First search for light fermionic dark matter absorption on electrons using germanium detector in CDEX-10 experiment

Using 205.4 kg·day of data from the CDEX-10 experiment with a 160 eVee threshold, the study reports the first search for sub-MeV fermionic dark matter absorption on germanium electrons, finding no significant signals and setting new upper limits on the DM-electron interaction cross section for vector and axial-vector interactions in the 0.1–10 keV/$c^2$ mass range.

The Gist

Imagine the universe is a giant, dark ocean. We know there's something huge swimming in it called Dark Matter, but we've never seen it, touched it, or heard it. It's like a ghost that makes up about a quarter of everything in existence, yet it ignores us completely.

For decades, scientists have been trying to catch these ghosts. The usual strategy is to wait for a heavy ghost (called a WIMP) to bump into a heavy object (like an atom's nucleus) and give it a little shove. But what if the ghosts are actually tiny, feather-light particles? If they are too light, they won't have enough "oomph" to bump a heavy nucleus. They would just bounce off without leaving a trace.

The New Strategy: The "Absorption" Trick

This paper from the CDEX-10 experiment in China tries a completely different approach. Instead of waiting for a ghost to bump into something, they are looking for a ghost to get eaten.

Think of it like this:

• Old Way: A tiny mosquito (Dark Matter) tries to hit a bowling ball (Atomic Nucleus). The bowling ball barely moves.
• New Way: The mosquito flies into a vacuum cleaner (an Electron). The vacuum cleaner sucks it up. The energy of the mosquito doesn't just push the vacuum; it gets absorbed, giving the vacuum a sudden, sharp jolt of energy.

The scientists are looking for these "jolts" in a very sensitive detector made of Germanium (a material used in computer chips).

The Detective Work: The CDEX-10 Experiment

The experiment is located deep underground in a mountain in China (the China Jinping Underground Laboratory). Why so deep? To block out cosmic rays from space that would create too much noise, like trying to hear a whisper in a rock concert.

They used a detector called CDEX-10, which is essentially a super-sensitive Germanium crystal.

• The Sensitivity: This detector is so sensitive it can hear a sound as quiet as a single drop of water hitting a lake from a mile away. In energy terms, it can detect a tiny amount of energy called 160 eVee.
• The Data: They collected data for about 205 days (measured in "kilogram-days," which is like weighing the detector and the time it ran).

What They Were Looking For

The team was hunting for fermionic dark matter (a specific type of ghost particle) that is very light—weighing between 0.1 and 10 keV. To put that in perspective, an electron is about 511 keV, so these dark matter particles are much lighter than an electron, but heavier than a neutrino.

They were looking for a specific signature:

1. A dark matter particle flies into the Germanium crystal.
2. It gets absorbed by an electron inside the crystal.
3. The electron gets a sudden kick of energy and jumps to a higher level.
4. The detector records this tiny flash of energy.

They calculated exactly what this "flash" should look like for different weights of dark matter. It's like knowing exactly what the sound of a specific bird should be so you can pick it out of a forest full of noise.

The Result: The Silence

After analyzing millions of data points, the scientists found nothing.

There was no mysterious "jolt" that matched the pattern of dark matter being absorbed. The detector only saw the usual background noise: tiny bits of radiation from the rocks around them, cosmic dust, and the natural radioactivity of the detector materials themselves.

The Good News:
Even though they didn't find the ghost, they found out where the ghost isn't.

They set a new "No-Go Zone." They can now say with 90% confidence: "If this type of dark matter exists, it interacts with electrons less than [a specific tiny number] times."

• For the "Vector" interaction (one type of handshake between particles), the limit is 6.8 × 10⁻⁴⁶ cm².
• For the "Axial-Vector" interaction (a slightly different handshake), the limit is 2.3 × 10⁻⁴⁶ cm².

These numbers are incredibly small. Imagine trying to hit a specific atom on a specific grain of sand on a beach the size of the Earth, but the "hit" has to happen less than once in a trillion years.

Why This Matters

This is a major step forward because:

1. It's the Lightest: Previous experiments mostly looked for heavy dark matter. This experiment is the first to set such strict limits on very light dark matter (the "feather-light" ghosts) using the absorption method.
2. It's a New Tool: It proves that using low-threshold Germanium detectors is a viable way to hunt for these elusive, light particles.
3. It Closes the Door: By ruling out these specific interaction strengths, they force theorists to rethink their ideas. If dark matter exists, it must be even more elusive or interact in a way we haven't thought of yet.

In Summary:
The CDEX-10 team built a super-sensitive ear to listen for the universe's lightest ghosts. They didn't hear the ghosts, but they successfully proved that the ghosts aren't hiding in the specific spot they were looking at. They have narrowed the search area, bringing us one step closer to solving the mystery of what the dark universe is made of.

Technical Summary

1. Problem Statement

• The Dark Matter Gap: While Weakly Interacting Massive Particles (WIMPs) in the GeV–TeV mass range have been extensively searched for via nucleus scattering, lighter sub-GeV dark matter (DM) remains less constrained.
• Threshold Limitation: In direct detection experiments, sub-MeV DM particles typically deposit energy below the standard experimental thresholds (usually $\sim$keV) via kinetic recoil, making them undetectable.
• The Specific Challenge: Existing searches for sub-MeV DM often rely on boosting mechanisms (e.g., cosmic ray interactions) or specific scattering channels. However, a new paradigm involves DM absorption, where the DM particle is absorbed by a target, releasing its rest mass energy ($E=mc^2$) rather than just kinetic energy.
• The Gap in Literature: While bosonic DM absorption (e.g., dark photons, axions) has been studied, the search for fermionic DM absorption by electron targets ($\chi + e^- \to \nu + e^-$) in the keV mass scale had not been experimentally realized with high sensitivity until this work.

