Cosmic-Ray Boosted Dark Matter

• Cosmic-ray boosted dark matter is a scenario where high-energy cosmic rays upscatter nonrelativistic dark matter to relativistic energies, enabling detection of sub-GeV particles.
• This mechanism relies on elastic and inelastic scattering processes with energy-dependent DM–SM cross sections that shape the observable flux and attenuation signatures.
• Experimental strategies leverage unique features like directional modulation and high recoil energies to extend the search beyond traditional direct detection thresholds.

Cosmic-ray boosted dark matter (CRBDM) denotes a class of dark matter (DM) detection scenarios in which otherwise slow and nonrelativistic Galactic DM particles are “upscattered” to relativistic energies via collisions with highly energetic cosmic rays (CRs)—protons, nuclei, or electrons—anywhere in the Galaxy or in particular astrophysical environments. The resulting flux of relativistic DM can produce observable signals in ground-based detectors that would be entirely inaccessible due to kinematic thresholds for standard nonrelativistic DM. This mechanism plays a pivotal role in extending the reach of direct detection experiments to the sub-GeV or even sub-MeV DM mass regime, opens new avenues for indirect detection at neutrino, gamma, and cosmic ray telescopes, and substantially impacts constraints on DM–Standard Model (SM) interaction properties.

1. Physical Mechanism: Cosmic-Ray Upscattering of Dark Matter

CRBDM production is based on elastic or inelastic two-body scattering of a high-energy cosmic ray particle and a cold DM particle in the Galactic halo or other high-CR-density astrophysical regions. The particle kinematics are governed by standard two-body collision relations. For elastic scattering, the DM kinetic energy after the collision is given by

$$T_\chi = \frac{(T_i^2 + 2 m_i T_i)}{T_i + (m_i + m_\chi)^2/(2 m_\chi)} \cdot \frac{1 - \cos\theta}{2},$$

where $T_i$ and $m_i$ are the kinetic energy and mass of the incident CR (proton, nucleus, or electron), $m_\chi$ is the dark matter mass, and $\theta$ is the center-of-mass scattering angle (Guha et al., 15 Jan 2024, Herbermann et al., 5 Aug 2024).

In astrophysical environments such as the Milky Way, AGN, or environments with dark matter spikes, the spatial integral over the cosmic ray and DM densities defines the effective production rate and morphology of the CRBDM flux. The upscattered DM population acquires kinetic energies $T_\chi$ well above the $\mathcal{O}(\mathrm{keV})$ scale typical of halo DM, reaching MeV or higher (corresponding to semi-relativistic or relativistic velocities). Inelastic processes (quasi-elastic nucleon knockout, resonance production, or deep-inelastic scattering) must also be considered for high transferred momentum or for models with inelastic dark sectors (Diurba et al., 9 Sep 2024, Gustafson et al., 28 Aug 2025).

The resulting CRBDM flux arriving at Earth is computed via

$$\frac{d\Phi_\chi}{dT_\chi} = D_{\mathrm{eff}} \frac{\rho_\chi^{\mathrm{loc}}}{m_\chi} \sum_i \int_{T_{i,\min}}^\infty dT_i \frac{d\sigma^{}_{\chi i}}{dT_\chi}\, \frac{d\Phi^{{\rm LIS}}_{i}}{dT_i},$$

where $D_{\mathrm{eff}}$ is an effective distance parameter, $\rho_\chi^{\mathrm{loc}}$ is the local DM density, $d\sigma_{\chi i}/dT_\chi$ is the differential cross section, and $d\Phi^{\rm LIS}_i/dT_i$ is the local interstellar CR flux (Xia et al., 2021, Maity et al., 2022). Calculations often include protons, helium, heavier nuclei, and leptons as CR species, and must also integrate over sky direction accounting for spatial inhomogeneities (Xu et al., 2022, Xia et al., 2021).

2. Impact of Energy-Dependent Interactions and Model Structure

The DM–SM scattering cross section entering CRBDM production is in general momentum-transfer dependent and model-specific. For a process mediated by a particle of mass $m_{\rm med}$ (e.g., a dark photon, new scalar or vector), the cross section typically scales as

$$d\sigma/dT_\chi \sim \frac{g_\chi^2 g_{SM}^2}{(q^2 + m^2_{\rm med})^2},$$

where $q^2 \sim 2 m_\chi T_\chi$ is the momentum transfer squared, $g_\chi$ and $g_{SM}$ are the couplings to DM and the SM particle, respectively (Guha et al., 15 Jan 2024, Bell et al., 2023).

