Cosmic Ray Boosted Dark Matter in COSINUS: Modeling and Constraints

This paper presents a catalog of dark matter-nucleon scattering cross sections for various mediator types and derives projected constraints on sub-GeV boosted dark matter for the COSINUS experiment, demonstrating its potential to probe light dark matter masses despite higher energy thresholds.

The Gist

The Big Mystery: The Invisible Ghost

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 don't interact with light. Scientists have been trying to catch these ghosts for decades using giant detectors deep underground.

The Problem: Most of these ghosts are very light and move very slowly. Imagine trying to catch a feather floating gently in a room with a net that only catches heavy bowling balls. The detectors are usually set to ignore tiny, gentle nudges because they think those are just background noise (like a leaf rustling). So, the lightest, fastest ghosts slip right through the net unnoticed.

The Solution: The "Cosmic Ray" Pinball Machine

This paper proposes a clever trick to catch those light ghosts. Instead of waiting for them to wander into the detector on their own, the scientists suggest we give them a boost.

Think of Cosmic Rays as high-speed bullets flying through space. Occasionally, a cosmic ray bullet smashes into a slow-moving dark matter ghost.

• The Analogy: Imagine a slow-moving billiard ball (the dark matter) sitting on a table. A super-fast cue ball (the cosmic ray) hits it. Suddenly, the slow ball shoots across the table at high speed.
• The Result: This "boosted" dark matter is now moving fast enough to hit the detector hard enough to be seen, even if the detector isn't sensitive enough to catch the slow ones.

The Experiment: COSINUS

The paper focuses on a specific experiment called COSINUS, located deep underground in Italy (to shield it from other noise).

• The Detector: It uses crystals made of Sodium Iodide (like table salt mixed with iodine).
• How it works: When a particle hits the crystal, it creates two things: a tiny flash of light (scintillation) and a vibration in the crystal lattice (phonons). By measuring both, the detector can tell the difference between a "ghost" (dark matter) and a "human" (background radiation).
• The Goal: The team wants to see if they can detect these "boosted" dark matter particles that have been kicked into high gear by cosmic rays.

The "Menu" of Possibilities

The scientists didn't just guess; they built a detailed menu of how these interactions could happen. They considered different types of dark matter (like heavy fermions, scalars, or vectors) and different types of "messengers" (mediators) that carry the force between the cosmic ray and the dark matter.

• The Heavy Mediator: Imagine the force between particles is carried by a heavy brick. If the brick is heavy enough, the interaction looks simple and consistent.
• The Findings: They found that for most types of interactions, the "boosted" scenario makes the detector much more sensitive. However, there is one tricky case (the "pseudoscalar" mediator) where the interaction is suppressed, making it harder to see.

The "Double Boost" (Neutrinos)

The paper also looked at a second source of boosts: Neutrinos.

• The Source: When massive stars explode (supernovae), they shoot out a flood of neutrinos. These are like a gentle rain of invisible particles.
• The Effect: If dark matter interacts with these neutrinos, they can get a second boost. The paper shows that adding this "neutrino boost" to the "cosmic ray boost" creates an even stronger signal, especially for very light dark matter.

The Conclusion: What's Next?

The authors ran the numbers to see what COSINUS could achieve if it runs for a while (collecting data equivalent to 100 kilograms of detector running for a day).

• The Verdict: Even though they haven't found dark matter yet, this study shows that COSINUS has the potential to rule out (or find) dark matter particles that are much lighter than previously thought possible.
• The Takeaway: By using the universe's own high-energy particles (cosmic rays and neutrinos) as a "slingshot," we can turn our detectors into much more powerful hunters for the elusive, lightest dark matter.

In a nutshell: We are trying to catch invisible, slow-moving ghosts. They are too light to trigger our alarms. But if we wait for a cosmic "bullet" to hit them first, they get a speed boost, fly into our detector, and finally ring the bell! This paper maps out exactly how that could happen and how good our detector is at hearing that bell.

Technical Summary

1. Problem Statement

Direct detection of sub-GeV dark matter (DM) is hindered by the low kinetic energy of non-relativistic DM particles in the galactic halo ($v \sim 10^{-3}c$). Standard detectors typically have energy thresholds of a few keV, making them insensitive to DM masses below a few GeV because the resulting nuclear recoil energy falls below the detection threshold. While low-threshold detectors have improved sensitivity down to hundreds of MeV, they are increasingly limited by background event rates rather than energy thresholds.

The paper addresses how to probe sub-MeV to sub-GeV dark matter by utilizing the Boosted Dark Matter (BDM) framework. In this scenario, high-energy cosmic rays (CRs) or neutrinos scatter off halo DM particles, transferring significant kinetic energy and "boosting" them to relativistic or semi-relativistic speeds. These boosted particles can then induce nuclear recoils above the detector threshold, even for very light DM masses.

2. Methodology

A. Theoretical Framework & Flux Calculation

The authors model the BDM flux generated by the scattering of halo DM with:

1. Cosmic Rays (CRs): Primarily protons and Helium nuclei from the Local Interstellar Spectra (LIS).
2. Diffuse Supernova Neutrino Background (DSNB): High-energy neutrinos from past supernovae.

