Sub-GeV dark matter from cosmic ray bremsstrahlung in the atmosphere

This paper investigates the sensitivity of neutrino observatories and direct detection experiments to sub-GeV dark matter boosted by cosmic ray bremsstrahlung in the atmosphere, specifically modeling initial state radiation and $\rho/\omega$ resonances to extend mass limits and compare the capabilities of LZ, PandaX-4T, Borexino, and Super-K.

The Gist

Imagine the universe is filled with a mysterious, invisible substance called Dark Matter. For decades, scientists have been trying to catch a glimpse of it, but it's like trying to catch a ghost with a butterfly net. Most of the time, we look for "slow" dark matter drifting through our galaxy, but if that dark matter is very light (sub-GeV), it moves too gently to bump into our detectors hard enough to be noticed.

This paper proposes a clever new strategy: Don't wait for the ghost to walk by; build a cannon to shoot it at us.

Here is the breakdown of the paper's ideas using simple analogies:

1. The Cosmic Ray "Cannon"

Usually, we think of cosmic rays (high-energy particles from space) as a nuisance that creates background noise. But the authors say, "Let's use them as a weapon!"

• The Analogy: Imagine the Earth's atmosphere as a giant, natural billiard table. High-energy protons (cosmic rays) are the "cue balls" zooming down from space. When they hit the "cushions" (air molecules in the atmosphere), they don't just bounce; they smash into each other.
• The Result: In these violent collisions, a tiny bit of energy is converted into a new, invisible particle: Dark Matter. Because the original cosmic rays are moving so fast, the new dark matter particles get "boosted" to incredible speeds, much faster than the slow dark matter floating around in the galaxy.

2. The "Bremsstrahlung" Effect (The Brake Light)

The paper focuses on a specific way these particles are made, called bremsstrahlung. This is a German word meaning "braking radiation."

• The Analogy: Think of a car speeding down a highway. If the driver slams on the brakes, the car shudders and emits a sound or heat. In physics, when a charged particle (like a proton) is forced to change direction or slow down during a collision, it emits a burst of energy.
• The Twist: In this scenario, instead of emitting light, the proton emits a "dark photon" (a carrier of dark force), which immediately decays into two dark matter particles. The authors used a new, more precise mathematical model (like upgrading from a blurry photo to a 4K video) to calculate exactly how many of these particles are created.

3. The "Resonance" Sweet Spot

One of the paper's most exciting findings is about a specific "tuning fork" frequency in nature.

• The Analogy: Imagine pushing a child on a swing. If you push at random times, they don't go very high. But if you push exactly when the swing is at the top of its arc (the resonance), they fly super high.
• The Science: The authors found that if the "dark photon" has a specific mass (around 0.76 GeV), it hits a "resonance" with known particles called the rho and omega mesons. This acts like the perfect push on the swing, creating a massive spike in the number of dark matter particles produced. It's a "sweet spot" where the atmosphere becomes a super-efficient dark matter factory.

4. The Detectors: From Butterfly Nets to Fishnets

Because these dark matter particles are now moving super-fast (boosted), they hit detectors much harder than usual.

• The Old Way: Traditional dark matter detectors (like LZ and PandaX) are like butterfly nets. They are designed to catch slow, heavy ghosts. They are great at catching "nuclear recoils" (when a dark particle hits an atomic nucleus).
• The New Way: Because the boosted dark matter is so energetic, it can also knock electrons loose. This allows Neutrino Telescopes (like Super-Kamiokande and Borexino) to join the hunt.
• The Analogy: If the old detectors are butterfly nets, these neutrino telescopes are giant fishing nets. They are huge (holding thousands of tons of water) and are designed to catch fast-moving particles. Even though they usually look for neutrinos, they can now "feel" the heavy thud of a fast-moving dark matter particle hitting an electron.

5. The Verdict: What Did They Find?

The authors ran the numbers to see if these detectors could actually see this "boosted" dark matter.

