Constraints on ultraheavy dark matter from the CDEX-10 experiment at the China Jinping Underground Laboratory

The CDEX-10 experiment at the China Jinping Underground Laboratory reports the first search for ultraheavy dark matter using p-type point-contact germanium detectors, setting the most stringent constraints to date on spin-independent scattering cross sections for masses between $10^6$ and $10^{11}$ GeV based on an analysis of 205.4 kg$\cdot$day of data with no observed excess above background.

The Gist

Imagine the universe is filled with invisible "ghosts" called Dark Matter. For decades, scientists have been hunting for the most famous type of these ghosts: the WIMPs (Weakly Interacting Massive Particles). Think of WIMPs as tiny, elusive mice that might be hiding in the walls of the universe. We've built incredibly sensitive traps (detectors) to catch them, but so far, the traps are empty.

But what if the ghosts aren't mice at all? What if they are elephants? Or even blue whales?

This is the story of the CDEX-10 experiment, a team of scientists in China who decided to stop looking for mice and start looking for Ultraheavy Dark Matter (UHDM). These are hypothetical particles so massive that a single one could weigh as much as a small asteroid, yet they are so rare that only a few might pass through the entire Earth in a year.

Here is a simple breakdown of their adventure:

1. The Deep Underground Lab

To catch these ghosts, you need to hide from the noise of the surface world (like cosmic rays from space). The CDEX team built their lab inside a mountain in China, 2,400 meters (about 1.5 miles) underground.

• The Analogy: Imagine trying to hear a whisper in a library. To do that, you need to be in a soundproof basement. The mountain acts as a giant, thick blanket that blocks out the "noise" of the universe, leaving only the quietest, most subtle signals.

2. The Detector: A Super-Sensitive Scale

Inside this deep lab, they use a detector made of Germanium (a shiny, pure metal). It's cooled down to the temperature of liquid nitrogen (colder than outer space) to make it incredibly sensitive.

• The Analogy: Think of this detector as a super-precise bathroom scale. If a single feather (a tiny particle) lands on it, the scale should jump. The CDEX detector is so good it can weigh the "feather" of a dark matter particle hitting a single atom inside the metal.

3. The Problem: The "Earth Shield"

Here is the tricky part. Because these Ultraheavy Dark Matter particles are so massive, they interact with matter much more strongly than the tiny WIMPs.

• The Analogy: Imagine shooting a bullet (a normal particle) through a wall; it goes right through. Now imagine shooting a bowling ball (an Ultraheavy particle) through a wall. It hits the wall, loses energy, slows down, and might not even make it to the other side.
• The Earth Effect: As these heavy particles try to get to the lab, they have to travel through the Earth's atmosphere, the crust, the mantle, and the core. The Earth acts like a giant speed bump. If the particles interact too strongly, the Earth stops them completely before they reach the detector. If they interact too weakly, they zip right through without leaving a trace.

4. The Simulation: A Digital Time Machine

Since they couldn't catch the particles, the scientists built a virtual world on their computers.

• They simulated billions of these heavy particles trying to travel from space, through the Earth's core, and into their detector.
• They calculated how much the Earth would slow them down (the "Earth Shielding Effect").
• They figured out that if the particles are too heavy or interact too strongly, the Earth acts like a filter, blocking them out. If they are just right, they arrive with a specific "speed signature" that the detector can see.

5. The Result: The Great Silence

The team collected data for a long time (equivalent to 205.4 kilograms of detector running for a day). They looked for a "blip" on their scale—a tiny jump in energy that would say, "Hey, a heavy ghost just hit us!"

The result? Nothing. No blips. No ghosts. Just background noise.

6. What This Means

Even though they didn't find the particles, this is a huge success.

• The Analogy: Imagine you are looking for a specific type of lost key in a giant field. You don't find it, but you prove that the key cannot be in the northern half of the field because you checked every inch there.
• The Conclusion: The CDEX team has drawn a new "No Entry" zone on the map of physics. They have proven that Ultraheavy Dark Matter particles with certain masses and interaction strengths do not exist (or at least, they aren't interacting the way we thought).
• They set the strictest rules yet for these heavy particles, especially for those lighter than 100 million times the mass of a proton.

The Future

The scientists are already planning CDEX-50, a bigger, even more sensitive version of their detector.

• The Analogy: They are upgrading from a bicycle to a Ferrari. With the new machine, they hope to either catch these heavy ghosts or prove they are even more elusive than we thought, pushing the boundaries of our understanding of the universe.

In short: The CDEX team went deep underground with a super-sensitive scale, simulated how the Earth blocks heavy dark matter, and found nothing. But by finding nothing, they successfully ruled out a massive chunk of possibilities, helping us narrow down where the true nature of Dark Matter might be hiding.

Technical Summary

1. Problem Statement

While Weakly Interacting Massive Particles (WIMPs) in the GeV–TeV mass range are the most popular dark matter (DM) candidates, no direct detection signal has been observed. Consequently, theoretical interest has expanded to Ultraheavy Dark Matter (UHDM) with masses ranging from $10$ TeV to the Planck mass ($10^{19}$ GeV).

• The Challenge: UHDM has a significantly lower number density than WIMPs due to its high mass. To be detectable, UHDM must have a much larger interaction cross-section.
• The Earth Shielding Effect: High cross-sections cause UHDM particles to lose significant energy (velocity) as they traverse the Earth's atmosphere and crust before reaching underground detectors. This "Earth shielding" creates an upper limit on the detectable cross-section and alters the expected energy spectrum, making standard WIMP analysis methods insufficient.
• The Gap: Previous experiments (e.g., DAMA, CDMS, LZ) have set limits, but there is a need for more stringent constraints, particularly for solid-state detectors in the mass range below $10^8$ GeV, and a more rigorous simulation of the Earth shielding effect.

