Direct Detection of Mechanism-Agnostic Fast-Moving Dark Matter

We present a comprehensive framework for interpreting electron recoil signals induced by fast-moving dark matter (DM), applicable across a wide range of theoretically motivated models. Amid both null results in conventional weakly interacting massive particle searches and growing interest in alternative DM scenarios, we focus on (semi-)relativistic DM components that can arise from mechanisms such as DM annihilation, decay, or cosmic-ray acceleration. These boosted DM candidates produce distinct experimental signatures that differ qualitatively from non-relativistic DM, necessitating a dedicated treatment. Our framework incorporates relativistic kinematics and atomic effects through ionization form factors, enabling accurate predictions of differential cross sections in both low- and high-energy regimes. We demonstrate how atomic effects become negligible at high recoil energies, validating the free-electron approximation in specific parameter regions. Furthermore, we highlight the complementarity between low-threshold direct detection experiments and high-threshold neutrino observatories in probing fast-moving DM across broad kinematic domains. This formalism provides a robust and model-independent foundation for interpreting current and future searches for relativistic DM.