Cosmic-ray boosted inelastic dark matter from neutrino-emitting active galactic nuclei

This paper proposes that cosmic-ray boosted inelastic dark matter from neutrino-emitting active galactic nuclei like NGC 1068 and TXS 0506+056 can be detected by experiments such as Super-K and XENONnT, offering a novel way to probe light dark matter models that reproduce the observed relic abundance but are otherwise inaccessible.

The Gist

The Big Picture: Hunting for the Invisible

Imagine the universe is filled with invisible "ghosts" called Dark Matter. We know they are there because they have gravity (they hold galaxies together), but we can't see them, and they rarely bump into normal stuff like atoms.

For decades, scientists have been trying to catch these ghosts by building huge detectors deep underground (like Super-Kamiokande in Japan or XENONnT in Italy). They wait for a ghost to bump into a nucleus in their detector. So far, the ghosts have been very good at hiding.

This paper proposes a new way to catch them. Instead of waiting for a slow, lazy ghost from our own neighborhood (the Milky Way), the authors suggest we look for ghosts that have been super-charged by cosmic monsters far away in the universe.

The Setup: The Cosmic Pinball Machine

The paper focuses on two specific cosmic monsters, known as Active Galactic Nuclei (AGN):

1. TXS 0506+056: A "blazar," which is a galaxy with a jet of energy shooting straight at Earth.
2. NGC 1068: A galaxy with a massive black hole in the center, but no jet pointing at us.

These places are like massive cosmic pinball machines. They are churning out huge amounts of high-speed particles called Cosmic Rays (mostly protons).

The Mechanism:

1. The Setup: Around the black holes in these galaxies, there is a dense cloud of dark matter (the ghosts).
2. The Collision: The high-speed cosmic rays (the pinballs) crash into the dark matter ghosts.
3. The Boost: When they crash, the dark matter gets a massive energy boost. It goes from being a slow, lazy ghost to a speeding bullet.
4. The Journey: These super-fast ghosts travel across the universe and hit Earth.
5. The Detection: Because they are moving so fast, they have enough energy to knock into atoms in our detectors, creating a signal we can actually see.

The Twist: The "Inelastic" Ghost

The paper introduces a special type of dark matter called "Inelastic Dark Matter."

• Normal (Elastic) Collision: Imagine a billiard ball hitting another billiard ball. They bounce off, but they stay the same ball.
• Inelastic Collision: Imagine a billiard ball hitting another ball, but the second ball is actually a transformer. When hit, it instantly changes into a slightly heavier, excited version of itself.

In this paper, the dark matter has two states: a light one ($\chi_1$) and a heavy one ($\chi_2$).

• When a cosmic ray hits the light dark matter, it bumps it up to the heavy state ($\chi_2$).
• This heavy state is unstable. It quickly decays (falls apart) back into the light state, releasing a tiny bit of energy (like a photon or an electron pair).
• This "transformation" makes the dark matter much harder to catch with traditional detectors, which is why this new method is so important.

The New Strategy: Using Deep Inelastic Scattering

The authors did something clever that previous studies missed. They looked at "Deep Inelastic Scattering" (DIS).

• The Old Way: Scientists usually thought about cosmic rays hitting the dark matter like a bowling ball hitting a single pin.
• The New Way: The authors realized that at the incredibly high speeds found in these galaxies, the cosmic rays don't just hit the whole dark matter particle; they smash into the tiny quarks (the building blocks) inside the protons.
• The Result: This is like hitting a watermelon with a sledgehammer instead of a ping-pong ball. It creates a much bigger explosion of energy. This "Deep Inelastic" effect significantly increases the number of boosted dark matter particles reaching Earth, making them much easier to spot.

The Results: Catching the Ghosts

The team calculated how many of these super-charged ghosts would reach Earth from NGC 1068 and TXS 0506+056.

