Constraints on light dark matter from primordial black hole evaporation at dark matter direct detection experiments

This paper utilizes recent data from underground direct detection experiments (XENONnT, PandaX-4T, and LZ) to constrain the scattering cross sections of light dark matter and the fraction of dark matter composed of primordial black holes by analyzing the flux of boosted dark matter particles produced via Hawking radiation from both partially and fully evaporated primordial black holes.

The Gist

The Big Idea: Hunting Ghosts with "Hot" Dark Matter

Imagine the universe is filled with Dark Matter. We know it's there because it holds galaxies together, but we've never seen it. For decades, scientists have been looking for "cold" dark matter—particles that are heavy and move very slowly, like a sleepy bear wandering through a forest.

But this paper asks a different question: What if some of that dark matter is actually "hot" and moving incredibly fast?

The authors propose a scenario involving Primordial Black Holes (PBHs). These aren't the black holes made from dead stars; they are tiny, ancient black holes formed in the very first split second of the Big Bang. Think of them as microscopic time capsules.

The Mechanism: The Black Hole "Popcorn Machine"

According to a famous theory by Stephen Hawking, black holes aren't truly black; they slowly leak energy and particles. This is called Hawking Radiation.

• The Analogy: Imagine a PBH is a tiny, super-hot popcorn machine. As it gets smaller, it gets hotter. Eventually, it starts popping out particles at high speeds.
• The Twist: If there is a type of light dark matter particle (let's call it a "ghost") that is light enough, this popcorn machine will shoot it out at near-light speeds.
• The Result: Instead of a sleepy bear, we have a bullet train of dark matter zooming through the galaxy. This is what the paper calls "Boosted Dark Matter."

The Challenge: The Earth Shield

Here is the problem: These "bullet trains" of dark matter are heading toward Earth. But to catch them, we have detectors buried deep underground (like XENONnT, PandaX, and LZ).

• The Analogy: Imagine the dark matter particles are trying to run a marathon to reach the finish line (the detector). But to get there, they have to run through a thick wall of mud (the Earth's crust).
• The Attenuation Effect: As these fast particles run through the mud, they bump into atoms and lose energy. Some stop completely; others slow down significantly.
• The Paper's Contribution: The authors did the math to figure out exactly how much energy these particles lose before they even reach the detector. They realized that if the dark matter interacts too strongly with the Earth, it gets stopped before it can trigger the alarm. If it interacts too weakly, it might pass right through without being noticed.

The Investigation: Listening for the "Ping"

The scientists used data from three massive, ultra-sensitive detectors deep underground. These detectors are like incredibly sensitive microphones waiting to hear a single drop of water hit a pool.

1. The Setup: They calculated how many "bullet train" dark matter particles should be hitting the detector based on the PBH theory.
2. The Comparison: They compared their predictions against the actual data from the detectors.
3. The Result: The detectors didn't hear any "pings." The background noise was exactly what they expected from normal radioactive decay, with no extra signals from dark matter bullets.

The Conclusion: Ruling Out the Suspects

Because they didn't find any signals, the authors had to draw a line in the sand. They said:

• "If dark matter interacts with electrons or atomic nuclei this strongly, we would have seen it by now."
• Since we didn't see it, those specific combinations of "how heavy the dark matter is" and "how strongly it interacts" are ruled out.

They also looked at the Primordial Black Holes themselves. They calculated: "If the universe was made of 100% of these tiny black holes, we would have seen their evaporation signals." Since we didn't, they placed strict limits on how many of these black holes can exist.

The "Fully Evaporated" Mystery

The paper also looked at black holes that were so small they have already completely evaporated (turned into pure energy). Even though they are gone, the "ghosts" they shot out billions of years ago might still be flying around today. The authors calculated that even these "ghosts" from dead black holes would have left a trace in our detectors. The fact that we see nothing means we can also rule out certain theories about how many of these ancient black holes were created in the beginning of time.

Summary in One Sentence

This paper uses the silence of our deepest underground detectors to prove that if tiny, ancient black holes are shooting out fast-moving dark matter particles, those particles can't be interacting with normal matter as strongly as some theories suggest, and there can't be as many of those black holes as some people hoped.

