Characterization of the Low Energy Excess using a NUCLEUS $Al_2O_3$ detector

The NUCLEUS experiment characterizes the unidentified low energy excess in its sapphire detector by demonstrating that the excess rate is independent of particle background levels but decreases with slower cooling procedures, following a universal power-law decay over time.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: Hunting Ghosts in a Silent Room

Imagine you are trying to hear a single, tiny whisper in a very quiet room. This is what the NUCLEUS experiment is trying to do. They are looking for a specific type of "ghost" interaction called Coherent Elastic Neutrino-Nucleus Scattering (CEνNS).

Neutrinos are like invisible, ghostly particles that pass through everything. When they hit an atom in their detector, they give it a tiny little nudge. The detector is so sensitive (it's a super-cooled crystal the size of a sugar cube) that it can feel that nudge.

The Problem:
The problem is that the detector is too sensitive. It's hearing a lot of static noise. Specifically, there is a mysterious "hiss" of extra events happening at very low energies (below a few hundred electron-volts). The scientists call this the Low Energy Excess (LEE).

It's like trying to hear that one ghostly whisper, but there's a constant, unexplained buzzing sound in the room that drowns it out. The scientists don't know what causes this buzz. Is it background radiation? Is it the detector itself? Is it a glitch?

The Investigation: The "Sapphire Microphone"

To figure out what's causing the buzz, the team used a special detector made of Sapphire (Aluminum Oxide). Think of this sapphire crystal as a high-fidelity microphone. It has two tiny sensors (called TESs) attached to it, like two ears listening to the same sound.

They ran this detector in different places:

1. On the surface: Where there is lots of cosmic radiation (like being in a busy city square).
2. Underground: Where the earth blocks most radiation (like being in a quiet basement).
3. With different shields: Sometimes they put lead and plastic walls around it; sometimes they took them off.

The Detective Work: What Caused the Buzz?

The team asked three main questions to solve the mystery of the LEE:

1. Is it the "Noise" from the outside world?

• The Test: They compared the detector's performance on the surface (high noise) vs. underground (low noise). They also opened the protective shields to let more radiation in.
• The Result: Nope. Even when they let in more radiation, the "buzz" (LEE) didn't get louder. In fact, sometimes it got quieter! This proves the buzz isn't caused by outside particles like cosmic rays or radiation.

2. Is it the "Muons" (Cosmic Rays)?

• The Test: They used a "Muon Veto" (a special alarm that detects when a cosmic ray passes through). They checked if the buzz happened at the exact same time as a cosmic ray.
• The Result: Nope. The buzz happens almost entirely on its own, unrelated to the cosmic rays passing by.

3. So, what is it?

• The Discovery: The team noticed something strange about how fast the detector cooled down.
  • When they cooled the detector down quickly (like putting a hot pan in the freezer), the "buzz" was very loud at the start.
  • When they cooled it down slowly (like letting a hot pan cool on the counter), the "buzz" was much quieter.
• The Analogy: Imagine a glass of water. If you freeze it instantly, it might crack or get cloudy. If you freeze it slowly, it stays clear. The detector seems to have a similar reaction to temperature changes. The "buzz" is likely caused by the physical stress or chemical changes happening inside the crystal as it settles into the extreme cold.

The "Magic Formula"

The scientists found a mathematical pattern to describe this "buzz."

• The Pattern: The buzz gets quieter over time, following a specific curve (a power law).
• The Trigger: The clock starts ticking the moment the detector hits 4 Kelvin (a very specific cold temperature where helium gas turns into liquid).
• The Rule: If you cool the detector slowly, the starting volume of the buzz is lower. If you cool it fast, the starting volume is high. But once the clock starts at 4 Kelvin, everyone follows the same rule for how fast the buzz fades away.

The Conclusion: How to Fix the Radio

The paper concludes that the "Low Energy Excess" is not caused by bad particles or electronic noise. It is caused by the cooling process itself.

The Takeaway for the Future:
If the NUCLEUS team wants to hear the ghostly neutrinos clearly, they don't need better shields or quieter rooms. They just need to slow down the cooling process. By being patient and letting the detector cool down gently, they can significantly reduce the "buzz" and finally hear the whisper they are looking for.

In a nutshell: The detector was screaming because it was shocked by the cold. If you let it chill out slowly, it stops screaming, and you can finally hear the neutrinos.

Technical Summary

Here is a detailed technical summary of the paper "Characterization of the Low Energy Excess using a NUCLEUS Al2O3 detector."

1. Problem Statement

The NUCLEUS experiment aims to detect Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) from reactor antineutrinos using low-threshold, gram-scale cryogenic calorimeters. A major obstacle to this goal is the Low Energy Excess (LEE): a sharp, unidentified rise in the event rate below a few hundred eV.

• The Challenge: The LEE dominates the region of interest for CE$\nu$NS and light dark matter searches. Its origin is unknown, and it limits the sensitivity of current experiments.
• The Hypothesis: Previous studies suggested the LEE might be caused by particle backgrounds (e.g., muons, environmental radiation) or noise. However, the time-dependent decay of the LEE rate (observed in other experiments like CRESST and EDELWEISS) suggests a different mechanism, potentially related to detector cooldown procedures or thermal history.

