Cosmic-Ray Boosted Dark Matter (CRDM)

• CRDM is a dark matter phenomenon where sub-GeV particles are upscattered by high-energy cosmic rays, overcoming traditional detection limits.
• It involves elastic scattering processes with light mediators, resulting in energy-dependent interaction signatures that are key to experimental identification.
• Detector strategies using xenon, germanium, and emulsion setups exploit CRDM’s high recoil energies to explore previously inaccessible regions in DM parameter space.

Cosmic-Ray Boosted Dark Matter (CRDM) encompasses the class of dark matter (DM) phenomenology in which otherwise nonrelativistic, often sub-GeV DM particles are upscattered to relativistic energies through collisions with energetic astrophysical cosmic rays (CRs) in the Galaxy or extragalactic sources. This mechanism enables a small but energetic DM population capable of generating detectable recoils in terrestrial or subterranean detectors—overcoming kinematic limitations that typically preclude the discovery of low-mass DM in direct detection experiments. CRDM has developed into a broad research field with deep interplay between theoretical particle physics, cosmic-ray astrophysics, detector phenomenology, and even the paper of astrophysical objects such as neutron stars and active galactic nuclei.

1. Production Mechanisms and Theoretical Frameworks

The canonical CRDM production mechanism is elastic two-body scattering of a high-energy CR—typically a proton, helium nucleus, or electron—with a DM particle $\chi$. The maximum kinetic energy transferable to DM is set by kinematic constraints: $$T_\chi^{\rm max}(T_{\rm CR}) = \frac{T_{\rm CR}^2 + 2 m_{\rm CR} T_{\rm CR}}{T_{\rm CR} + \frac{(m_{\rm CR} + m_\chi)^2}{2m_\chi}}$$ with $T_{\rm CR}, m_{\rm CR}$ respectively the incident CR kinetic energy and mass (see (Dent et al., 2019, Xia et al., 2021, Lei et al., 2020)). The resulting CRDM flux at the Earth is calculated as: $$\frac{d\Phi_\chi}{dT_\chi} = D_{\rm eff}\, \frac{\rho_\chi}{m_\chi} \sum_i \int_{T_i^{\rm min}(T_\chi)}^\infty \frac{d\sigma_{\chi i}}{dT_\chi} \frac{d\Phi_i^{\rm LIS}}{dT_i} dT_i$$ where $D_{\rm eff}$ is an effective propagation distance incorporating Galactic geometry and spatial variations in both DM and CR densities (Xia et al., 2021), $\frac{d\Phi_i^{\rm LIS}}{dT_i}$ is the local interstellar CR flux, and $\frac{d\sigma_{\chi i}}{dT_\chi}$ is the relevant differential cross section.

For more complex CRDM origins, active galactic nuclei (AGN) have been proposed as CR acceleration sites where CRs encounter DM overdensities (“spikes”), producing a flux of boosted, and in some cases, inelastically excited DM via $p + \chi_1 \rightarrow p + \chi_2$ (Gustafson et al., 28 Aug 2025).

2. Energy-Dependent Interactions and Mediation

CRDM–Standard Model interactions can be parametrized by a variety of simplified models featuring light mediators. Frequently studied are:

• Vector (dark photon) and axial vector mediators (often with $U(1)'$ gauge structure, e.g., $U(1)_D$, $U(1)_{B-L}$, $U(1)_{L_e-L_\mu}$), yielding interactions such as $$\mathcal{L} \supset g_\chi V_\mu \bar\chi\gamma^\mu\chi + g_{SM} V_\mu \bar\psi\gamma^\mu\psi$$ (Cho et al., 2020, Guha et al., 15 Jan 2024).
• Scalar and pseudoscalar mediators coupling DM and SM through Yukawa-like operators.

