Sensitivity of neutrinoless double beta decays from a combined analysis of ground and excited states

This paper proposes that combining the analysis of neutrinoless double-beta decay transitions to both ground and excited states in large liquid xenon detectors can significantly enhance discovery sensitivity and mitigate nuclear matrix element uncertainties in the search for the inverted neutrino mass ordering.

The Gist

Imagine you are a detective trying to solve the ultimate cosmic mystery: Why does the universe exist at all?

To crack this case, scientists are looking for a very rare event called neutrinoless double-beta decay. Think of this as a nuclear "magic trick" where an atom spontaneously changes its identity, spitting out two electrons but no neutrinos. If we see this happen, it proves that neutrinos are their own antiparticles (Majorana particles) and helps us understand the fundamental rules of the universe.

However, there's a huge problem: It's incredibly hard to find. It's like trying to hear a single whisper in a hurricane. The current experiments are huge, but they are still struggling to catch enough of these whispers to be sure.

This paper proposes a clever new strategy to make the "whisper" louder without building a bigger microphone. Here is the breakdown in simple terms:

1. The Problem: The "Fuzzy" Math

Scientists have a formula to calculate how often this decay happens. But the formula relies on something called Nuclear Matrix Elements (NMEs).

• The Analogy: Imagine trying to guess the weight of a hidden elephant. You have a scale, but the scale is broken and gives you a reading that could be anywhere from 2 tons to 6 tons. Because the math is so "fuzzy" (uncertain), even if you see a signal, you aren't sure if it's the real deal or just a fluke. This uncertainty is the biggest bottleneck in the field.

2. The Old Strategy: Listening to the "Main Channel"

Currently, experiments only listen for the decay where the atom settles into its ground state (its calmest, lowest-energy state).

• The Analogy: This is like listening for a specific song on the radio. But the signal is weak, and there's a lot of static (background noise). To hear it clearly, you have to stand in a tiny, quiet room in the center of a massive, noisy stadium. You have to ignore 80% of the stadium to avoid the noise, which means you miss a lot of potential signals.

3. The New Strategy: Tuning into the "Bonus Channel"

The authors suggest we shouldn't just listen to the main song. We should also listen for a bonus track where the atom lands in a slightly excited state before settling down.

• The Analogy: When the atom lands in this excited state, it doesn't just sit there; it immediately "sings" by releasing two distinct gamma-ray "notes" (like a chime or a bell) as it calms down.
• Why this helps:
  1. The Signature: In the giant liquid xenon detectors (like the proposed PandaX-xT or XLZD), the main signal looks like a single flash of light. But this "bonus channel" looks like a flash of light followed by two distinct chimes at specific locations.
  2. Noise Cancellation: Because this pattern (Flash + Chime + Chime) is so unique, the computer can easily tell it apart from the background noise. It's like hearing a specific three-note melody in a crowded room; you can ignore the chatter much more easily.
  3. More Space: Because the signal is so distinct, scientists don't need to hide in the tiny, quiet center of the detector. They can use a much larger area (the "fiducial volume") to listen. It's like being allowed to stand in the middle of the stadium because your headphones are so good at filtering out the crowd noise.

4. The Result: A Bigger Net

By combining the search for the "main song" (ground state) and the "bonus track" (excited state), the experiment becomes much more sensitive.

• The Outcome: The paper shows that this combined approach could improve the sensitivity by 2 to 9 times, depending on the specific nuclear physics models used.
• The Goal: This boost is enough to potentially cover the entire range of possibilities for the "inverted mass ordering" of neutrinos (a specific way the universe is structured) within the next decade, without needing to build a detector twice as big.

Summary

Think of the current experiments as trying to find a needle in a haystack by looking at the top 10% of the hay. This paper suggests: "Hey, the needle we are looking for has a tiny, unique magnet on it that makes it glow blue. If we look for the blue glow, we can search the entire haystack and ignore the rest of the hay."

By using the unique "glow" (the gamma rays from the excited state) to filter out noise and expand the search area, scientists can find the needle (the neutrinoless double-beta decay) much faster and with greater certainty. This could finally answer the question of whether neutrinos are their own antiparticles, unlocking a deeper secret of the universe.

Technical Summary

1. Problem Statement

The primary goal of next-generation neutrinoless double-beta ($0\nu\beta\beta$) decay experiments (e.g., PandaX-xT, XLZD) is to probe the inverted neutrino mass ordering (IO) region, requiring half-life sensitivities approaching $10^{28}$ years. However, the discovery potential is severely limited by large uncertainties in Nuclear Matrix Elements (NMEs).

• Current Limitation: NME calculations vary by a factor of three or more across different nuclear models (e.g., RQRPA, IBM-2, ISM, MR-CDFT). This uncertainty prevents a definitive determination of the effective Majorana neutrino mass ($|m_{\beta\beta}|$) even if a signal is observed.
• The Gap: Standard searches focus almost exclusively on the transition from the ground state to the ground state ($0\nu\beta\beta$-gs). Transitions to excited states ($0\nu\beta\beta$-ex) are typically suppressed by phase-space factors and are often ignored or treated as background.
• The Question: Can the $0\nu\beta\beta$-ex channel be exploited to enhance experimental sensitivity and mitigate NME uncertainties without increasing detector size?

2. Methodology

The authors propose a combined analysis strategy that simultaneously utilizes both the ground-state ($0\nu\beta\beta$-gs) and the first excited $0^+$ state ($0\nu\beta\beta$-ex) decay channels of $^{136}\text{Xe}$.

