Precise $^{136}$Xe Double Beta Decay Measurement in PandaX-4T with Implications on the Nuclear Matrix Elements and Majorons

Using 39.1 kg·yr of exposure from the PandaX-4T experiment, this study presents the most precise measurement to date of the $^{136}$Xe two-neutrino double beta decay half-life, provides a consistent measurement of the nuclear matrix element ratio $\xi_{31}^{2\nu}$, and establishes the world's most stringent limit on Majoron-emitting modes with spectral index $n=7$.

The Gist

Imagine you are a detective trying to solve a mystery about the universe's most elusive particles: neutrinos. These are tiny, ghost-like particles that zip through everything without leaving a trace.

This paper is a report from the PandaX-4T experiment, a massive, ultra-sensitive detector buried deep underground in a gold mine in China. Think of PandaX-4T as a giant, high-tech "fish tank" filled with 3.7 tons of liquid xenon (a noble gas), designed to catch rare events that happen very, very rarely.

Here is the story of what they found, explained simply:

1. The Mystery: The Double Beta Decay

In the atomic world, some atoms are unstable and want to become stable. Usually, they do this by shooting out a particle called a "beta particle" (an electron). Sometimes, an atom tries to do this twice at the same time. This is called Double Beta Decay.

There are two main theories about how this happens:

• The "Standard" Version (2νββ): The atom shoots out two electrons and two neutrinos. This is allowed by our current laws of physics (the Standard Model). It's like a car driving down a road with two passengers.
• The "Ghost" Version (0νββ): The atom shoots out two electrons but zero neutrinos. This would mean neutrinos are their own antiparticles (Majorana particles). If we find this, it breaks the current rulebook and could explain why the universe has more matter than antimatter. It's like a car driving down a road with two passengers, but the passengers vanish into thin air.

The Problem: The "Ghost" version is so rare that no one has ever seen it yet. To find it, scientists need to understand the "Standard" version perfectly first, because the Standard version creates a background "noise" that can hide the Ghost signal.

2. The Detective Work: Listening to the "Music"

When the atom decays, the electrons it shoots out carry energy. If you measure the total energy of these electrons, it creates a specific "song" or spectrum.

• The Standard Song: The energy is spread out in a smooth curve (a continuous spectrum).
• The Ghost Song: The energy would be a sharp, single spike (because no energy is lost to neutrinos).

The PandaX-4T team didn't just look for the spike; they listened very carefully to the Standard Song to see if they could hear any subtle changes in its melody.

3. The Key Discovery: Tuning the Instrument

The paper focuses on a specific detail in the Standard Song called $\xi_{31}^{2\nu}$.

• The Analogy: Imagine the Standard Song is a piece of music played by a piano. The main notes are the "leading" components, but there are also faint, subtle harmonics (the "subleading" components) that make the sound unique.
• The Measurement: The team measured the ratio of these harmonics to the main notes. They found a value of 0.59.
• Why it matters: This value acts like a fingerprint for the atomic nucleus. By measuring it precisely, they can test different theories about how the nucleus behaves. Their result matches the predictions of the "Quasiparticle Random-Phase Approximation" (a complex math model), but it's not precise enough yet to rule out other theories. It's like confirming the piano is in tune, but we need even better microphones to hear if the piano is made of wood or plastic.

The Result: They measured the "half-life" (how long it takes for half the atoms to decay) of this process with the highest precision ever recorded: $2.14 \times 10^{21}$ years. That's 2,140,000,000,000,000,000,000 years!

4. The Hunt for "Majorons" (The Exotic Bosons)

The team also looked for a different kind of "Ghost" signal. Some theories suggest that instead of neutrinos, the atom might shoot out a mysterious particle called a Majoron (a hypothetical particle related to dark matter).

• The Analogy: If the Standard Song is a piano, the Majoron signal would be a completely different instrument, like a flute, playing a specific note.
• The Search: They looked for these "flute notes" in the data. They found nothing.
• The Victory: Even though they didn't find the Majoron, they set the strictest limit ever for a specific type of Majoron signal (spectral index $n=7$). It's like saying, "We didn't find the thief, but we proved with 99.9% certainty that the thief didn't enter through the front door."

