Sensitivity of the CUPID experiment to $0νββ$ decay of $^{100}$Mo

This paper presents a numerical sensitivity study for the CUPID experiment's search for neutrinoless double-beta decay of $^{100}$Mo, establishing a Bayesian exclusion limit of $T_{1/2} > 1.6 \times 10^{27}$ years and a Frequentist 3$\sigma$ discovery sensitivity of $T_{1/2} = 1.0 \times 10^{27}$ years under its baseline operational scenario.

The Gist

The Great Neutrino Hunt: CUPID's Mission to Catch a Ghost

Imagine the universe is filled with tiny, invisible ghosts called neutrinos. They zip through everything—stars, planets, and even your body—without ever bumping into anything. For decades, physicists have wondered: Are these ghosts their own anti-ghosts?

If a neutrino is its own anti-particle (a "Majorana" particle), it would break the rules of physics as we know them and help explain why the universe is made of matter instead of being empty. To prove this, scientists are looking for a very rare event called neutrinoless double-beta decay.

Think of it like this: Imagine two twins (neutrons) in a house (an atom) decide to transform into two other twins (protons) and run out the door (electrons). In the normal version of this event, they also throw two "ghosts" (antineutrinos) out the door with them. But in the special version scientists are hunting for, the twins transform and run out without throwing any ghosts. If we catch this happening, we prove the ghosts are their own anti-ghosts.

The Detective: CUPID

The CUPID experiment is a giant, ultra-sensitive detective designed to catch this rare event. It's the successor to a previous experiment called CUORE, which was like a very good detective but got distracted by background noise.

Here is how CUPID works, using some everyday analogies:

1. The Crime Scene (The Crystals)
CUPID uses 1,596 giant, super-pure crystals made of a special material (Lithium Molybdate) enriched with a specific isotope called Molybdenum-100. Think of these crystals as a massive library of "suspects." If a neutrinoless decay happens, it will happen inside one of these crystals.

2. The Super-Cold Freezer
To hear the faintest whisper of a decay, the whole experiment is frozen to a temperature near absolute zero (about -273°C). This is like turning off the wind and traffic noise in a city so you can hear a single pin drop. At this temperature, the crystals become incredibly sensitive thermometers.

3. The Two-Step Alarm System
When a particle hits a crystal, it creates heat (a tiny temperature rise) and light (a flash of photons).

• The Heat: Tells the scientists something happened.
• The Light: Tells them what happened.

This is the key innovation. Most background noise (like dust or radioactive dust on the surface) acts like a heavy thud that makes a lot of heat but very little light. The signal we want (the decay) is like a sharp click that makes heat and light in a specific ratio. CUPID uses two detectors for every crystal: one to feel the heat and one to catch the light. This allows it to reject 99.9% of the background noise, acting like a bouncer at a club who only lets the VIPs (the signal) in and kicks out the troublemakers (the noise).

4. The Goal: A Perfect Score
The experiment aims to run for 10 years. During this time, it hopes to see a specific "peak" in the energy data—a perfect spike at exactly the right energy level where the decay should happen.

• If they see the spike: They have discovered the neutrinoless decay and proven the neutrino is its own anti-particle.
• If they don't see it: They can set a "limit," saying, "If this decay exists, it must be rarer than we can detect." This still tells us something important about how heavy the neutrino is.

What the Paper Says (The Results)

The paper doesn't present new data from the experiment yet (it's still being built and tested); instead, it presents a simulation of what CUPID will be able to do.

• The Baseline Scenario: If everything goes according to plan (clean crystals, perfect cold, and low background noise), CUPID will be able to:

  • Discover the decay if it happens with a frequency of about 1 event every 100 septillion years (a 1 followed by 27 zeros).
  • Exclude (rule out) the decay if it happens faster than that.
  • In terms of the "weight" of the neutrino, this sensitivity covers the range where the neutrino mass is between 9.6 and 28 "meV" (a tiny unit of mass). This range is crucial because it covers the "Inverted Ordering" scenario, which is a major theory about how neutrino masses are arranged.

• The "What-If" Scenarios: The scientists also ran simulations to see what happens if things aren't perfect:

  • If the background noise is slightly higher, the sensitivity drops a bit, but the experiment is still very powerful.
  • If the energy resolution (how sharp the "spike" looks) is a bit blurry, it's harder to find the signal, but CUPID is designed to handle this.

• The "Staged" Approach: CUPID won't turn on all 1,596 crystals at once. It will start with a smaller group (about 1/3 of the total) after 3 years. Even with this smaller "Stage-I" version, the paper shows they could start seeing results much earlier than waiting for the full 10 years.

The Bottom Line

The CUPID experiment is a high-tech, super-cold, light-sensing machine built to catch the rarest event in the universe. The paper calculates that if the universe plays by the rules of the "Inverted Ordering" theory, CUPID has a very high chance of finding the answer.

If it finds the decay, it changes our understanding of the universe. If it doesn't find it, it tells us that the neutrino is even lighter or rarer than we thought, forcing physicists to rewrite their theories. Either way, CUPID is designed to be the ultimate judge in the case of the neutrino's identity.

