Search for Sterile Neutrinos with CUPID-0

Using 9.95 kg·yr of exposure from the CUPID-0 experiment, researchers found no evidence of sterile neutrinos in the double beta decay of $^{82}$Se and established the most stringent upper limit to date on the active-sterile mixing probability ($\sin^2\theta < 8\times 10^{-3}$) for a sterile neutrino mass of 0.7 MeV.

The Gist

The Big Picture: Hunting for "Ghost" Particles

Imagine the universe is a giant, crowded party. We know about the "regular" guests: the three types of neutrinos (tiny, ghost-like particles) that interact with matter, albeit very rarely. These are the "Active Neutrinos."

But physicists have a hunch that there might be a secret VIP section at this party where "Sterile Neutrinos" are hiding. These are hypothetical particles that are so shy they don't interact with anything—not even the weak force that regular neutrinos use. They only exist if they can "mix" with the regular neutrinos, kind of like a chameleon blending into a crowd.

The Goal: The CUPID-0 experiment wanted to find evidence of these shy "Sterile Neutrinos" by watching a very specific, rare event: Double Beta Decay.

The Experiment: A Super-Sensitive Ice Cube

To catch these ghosts, the scientists built a detector called CUPID-0 deep underground (to block out cosmic rays from space).

• The Setup: Imagine a tower made of 24 special crystals (Zinc Selenide) that are super cold—colder than outer space (about 10 millikelvin).
• The Trick: These crystals act like a two-in-one sensor. When a particle hits them, the crystal gets slightly warmer (Heat) and also flashes a tiny bit of light (Scintillation).
• Why two signals? It's like having a security guard who checks both your ID card and your face. This helps the scientists tell the difference between a "good" particle (like an electron from a decay) and a "bad" background noise (like an alpha particle from natural radioactivity).

The Mystery: The "Missing" Energy

In a standard Double Beta Decay, two neutrons in an atom turn into two protons, shooting out two electrons and two regular neutrinos. The energy of the two electrons adds up to a specific maximum number (the "Q-value"). It's like a bucket filling up with water to a specific line.

The Sterile Neutrino Twist:
If a heavy, invisible Sterile Neutrino is also born in this process, it steals some of the energy.

• Analogy: Imagine you are baking a cake that is supposed to weigh exactly 1 kg. If a thief (the Sterile Neutrino) sneaks in and steals a slice of the cake, the final weight will be less than 1 kg.
• The Effect: Instead of the energy of the electrons stopping at the usual maximum, the "cake" (the energy spectrum) would stop earlier. The shape of the energy curve would get distorted, looking like a hill that was cut off too early.

The Investigation: Cleaning the Mess

The scientists didn't just look for the distortion; they had to prove it wasn't just a mess of background noise.

1. The Background Noise: The detector is surrounded by natural radioactivity (like radon gas or uranium traces in the rocks). It's like trying to hear a whisper in a room full of people talking.
2. The Model: The team spent a lot of time building a super-detailed computer model of every possible source of noise. They simulated 33 different types of radioactive contaminants.
3. The Result: They successfully mapped out the "noise" from 200 keV all the way up to 11 MeV. They proved their model was perfect by showing that the "residuals" (the difference between their model and the real data) looked like random static, not a hidden signal.

The Findings: No Ghosts Found (Yet)

After analyzing 9.95 years of data (measured in "kilogram-years" of exposure), they looked for the "cut-off" shape that would indicate a Sterile Neutrino.

• The Verdict: They found nothing. The energy spectrum looked exactly like the Standard Model predicted, with no signs of a heavy sterile neutrino stealing energy.
• The Limit: Because they didn't find a ghost, they set a "speed limit" for how likely it is that these ghosts exist. They calculated that if a Sterile Neutrino with a mass between 0.5 and 1.5 MeV exists, the chance of it mixing with regular neutrinos is incredibly small.
• The Best Limit: For a neutrino mass of 0.7 MeV, they proved that the mixing probability is less than 0.008 (less than 1%). This is the tightest constraint (the most strict rule) ever set for this specific mass range using this method.

Why This Matters

Think of this like searching for a specific type of fish in a massive ocean.

• CUPID-0 used a very large net (a lot of data) and a very smart sonar (the background model).
• They didn't catch the fish, but they proved that if the fish is there, it must be extremely rare or very hard to catch.
• This result is better than previous attempts by other experiments (CUPID-Mo and GERDA) because CUPID-0 had more data and a better ability to distinguish the signal from the noise.

In short: The CUPID-0 team built a super-sensitive, ultra-cold detector to look for a "missing piece" of energy that would prove the existence of a new, invisible particle. They didn't find the particle, but they successfully ruled out many possibilities, narrowing the search for the "Ghost Neutrino" significantly.

Technical Summary

1. Problem Statement

The Standard Model (SM) describes neutrinos as massless, but experimental evidence of neutrino oscillations confirms they have mass. This discrepancy suggests the existence of physics beyond the SM, potentially involving sterile neutrinos—hypothetical fermions that do not interact via the weak force but mix with active neutrinos. Sterile neutrinos are motivated by theories explaining neutrino mass generation (e.g., the see-saw mechanism) and are candidates for dark matter.

While oscillation experiments probe light sterile neutrinos, this paper focuses on MeV-scale sterile neutrinos ($m_N$). The authors investigate whether these particles are emitted during the two-neutrino double beta decay ($2\nu\beta\beta$) of Selenium-82 ($^{82}\text{Se}$).