1. NGC 1068 is the Surprise Winner: Even though TXS 0506+056 has a powerful jet, the authors found that NGC 1068 actually produces a stronger signal for this specific type of dark matter. Why? Because it has a denser cloud of dark matter around its black hole, and it emits cosmic rays steadily (like a steady stream) rather than just in short bursts.
2. New Limits: By looking at data from the Super-Kamiokande detector, the authors set new rules. They said, "If dark matter behaves like this, we should have seen it by now. Since we didn't, this type of dark matter cannot exist in these specific configurations."
3. Ruling Out the "Thermal" Ghosts: They found that their method can test regions of dark matter that are theoretically predicted to exist (specifically, the kind of dark matter that would naturally fill the universe to the right amount). Previous experiments couldn't see these because the dark matter was too light or changed its form too quickly.

The Bottom Line

This paper is like upgrading from a net with big holes to a net with tiny holes. By realizing that cosmic rays in distant galaxies can smash into dark matter in a way that creates a "deep inelastic" explosion, the authors showed that we can use existing detectors (like Super-K) to hunt for a specific, tricky type of dark matter that was previously invisible to us. They didn't find the ghost, but they successfully narrowed down the hiding spots, telling us exactly where the ghost isn't.

Technical Summary

Technical Summary: Cosmic-ray boosted inelastic dark matter from neutrino-emitting active galactic nuclei

Problem Statement
Direct detection experiments have established stringent constraints on dark matter (DM) with masses in the GeV–TeV range, yet light DM (MeV scale) and inelastic DM models remain less constrained or entirely inaccessible to current terrestrial searches. In inelastic DM scenarios, the elastic scattering channel is often suppressed or forbidden (e.g., due to Majorana nature or mass splittings), while the inelastic channel ($\chi_1 \to \chi_2$) dominates. Standard direct detection relies on galactic halo DM, which lacks the kinetic energy to overcome the mass splitting threshold in many inelastic models. Previous works suggested that cosmic rays (CRs) scattering off DM in the Milky Way could produce a "boosted" flux, but these were limited to parameter spaces already ruled out by other probes. Furthermore, previous studies of CR-DM interactions in Active Galactic Nuclei (AGN) often focused on spectral distortions or specific blazar flares without fully addressing deep inelastic scattering (DIS), realistic CR distributions, or steady neutrino-emitting sources.

Methodology
The authors calculate the flux of CR-boosted DM reaching Earth from two specific multi-messenger sources: the blazar TXS 0506+056 and the Seyfert Type-II galaxy NGC 1068. The methodology involves:

1. Cosmic Ray Modeling: The authors model the CR proton spectra for both sources using leptohadronic models constrained by IceCube neutrino and electromagnetic observations. For TXS 0506+056, they utilize a jetted model with a Lorentz boost factor $\Gamma_B \approx 20$. For NGC 1068, they consider three cases (C1, C2a, C2b) representing different normalizations and spectral indices based on X-ray and neutrino data, assuming no jet ($\Gamma_B = 1$).
2. Dark Matter Distribution: They assume a "spike" profile for DM density around the supermassive black holes (SMBHs) of these AGN, formed by adiabatic growth. The column density of DM traversed by CRs is calculated analytically, accounting for the NFW profile outside the spike and saturation effects.
3. Scattering Physics: The interaction is modeled via a vector mediator $Z'$ coupling to SM fermions and a Dirac fermion DM pair ($\chi_1, \chi_2$) with a mass splitting $\delta$. The calculation includes:
   • Elastic/Inelastic Scattering: CR protons scatter off $\chi_1$ to produce $\chi_2$ ($\chi_1 + p \to \chi_2 + p$).
   • Deep Inelastic Scattering (DIS): At high energies, the scattering is treated as occurring off partons (quarks) within the proton, utilizing parton distribution functions (PDFs).
   • Decays: The excited state $\chi_2$ is assumed to decay rapidly back to $\chi_1$ (plus a photon or $e^+e^-$ pair) before reaching Earth, affecting the final flux geometry and energy.
   • Attenuation: The attenuation of the DM flux as it passes through the Earth is calculated using the Preliminary Reference Earth Model (PREM) to determine optical depth.
4. Experimental Constraints: The resulting boosted flux is propagated to Earth and compared against data from Super-Kamiokande (Super-K) and XENONnT.
   • Super-K: Constraints are derived from electron scattering (with and without angular cuts) and proton recoil data. DIS events in the detector are also considered.
   • XENONnT: Constraints are derived from nuclear recoil limits in the 3.3–60.5 keV energy window.

