Direct Measurement of the $^{212}\mathrm{Pb}$ and $^{214}\mathrm{Pb}$ $\beta$ Decay Branching Ratios with the XENONnT Experiment

Using calibration data from the XENONnT detector, this study presents the most precise direct measurements to date of the ground-state $\beta$ decay branching ratios for $^{212}\mathrm{Pb}$ and $^{214}\mathrm{Pb}$, thereby significantly improving background modeling for rare-event searches like dark matter and neutrino experiments.

The Gist

Imagine the XENONnT experiment as a giant, ultra-sensitive underwater camera sitting deep underground in Italy. Its job is to take pictures of the universe's rarest and most elusive events, like dark matter particles or solar neutrinos. To do this, the camera needs to be in a perfectly quiet room, free from any "noise" that could look like a signal.

Unfortunately, the room isn't perfectly quiet. There is a constant, faint hum coming from natural radioactive elements called Radon. As Radon decays, it creates "children" isotopes, specifically Lead-212 and Lead-214. These lead isotopes are like tiny, mischievous ghosts that emit energy (beta decay) right in the low-energy range where the scientists are trying to find their precious signals.

For years, scientists had a "Wanted Poster" for these ghosts, but the descriptions were fuzzy. They knew the ghosts existed, but they weren't sure exactly how often they chose to take a specific path (a "branching ratio") versus other paths. It was like knowing a thief steals 100 times a year, but not knowing if they steal a watch 10% of the time or 50% of the time. This uncertainty made it hard to tell the difference between a real discovery and just a ghost passing by.

The Experiment: A Controlled "Ghost Hunt"

Instead of waiting for these ghosts to appear randomly in the background, the XENONnT team decided to invite them in on purpose. They introduced a controlled amount of Radon into their detector tank. This created a massive, predictable swarm of Lead-212 and Lead-214, giving them a high-quality dataset to study.

Think of it like a music producer trying to understand a specific instrument. Instead of listening to a chaotic orchestra, they isolate that one instrument and play it loudly so they can hear every nuance.

How They Measured It

The detector works by watching for two things when a particle hits the liquid xenon: a flash of light (S1) and a second flash caused by electrons being pulled out (S2).

• The Single-Site Trick: When a Lead isotope decays directly to its stable state (the "Ground State"), it acts like a single bullet hitting a target. It leaves one clean spot of energy.
• The Multi-Site Trick: When it decays to an excited state, it's like a bullet hitting a target and then shattering, sending shards (gamma rays) flying elsewhere. This leaves multiple spots of energy.

By counting how many "single-bullet" hits they saw versus "shattered" hits, and knowing exactly how many Lead atoms they started with, they could calculate the exact percentage of times the Lead chose the direct path.

The Results: Sharper Descriptions

The team used a sophisticated mathematical model (a "best fit" line) to match their data against the theoretical predictions. Here is what they found:

1. Lead-212: They found that about 14.75% of the time, it decays directly to the ground state. This is a much sharper number than before, reducing the uncertainty by three times. It's like upgrading a blurry photo of a face into a high-definition portrait.
2. Lead-214: They found that about 9.8% of the time, it decays directly to the ground state. This result is particularly important because previous scientific references disagreed on this number (one said ~9%, another said ~12%). The XENONnT data sides with the lower number, helping to resolve a long-standing argument in the physics community.

Why This Matters (According to the Paper)

The paper states that these results are crucial for the "noise cancellation" of future experiments. By knowing the exact "song" these radioactive ghosts sing, scientists can subtract that noise more accurately from their data.

This doesn't just help XENONnT; it helps the entire field of dark matter and solar neutrino research. With a cleaner background, these experiments can become more sensitive, potentially allowing them to see the faintest whispers of new physics or solar particles that were previously hidden in the static.

In short, the paper is a high-precision measurement of how two specific radioactive isotopes behave, providing the "instruction manual" needed to tune out background noise in the search for the universe's biggest mysteries.

Technical Summary

Technical Summary: Direct Measurement of the 212Pb and 214Pb β Decay Branching Ratios with the XENONnT Experiment

Problem Statement
Radon radioactivity constitutes a primary background source in liquid xenon (LXe) Time Projection Chambers (TPCs) used for rare-event searches, such as dark matter detection and solar neutrino scattering. The decay chains of $^{220}\text{Rn}$ and $^{222}\text{Rn}$ involve the $\beta$ decays of $^{212}\text{Pb}$ and $^{214}\text{Pb}$, respectively. Accurate characterization of these isotopes is essential for distinguishing new physics from known processes. Specifically, the ground-state (GS) $\beta$ decay branches of these isotopes directly impact the low-energy region of interest.

Current knowledge of these branching ratios (BRs) suffers from significant uncertainties and discrepancies. For $^{212}\text{Pb}$, GS BRs were indirectly determined via $\gamma$-ray spectroscopy and internal conversion intensities in the 1990s, leaving a relative uncertainty of approximately 7.7%. For $^{214}\text{Pb}$, the situation is more critical: the absolute precision for the GS transition is estimated at 7–10%, but literature values exhibit notable tension. The Laboratoire National Henri Becquerel (LNHB) reports a GS BR of $(9.2 \pm 0.6)\%$, while the Nuclear Data Sheet (NDS) reports $(12.7 \pm 1.1)\%$. This discrepancy, attributed to the high $\gamma$-ray multiplicity of the decay, necessitates a re-evaluation using direct measurement techniques.

