Resolution Studies for Axion Searches with CUPID-0

This paper presents a resolution study for high-energy solar axion searches at 5.5 MeV using CUPID-0 Phase I and II data, demonstrating an energy resolution of approximately 39.8 keV and a background level below $10^{-3}$ counts/(keV kg y) that enable sensitive axion detection.

The Gist

Imagine the universe is a giant, noisy room, and scientists are trying to hear a single, specific whisper from a distant friend. This "whisper" is a hypothetical particle called an axion. Scientists think axions might be the invisible "dark matter" that holds the universe together, and they might also be the reason why the laws of physics don't break in certain ways.

The paper you shared is about a team of scientists using a very special, super-sensitive listening device called CUPID-0 to try and catch this whisper. Here is the story of what they did, explained simply:

1. The Listening Device (The Detector)

Think of the CUPID-0 detector as a giant, ultra-cold refrigerator filled with 26 tiny, glowing crystals (like high-tech ice cubes).

• How it works: When a particle hits one of these crystals, it creates two things: a tiny bit of heat (like a warm breath on a cold window) and a flash of light (like a firefly blinking).
• The Superpower: Because the device is so cold and sensitive, it can measure both the heat and the light at the exact same time. This allows the scientists to tell the difference between a "real" signal (the axion whisper) and "noise" (background static from the environment).

2. The Target (The Solar Axion)

The scientists are looking for axions coming from the Sun.

• Imagine the Sun is a factory churning out these particles. The specific axions they are hunting for are like a pure, single-note tone at a very high pitch (5.5 million electron-volts, or 5.5 MeV).
• If these axions hit the crystals in the detector, they should create a sharp, distinct spike in the data, right at that 5.5 MeV mark.

3. The Problem: Tuning the Radio

The CUPID-0 detector was originally built to listen for lower-pitched sounds (lower energies, around 3 MeV). The scientists needed to know: "If we tune our radio up to this very high 5.5 MeV frequency, will the sound still be clear, or will it get fuzzy?"

If the "sound" gets too fuzzy (poor resolution), the axion signal might get lost in the background noise. They needed to test how sharp their "ears" were at this high pitch.

4. The Test Drive (Calibration)

To test the detector, the scientists didn't wait for axions (which might not exist yet). Instead, they used a calibration source (a safe, known radioactive source) to create signals at various known frequencies.

• They looked at the "peaks" in their data—these are like clear, loud notes played by the calibration source.
• They measured how "wide" or "blurry" each note was. A sharp, narrow note means the detector has great resolution. A wide, blurry note means it's fuzzy.

5. The Prediction (Extrapolation)

The scientists couldn't test the detector exactly at 5.5 MeV with their calibration source because that specific energy wasn't available in their test kit. So, they used math to extrapolate (predict) what would happen at 5.5 MeV.

• They plotted the "blurriness" of the notes they could hear against their energy levels.
• They drew a straight line through these points and extended it out to the 5.5 MeV mark.

6. The Result: A Clear Whisper

The study found that even at this high energy, the detector remains incredibly sharp.

• The Resolution: At 5.5 MeV, the "fuzziness" of the signal is only about 40 keV.
• The Analogy: Imagine trying to hear a specific note on a piano. If the note is 5.5 million Hz, and your ear can distinguish it from the neighbors within a tiny range of 40 Hz, that is an incredibly precise ear.
• The Background: Because the signal is so sharp (narrow) and the detector is so quiet (low background), the scientists calculated that there would be almost no "static" (background noise) in the window where they are looking for the axion.

Summary

In simple terms, this paper is a quality control report. The scientists took their ultra-sensitive detector, tested it with known signals, and mathematically proved that it is sharp enough to spot a high-energy axion from the Sun if one exists. They confirmed that the "window" they need to look through is narrow and clear, giving them a very good chance of finding this mysterious particle without getting confused by background noise.

Technical Summary

1. Problem Statement

The Standard Model of particle physics fails to explain several fundamental phenomena, including the nature of dark matter and the strong CP problem. Axions are hypothetical particles proposed to solve the strong CP problem and are strong candidates for dark matter. Specifically, the Sun is predicted to produce high-energy axions via nuclear reactions (specifically the $p+p \to {}^3\text{He} + a$ channel), resulting in a monochromatic flux at 5.5 MeV.