For composite or "puffy" DM models, an additional DM form factor appears: $$F_{\mathrm{DM}}(q^2) = \frac{1}{(1 + r^2_{\rm DM} q^2)^2},$$ where $r_{\rm DM}$ is the DM radius (Wang et al., 2023). The interplay between mediator and DM structure-induced form factors can enhance or suppress the cross section at high $q^2$, directly shaping the spectrum and attenuation of the CRBDM flux.

Energy-dependent cross sections (from light mediators or finite DM structure) influence both the production rate and the attenuation of CRBDM flux as DM traverses the Earth before reaching an underground detector. In cases where form factor suppression is significant at high recoil, attenuation through the Earth’s crust is mitigated, allowing the high-energy tail of the CRBDM flux to remain intact (Xia et al., 2021, Herbermann et al., 5 Aug 2024). The energy dependence of the cross section is essential when setting accurate exclusion limits, and simplifying the analysis with constant cross section assumptions can significantly misrepresent the boundaries of exclusion (Herbermann et al., 5 Aug 2024).

3. Propagation, Attenuation, and Experimental Signatures

CRBDM particles, after production, traverse the interstellar medium, the Earth's atmosphere, and potentially kilometers of rock before reaching a detector. The same cross section that produces the boosted flux causes attenuation by scattering with atmospheric and crustal electrons or nuclei, leading to energy loss and angular deflection. Attenuation is described by

$$\frac{dT_\chi}{dz} = -\sum_T n_T \int dE_R\, \frac{d\sigma_{\chi T}}{dE_R} E_R,$$

where $z$ is the distance traveled and $n_T$ is the number density of target $T$ (Bell et al., 2023, Xia et al., 2021). For high-energy CRBDM, nuclear form factors suppress attenuation at large $q^2$, permitting even relatively large cross sections without blinding the detectors to the flux (Xia et al., 2021).

A crucial phenomenological consequence is the appearance of an “attenuation ceiling” in the cross section–mass plane. Above this ceiling, the boosted DM flux is exponentially depleted before reaching the detector (Herbermann et al., 5 Aug 2024). The position and sharpness of the ceiling depend on the DM mass, mediator mass, and cross section energy dependence.

Experimental signals from CRBDM predominantly occur via nuclear recoils for spin-independent or spin-dependent interactions, or via electron recoils for leptophilic DM. The boosted kinetic energies can be many MeV, and the resulting recoils are readily distinguishable from those produced by nonrelativistic DM, but overlap with neutrino backgrounds in energy.

Experimental strategies exploit distinct features of CRBDM, including:

• Nuclear recoil energy spectrum extending to higher energies than expected for standard halo DM,
• Diurnal, sidereal, or directional modulation (due to anisotropic CR flux or attenuation), which can suppress isotropic background (Ge et al., 2020, Cui et al., 2021, Agafonova et al., 2023, Xia et al., 2022),
• Azimuthal asymmetries reflecting the underlying CR flux morphology and source positioning (Xia et al., 2022),
• Distinct event topologies in neutrino detectors from deep inelastic DM–nucleon scatterings (hadronic activity, single lepton emission) (Diurba et al., 23 Apr 2025).

4. Experimental Results and Constraints

A variety of direct detection (xenon, germanium) and large-scale neutrino experiments (Super-Kamiokande, DUNE, IceCube) have established constraints on DM interaction cross sections via the CRBDM channel:

Experiment	Mass Sensitivity	Best SI σ (cm²)	Notable Features
LUX-ZEPLIN	0.1–1 GeV/c²	$3.9 \times 10^{-33}$	Largest LXe TPC, power-constrained analysis (Aalbers et al., 23 Mar 2025)
PandaX-II	0.1 MeV–0.1 GeV/c²	$10^{-31}$–$10^{-28}$	Exploits diurnal modulation (Cui et al., 2021)
CDEX-10	10 keV–1 GeV	$1.7\times10^{-30}$–$10^{-26}$	Lower mass reach, includes heavy CR nuclei (Xu et al., 2022)
XENON1T	0.1–10 MeV	$\sim10^{-35}$ (SI, grav. med.)	Includes momentum dependence, tight low-mass limits (Wang et al., 2019)
DUNE	MeV–GeV	SI/SD: competitive with LZ	QE and DIS channels, sensitivity to SD (Diurba et al., 23 Apr 2025)
NEWSdm	1 keV–1 GeV	$10^{-30}$	Directional surface search, up to factor 3.5 asymmetry (Agafonova et al., 2023)
Super-K	1–100 MeV ($m_\chi$)	$2.4\times10^{-33}$ (e$^-$)	Azimuthal/sky asymmetries in event map (Xia et al., 2022)
IceCube	$< 100$ keV (e$^-$), MeV ($N$)	Model-dependent	Both elastic and DIS event classes (Cappiello et al., 30 Apr 2024)