A. Detector Physics & Signal Identification

The study focuses on large-scale Natural Liquid Xenon (NNLXe) Time Projection Chambers (TPCs) like PandaX-xT and XLZD.

• $0\nu\beta\beta$-gs Signature: Appears as a Single-Site (SS) event where two electrons deposit energy at a single location near the Q-value (2.46 MeV).
• $0\nu\beta\beta$-ex Signature: The decay to the excited $0^+_2$ state (Q-value $\approx$ 0.88 MeV) is followed by the emission of two de-excitation $\gamma$-rays (0.76 MeV and 0.82 MeV). This creates a Multi-Site (MS) event with spatially separated energy depositions.
• Background Suppression: The MS topology of the $0\nu\beta\beta$-ex signal allows for much looser fiducial volume (FV) cuts compared to the SS search. While SS searches must restrict the FV to the inner 20% of the detector to shield against external radioactivity, the MS signature allows the use of a much larger FV (up to 3x larger) while maintaining low background rates.

B. Simulation Framework

• Tools: Used BambooMC (Geant4-based) to simulate detector response.
• Scenarios:
  1. Nominal Scenario: Based on current XLZD/PandaX-xT parameters (60t active mass, 8.2t FV for gs, 20t FV for ex).
  2. Ideal Scenario: A hypothetical 100t detector with a 60t FV for the excited state and significantly reduced background rates ($10^{-4}$ counts/yr).
• Statistical Analysis: Constructed a $\chi^2$ function based on Poisson likelihood to combine signal ($S_i$) and background ($B_i$) from both channels. The sensitivity to $|m_{\beta\beta}|$ is derived at the $3\sigma$ confidence level ($\Delta\chi^2 \geq 9$).

C. Nuclear Physics Inputs

The analysis incorporates NMEs from seven different nuclear models:

• RQRPA (with Recoupling Method RCM and Boson Expansion Method BEM)
• Multiple-Commutator Model (MCM with UCOM and Jastrow correlators)
• Interacting Boson Model (IBM-2)
• Interacting Shell Model (ISM)
• Multi-Reference Covariant Density Functional Theory (MR-CDFT)

3. Key Contributions

1. Novel Strategy: First proposal to combine $0\nu\beta\beta$-gs and $0\nu\beta\beta$-ex channels specifically for $^{136}\text{Xe}$ to enhance sensitivity without scaling up detector mass.
2. Fiducial Volume Optimization: Demonstrated that the unique multi-site topology of excited-state decays in liquid xenon allows for a 3-fold increase in fiducial mass for the excited channel, drastically improving the signal-to-background ratio.
3. Model-Independent Robustness: Showed that the sensitivity enhancement depends on the ratio of NMEs ($M_{ex}^{0\nu} / M_{gs}^{0\nu}$). Even with large model discrepancies, the combined approach consistently outperforms single-channel searches.
4. Feasibility for Future Experiments: Provided concrete sensitivity projections for upcoming experiments (PandaX-xT, XLZD), proving they are uniquely suited for this search due to their excellent spatial and energy resolution.

4. Results

The study evaluated the sensitivity to the effective neutrino mass ($|m_{\beta\beta}|$) over a 10-year data acquisition period.

• Sensitivity Enhancement:
  • Nominal Scenario: The combined analysis improves sensitivity by a factor of 2 to 9 depending on the nuclear model. For the RQRPA (RCM) model, sensitivity improves from 69.5 meV (gs-only) to 32.8 meV (combined).
  • Ideal Scenario: Under ideal background conditions, the improvement is even more significant. For models like MCM (UCOM), sensitivity reaches 6.4 meV, well below the lower bound of the inverted ordering.
• Coverage of Inverted Ordering (IO):
  • In the Nominal scenario, the combined analysis brings the sensitivity into the IO region for models where $M_{ex}^{0\nu} \geq M_{gs}^{0\nu}$.
  • In the Ideal scenario, the combined analysis fully covers the entire IO parameter space (down to $\sim$6–8 meV) within a few years for several models.
• NME Dependence: The enhancement is most pronounced when the NME for the excited state is comparable to or larger than that of the ground state. Notably, for $^{150}\text{Nd}$, the paper suggests the excited state NME could be significantly larger, making it an even more promising candidate for this strategy.

5. Significance

• Overcoming Theoretical Uncertainty: By utilizing multiple decay channels, the experiment becomes less reliant on a single, potentially inaccurate NME calculation. If a signal is found in both channels, it provides a self-consistency check against background or non-standard mechanisms.
• Maximizing Discovery Potential: This approach allows next-generation ton-scale experiments to fully probe the inverted mass ordering region without the prohibitive cost of building significantly larger detectors.
• Future Directions: The paper highlights that other isotopes like $^{100}\text{Mo}$ and $^{150}\text{Nd}$ may offer even greater sensitivity gains due to favorable NME ratios. It also suggests that transitions to $2^+$ states should be included in future combined analyses.
• Call to Action: The results underscore the urgent need for theoretical advancements to reduce NME uncertainties and provide systematic error quantification, which will further refine the sensitivity projections of these combined analyses.

In conclusion, this work provides a robust, physics-driven pathway to maximize the discovery potential of the next generation of $0\nu\beta\beta$ experiments by leveraging the unique capabilities of liquid xenon TPCs to detect excited-state transitions.