The calculation involves:

• Kinematics: Deriving the maximum kinetic energy ($T_{\chi}^{max}$) a DM particle can acquire after scattering with a CR or neutrino.
• Differential Flux: Calculating the differential BDM flux ($d\Phi_\chi/dT_\chi$) by integrating the LIS/DSNB flux over the scattering cross-section.
• Form Factors: Incorporating nuclear form factors (dipole form for CRs, Helm form for detector nuclei) to account for finite nuclear size effects.
• Attenuation: Solving the differential equation for energy loss as BDM particles traverse the Earth's crust (Gran Sasso depth). The authors found attenuation negligible for their specific exposure assumptions.

B. Interaction Models

The study systematically categorizes DM-nucleon interactions in the heavy mediator limit ($m_\phi^2 \gg q^2$), covering various spin configurations for DM and mediators:

• DM Types: Fermion, Scalar, and Vector.
• Mediator Types: Scalar, Pseudoscalar, Vector, and Axial-Vector.
• Cross-Sections: The authors derive energy-dependent differential cross-sections ($d\sigma/dT_\chi$) for all combinations. They compare these against a baseline energy-independent contact interaction model.

C. Experimental Setup: COSINUS

The analysis is applied to the COSINUS experiment, which uses Sodium Iodide (NaI) cryogenic scintillating calorimeters at the Gran Sasso National Laboratory (LNGS).

• Exposure: Projected 100 kg·d.
• Threshold: 1 keV nuclear recoil energy.
• Resolution: 0.2 keV baseline.
• Background: Modeled using a simulation-based background model with particle discrimination (phonon + light readout) to distinguish nuclear recoils from electron recoils.

D. Statistical Analysis

• Likelihood Analysis: A Monte Carlo procedure generates random event counts based on a Poisson distribution for 50 energy bins (1–51 keV).
• Hypothesis Testing: A likelihood ratio test compares the background-only hypothesis ($\bar{\sigma}_{\chi i} = 0$) against the signal hypothesis to determine 90% Confidence Level (CL) exclusion limits.
• Parameters: The free parameters are the DM mass ($m_\chi$) and the reference DM-nucleon cross-section ($\bar{\sigma}_{\chi i}$).

3. Key Contributions

1. Comprehensive Catalog of Cross-Sections: The paper provides a complete set of analytical expressions for the differential cross-sections of BDM scattering for Fermion, Scalar, and Vector DM interacting via Scalar, Pseudoscalar, Vector, and Axial-Vector mediators.
2. Model-Dependent Sensitivity: It demonstrates that assuming an energy-independent contact interaction is a conservative estimate. Most energy-dependent models (specifically those involving Scalar, Vector, and Axial-Vector mediators) yield significantly stronger constraints (orders of magnitude better) than the contact interaction limit.
3. DSNB Contribution: The study quantifies the contribution of the Diffuse Supernova Neutrino Background to the BDM flux. It shows that neutrino scattering adds a secondary peak to the BDM flux at lower energies, enhancing sensitivity specifically for energy-independent and pseudoscalar mediator scenarios.
4. COSINUS Projections: It presents the first projected constraints for the COSINUS experiment on sub-GeV BDM, filling a gap in the sensitivity landscape between low-threshold experiments and heavy-target experiments like LZ.

4. Results

• Fermion DM:

  • The Pseudoscalar mediator scenario yields the weakest constraints due to momentum-transfer suppression ($\propto T_\chi^2$).
  • Scalar, Vector, and Axial-Vector mediators provide significantly tighter bounds compared to the energy-independent case.
  • COSINUS projections are competitive with or superior to current BDM limits from LZ (LUX-ZEPLIN) in specific mass ranges, particularly for light DM.

• Scalar DM:

  • Similar to Fermion DM, the Pseudoscalar case is suppressed (linear in $T_\chi$), while other mediators offer improved sensitivity.
  • The Vector mediator provides slightly stronger bounds than the Axial-Vector case in this scenario.

• Vector DM:

  • The analysis extends to Vector DM, deriving new scattering functions. The results follow the trend where heavy mediator scenarios (excluding Pseudoscalar) outperform the contact interaction limit.

• Impact of Neutrinos (DSNB):

  • Including DSNB interactions significantly improves sensitivity for the energy-independent and Pseudoscalar cases.
  • For other mediator types, the CR contribution dominates, making the neutrino addition less critical but still non-negligible.

• Comparison: The projected limits for COSINUS (100 kg·d) are shown to be competitive with CRESST-III and LZ results, particularly in the sub-GeV mass region where traditional direct detection fails.

5. Significance

• Extending the Reach: This work demonstrates that experiments with higher energy thresholds (like COSINUS) can effectively probe sub-GeV dark matter if the BDM framework is utilized, bypassing the need for ultra-low thresholds that are difficult to achieve experimentally.
• Model Discrimination: By providing constraints for specific mediator spins and parities, the paper moves beyond generic "contact interaction" limits, allowing for more rigorous testing of specific Beyond Standard Model (BSM) theories.
• Synergy of Sources: It highlights the importance of considering multiple astrophysical sources (CRs and Neutrinos) for boosting DM, showing that the DSNB is a crucial component for probing specific interaction types (like pseudoscalar couplings) that are otherwise difficult to constrain.
• Future Guidance: The results provide a roadmap for the COSINUS collaboration and similar experiments to optimize their search strategies for light dark matter, emphasizing the need to account for energy-dependent cross-sections in data analysis.

In summary, the paper establishes that COSINUS has the potential to set world-leading constraints on sub-GeV Boosted Dark Matter, provided that the specific energy-dependent nature of the DM-mediator interaction is correctly modeled, and that neutrino-induced boosting is considered for a complete picture.