In the light mediator regime, the differential cross section develops a strong energy and momentum transfer dependence (propagator suppression or enhancement depending on whether $m_{\rm med}^2 \gtrless q^2$), typically

$$\frac{d\sigma}{dT} \propto \frac{g_\chi^2 g_{SM}^2}{(2 m_\chi T + m_{\rm med}^2)^2}$$

(Dent et al., 2019, Guha et al., 15 Jan 2024). This energy dependence has outsize impact on both the generation of CRDM and their subsequent detection, especially at low DM masses, and can produce bounds several orders of magnitude more stringent than for constant cross-section assumptions.

For inelastic DM (e.g., with $\chi_1$ and $\chi_2$), dedicated calculations are needed to capture upscattering, nuclear resonance, and deep inelastic scattering (DIS) channels, as well as inelastic nuclear form factors, with tools such as GENIE used for high-energy event simulation (Diurba et al., 9 Sep 2024, Gustafson et al., 28 Aug 2025).

3. Signal Characteristics, Detector Analysis, and Earth Attenuation

The striking phenomenological feature of CRDM is the presence of a population of highly energetic DM particles capable of exceeding nuclear or electronic recoil thresholds in direct detection experiments, for DM masses—as low as $\sim$keV to MeV—where canonical nonrelativistic DM would be invisible (Cui et al., 2021, Aalbers et al., 23 Mar 2025, Lei et al., 2020).

A central issue is Earth attenuation: as CRDM propagate through the Earth's crust, they lose energy and flux via further scatterings with electrons or nuclei. The energy loss is described analytically through a mean energy loss equation

$$\frac{dT_\chi}{dx} = -\sum_N n_N \int (d\sigma/dT_r) T_r dT_r$$

for traversal length $x$ through the Earth, and is further suppressed by nuclear form factors, especially at high momentum transfer (Xia et al., 2021, Herbermann et al., 5 Aug 2024). The “attenuation ceiling” marks the cross-section above which few if any CRDM particles reach the detector with sufficient energy, and is found to be nearly model-independent for $m_\chi, m_{\rm med} > m_e$ (Herbermann et al., 5 Aug 2024).

Detector analyses exploit both the high recoil energy and distinctive event topology of CRDM. State-of-the-art analyses use:

• Profile likelihood methods to exploit spectral and event-level discrimination (e.g., S1/S2 in xenon TPCs, diurnal or directional information) (Cui et al., 2021, Agafonova et al., 2023, Aalbers et al., 23 Mar 2025).
• Simulations for overburden and topography (e.g., DarkProp, CJPL_ESS) that track energy loss and angular scattering in realistic Earth models (Xia et al., 2021, Xu et al., 2022).

4. Experimental Results and Astrophysical Implications

CRDM has been actively searched for in an expanding roster of high- and low-background experiments:

Experiment	Target	Mass/Exposure	CRDM Mass Range Probe (typ.)	Ref.
LZ	Xe TPC	4.2 t·yr	$0.1~\mathrm{MeV} - 1~\mathrm{GeV}$	(Aalbers et al., 23 Mar 2025)
PandaX-II	Xe TPC	100 t·day	$0.1~\mathrm{MeV} - 0.1~\mathrm{GeV}$	(Cui et al., 2021)
CDEX-10	Ge PPC	205.4 kg·day	$10~\mathrm{keV} - 1~\mathrm{GeV}$	(Xu et al., 2022)
Super-Kamiokande	Water Cher.	200 t·yr	$1~\mathrm{MeV}$ and above	(Xia et al., 2022)
NEWSdm (proj.)	Emulsion	10 kg·yr	$1~\mathrm{keV} - 1~\mathrm{GeV}$	(Agafonova et al., 2023)

Experiments report step-function-like exclusion contours in cross-section vs. $m_\chi$, with a prominent “neutrino floor” at low cross-section—determined by coherent elastic neutrino-nucleus scattering (Dent et al., 2019, Lei et al., 2020). CRDM searches have closed parameter gaps between accelerator and astrophysical constraints and extended reach down to $\sigma \sim 10^{-33}$ cm$^2$ for sub-GeV DM (Aalbers et al., 23 Mar 2025, Xia et al., 2021).

