Illuminating Light Dark Matter with Fixed-Target Experiments

Astronomical and cosmological observations provide overwhelming evidence for a non-luminous matter component, dark matter (DM), whose particle nature remains unknown. Experimental searches for non-gravitational DM interactions have largely targeted DM with GeV-TeV masses via nuclear recoils, yielding no discovery thus far. DM in the MeV-GeV mass range, however, is theoretically motivated, reproducing the observed relic abundance while remaining invisible to nuclear recoil searches. Such light DM is better probed via electron recoils or at fixed-target experiments. This thesis advances the theoretical and statistical toolkit for light DM searches at fixed-target experiments, spanning model building, statistical inference, global fits, and signal simulation. We survey the landscape of fixed-target searches for light DM, focusing on the Light Dark Matter eXperiment (LDMX). We also simulate DM signatures at the next-generation experiment SHiP to assess its sensitivity. Within minimal DM models, we present a likelihood-based statistical framework for LDMX using the full two-dimensional recoil electron distribution, spanning exclusion, discovery, parameter estimation, and model comparison in frequentist and Bayesian formulations. This establishes the discovery potential of LDMX, and we quantify the direct detection exposure needed to independently confirm a potential signal. Beyond this paradigm, we perform global fits of scalar and fermionic light DM, combining cosmological, astrophysical, and laboratory constraints. We then extend fixed-target searches to spin-1 DM and higher electromagnetic moment dark photons, yielding rich signatures with strong complementarity to other probes. Finally, we go beyond standard nuclear modelling of dark photon production, incorporating elastic nuclear form factors and spectral functions from many-body ab initio methods in place of analytic treatments.