Exploring the keV-scale physics potential of CUORE

This paper presents an analysis of over two tonne-years of CUORE data demonstrating that optimized selection techniques enable the experiment to effectively explore the keV-scale energy region with improved resolution and reduced background, thereby validating tonne-scale cryogenic calorimeters as versatile tools for rare event and dark matter physics across a wide energy range.

The Gist

Imagine the CUORE experiment as a massive, ultra-sensitive library of 988 tiny, frozen crystal "ears" buried deep underground in Italy. These ears are designed to listen for the faintest whispers of energy in the universe, specifically looking for a rare event called "neutrinoless double beta decay" (which happens at high energy levels, like a loud shout).

However, this paper is about a different mission: listening to the whispers.

The researchers wanted to see if these giant, frozen ears could also hear very quiet, low-energy sounds (in the "keV" range) that might reveal secrets about dark matter or rare atomic decays. The problem? When you turn the volume down to hear a whisper, you also hear a lot of static, wind, and vibrations that drown out the signal.

Here is a simple breakdown of what they did and found:

1. The Challenge: Tuning the Radio

Think of the CUORE detectors like a radio. Usually, they are tuned to listen to loud stations (high energy). To hear the quiet whispers (low energy), they had to:

• Turn down the static: They developed new software filters to ignore the "wind noise" (vibrations from the earth, electronics, or the building).
• Pick the best ears: Not all 988 crystals were equally good at hearing whispers. Some were too "noisy" or sensitive to vibrations. The team had to carefully select only the best-performing crystals for this specific low-energy task.

2. The Strategy: Two Listening Modes

The team created two different "listening modes" to test how well they could hear:

• The "Conservative" Mode (10 keV threshold): They set the volume so they could hear whispers that were 10 units loud. This kept a lot of data (691 kg-years of exposure) but filtered out the very faintest sounds.
• The "Strict" Mode (3 keV threshold): They turned the volume down even further to hear 3-unit whispers. This was much harder. They had to be extremely picky, discarding most of the data and only keeping the cleanest signals from the best crystals. This resulted in a tiny amount of data (11 kg-years), but the quality was incredibly high.

3. The Results: Clearing the Noise

By using these new techniques, they achieved some impressive feats:

• Sharper Hearing: They improved the clarity of the signal. In the "Strict" mode, their ability to distinguish a real sound from static improved significantly (getting down to a resolution of about 1.2 keV).
• Quieter Background: They managed to reduce the background "hiss" by about 10 times. It's like going from a noisy coffee shop to a quiet library.
• Finding the "Whispers": Once the noise was cleared, they could see specific features in the energy spectrum that were previously hidden. They found:
  • Known sounds: Peaks from natural radioactive elements (like Tellurium X-rays) and surface contamination.
  • Mysterious bumps: They spotted small excesses of energy at around 4.7 keV, 10 keV, and 13 keV. These could be new physics, or just unknown background noise, but now they are visible for the first time in this experiment.

4. The Big Picture: A Versatile Tool

The most important takeaway is that this experiment proved a tonne-scale (huge) detector can work across a massive range of energies.

• Previously, they were known for hearing the "shouts" (MeV scale).
• Now, they proved they can also hear the "whispers" (keV scale).

This is like discovering that a massive concert hall microphone, originally built to record a full orchestra, can also be used to record a single violin playing a very quiet note, provided you clean up the room and use the right filters.

Why Does This Matter?

The paper suggests this opens the door to searching for:

• Dark Matter: Particles that might interact very weakly with matter, creating tiny energy blips.
• Axions: Hypothetical particles that could turn into electrons and create a specific energy spike.
• Rare Decays: Uncommon nuclear events that happen very slowly.

The researchers conclude that by refining how they handle data and select their detectors, they have turned CUORE into a "Swiss Army knife" for particle physics, capable of hunting for new physics across a wide range of energy levels, not just the high-energy ones it was famous for. This success also gives hope for future, even larger experiments (like CUPID) to operate effectively at these low energies.

Technical Summary

Technical Summary: Exploring the keV-scale physics potential of CUORE

Problem Statement
The CUORE (Cryogenic Underground Observatory for Rare Events) experiment is primarily designed to search for neutrinoless double beta decay ($0\nu\beta\beta$) of $^{130}\text{Te}$ at the MeV scale ($\sim2.5$ MeV). Standard analysis for this search employs an energy threshold of 40 keV to ensure high signal-to-noise ratios and minimize background. However, the detector technology—tonne-scale cryogenic calorimeters operating at millikelvin temperatures—possesses intrinsic sensitivity down to the keV scale. Exploring this lower energy regime is crucial for investigating new physics scenarios, such as dark matter candidates (WIMPs and axions) and rare nuclear decays, which hypothesize energy deposits in the few-keV range. The challenge lies in the fact that near the trigger threshold, the energy spectrum is heavily polluted by noise, spurious pulses from environmental sources (vibrations, electronics), and a lower signal-to-noise ratio, making standard analysis techniques insufficient for reliable reconstruction.

Methodology
To address these challenges, the authors developed a dedicated analysis chain optimized for low-energy deposits using over 2 tonne-years of data collected over five years. The methodology focuses on strict data selection to prioritize quality over total exposure, enabling operation at lower thresholds.