Methodology
The XENONnT experiment, a dual-phase LXe TPC located at the Laboratori Nazionali del Gran Sasso (LNGS), was utilized to perform direct, high-precision measurements of these branching ratios. The study leveraged calibration data from two distinct campaigns:

• $^{212}\text{Pb}$ Analysis: Utilized $^{220}\text{Rn}$ calibration data from the first science run (SR0).
• $^{214}\text{Pb}$ Analysis: Utilized $^{222}\text{Rn}$ calibration data from the second science run (SR1).

In these campaigns, gaseous xenon was exposed to implanted $^{226}\text{Ra}$ and $^{228}\text{Th}$ sources, flushing radon atoms into the TPC to create a homogeneous distribution of Pb isotopes. The analysis focused on modeling the complete $\beta + \gamma$ signal rather than relying solely on $\gamma$-ray de-excitation.

Key methodological steps included:

1. Event Selection: Events were reconstructed using standard XENONnT pipelines. Selection criteria required at least 3 PMTs for the S1 signal and an S2 threshold >500 PE. Events were classified as single-site (SS) or multiple-site (MS). To ensure a cleaner signal, the analysis primarily selected SS events, as $\beta$ transitions to the nuclear ground state appear exclusively as SS events due to the short range of electrons in LXe. Excited state decays, which emit prompt de-excitation $\gamma$ rays, could manifest as SS or MS topologies.
2. Efficiency Modeling: Selection efficiencies for various decay channels (GS and excited states EX1–EX4) were determined using Geant4 simulations modified to isolate individual Pb $\to$ Bi decay branches. These simulations incorporated LXe microphysics and detector effects. A data-driven approach was used for the S2 light fraction selection.
3. Spectral Modeling: The analysis employed a binned maximum likelihood fit to the reconstructed energy spectra.
   • For $^{212}\text{Pb}$, three channels were modeled: GS, EX1 (238.6 keV), and EX2 (415.3 keV).
   • For $^{214}\text{Pb}$, five channels were modeled: GS, EX1 (295.2 keV), EX2 (351.9 keV), EX3 (533.7 keV), and EX4 (839.0 keV).
   • Theoretical shapes for first-forbidden non-unique GS $\beta$ decays were taken from existing literature [9]. For excited states, where theoretical calculations were unavailable, spectral shapes were simulated using Geant4's Radioactive Decay Module, assuming allowed transition shapes ($S=1$) due to current framework limitations.
4. Background Handling: Backgrounds were modeled using a combination of data-driven templates (from science runs) and simulation-based components, including contributions from $^{212}\text{Bi}$/$^{214}\text{Bi}$ decays outside the active volume, PTFE surface events, and neutron-activated xenon isotopes.

Key Results
The study reports the first direct, high-precision measurements of the GS branching ratios for both isotopes:

• $^{212}\text{Pb}$ Ground State: The measured branching ratio is $(14.75 \pm 0.20(\text{stat}) +0.14_{-0.40}(\text{sys}))\%$. This result reduces the relative uncertainty by a factor of three compared to previous indirect determinations. The measurement is compatible within $2\sigma$ with both LNHB and NDS literature values.
• $^{214}\text{Pb}$ Ground State: The measured branching ratio is $(9.8 \pm 0.3(\text{stat}) +0.8_{-0.2}(\text{sys}))\%$. This result shows better agreement with the LNHB evaluation and other direct measurements than with the NDS value. It addresses the existing $4.7\sigma$ tension between LNHB and NDS literature values, favoring the lower value.

The analysis also provided measurements for the excited state branching ratios, though these carry larger systematic uncertainties and strong correlations between the EX1 and EX2 channels for $^{214}\text{Pb}$.

Significance and Claims
The authors claim that these results represent the most precise direct measurements of these transitions to date. The primary significance of this work lies in:

1. Resolving Nuclear Data Tensions: The $^{214}\text{Pb}$ measurement helps resolve the long-standing discrepancy between major nuclear data evaluations (LNHB vs. NDS).
2. Background Modeling: As $^{214}\text{Pb}$ constitutes the dominant background in XENONnT, these precise BRs are critical for enhancing background modeling in dark matter and neutrino experiments.
3. Sensitivity Improvement: By refining the understanding of low-energy electronic recoil backgrounds, these results improve the sensitivity of current and future experiments to solar neutrinos and physics beyond the Standard Model.
4. Validation of LXe-TPCs: The study demonstrates that low-background LXe-TPCs are highly suitable for precision nuclear physics measurements, providing crucial experimental benchmarks to refine theoretical calculations of $\beta$ decay spectra.

The paper notes that while the results are robust, future improvements could be achieved by adopting more sophisticated theoretical spectral shapes, increasing statistics, and incorporating multi-site (MS) events into the analysis. The results are also consistent with a recent preprint from the PandaX collaboration, further validating the measurement.