These experiments have collectively closed the previously untested region in the DM–nucleon cross section versus mass plane between astrophysical exclusions (from CMB, gas cloud cooling, and SNe) and the “floor” of direct detection sensitivity, particularly for light (keV–GeV) DM (Xia et al., 2021, Xu et al., 2022, Aalbers et al., 23 Mar 2025).

5. Advanced Model Phenomenology and Theoretical Implications

The theoretical landscape of CRBDM encompasses a range of DM interactions:

• Spin-independent and spin-dependent nucleon cross sections, with coherent (A²-enhanced) and incoherent (partonic) regimes, including contributions from both elastic and inelastic (QE, resonance, DIS) scatterings (Diurba et al., 9 Sep 2024, Diurba et al., 23 Apr 2025).
• Mediation via light vector or scalar bosons (including $Z^\prime$, dark photons, $U(1)_{B-L}$, $U(1)_{L_e-L_\mu}$) with energy-dependent cross sections (Guha et al., 15 Jan 2024, Bell et al., 2023).
• Leptophilic and composite/puffy DM scenarios, where the CR source population and the underlying DM form factors profoundly affect the observable flux (Wang et al., 2023, Herbermann et al., 5 Aug 2024).
• Inelastic DM models (with mass splitting $\delta$), for which the boosted kinetic energy enables transitions otherwise forbidden for stationary halo DM. This opens the parameter space of such models for discovery (or exclusion), even for $\delta \sim 0.4 m_\chi$ (Gustafson et al., 28 Aug 2025).

The distinctive CRBDM angular, energy, and modulation signatures provide a key handle for separating signal from backgrounds—including the diurnal modulation induced by Earth rotation and the anisotropic sky distributions mapped to the CR density and propagation (Ge et al., 2020, Cui et al., 2021, Agafonova et al., 2023).

In AGN environments, the presence of DM density spikes and intense local CR fluxes can enhance the CRBDM flux by several orders of magnitude, possibly probing thermal relic cross section targets for light and inelastic DM models, a region otherwise inaccessible to direct detection, collider, or indirect probes (Gustafson et al., 28 Aug 2025).

Constraints from CRBDM are fundamentally limited by existing bounds on the interaction mediators from laboratory, cosmological, and astrophysical observations. In many minimal scenarios, the cross section required for significant boosting is already in tension with such constraints, motivating focused model-dependent studies for viable open parameter space (Bell et al., 2023).

6. Outlook and Future Directions

Prospects for CRBDM research include further improvements in detector energy thresholds, mass, and background discrimination, notably in upcoming multi-ton xenon/noble liquid and advanced low-threshold cryogenic experiments (e.g., Darwin, DUNE, ICECube-Gen2, PandaX-4T, NEWSdm surface upgrades). Enhanced sensitivity to both SI and SD interactions, deeper modeling of inelastic contributions (via adaptations of neutrino event generators such as GENIE), and increased exposure will further probe the low-mass DM frontier (Aalbers et al., 23 Mar 2025, Maity et al., 2022, Diurba et al., 9 Sep 2024, Diurba et al., 23 Apr 2025).

Integrated theoretical–experimental research will focus on:

• Detailed treatment of energy dependence in DM–SM cross sections, including robust Earth attenuation and overburden propagation,
• Morphological and directional analyses leveraging CR anisotropies and diurnal/asymmetry observables,
• Inclusion of exotic sources of boosting (e.g., AGN, DSNB neutrinos (Ghosh et al., 18 Nov 2024)), and the resulting multi-source restriction on DM–neutrino couplings,
• Model-building efforts to realize leptophilic/inter-generational seclusion or inelasticity required by viable CRBDM signatures.

CRBDM will remain a unique complement to velocity-blind direct detection, accelerator, and cosmological searches, probing DM interactions and properties in regimes that are otherwise inaccessible due to the nonrelativistic nature of halo dark matter. As direct detection technologies mature and new analysis strategies are developed, CRBDM scenarios will play a central role in the future of sub-GeV and hidden sector dark matter exploration.