2. Methodology

The CDEX Collaboration utilized data from the CDEX-10 experiment, located at the China Jinping Underground Laboratory (CJPL) with a rock overburden of 2400 meters (6720 mwe).

• Detector System: The experiment uses a 10 kg array of p-type point-contact germanium (pPCGe) detectors. These are chosen for their ultralow energy threshold and excellent energy resolution. The system is shielded by high-purity oxygen-free copper, lead, and polyethylene, operating in liquid nitrogen.
• Data Set: The analysis covers an exposure of 205.4 kg·day collected between February 2017 and August 2018, focusing on the energy range of 0.16–4.16 keVee.
• Monte Carlo Simulation Framework:
  • Propagation Model: The authors developed a comprehensive simulation incorporating the Earth shielding effect. They modeled UHDM propagation as straight-line trajectories (valid for $m_\chi > 10^5$ GeV) through the atmosphere, Earth's core/mantle/crust, the Jinping mountain, and the detector's lead shield.
  • Velocity Attenuation: The simulation calculates velocity loss ($dv/dD$) based on the continuous energy attenuation method, accounting for the density profiles of different Earth layers and the specific incident angles of particles.
  • Cross-Section Models: Two scaling relations were tested:
    1. $A^4$ scaling: Cross-section scales with the square of the atomic mass number ($A^2$) for the nucleus, leading to an $A^4$ dependence relative to nucleon cross-sections.
    2. $A$-independent scaling: Cross-section is independent of the nucleus mass (per-nucleus scaling).
  • Energy Deposition: The simulation calculates energy deposition in the germanium detector, converting nuclear recoil energy to electron-equivalent energy using the Lindhard quenching factor. It handles both sparse collision regimes (simulating individual collisions) and dense regimes (continuous deposition).
• Data Analysis:
  • A background model was constructed by fitting K-shell and L-shell X-ray peaks from internal cosmogenic radionuclides.
  • A $\chi^2$ minimization method was applied to the residual spectrum (0.16–4.16 keVee) to compare the observed data against the simulated UHDM signal plus a flat background.
  • A 90% confidence level (CL) one-sided upper limit was derived using $\Delta\chi^2 = 1.64$.

3. Key Contributions

• Refined Earth Shielding Model: The paper introduces a detailed simulation that categorizes UHDM trajectories based on the specific Earth structures they traverse (Core, Mantle, Crust, Mountain). It demonstrates that the Earth's layered density structure significantly shapes the velocity distribution and energy spectrum of UHDM reaching the detector.
• Linear Propagation Validity: The authors provide a rigorous derivation and validation for the straight-line propagation approximation, calculating radial deviations due to multiple scattering. They establish that for the relevant mass range, the probability of UHDM missing the detector due to transverse deviation is negligible ($O(10^{-5})$).
• Dual Scaling Analysis: The study provides constraints for both the $A^4$ (nucleon) and $A$-independent (nucleus) cross-section scaling models, allowing for broader comparison with other experiments.
• Spectral Fitting: Unlike simple event counting, this work utilizes the shape of the expected energy spectrum to set limits, optimizing sensitivity to the specific signatures of UHDM after Earth shielding.

4. Results

• No Excess Observed: The analysis of the 205.4 kg·day dataset revealed no excess events above the expected background in the 0.16–4.16 keVee range.
• Exclusion Limits:
  • The study establishes the first exclusion limits for UHDM by the CDEX Collaboration.
  • Mass Range: Constraints are set for UHDM masses from $10^6$ to $10^{11}$ GeV.
  • Cross-Section Limits:
    • For the $A^4$ scaling model, the experiment excludes spin-independent UHDM-nucleon cross-sections.
    • For the $A$-independent scaling model, limits on UHDM-nucleus cross-sections are provided.
• Comparison with Other Experiments:
  • CDEX-10 provides the most stringent constraints for solid-state detectors below $10^8$ GeV.
  • The results are competitive with or superior to liquid scintillator experiments (like DEAP-3600) and other solid-state experiments (like Majorana and CDMS) in the lower mass range, primarily due to the low energy threshold and low background of the pPCGe detectors.
  • The exclusion region shape is directly influenced by the Earth's shielding structure; for instance, particles passing through the Earth's core are attenuated at lower cross-sections than those passing only through the mountain.

5. Significance

• Validation of Low-Threshold Detectors: The results demonstrate that low-background, low-threshold solid-state detectors are highly effective for searching for UHDM, particularly in the mass range where Earth shielding effects become dominant.
• Theoretical Constraints: By excluding specific regions of the mass-cross-section parameter space, the paper constrains theories of supersymmetry and other models predicting ultraheavy composite particles or primordial black holes.
• Future Outlook: The paper highlights the potential of the next-generation CDEX-50 experiment (50 kg of detectors). With a projected background reduction of two orders of magnitude, CDEX-50 is expected to probe even lower cross-sections and extend the exclusion limits to heavier mass regions ($>10^{12}$ GeV) by analyzing multiple interactions across the detector array.

In summary, this work represents a significant advancement in the direct detection of ultraheavy dark matter, leveraging the unique capabilities of the CDEX-10 experiment and a sophisticated Earth-shielding simulation to set the world's leading limits for solid-state detectors in the sub-$10^8$ GeV mass range.