• The Good News: They found that for certain types of dark matter (specifically those interacting via a "dark photon"), these experiments are actually quite sensitive. The "resonance" sweet spot makes the signal much stronger, potentially allowing us to see dark matter that was previously invisible.
• The Bad News: When they compared their results to other experiments (like particle accelerators that smash protons together in labs), the accelerators are still the "champions." They have tighter limits on what dark matter can be.
• The Takeaway: While we might not discover dark matter first with this method, it offers a complementary view. It's like looking at a sculpture from a different angle. If the dark matter has specific properties, these atmospheric experiments might be the only ones sensitive enough to find it, especially if the dark matter interacts with protons but not electrons.

Summary

This paper suggests we stop waiting for slow, shy dark matter to visit us. Instead, we should look at the "shrapnel" created when cosmic rays smash into our atmosphere. By using a more precise map of how these collisions work, we might find that our existing giant water tanks (neutrino detectors) and underground tanks (dark matter detectors) are already sitting on a goldmine of data, waiting for us to look at it with the right "lens."

Technical Summary

1. Problem Statement

The search for sub-GeV Dark Matter (DM) faces significant challenges in conventional direct detection experiments due to low nuclear recoil energy thresholds, which are optimized for Weakly Interacting Massive Particles (WIMPs). While accelerator-based searches and low-threshold experiments have made progress, there remains a need to explore alternative production mechanisms that can boost DM particles to higher energies, making them detectable in existing large-volume detectors.

Previous work on "atmospheric DM" focused primarily on DM production via meson decays. However, this paper addresses the need to extend the sensitivity reach to higher DM masses and explore the proton bremsstrahlung production mode. Specifically, the authors aim to:

• Revisit the atmospheric production mechanism using a more rigorous formalism for proton initial state radiation (ISR).
• Investigate the impact of vector mediator mixing with hadronic resonances (specifically $\rho/\omega$) on the DM flux.
• Determine the sensitivity of current direct detection experiments (LZ, PandaX-4T) and neutrino observatories (Borexino, Super-Kamiokande) to this boosted DM flux.

2. Methodology

A. Production Mechanism: Proton Bremsstrahlung

The authors model the production of Dark Vectors ($V$) via the inelastic scattering of cosmic ray protons in the Earth's atmosphere ($p + p \to p + V + X$).

• Formalism: They utilize a recently developed framework for proton ISR (based on Refs. [21–23]) which focuses on initial state radiation rather than the traditional Weizsäcker-Williams approximation.
• Cross-Section: The differential cross-section is factorized into a splitting function $w(z, p_T)$, a non-single diffractive $pp$ cross-section $\sigma_{NSD}$, and proton form factors ($F_p$).
  $$\frac{d^2\sigma_{br}}{dE_V d\theta} \approx 2\epsilon^2 p_T z \sigma_{NSD}(s') w(z, p_T^2) |F_p(m_V^2)|^2 K(p_V)$$
• Resonance Enhancement: A key feature of their model is the inclusion of precision fits for proton monopole and dipole form factors. This allows for significant enhancement in DM production when the dark vector mass ($m_V$) aligns with hadronic vector meson resonances, particularly the $\rho$ and $\omega$ mesons.
• Flux Calculation: The DM flux is derived by convolving the cosmic ray proton spectrum (modeled as a power law $E_p^{-2.7}$ above $\sim 10$ GeV) with the splitting probability. The calculation assumes all cosmic ray protons scatter in the atmosphere due to the short mean free path.

B. Detection Signatures

The paper analyzes the detection of these boosted DM particles ($\chi$) via two channels:

1. Nuclear Recoil: Scattering off nuclei in direct detection experiments (LZ, PandaX-4T).
2. Electron Recoil: Scattering off electrons in neutrino telescopes (Borexino, Super-K).

The event rate is calculated by integrating the differential DM flux over the detector's recoil energy range ($T_1$ to $T_2$):
$$N(m_\chi, R, \epsilon) = \mathcal{E} \int_{T_1}^{T_2} dT_r \, \epsilon(T_r) \int_{E_{min}}^\infty dE_\chi \frac{d\Phi_\chi}{dE_\chi} \frac{d\sigma_{\chi r}}{dT_r}$$
Where $R = m_V/m_\chi$ is the mass ratio. The analysis considers two benchmark scenarios:

• Canonical Slice: $R = 2.5$.
• Resonant Slice: $m_V = 0.76$ GeV (near the $\rho/\omega$ resonance peak).