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains unknown. While Weakly Interacting Massive Particles (WIMPs) have been the leading candidate, null results from direct detection (DD) experiments have pushed the exclusion limits for DM-nucleon scattering cross-sections down to $\sim 10^{-46} \text{--} 10^{-47} \text{ cm}^2$. This has spurred interest in alternative scenarios, specifically:

1. Light Dark Matter (LDM): Sub-GeV particles that evade traditional WIMP constraints due to suppressed nuclear recoil energies.
2. Primordial Black Holes (PBHs): Black holes formed in the early universe that could constitute a fraction of DM.

A specific gap exists in the literature regarding the production of Boosted Dark Matter (BDM) via Hawking radiation from PBHs. Previous studies often:

• Relied on older DD data with lower exposure.
• Focused exclusively on either DM-electron or DM-nucleus scattering, rather than both.
• Assumed a monochromatic PBH mass distribution that has not fully evaporated, neglecting the contribution from PBHs that have already completely evaporated (mass $< M_{th} \approx 7.5 \times 10^{14}$ g).
• Often ignored the attenuation effect of DM particles traversing the Earth's matter before reaching underground detectors.

This paper aims to provide a comprehensive analysis using the latest data from XENONnT, PandaX-4T, and LZ to constrain light DM produced by PBH evaporation, accounting for both scattering channels, Earth attenuation, and the full mass evolution of PBHs.

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2. Methodology

A. Theoretical Framework: PBH Evaporation and DM Flux

• Hawking Radiation: The authors model the emission of Dirac fermionic DM particles ($\chi$) from PBHs. The differential spectrum is calculated using the BlackHawk v2.3 code, incorporating graybody factors.
• Flux Components: The total DM flux at Earth is the sum of:
  • Galactic (MW): Emission from PBHs currently residing in the Milky Way halo (modeled with an NFW profile).
  • Extragalactic (EG): Cumulative emission from PBHs throughout cosmic history, redshifted to the present.
• Mass Evolution Scenarios:
  1. Partially Evaporated ($M_{PBH} \gtrsim 9 \times 10^{14}$ g): PBHs are stable enough that their mass and Hawking temperature remain effectively constant over the age of the universe.
  2. Fully Evaporated ($10^{13} \text{ g} \lesssim M_{PBH} \lesssim 6 \times 10^{14}$ g): PBHs have completely evaporated by today. The authors perform a time-integrated calculation of the flux, accounting for the changing mass and temperature of PBHs during their lifetime. The initial abundance is parameterized by $\beta'_{PBH}$ rather than the current fraction $f_{PBH}$.

B. Attenuation in Earth Matter

A critical component of the analysis is the attenuation effect. As high-energy DM particles traverse the Earth to reach underground detectors, they lose energy via scattering with electrons and nuclei.

• The authors solve the energy loss differential equation ($dT/dx$) considering the Earth's density profile.
• They calculate the attenuated flux at the detector depth ($z$) as a function of the initial surface flux.
• Key Finding: For large scattering cross-sections, the flux is significantly suppressed. However, for specific masses (near the electron mass $m_e$), scattering can cause a "pile-up" of events at lower energies, enhancing the flux in specific kinematic regions.

C. Direct Detection Event Rates

The expected event rates are computed for three major liquid xenon (LXe) experiments: XENONnT, PandaX-4T, and LZ.

• Scattering Channels:
  • DM-Electron ($\chi$-$e$): Calculated using the response function for electron recoil (ER).
  • DM-Nucleus ($\chi$-$N$): Calculated for nuclear recoil (NR). Since these experiments report data in electron-equivalent energy, the authors apply the Lindhard quenching factor to convert NR energies to ER signals.
• Statistical Analysis:
  • XENONnT & PandaX: Gaussian $\chi^2$ analysis comparing predicted signal + background against observed data.
  • LZ: Poissonian $\chi^2$ analysis (due to lower event counts).
  • Exclusion Limits: Derived at $2\sigma$ confidence level ($\Delta \chi^2 \approx 6.18$).