Technical Summary

Technical Summary: Sensitivity of the CUPID Experiment to $0\nu\beta\beta$ Decay of $^{100}$Mo

Problem and Context
The observation of neutrinoless double-beta decay ($0\nu\beta\beta$) would confirm lepton number violation and establish the neutrino as a Majorana particle, offering a pathway to physics beyond the Standard Model and insights into the baryon asymmetry of the universe. The decay rate is proportional to the square of the effective Majorana neutrino mass ($m_{\beta\beta}$). The CUPID (CUORE Upgrade with Particle IDentification) experiment is designed to search for the $0\nu\beta\beta$ decay of $^{100}$Mo using scintillating $Li_2MoO_4$ crystals. While the preceding CUORE experiment demonstrated the feasibility of operating $\sim$1000 bolometers at $\sim$10 mK, its sensitivity was limited by background induced by $\alpha$ particles from surface contaminations. CUPID aims to overcome this by utilizing scintillating bolometers to discriminate $\alpha$ particles from $\beta/\gamma$ events via light yield differences, targeting a background reduction by a factor of 100 compared to CUORE.

Methodology
This paper presents a comprehensive statistical analysis to compute the discovery and exclusion sensitivities of CUPID to the $0\nu\beta\beta$ half-life ($T_{1/2}$) and the effective Majorana neutrino mass ($m_{\beta\beta}$). The analysis employs both Frequentist and Bayesian frameworks, utilizing an extended unbinned likelihood approach.

• Experimental Parameters: The baseline scenario assumes 1596 enriched $^{100}$Mo crystals (total mass 450 kg, $^{100}$Mo mass 240 kg) operating for 10 years. The design targets an energy resolution of 5 keV FWHM at the $Q$-value (3034 keV) and a background index ($B$) of $1.0 \times 10^{-4}$ counts/keV/kg/yr in a 30 keV region of interest.
• Statistical Framework:
  • Frequentist: Discovery sensitivity is determined by testing the null hypothesis ($\Gamma = 0$) against the alternative ($\Gamma > 0$) using a profile likelihood ratio test statistic ($t_P$). Exclusion sensitivity is calculated by determining the interval of $\Gamma$ values incompatible with the data at 90% confidence level (CL).
  • Bayesian: Exclusion limits are derived as 90% credible intervals (c.i.) from the marginalized posterior distribution of the decay rate, assuming a flat prior on the decay rate (or $m_{\beta\beta}^2$).
  • Simulation: Sensitivities are computed numerically using pseudo-experiments (toy Monte Carlo) generated from the likelihood model, which includes signal (Gaussian peak at $Q_{\beta\beta}$) and background (constant or MC-derived shapes).
• Nuclear Matrix Elements (NMEs): The translation from half-life limits to $m_{\beta\beta}$ limits utilizes a set of NMEs from various nuclear models (pn-QRPA, IBM-2, EDF, Shell Model) to account for theoretical uncertainties.

Key Contributions and Results
The paper provides quantitative sensitivity projections for CUPID under various scenarios of background index and energy resolution:

1. Baseline Scenario Sensitivity (10 years, $B=1.0 \times 10^{-4}$, 5 keV FWHM):

   • Discovery (Frequentist, $3\sigma$): The median discovery sensitivity corresponds to a half-life of $\hat{T}_{1/2} = 1.0^{+0.7}_{-0.3} \times 10^{27}$ yr. This translates to an effective Majorana mass range of $\hat{m}_{\beta\beta} = 12–36$ meV, depending on the NME model used.
   • Exclusion (Frequentist, 90% CL): The median exclusion sensitivity is $\hat{T}_{1/2} > 1.8^{+2.1}_{-0.8} \times 10^{27}$ yr, corresponding to $\hat{m}_{\beta\beta} < 9.0–26$ meV.
   • Exclusion (Bayesian, 90% c.i.): The median exclusion limit is $\hat{T}_{1/2} > 1.6^{+0.6}_{-0.5} \times 10^{27}$ yr, corresponding to $\hat{m}_{\beta\beta} < 9.6–28$ meV.

2. Impact of Parameters:

   • The study evaluates scenarios with improved backgrounds ($0.6 \times 10^{-4}$ and $0.2 \times 10^{-4}$ counts/keV/kg/yr) and degraded resolutions (7.5 keV and 10 keV). Improved background levels significantly enhance sensitivity, while degraded resolution has a moderate negative impact.
   • The spread in $m_{\beta\beta}$ sensitivity is dominated by the uncertainty in NME calculations rather than variations in experimental performance parameters.

3. Staged Deployment (CUPID Stage-I):

   • For a phased deployment involving 150 kg of crystals over 3 years, the median discovery sensitivity is projected at $\hat{T}_{1/2} \approx 0.2 \times 10^{27}$ yr ($\hat{m}_{\beta\beta} = 26–77$ meV), assuming a slightly higher background of $1.5 \times 10^{-4}$ counts/keV/kg/yr.

4. Discovery Probability:

   • For the baseline design, the probability of discovery (defined as 50% probability) is high for the inverted ordering (IO) regime of neutrino masses, particularly for favorable NME models (e.g., EDF), even at the lower bound of the IO region ($m_{\beta\beta} \approx 18.4$ meV).

Significance
The paper claims that the CUPID experiment, with its baseline design parameters, possesses the sensitivity to fully explore the neutrino mass regime in the inverted ordering scenario and the normal ordering regime for neutrino masses larger than 10 meV. The results highlight the competitiveness of CUPID against current and next-generation experiments. The analysis confirms that the combination of scintillating bolometer technology (providing $\alpha$ rejection) and the high $Q$-value of $^{100}$Mo allows CUPID to achieve the necessary background levels to probe the Majorana neutrino mass scale relevant to current cosmological and oscillation data. The work establishes the statistical foundation for interpreting future CUPID data in terms of fundamental neutrino properties.