Directional and diurnal signatures are a growing focus; e.g., CRDM arriving preferentially from the Galactic Center due to combined DM and CR density profiles induces anisotropy, providing a distinctive discrimination handle (Agafonova et al., 2023, Xia et al., 2022). Analyses exploiting sidereal modulation offer further sensitivity (Cui et al., 2021).

Importantly, several works have emphasized the need to consider constraints from AGN and extragalactic sources, with deep inelastic CR–DM scatterings in DM spikes near SMBHs producing a potentially detectable flux at Earth—sensitive to inelastic DM models and probing relic abundance–favored regions (Gustafson et al., 28 Aug 2025).

5. Energy Spectrum Evolution and Dark Sector Dynamics

Recent developments include the inclusion of dark sector parton shower (“final state radiation,” FSR) effects, where boosted DM can radiate dark photons (A′), redistributing its energy and modifying the CRDM flux reaching detectors (Chen et al., 15 Sep 2025). Monte Carlo frameworks with Sudakov form factors and kinematic dipole recoil show that, depending on mediator mass $m_{A'}$ and $g_D$, FSR can either enhance the flux in the sub-MeV regime or sharply suppress the high-energy tail (more than $50\%$ decrease around 100 MeV for $m_{A'} \lesssim 10^{-3}$ MeV, $g_D=3$). This leads to a relaxation of bounds on kinetic mixing, e.g., by up to factors of 1.6 in Super-Kamiokande depending on parameters.

Consistency with DM self-interaction limits (from the Bullet Cluster, $\sigma_T/m_\chi \lesssim 1~\text{cm}^2/\text{g}$) is maintained in allowed regions for dark photon models considered (Chen et al., 15 Sep 2025).

6. Constraints, Complementary Probes, and Model Dependence

While CRDM searches have rapidly improved constraints on DM–nucleon and DM–electron cross sections in previously inaccessible mass ranges, they are also subject to limitations from independent laboratory and astrophysical constraints, particularly on light mediators. For SI and SD interactions, the required large couplings to achieve observable CR upscattering often violate bounds from meson decay, stellar cooling, and supernova emission (Bell et al., 2023). Practically, this places tight restrictions on the applicability of CRDM results: exclusion contours derived for specific couplings often only survive in models with suppressed signals in these complementary channels.

Moreover, energy-dependent versus constant cross-section assumptions produce parametrically different exclusion curves, mandating case-by-case reinterpretation of experimental limits within consistent particle physics models (Herbermann et al., 5 Aug 2024).

7. Outlook and Future Directions

CRDM continues to motivate low-threshold, large-exposure detectors—liquid xenon (LZ, XENONnT), germanium (CDEX, EDELWEISS), and nanometric emulsion (NEWSdm)—as well as the inclusion of directional and diurnal sensitivity in data analysis (Aalbers et al., 23 Mar 2025, Agafonova et al., 2023, Cui et al., 2021). Future megaton-scale neutrino detectors (e.g., Hyper-Kamiokande, JUNO), direct detection facilities (DARWIN), and improved models of AGN and cosmic ray propagation promise further reach, especially in even-lower-mass and inelastic DM parameter space (Kamenetskaia et al., 21 Jan 2025, Gustafson et al., 28 Aug 2025).

A robust theoretical understanding of energy spectra (including showering and inelastic effects), Earth attenuation, and mediator model-dependence is critical for this field. Continued developments in simulation frameworks and astrophysical modeling will be needed as higher-statistics data become available and parameter space is further constrained.

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CRDM serves as an essential probe of the light, feebly interacting, and inelastic sectors of dark matter parameter space, leveraging the energetic environment of the Galaxy to unlock new detection channels and close gaps left by traditional nonrelativistic searches.