2. Methodology

• Experimental Setup:
  • Experiment: CDEX-10, located at the China Jinping Underground Laboratory (CJPL) with 2400 m rock overburden.
  • Detector: A p-type point contact germanium (PPCGe) detector (specifically the C10B-Ge1 module).
  • Exposure: 205.4 kg·day of data collected between February 2017 and August 2018.
  • Threshold: The analysis utilized an exceptionally low energy threshold of 160 eVee (electron-equivalent energy), with a combined efficiency of 4.5% at the threshold and 48.0% in the first bin (160–260 eVee).
• Theoretical Model:
  • Process: Fermionic DM ($\chi$) is absorbed by an atomic electron, producing a neutrino ($\nu$) and a recoiling electron: $\chi + e^- \to \nu + e^-$.
  • Interaction Types: The study considers two effective field theory (EFT) operators:
    1. Vector interaction ($O_V$): $(\bar{e}\gamma_\mu e)(\bar{\nu}_L \gamma^\mu \chi_L)$
    2. Axial-vector interaction ($O_A$): $(\bar{e}\gamma_\mu \gamma_5 e)(\bar{\nu}_L \gamma^\mu \chi_L)$
  • Signal Characteristics: The total detectable energy is $E_{det} = E_R + |E_{nl}^B|$, where $E_R$ is the electron recoil energy and $|E_{nl}^B|$ is the binding energy of the electron shell (K, L, M). The signal appears as a continuous spectrum starting from the binding energy of the specific shell.
  • Assumptions: Ge atoms are treated as isolated atoms (ignoring band structure effects for valence electrons), considering only core electrons (K, L, M shells) to ensure conservative results. The local DM density is assumed to be $0.3 \text{ GeV/cm}^3$.
• Data Analysis:
  • Background Modeling: The background in the 0.16–2.16 keV range includes cosmogenic isotopes ($^{68}\text{Ge}, ^{68}\text{Ga}, ^{65}\text{Zn}, ^{55}\text{Fe}, ^{54}\text{Mn}, ^{49}\text{V}$) producing L- and M-shell X-ray peaks, and Compton scattering from high-energy gammas.
  • Statistical Approach: A $\chi^2$ minimization fit was performed on the energy spectrum (0.16–2.16 keV). Nuisance parameters for detector efficiency and isotope intensities were constrained using covariance matrices.
  • Limit Setting: Since no significant excess was observed, 90% Confidence Level (CL) upper limits were derived using the Feldman-Cousins method.

3. Key Contributions

• First Search: This is the first experimental search for sub-MeV fermionic dark matter absorption by electron targets using a germanium detector.
• Low-Mass Sensitivity: By leveraging the low threshold (160 eVee) of the CDEX-10 PPCGe detector, the study extends the sensitivity to DM masses as low as 0.1 keV/c², a regime previously inaccessible to many direct detection experiments.
• New Constraints: The paper establishes the world's most stringent limits on the DM-electron absorption cross-section ($\sigma_e v_\chi$) for fermionic DM in the 0.1–10 keV/c² mass range.
• Validation of EFT: The analysis confirms the validity of the dimension-6 EFT framework for mediators with masses $\gg$ keV (e.g., dark photons), justifying the theoretical approach used.

4. Results

• Observation: No significant excess of events over the expected background was observed in the 0.16–2.16 keV energy range.
• Upper Limits on Cross Section:
  • For a DM mass of 5 keV/c²:
    • Vector Interaction: Upper limit on $\sigma_e v_\chi$ is $6.8 \times 10^{-46} \text{ cm}^2$.
    • Axial-Vector Interaction: Upper limit on $\sigma_e v_\chi$ is $2.3 \times 10^{-46} \text{ cm}^2$.
• Comparison:
  • These results provide the most stringent constraints for fermionic DM masses below 10 keV/c².
  • For masses above 35 keV/c², the PandaX-4T experiment (using liquid xenon) currently holds tighter constraints, but CDEX-10 dominates the sub-10 keV region due to its superior low-energy threshold.
• Astrophysical Consistency: The derived limits are consistent with constraints from X-ray/gamma-ray observations regarding DM decay channels (e.g., $\chi \to \gamma\gamma\nu$), though the direct detection limits are generally more competitive in the specific mass range studied.

5. Significance

• Probing the Lightest DM: This work demonstrates that semiconductor detectors with ultra-low thresholds are powerful tools for probing the "lightest" accessible dark matter candidates, filling a critical gap between astrophysical constraints and high-mass WIMP searches.
• New Physics Channel: It validates the "DM absorption" channel as a viable and sensitive method for detecting fermionic DM, distinct from the traditional scattering paradigm.
• Future Directions: The success of CDEX-10 sets the stage for future experiments (like CDEX-1T) with larger exposures and similar low thresholds, which could potentially discover or further constrain keV-scale fermionic dark matter, potentially explaining anomalies in other sectors or providing the first direct detection of such light particles.