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3. Key Contributions

1. Comprehensive Multi-Channel Analysis: Unlike previous works focusing on a single channel, this study simultaneously constrains both DM-electron and DM-nucleus scattering cross-sections using the same dataset.
2. Inclusion of Attenuation Effects: The paper rigorously models the energy loss of boosted DM in the Earth's crust, demonstrating how this effect creates non-trivial features in the exclusion contours (e.g., dips and bumps) depending on the DM mass and cross-section.
3. Full Mass Range Coverage:
   • Constraints on non-evaporated PBHs ($9 \times 10^{14} \text{--} 10^{16}$ g) in terms of the current DM fraction $f_{PBH}$.
   • Constraints on fully evaporated PBHs ($10^{13} \text{--} 6 \times 10^{14}$ g) in terms of the initial formation abundance $\beta'_{PBH}$.
4. Utilization of Latest Data: The analysis incorporates the most recent exposure and background rejection capabilities of XENONnT, PandaX-4T, and LZ, significantly improving sensitivity over prior studies.

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4. Key Results

A. Constraints on Scattering Cross-Sections

For a benchmark PBH mass of $M_{PBH} = 10^{15}$ g and a DM fraction $f_{PBH} = 1.6 \times 10^{-8}$:

• DM-Electron Scattering ($\sigma_{\chi e}$):
  • Excluded range: $7.8 \times 10^{-34} \text{ cm}^2 \lesssim \sigma_{\chi e} \lesssim 4.5 \times 10^{-28} \text{ cm}^2$ (for $m_\chi \lesssim 10^{-5}$ GeV).
  • Feature: A distinct dip in the exclusion limit occurs around $m_\chi \approx 0.5$ MeV (near the electron mass). This is due to the kinematic suppression of the response function and the maximization of the attenuation effect at this mass.
• DM-Nucleus Scattering ($\sigma_{\chi n}^{SI}$):
  • Excluded range: $3.8 \times 10^{-38} \text{ cm}^2 \lesssim \sigma_{\chi n}^{SI} \lesssim 4.5 \times 10^{-27} \text{ cm}^2$.
  • The exclusion contour is nearly flat for $m_\chi < 10^{-2}$ GeV because the heavy nuclear target washes out the kinematic features seen in electron scattering.

B. Constraints on PBH Abundance

• Partially Evaporated PBHs ($9 \times 10^{14} \text{--} 10^{16}$ g):
  • The upper limit on $f_{PBH}$ becomes more stringent as $M_{PBH}$ decreases (due to higher Hawking temperatures).
  • For $M_{PBH} = 9 \times 10^{14}$ g and $\sigma_{\chi e} = 10^{-30} \text{ cm}^2$, $f_{PBH} \lesssim 4.5 \times 10^{-12}$.
  • XENONnT provides the most stringent bounds among the three experiments due to better background modeling.
• Fully Evaporated PBHs ($10^{13} \text{--} 6 \times 10^{14}$ g):
  • Constraints are re-cast in terms of the initial abundance parameter $\beta'_{PBH}$.
  • For $M_{PBH} = 6 \times 10^{14}$ g, $\beta'_{PBH} \lesssim 2 \times 10^{-27}$ (for $\sigma_{\chi e} = 10^{-30} \text{ cm}^2$).
  • These limits are comparable to, and often stronger than, existing constraints from the Extragalactic Gamma-Ray Background (IGRB) and CMB anisotropies.

C. Spectral Evolution

The study confirms that for PBHs with lifetimes shorter than the age of the universe, the mass evolution significantly alters the emitted spectrum. However, for the mass range $10^{13} \text{--} 6 \times 10^{14}$ g, the time-dilation effect and the integration over cosmic time allow for a robust calculation of the residual flux observable today.

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5. Significance

• Enhanced Sensitivity: This work demonstrates that underground direct detection experiments are highly sensitive to Boosted Dark Matter scenarios, probing cross-sections orders of magnitude lower than those accessible to traditional WIMP searches for sub-GeV masses.
• Complementarity: The results highlight the complementarity between cosmological bounds (IGRB, CMB) and direct detection. While cosmological bounds constrain the total energy injection, DD experiments provide unique sensitivity to the specific interaction cross-sections of the DM particles.
• Model Independence: By treating the scattering as a general effective interaction (independent of specific UV-complete models), the constraints apply broadly to any light DM candidate produced by PBH evaporation.
• Future Prospects: The analysis establishes a robust framework for interpreting future data from next-generation detectors (e.g., DARWIN) in the context of PBH-evaporated dark matter, particularly for the fully evaporated mass window which was previously less explored in DD contexts.

In conclusion, this paper significantly tightens the constraints on light dark matter produced by primordial black holes, ruling out large regions of the parameter space for both scattering cross-sections and PBH abundance fractions, while providing a detailed methodology for handling attenuation and mass evolution effects.