5. Why This Matters

• Lowering the Noise: Previous experiments could only listen to the "music" starting from a high energy (like 500 keV). PandaX-4T lowered the microphone to hear the quietest, lowest notes (down to 20 keV). This gave them a much clearer picture of the whole song.
• Refining the Map: By measuring the Standard decay so precisely, they are helping physicists build a better map of the atomic nucleus. This map is crucial for the next step: finally hunting down the elusive "Ghost" decay (neutrinoless double beta decay).
• The Future: The PandaX-4T detector is getting bigger and better. With more data, they hope to finally hear that "Ghost" signal or prove once and for all that neutrinos are indeed their own antiparticles.

Summary

In short, the PandaX-4T team acted like master audiophiles. They listened to the faint, rare "music" of atoms decaying in a giant tank of liquid xenon. They didn't find the "ghost" they were hunting for, but they tuned their instruments so perfectly that they now have the clearest, most precise understanding of the "standard" music ever achieved. This clarity brings us one step closer to solving one of the biggest mysteries in physics: What is the true nature of the neutrino?

Technical Summary

1. Problem Statement and Motivation

Double beta decay ($\beta\beta$) is a rare nuclear process crucial for testing the Standard Model and searching for New Physics.

• Two-Neutrino Double Beta Decay ($2\nu\beta\beta$): Consistent with the Standard Model but requires precise measurement of Nuclear Matrix Elements (NMEs) to constrain theoretical models.
• Neutrinoless Double Beta Decay ($0\nu\beta\beta$): A hypothetical process that would prove neutrinos are Majorana particles. Its rate depends on the effective Majorana mass and NMEs. Accurate $2\nu\beta\beta$ measurements are essential to reduce uncertainties in $0\nu\beta\beta$ NME predictions.
• Majoron-Emitting Modes: Hypothetical decays where one or two bosons (Majorons) are emitted. These are signatures of lepton number violation and potential dark matter candidates.
• The Gap: Previous measurements of the $^{136}\text{Xe}$ $2\nu\beta\beta$ spectrum and searches for Majoron modes were limited to high energy thresholds (500–800 keV), leaving the lower energy region unexplored. This paper aims to utilize the full spectrum to improve precision and sensitivity.

2. Methodology

Experimental Setup:

• Detector: PandaX-4T, a dual-phase liquid xenon (LXe) Time Projection Chamber (TPC) located in the Jinping Underground Laboratory.
• Exposure: Utilized data from the commissioning run (Run0, 94.8 days) and the first science run (Run1, 163.5 days), totaling 39.1 $\pm$ 0.7 kg$\cdot$yr of $^{136}\text{Xe}$ exposure.
• Fiducial Volume (FV): Defined as the innermost, cleanest region to minimize background. FV masses were 625 kg (Run0) and 621 kg (Run1).
• Energy Range: The analysis extended the Region of Interest (ROI) down to 20 keV, a significant improvement over previous studies.

Data Analysis and Calibration:

• Energy Calibration: Used monoenergetic peaks ($^{83m}\text{Kr}$ at 41.5 keV, $^{131m}\text{Xe}$ at 164 keV, $^{127}\text{Xe}/^{129m}\text{Xe}$ at 236 keV) and high-energy sources ($^{137}\text{Cs}$, $^{60}\text{Co}$, $^{40}\text{K}$, $^{232}\text{Th}$ chain).
• Response Model: A 5-parameter model accounted for energy shifts and resolution (Gaussian width $\sigma(E)$) and nonlinearity. Parameters were derived from control regions outside the FV to avoid statistical correlation with the signal fit.
• Background Modeling: Primary backgrounds included:
  • Intrinsic: $^{85}\text{Kr}$, $^{124}\text{Xe}$, $^{125}\text{I}$, and xenon isotopes ($^{127}\text{Xe}$, etc.).
  • Material: Radioactive impurities ($^{232}\text{Th}$, $^{238}\text{U}$, $^{60}\text{Co}$, $^{40}\text{K}$) in detector components and the stainless steel platform (SSP).
  • External: Solar neutrinos ($pp$ and $^7\text{Be}$).
• Statistical Approach: A one-dimensional binned likelihood fit (Frequentist approach) was performed on the summed electron energy spectrum (20–2800 keV).