2. Methodology

The authors conducted a systematic study using a double Transition-Edge Sensor (TES) detector with an Aluminum Oxide (Al$_2$O$_3$, sapphire) absorber (0.75 g). The study utilized data from multiple runs in 2023–2024 at the Technical University of Munich (TUM) under varying conditions:

• Experimental Setups:
  • Surface (Surf): Above-ground facility with no dedicated shielding.
  • Underground (UGL): Shallow underground laboratory ($\sim$10 m.w.e.) with passive shielding (Lead + Borated Polyethylene) and an active Muon Veto (MV).
• Variable Conditions:
  • Shielding Configurations: Comparing runs with shields closed vs. open (UGL2 run).
  • Background Levels: Comparing surface runs (high background) vs. underground runs (low background).
  • Detector Maintenance: Cleaning and remounting the detector between runs to reduce radioactive contamination.
  • Cooldown Dynamics: Analyzing runs with different cooldown speeds and durations from room temperature to base temperature.
• Data Analysis Strategy:
  • Event Classification: Events were classified as "Shared" (simultaneous signals in both TESs, mimicking bulk energy deposition like CE$\nu$NS) or "Singles" (signals in only one TES, likely surface events or noise).
  • LEE Rate Definition: The LEE rate ($R_{LEE}$) was calculated in the 100–300 eV range, subtracting the background rate measured in the 1–3 keV range to isolate the excess.
  • Time Evolution Modeling: The decay of the LEE rate over time was modeled using a power law function: $R_{LEE}(t) = A \cdot (t - t_0)^{-k}$.

3. Key Contributions

1. First Dedicated Muon Veto Coincidence Analysis: The paper presents the first analysis of LEE events in coincidence with a muon veto in a shallow underground environment to test if cosmic muons drive the excess.
2. Systematic Background Correlation Test: By opening and closing shields within the same run (UGL2) and comparing surface vs. underground data, the authors rigorously tested the correlation between particle background rates and the LEE.
3. Identification of Cooldown as the Primary Driver: The study establishes a quantitative link between the cooldown speed (time taken to reach 4 K) and the initial magnitude of the LEE, proposing a universal power-law decay model for the LEE evolution.

4. Key Results

A. Independence from Particle Backgrounds

• Muon Veto: Applying a muon veto coincidence cut reduced the LEE rate by only a negligible amount. The probability of the LEE being coincident with muons ($p_{LEE} \approx 0.025$) is consistent with accidental coincidences ($p_{acc} \approx 0.012$). This implies >98% of the LEE is not caused by muons.
• Shielding & Surface vs. Underground:
  • Opening the external shield in the UGL2 run significantly increased the keV-range particle background but decreased the LEE rate.
  • Surface runs (high background) and underground runs (low background) showed comparable LEE rates.
  • Conclusion: There is no evidence that the LEE is induced by external particle backgrounds or environmental radiation.

B. Dependence on Cooldown Parameters

• Universal Time Decay: The LEE rate follows a power-law decay $R_{LEE}(t) \propto t^{-k}$ across all datasets when time $t$ is measured from the moment the detector reaches 4 K (the onset of helium condensation).
• Common Exponent: The decay exponent is consistent across all runs and detector materials (Al$_2$O$_3$ and CaWO$_4$), with a weighted average of $k = 0.59 \pm 0.06$.
• Impact of Cooldown Speed:
  • The normalization constant $A$ (initial LEE rate at 1 day post-4 K) is inversely correlated with the cooldown duration.
  • Slower cooldowns (taking longer to reach 4 K from room temperature) result in significantly lower initial LEE rates (up to an order of magnitude reduction).
  • Faster cooldowns result in higher initial excess rates.

C. Noise and Singles

• The study confirmed that negative triggers (noise fluctuations) do not account for the LEE in the 100–300 eV range.
• While "Singles" events dominate at very low energies (<100 eV), the "Shared" events (the focus of CE$\nu$NS searches) clearly exhibit the LEE behavior described above.

5. Significance and Outlook

• Ruling Out Backgrounds: The findings definitively rule out external particle backgrounds (muons, neutrons, gammas) and simple noise as the primary cause of the LEE in NUCLEUS detectors. This shifts the focus of mitigation strategies away from shielding improvements toward internal detector physics.
• Mitigation Strategy: The discovery that slower cooldowns reduce the LEE provides a practical, immediate experimental strategy. By optimizing the cooldown profile (specifically the phase around 4 K where helium condenses and materials undergo phase transitions), future experiments can significantly lower the background floor.
• Physical Mechanisms: The results suggest the LEE is driven by cooldown-related processes, such as:
  • Thermal stress relaxation in the detector mounting.
  • Helium condensation and penetration into micro-crevices.
  • Superconducting transitions of aluminum components (wiring/pads) near 1 K.
• Future Work: The authors plan to investigate the specific temperature ranges triggering these effects and study the correlation of noise between the two TES sensors to further reduce the background at the lowest energies.

In summary, this paper characterizes the Low Energy Excess not as a background artifact, but as a transient phenomenon intrinsic to the detector's thermal history, offering a clear path forward for optimizing cryogenic detector performance for neutrino and dark matter physics.