While the CUPID-0 experiment (a scintillating cryogenic calorimeter) is primarily designed to search for neutrinoless double beta decay ($0\nu\beta\beta$) at lower energies (up to ~3 MeV), its excellent energy resolution and low background make it a promising candidate for searching for these high-energy solar axions. However, the detector's performance at 5.5 MeV had not been characterized. To search for axions, it is critical to determine the detector's energy resolution at this specific energy to define the signal window and estimate the background levels.

2. Methodology

The study utilizes data from the CUPID-0 experiment, comprising exposures of 9.95 kg·yr (Phase I) and 5.74 kg·yr (Phase II). The analysis focuses on $\beta/\gamma$ events with multiplicity $M=1$ (single crystal interaction) and $M=2$ (summed energy of two simultaneous crystals).

• Data Sources:

  • Calibration Data: Collected using a ${}^{232}\text{Th}$ source to identify known spectral peaks.
  • Background Data: Collected under normal operating conditions without external sources.
  • Key Peaks: The analysis fits prominent peaks in the energy spectrum (e.g., ${}^{40}\text{K}$, ${}^{208}\text{Tl}$ at 2615 keV, ${}^{65}\text{Zn}$, ${}^{228}\text{Ac}$) to extract detector response parameters.

• Fit Model:

  • A double-Gaussian model is employed to account for the slightly non-Gaussian response of the detector (observed in previous experiments like CUORE).
  • The fit function combines an exponential background and a signal component $G$:
    $$f(E) = n_{\text{bkg}} \cdot e^{-\lambda E} + n_{\text{sig}} \cdot G(\mu_P, \sigma_P, \rho, \eta, \epsilon)$$
  • The signal $G$ is a weighted sum of a primary Gaussian and a secondary Gaussian (representing sub-optimal crystal modules).
  • Parameter Fixing: Shape parameters ($\rho, \eta, \epsilon$) are first determined using the high-statistics 2615 keV ${}^{208}\text{Tl}$ calibration line. These fixed values are then applied to fit other peaks across the energy range to reduce free parameters.

• Extrapolation Strategy:

  • The Full Width at Half Maximum (FWHM) is calculated for each fitted peak ($FWHM = 2.335 \sigma_P$).
  • FWHM values are plotted against peak energy to establish the energy dependence of the resolution.
  • A linear fit is applied to extrapolate the resolution to the target energy of 5.5 MeV.
  • Note on M=2 Data: Calibration data for $M=2$ was discarded due to systematic effects (accidental coincidences from high statistics in calibration runs artificially broadening peaks). Only background data was used for the $M=2$ extrapolation.

3. Key Contributions

• High-Energy Characterization: This work provides the first dedicated characterization of the CUPID-0 detector's energy resolution at 5.5 MeV, a region outside its primary design range for $0\nu\beta\beta$.
• Validation of Linear Extrapolation: The study confirms that the energy resolution follows a linear trend in the high-energy regime, dominated by an effective constant term rather than stochastic fluctuations, which is typical for cryogenic bolometers.
• Background Quantification: The analysis quantifies the background level in the region of interest (ROI) for axion searches, demonstrating the detector's capability to operate with extremely low background rates at high energies.

4. Results

• Energy Resolution at 5.5 MeV:
  • For $M=1$ events (fully contained in a single crystal), the extrapolated energy resolution is $(39.8 \pm 2.1)$ keV (FWHM).
  • For $M=2$ events (background only), the extrapolated resolution is $(57.7 \pm 8.3)$ keV, consistent with the quadrature sum of two $M=1$ resolutions.
• Signal Window: The narrow resolution (~40 keV) implies a very narrow search window for a monochromatic 5.5 MeV axion signal.
• Background Level: The background level in the 5.5 MeV region is measured to be $< 10^{-3}$ counts/(keV·kg·y).
• Consistency: The results are consistent with previous findings using ${}^{56}\text{Co}$ sources (Ref. [3]), with compatible slope and intercept parameters within statistical uncertainties.

5. Significance

This study establishes the technical feasibility of using CUPID-0 (and by extension, the future CUPID experiment) to search for high-energy solar axions.

• Discovery Potential: The combination of a narrow signal window (due to excellent resolution) and an extremely low background level creates a highly sensitive environment for rare-event searches.
• Strategic Foundation: The quantitative understanding of the detector response at 5.5 MeV allows for the definition of a robust signal search strategy.
• Broader Impact: It demonstrates that scintillating cryogenic calorimeters, originally built for neutrino physics, are versatile tools capable of probing new physics sectors, such as axion dark matter, well beyond their nominal energy ranges.