1. Energy Calibration and Validation: The energy scale was extrapolated from high-energy $\gamma$-ray lines ($^{232}\text{Th}$-$^{60}\text{Co}$ sources) and validated using Te X-ray peaks ($\sim27$ and $31$ keV) and coincident events with the $^{40}\text{K}$ 1461 keV line (producing a $\sim3.2$ keV X-ray). This confirmed calibration reliability down to the detector thresholds.
2. Optimum Trigger (OT): An offline trigger was implemented using an Optimum Filter (OF) to maximize the signal-to-noise ratio. Trigger thresholds were set per detector-dataset pair where the efficiency reached 90%.
3. Multi-Site Event Tagging: To distinguish single-site physics events from multi-site background, an anti-coincidence algorithm was optimized. The time window was expanded to $\pm15$ ms (compared to $\pm5$ ms for MeV searches) to account for pulse shape estimation uncertainties at low energies, and a spatial radius of 150 mm was applied.
4. Spurious Event Discrimination: A critical component was the rejection of spurious pulses (e.g., from vibrations) that mimic physics signals. The authors utilized the reduced $\chi^2$ ($\chi^2_{\text{OF}}$) computed between filtered events and the average signal pulse shape.
   • Detector Selection: Since noise characteristics vary by detector, the $\chi^2_{\text{OF}}$ cut was optimized individually. Two metrics were defined to select the best-performing detectors: Purity ($P$), the fraction of signal events in the Region of Interest (ROI), and $\Delta\chi^2_{\text{OF}}$, the difference in median $\chi^2$ values between the ROI and a Region of Reference (ROR). Detectors were selected to maximize the ratio of exposure to background ($M\Delta T / N_B$).
5. Efficiency Evaluation: Reconstruction efficiencies (trigger, energy reconstruction, pile-up rejection) were evaluated using injected thermal pulses ("pulsers") at various energies, while anti-coincidence and pulse shape cut efficiencies were derived from physical peaks ($^{40}\text{K}$ and Te X-rays).

Key Contributions and Results
The study presents the first comprehensive analysis of CUORE's performance at keV scales, establishing two distinct data selection classes:

• 10 keV Threshold: Optimized for solar axion searches.
• 3 keV Threshold: The lowest accessible energy, optimized for strict background suppression.

Performance Metrics:

• Exposure: The strict selection reduced the total exposure to 691 kg yr for the 10 keV threshold and 11 kg yr for the 3 keV threshold (representing 34% and 0.5% of the total collected exposure, respectively).
• Resolution: The analysis achieved an average baseline Full Width at Half Maximum (FWHM) resolution of 2.54 $\pm$ 0.14 keV at 10 keV and 1.18 $\pm$ 0.02 keV at 3 keV.
• Background Reduction: The combined application of pulse shape cuts and detector selection reduced the background by approximately one order of magnitude, reaching 2.06 $\pm$ 0.05 counts/(keV kg days) at 10 keV and 16 $\pm$ 2 counts/(keV kg days) at 3 keV.
• Efficiencies: The near-threshold reconstruction efficiencies were found to be 50 $\pm$ 2% at 10 keV and 26 $\pm$ 4% at 3 keV.

Spectral Features:
The resulting low-energy spectra revealed several distinct features:

• Known Origins: Te X-rays ($\sim27, 31$ keV), $^{125m}\text{Te}$ de-excitation ($\sim145$ keV), and nuclear recoils from $^{210}\text{Po}$ ($\sim90$ keV).
• Investigated Structures:
  • A broad structure at $\sim36$ keV (rate: $8.3 \pm 0.3$ counts/(kg d)), potentially related to $^{210}\text{Pb}$ but exhibiting a kink rather than a sharp peak.
  • A monochromatic peak at $\sim31$ keV (rate: $1.35 \pm 0.04$ counts/(kg d)), associated with $^{121}\text{Te}$ electron capture.
  • Excesses at $\sim10$ keV and $\sim13$ keV (rates $\sim0.66-0.67$ counts/(kg d)).
  • A peak at $\sim4.7$ keV (rate: $19.1 \pm 1.0$ counts/(kg d)), coincident with L1-shell electron capture of $^{121}\text{Te}$, though the lack of coincidence with high-energy gammas leaves its origin open.

Significance and Claims
The paper claims to demonstrate that tonne-scale cryogenic calorimeters can operate effectively across a wide energy range, spanning three orders of magnitude from a few keV to $\sim10$ MeV. By prioritizing stricter selection criteria, the authors successfully optimized data for low-energy thresholds, proving the scalability of this technology for versatile physics searches.

The significance of this work lies in:

1. Enabling New Physics Searches: Providing the necessary low-threshold, low-background data for searching for WIMP dark matter (via annual modulation and nuclear recoils) and axions (via monochromatic peaks, e.g., the 14.4 keV $^{57}\text{Fe}$ transition).
2. Background Modeling: Establishing the capability to reconstruct a detailed background model at energies below 100 keV, which is essential for future rare decay searches.
3. Future Optimization: Informing the design and operation of future large-mass cryogenic experiments (such as CUPID). The results highlight the critical impact of vibration damping and operating temperature (12 mK vs. 15 mK) on low-energy performance, suggesting that upgrades to the cryogenic facility (specifically pulse tube pre-cooling) will be vital for enhancing sensitivity to low-energy phenomena in next-generation detectors.