Enhanced Cosmic-Ray Cooling in AGN from Dark Matter Deep Inelastic Scattering

TL;DR

The study targets sub-GeV dark matter interacting with protons in AGN dark matter spikes through a vector portal mediator. It develops a minimal Dirac fermion DM model and computes both elastic and DIS cross sections, incorporating nucleon structure via Sachs form factors and CT10nlo PDFs. The CR cooling timescale t_chi_p is defined from the energy-loss rate, and a cooling criterion t_chi_p <= C t_SM with C ~ 0.1 yields exclusion limits on the DM–proton cross section across m_chi in [1e-6, 1] GeV and m_A' around 10 GeV. The results show DIS can dominate energy loss at TeV–PeV CR energies for heavy mediators, shortening the cooling times by orders of magnitude and producing cross-section constraints surpassing XENON1T, LZ, SK, Borexino, PandaX Migdal, and BBN bounds, thus providing a new astrophysical probe of sub-GeV DM interactions. Uncertainties from the DM spike profile and potential annihilation or self-interactions are discussed.

Abstract

The diffusion of high-energy cosmic rays (CRs) through the dark matter (DM) spikes of active galactic nuclei entails significant energy loss via interactions with DM. While previous studies of sub-GeV DM have focused on elastic scattering, this process becomes insufficient at higher proton energies and DM masses. In this work, we investigate the CR-DM deep inelastic scattering (DIS) as mediated by a vector portal. We calculate the DIS contribution to the CR energy loss rate and derive stringent exclusion limits on the CR-DM scattering cross-section for DM masses between $10^{-6}$ GeV and $1$ GeV. For higher CR energies and mediator masses, the resulting CR cooling timescales are reduced by orders of magnitude after involving the DIS contribution, producing stringent constraints that surpass most of current experimental limits.

Figures (4)

• Figure 1: Ratio $\dot{E}_{DIS}/\dot{E}_{ES}$ as a function of DM mass $m_{\chi}$ and mediator mass $m_{A'}$ for cosmic ray energies, $10^{3} ~\mathrm{GeV}$ (Left panel) and $10^{6}~\mathrm{GeV}$ (Right panel). The white contour denotes $\dot{E}_{DIS}/\dot{E}_{ES}=1$, where DIS and elastic scattering contribute equally to energy loss rate. Both panels show maximal ratio in the upper-right quadrant where $m_{A'}$ and $m_{\chi}$ are simultaneously large.
• Figure 2: Cooling timescale for CRs interacting with DM as a function of CR kinetic energy. The dashed lines correspond to DM-proton elastic scattering processes, and the solid lines correspond to the combination of both elastic and deep inelastic scattering processes. Additionally, the gray line indicates CR cooling via standard model processes. Here, we fix the DM mass $m_{\chi}=0.1~\mathrm{GeV}$.
• Figure 3: Constraint on the DM-proton elastic and deep inelastic scattering cross-section from the CR cooling effect, with a mediator mass of $m_{A'} = 10 \text{ GeV}$. Solid curves represent the limits including both elastic and DIS, while dashed curves correspond to elastic-only limits. Red and blue colours indicate kinetic energy of $T = 10^6 \text{GeV}$ and $T = 10^3 \text{GeV}$, respectively. The bounds from XENON1T (light red) Dent:2019krz, LZ (sky blue) Wang:2025ztbLZ:2025iaw, SK (yellow) Bell:2023sdq, Borexino (purple) Wang:2025ztbBorexino:2013bot, PandaX-4T (halo DM, Migdal effect, green) PandaX:2023xgl, and BBN (gray) Giovanetti:2021izc are shown.
• Figure 4: (Left) Cross-section ratio, $\sigma_{\rm DIS}/(\sigma_{\rm ES}+\sigma_{\rm DIS})$, versus cosmic ray kinetic energy $T$ for DM masses: 0.1 MeV (yellow), 10 MeV (blue), 1 GeV (red). Solid curves represent the heavy mediator case ($m_{A'}=10~\mathrm{GeV}$), while dashed curves show the light mediator scenario ($m_{A'}=1~\mathrm{MeV}$). (Right) Corresponding energy loss rate ratio versus CR kinetic energy, using identical color and line-style coding.