Key Parameters Investigated:

1. $\xi_{31}^{2\nu}$: A parameter defined as the ratio of subleading to leading components of the $2\nu\beta\beta$ NME ($M_{GT-3}^{2\nu} / M_{GT}^{2\nu}$). It distinguishes between "single-state dominance" and "higher-state dominance" hypotheses.
2. Majoron Modes: Searches for spectral indices $n = 1, 2, 3, 7$, corresponding to different Majoron emission scenarios.

3. Key Contributions

• Extended Energy Range: First analysis of the $^{136}\text{Xe}$ $\beta\beta$ spectrum extending down to 20 keV, allowing for a nearly complete spectral fit.
• Precision Measurement: Achieved the most precise measurement of the $^{136}\text{Xe}$ $2\nu\beta\beta$ half-life to date, reducing uncertainty by a factor of 2 compared to previous PandaX results.
• NME Constraint: Provided a direct measurement of the parameter $\xi_{31}^{2\nu}$, offering new constraints on theoretical NME calculations used for $0\nu\beta\beta$ searches.
• Majoron Limits: Established the most stringent limits to date for the Majoron-emitting mode with spectral index $n=7$.

4. Results

A. $2\nu\beta\beta$ Half-Life:

• Measured half-life: $(2.14 \pm 0.05) \times 10^{21}$ years.
• This result is the most precise to date, with a total uncertainty smaller than any previous measurement.
• The value is slightly lower than the previous PandaX Run0 result, attributed to an updated $^{136}\text{Xe}$ abundance value (8.584% vs. 8.857%).

B. Nuclear Matrix Element Parameter ($\xi_{31}^{2\nu}$):

• Measured value: $0.59^{+0.41}_{-0.38}$.
• Significance: The result is consistent with theoretical predictions (Quasiparticle Random Phase Approximation and Shell Model) within $1\sigma$ and $2\sigma$ respectively.
• Comparison: The result is consistent with zero ($\xi_{31}^{2\nu} = 0$), which supports the "higher-state dominance" hypothesis, though the current precision cannot conclusively exclude the "single-state dominance" hypothesis.
• Discrepancy: The measured value has the opposite sign to the KamLAND-Zen result ($-0.26^{+0.31}_{-0.25}$), differing by approximately $1.7\sigma$.

C. Majoron-Emitting $\beta\beta$ Search:

• No statistically significant evidence for Majoron-emitting decays was found for any mode ($n=1, 2, 3, 7$).
• 90% Confidence Level (CL) Lower Limits on Half-lives:
  • $n=1$: $> 2.4 \times 10^{23}$ yr
  • $n=2$: $> 1.2 \times 10^{23}$ yr
  • $n=3$: $> 5.7 \times 10^{22}$ yr
  • $n=7$: $> 7.0 \times 10^{22}$ yr (Most competitive result; improved sensitivity due to the low-energy threshold where the $n=7$ spectrum peaks).

5. Significance and Future Outlook

• Physics Impact: The precise determination of the $2\nu\beta\beta$ half-life and the parameter $\xi_{31}^{2\nu}$ provides critical benchmarks for refining Nuclear Matrix Element calculations, which are the dominant source of uncertainty in interpreting $0\nu\beta\beta$ searches.
• Detector Capability: The successful reconstruction of the spectrum down to 20 keV demonstrates the PandaX-4T detector's capability to operate effectively in the MeV range, validating its dual-purpose design for both dark matter and rare decay searches.
• Future Potential: With the detector currently in its second science run (Run2) following upgrades, the collaboration expects to further enhance sensitivity. The ability to reconstruct the nearly complete $\beta\beta$ spectrum will allow for even more precise discrimination between theoretical models and tighter constraints on Majoron models and $0\nu\beta\beta$ physics.