Direct Detection of Mechanism-Agnostic Fast-Moving Dark Matter

TL;DR

This work develops a mechanism-agnostic, fully relativistic framework for interpreting electron recoils from fast-moving dark matter across fermionic and scalar DM with vector, scalar, axial-vector, and pseudoscalar mediators. It introduces a generalized differential cross section that combines a relativistic DM form factor |F_DM|^2 with an atomic ionization form factor |f_ion|^2, and demonstrates that the high-recoil-energy limit recovers the free-electron result while atomic effects can dominate at lower energies. The authors show how to determine the regimes where atomic effects matter, quantify the complementarity between low-threshold direct-detection experiments and high-threshold neutrino observatories, and apply the formalism to two benchmarks: two-component boosted DM and cosmic-ray–boosted DM, including a practical method to reinterpret fixed-flux exclusions for realistic flux models. Overall, the framework provides a model-independent, cross-experiment map between flux, mediator dynamics, and detector response, enabling robust interpretation of current and future searches for relativistic DM.

Abstract

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.

Figures (13)

• Figure 1: Feynman diagram depicting the interaction between a DM particle and a target electron.
• Figure 2: The asymptotic behavior of the ionization form factor of the xenon atom for the 2p (top) and 3s (bottom) shells. All ionization form factor curves are estimated at various electron recoil energies: 100 keV (black), 1 MeV (red), 10 MeV (green), and 100 MeV (blue). The four mediator cases are represented by solid (vector), dashed (axial vector), dot-dashed (scalar), and dotted (pseudoscalar) curves. The vertical dotted lines represent the corresponding $k'$ value for each of the given $E_r$ values.
• Figure 3: $R_{\sigma}$ for the FV case representing different mediator mass regimes of $m_X =$ 50 keV (left), $m_X =$ 100 MeV (center), and $m_X = 3 \, m_{\chi}$ (right). The color scale in each panel is normalized to the maximum $R_\sigma$ value within that panel.
• Figure 4: Differential cross sections for the FV case in terms of the electron recoil energy for the free-electron assumption in solid blue and for the relativistic ionization form factor in dashed red. Left, center, and right panels respectively correspond to mediator masses $m_X =$ 50 keV, $m_X =$ 100 MeV, and $m_X = 3 \, m_{\chi}$. Top, middle, and bottom panels respectively correspond to points A, B, and C as indicated on Figure \ref{['fig:csvar_ABC_FV']}.
• Figure 5: $R_{\sigma}$ for the FP case representing different mediator mass regimes of $m_X =$ 50 keV, $m_X =$ 100 MeV, and $m_X = 3 \, m_{\chi}$ in the left, center, and right panels, respectively. The color scale in each panel is normalized to the maximum $R_\sigma$ value within that panel.