suggests that the luminosity-limited sensitivity of LDMX can be
realized at 4 GeV and higher beam energies.