• Theoretical Mechanism: If a sterile neutrino ($N$) mixes with the electron antineutrino, the decay $(A, Z) \to (A, Z+2) + 2e^- + \bar{\nu}_e + N$ (denoted $N\nu\beta\beta$) becomes possible.
• Observable Signature: Unlike the continuous spectrum of standard $2\nu\beta\beta$ ending at the Q-value ($Q_{\beta\beta} \approx 2998$ keV), the emission of a massive sterile neutrino shifts the kinematic endpoint to $Q_{\beta\beta} - m_N$. This results in a characteristic distortion in the summed electron energy spectrum, specifically a shift in the spectral peak and a truncation of the high-energy tail.

2. Methodology

The analysis utilizes data from the CUPID-0 experiment, a scintillating bolometer array located at the Gran Sasso National Laboratories (LNGS).

• Detector Technology: CUPID-0 employs 26 ZnSe crystals (24 enriched to 95.3% in $^{82}\text{Se}$) operating at cryogenic temperatures (~10 mK). It utilizes a dual-readout technique (heat and scintillation light) to discriminate between $\beta/\gamma$ events (signal region) and $\alpha$ particles (background).
• Dataset: The analysis covers data collected from June 2017 to December 2018, corresponding to an exposure of 9.95 kg·yr of enriched $^{82}\text{Se}$.
• Background Modeling:
  • A detailed background model was constructed using Monte Carlo simulations (GEANT4 via the Arby toolkit) covering energies down to 200 keV (an extension of previous CUPID-0 studies).
  • The model accounts for 33 background sources, including natural radioactivity ($^{232}\text{Th}$, $^{238}\text{U}$, $^{40}\text{K}$) and cosmogenic activation.
  • The data was analyzed across four spectral classes to disentangle sources:
    1. M1$\beta/\gamma$: Single-crystal $\beta/\gamma$ events (200 keV – 5 MeV).
    2. M1$\alpha$: Single-crystal $\alpha$ events (2 MeV – 11 MeV).
    3. M2: Individual energies of coincident two-crystal events.
    4. $\Sigma_2$: Total energy of coincident two-crystal events.
• Statistical Framework:
  • A multivariate Bayesian fit was performed simultaneously on all four spectral classes.
  • The sterile neutrino signal was introduced as an additional template with a free scaling parameter.
  • The mixing probability $\sin^2\theta$ was derived from the fitted decay rate using phase-space factors ($G_{\nu N}$) calculated specifically for this work.
  • Systematic Uncertainties: Extensive tests were conducted, varying binning strategies, energy thresholds (up to 300 keV), energy scale calibrations ($\pm 3-5$ keV), and background composition (removing degenerate sources or specific internal/external components).

3. Key Contributions

• First Search in $^{82}\text{Se}$: This is the first dedicated search for MeV-scale sterile neutrino emission in the double beta decay of $^{82}\text{Se}$.
• Novel Phase-Space Factors: The authors computed the phase-space factors ($G_{\nu N}$) for the $N\nu\beta\beta$ decay of $^{82}\text{Se}$ for the first time, accounting for the mass-dependent kinematic suppression.
• Extended Background Model: The background model was successfully extended down to 200 keV, allowing for a more robust characterization of low-energy spectral distortions where the signal for heavier sterile neutrinos would appear.
• Rigorous Systematic Treatment: The paper employs a sophisticated method to combine results from various systematic models using the law of total probability, weighting each model by its evidence (Bayesian model comparison).

4. Results

• Signal Observation: No evidence of a sterile neutrino signal was observed in any of the tested mass hypotheses ($0.5 \text{ MeV} \leq m_N \leq 1.5 \text{ MeV}$). The data is fully compatible with the background-only hypothesis (standard $2\nu\beta\beta$).
• Upper Limits: The authors derived 90% Credible Interval (C.I.) upper limits on the active-sterile mixing probability $\sin^2\theta$.
  • Most Stringent Limit: $\sin^2\theta < 8 \times 10^{-3}$ for a sterile neutrino mass of $m_N = 0.7$ MeV.
  • Mass Dependence: Limits are strongest between 0.5 and 1.2 MeV. For masses $> 1.2$ MeV, limits weaken due to the signal peak shifting below the analysis threshold and reduced phase-space factors.
• Comparison with Other Experiments:
  • The results improve upon constraints set by CUPID-Mo (using $^{100}\text{Mo}$) and GERDA (using $^{76}\text{Ge}$) across the explored mass range.
  • The improvement over CUPID-Mo is attributed to the larger exposure of CUPID-0.
  • The improvement over GERDA is attributed to the higher $2\nu\beta\beta$ decay rate of $^{82}\text{Se}$, which provides greater statistical power for spectral shape analysis.

5. Significance

This work demonstrates the capability of scintillating bolometer technology to perform high-precision spectral shape analyses, extending their utility beyond the search for neutrinoless double beta decay ($0\nu\beta\beta$) to the study of exotic decay modes. By setting the most stringent limits to date on MeV-scale sterile neutrino mixing in $^{82}\text{Se}$, the CUPID-0 collaboration significantly constrains the parameter space for these hypothetical particles. The results provide a complementary constraint to limits derived from single beta decay and nuclear structure tests, reinforcing the exclusion of certain sterile neutrino scenarios as dark matter candidates or solutions to short-baseline anomalies in this mass range.