Key Contributions

• Inclusion of DIS: The paper explicitly incorporates deep inelastic scattering at both the source (AGN) and the detector (Super-K). This significantly enhances the boosted DM flux at high energies where form-factor suppression in elastic scattering would otherwise reduce the signal.
• Steady vs. Flaring Sources: Unlike previous works focusing solely on flaring blazars, this study includes NGC 1068, a steady neutrino emitter. The authors find that when DIS is included, the boosted flux from NGC 1068 can exceed that of TXS 0506+056 due to the higher DM column density inferred from its SMBH mass, despite the lack of a relativistic jet boost.
• Comprehensive Parameter Space: The analysis covers a wide range of DM masses ($m_\chi$), mass splittings ($\delta$), and mediator masses ($m_{Z'}$), specifically targeting regions where inelastic DM evades standard direct detection bounds.
• Realistic Attenuation: The study provides a detailed treatment of Earth attenuation, establishing a "ceiling" on the coupling strength beyond which the flux is completely blocked, preventing unphysical constraints.

Results

• Flux Characteristics: The boosted DM flux peaks at low energies for TXS 0506+056 due to jet kinematics, while NGC 1068 provides a broader spectrum. DIS contributions become dominant at higher energies, increasing the flux by orders of magnitude compared to elastic-only scenarios.
• Exclusion Limits:
  • Using Super-K electron scattering data, the authors derive upper limits on the DM-proton/electron scattering cross-sections.
  • For light DM ($m_\chi \lesssim 0.1$ GeV) with moderate mass splittings, the constraints improve upon previous bounds from beam dump experiments and CR cooling in AGN.
  • For larger mass splittings ($\delta \gtrsim 400$ keV), where direct detection is insensitive, the CR-boosted method probes thermal freeze-out regions that were previously uncharted.
  • The inclusion of DIS significantly tightens constraints for heavier DM masses ($m_\chi \gtrsim 0.1$ GeV) compared to elastic-only analyses.
• Source Comparison: While TXS 0506+056 is a powerful source due to its jet, NGC 1068 provides competitive or superior constraints in the DIS regime due to its steady emission and high DM density.
• XENONnT vs. Super-K: Constraints from XENONnT are generally weaker than those from Super-K for the scenarios considered, primarily due to significant attenuation of the DM flux through the Earth's atmosphere and crust for the parameter space where Super-K is sensitive.

Significance and Claims
The paper claims to provide novel bounds on light and inelastic dark matter models that are otherwise experimentally inaccessible. By leveraging the high CR luminosities and dense DM environments of neutrino-emitting AGN, the authors demonstrate that:

1. Thermal Relic Testing: The method can test regions of parameter space favored to reproduce the observed relic abundance of the Universe via thermal freeze-out, particularly for inelastic DM models.
2. Complementarity: The constraints are complementary to, and in some mass-splitting regimes superior to, those from colliders, beam dumps, and traditional direct detection.
3. Feasibility: The scenario remains viable even with mass splittings, offering a new avenue to probe DM that evades standard elastic scattering searches.

The authors note that their results depend on the assumed DM density profile (spike vs. NFW) and CR acceleration models. They suggest that future observations (e.g., Hyper-Kamiokande) and improved understanding of DM distributions in AGN could further strengthen these constraints. The work does not claim a detection but establishes robust exclusion limits that rule out specific thermal inelastic DM scenarios.