3. Key Contributions

1. Refined Production Model: The authors extend the atmospheric DM mass reach by implementing a sophisticated ISR formalism that incorporates proton form factors. This allows for a more accurate calculation of the production rate, particularly near vector meson resonances.
2. Resonance-Driven Enhancement: They demonstrate that the cosmic ray flux peak combined with vector mixing near the $\rho/\omega$ resonances leads to a dramatic enhancement in the DM flux, significantly boosting the sensitivity of detectors for specific mediator masses.
3. Comprehensive Detector Comparison: The study provides a unified comparison of sensitivity across:
   • Direct Detection: LZ and PandaX-4T (sensitive to nuclear scattering).
   • Neutrino Detectors: Borexino and Super-K (sensitive to electron scattering).
   • Accelerator Limits: Comparison with BaBar, NA64, and others.
4. Threshold Advantage: The paper highlights that while direct detection experiments are limited by $\mathcal{O}(10 \text{ keV})$ thresholds, neutrino detectors with $\mathcal{O}(\text{MeV}-\text{GeV})$ thresholds are uniquely suited to detect the high-energy recoil signatures of boosted atmospheric DM.

4. Results

• Flux Characteristics: The calculated DM flux exhibits a "box" distribution in energy due to the two-body decay of the vector mediator. The flux is strongly correlated with the incoming proton energy, with a steep fall-off at low energies due to the relativistic cutoff applied to the cosmic ray spectrum.
• Sensitivity Contours:
  • Canonical Case ($R=2.5$): For this mass ratio, the sensitivity contours for atmospheric DM are largely excluded by existing direct detection limits (e.g., CRESST-III for nuclear scattering and PandaX-4T/DarkSide for electron scattering).
  • Resonant Case ($m_V \approx 0.76$ GeV): When the mediator mass is tuned to the $\rho/\omega$ resonance, the production rate is enhanced. In this regime, the sensitivity of LZ and Super-K exceeds conventional direct detection limits for specific parameter slices.
• Comparison with Accelerators:
  • The sensitivity of atmospheric production is generally not competitive with current fixed-target and collider experiments (like BaBar) in the $\rho/\omega$ resonance regime, where BaBar's missing mass limits dominate.
  • However, the atmospheric limits are significant because they rely on hadronic couplings (proton bremsstrahlung) and do not strictly require leptonic couplings, whereas many accelerator limits (like BaBar) rely heavily on electron couplings.
• Detector Performance:
  • Neutrino Detectors: Super-K and Borexino show superior sensitivity for electron scattering due to their large volume and ability to handle higher recoil energies.
  • Direct Detection: LZ and PandaX-4T provide competitive constraints for nuclear scattering, particularly when the DM mass is low enough to produce detectable nuclear recoils despite the high boost.

5. Significance and Future Outlook

• Complementarity: This work establishes atmospheric bremsstrahlung as a complementary probe to meson-decay production and accelerator searches. It is particularly valuable for models where DM couples primarily to quarks (baryons) rather than leptons.
• Future Potential: The authors note that the sensitivity of this method scales with exposure. Future large-volume neutrino detectors (Hyper-K, DUNE, JUNO) could significantly improve these limits, potentially surpassing current accelerator bounds in specific kinematic regimes.
• Theoretical Robustness: By utilizing the latest form-factor parameterizations and ISR formalisms, the paper provides a more robust theoretical foundation for interpreting null results or potential signals in the context of sub-GeV DM.

In conclusion, the paper demonstrates that while terrestrial accelerators currently hold the strongest constraints for vector-mediated sub-GeV DM, atmospheric production via cosmic ray bremsstrahlung offers a unique, resonance-enhanced channel that probes different coupling structures and remains a viable target for next-generation neutrino and direct detection experiments.