Determination of the Muon Lifetime in $^{76}$Se with the MONUMENT experiment

The MONUMENT collaboration determined the muon lifetime in $^{76}$Se with improved accuracy to be (135.1 $\pm$ 0.5) ns, a result that aligns with phenomenological calculations using unquenched axial-vector coupling and serves as a benchmark for neutrinoless double beta decay models.

The Gist

The Big Picture: Why Are We Doing This?

Imagine you are trying to solve a massive, cosmic mystery: Why does the universe exist?

Scientists believe the answer lies in a rare, ghostly particle called the neutrino. Specifically, they are looking for proof that neutrinos are their own "twins" (antiparticles). If they are, it could explain why there is more matter than antimatter in the universe.

To find this proof, physicists are watching for a super-rare event called Neutrinoless Double Beta Decay. It's like watching a specific type of atom (Germanium-76) spontaneously split into two electrons without emitting any neutrinos. If they see this, it's a Nobel Prize-winning discovery.

But there's a problem: The math used to predict how often this should happen is messy. Different teams get different answers, like trying to measure the weight of a cloud with a kitchen scale. The numbers vary by a factor of 2 or 3, which is huge in physics.

The Solution: The "Muon Stopwatch"

To fix the math, the scientists needed a way to test their models. They decided to use a "practice run" called Ordinary Muon Capture (OMC).

Think of the atom (Germanium-76) as a house.

1. The Real Mystery: The house is supposed to spontaneously collapse (Double Beta Decay).
2. The Practice Run: Instead of waiting for the collapse, the scientists throw a heavy, fast-moving ball (a Muon) at the house. The ball gets stuck inside, and the house reacts.

This reaction is very similar to the real mystery, but it happens much faster and is easier to measure. By timing exactly how long the Muon stays stuck in the house before it disappears (decays or is captured), they can check if their "house blueprint" (the nuclear physics model) is accurate.

The Experiment: The MONUMENT Team

The team, called MONUMENT, went to the Paul Scherrer Institute in Switzerland, which has a giant machine that shoots these Muon balls at a target.

• The Target: They used a small pile of Selenium powder (specifically the isotope Selenium-76). Selenium is the "sister" of Germanium. If you understand how Selenium reacts to a Muon, you understand how Germanium behaves in the real mystery.
• The Detectors: They surrounded the target with high-tech cameras (Germanium detectors) that can "see" the flashes of light (gamma rays) the house makes when it reacts to the Muon.

The Problem with the Old Data

A few years ago, the same team tried this experiment and got a result. But, as the paper admits, their old equipment had a glitch. It was like trying to time a sprinter with a stopwatch that sometimes skipped a second. Their old result said the Muon lived for 148.5 nanoseconds.

The new paper says: "We fixed the stopwatch. Let's try again."

The New Method: Two Different Clocks

To make sure they didn't make the same mistake twice, they used two completely different ways to record the data:

1. The "MIDAS" System: This is like a standard digital camera that takes a photo every time something happens. It's fast but might miss tiny details if things happen too quickly.
2. The "ALPACA" System: This is like a high-speed video camera that records the entire movie of the event, not just a snapshot. It's slower to process but captures every tiny detail.

By running both systems side-by-side, they could cross-check their results. If both clocks agreed, they knew the time was real.

The Results: The New Time

After analyzing millions of events, the team found the new, corrected time.

• Old Time: 148.5 nanoseconds (billionths of a second).
• New Time: 135.1 nanoseconds.

This new number is much more precise (the error margin is tiny, only ±0.5).

Why Does This Matter?

When they compared this new time to the theoretical "blueprints" (math models), something interesting happened:

• The "Quenched" Models: Some old math models assumed the forces inside the nucleus were "dampened" or "muted" (like wearing earplugs). These models predicted a much shorter time (around 59 ns). The new data proves these models are wrong.
• The "Unquenched" Models: Newer models that assume the forces are loud and clear (no earplugs) predicted a time of roughly 134.5 ns. The new data matches this almost perfectly.

The Takeaway

The MONUMENT team successfully fixed their "stopwatch" and proved that the "loud and clear" math models are the correct ones to use.

In simple terms:
They fixed a broken ruler, measured a specific atom, and found that the ruler they were using to predict the "Big Mystery" (Double Beta Decay) was actually accurate all along, provided they didn't try to "mute" the physics.

This gives the scientists hunting for the Big Mystery (Neutrinoless Double Beta Decay) much more confidence in their calculations. They now know exactly how to tune their search, bringing them one step closer to solving the mystery of why the universe exists.

Technical Summary

1. Problem Statement and Motivation

The primary motivation for this research is to improve the accuracy of nuclear physics models used to predict neutrinoless double beta decay ($0\nu\beta\beta$).

• The Challenge: The half-life of $0\nu\beta\beta$ decay depends heavily on the Nuclear Matrix Element (NME). Current theoretical calculations of NMEs using different many-body methods (e.g., Quasiparticle Random Phase Approximation - QRPA) exhibit a significant spread (factors of 2 to 3), creating the largest source of uncertainty in interpreting experimental limits.
• The Solution: Ordinary Muon Capture (OMC) serves as an experimental benchmark for $0\nu\beta\beta$ decay. Both processes involve similar momentum transfers ($\sim 100$ MeV/c) and populate similar intermediate nuclear states.
• Specific Target: The study focuses on $^{76}$Se, the daughter nucleus of the $0\nu\beta\beta$-decay candidate $^{76}$Ge (used in experiments like LEGEND).
• Previous Limitation: A previous measurement of the muon lifetime in $^{76}$Se (Zinatulina et al., 2019) suffered from instrumental issues regarding timing information, resulting in a value of $148.5 \pm 0.1$ ns that was likely inaccurate. This paper aims to correct that value with improved precision.

2. Methodology and Experimental Setup

The experiment was conducted at the Paul Scherrer Institute (PSI) in Switzerland, utilizing the $\pi$E1 muon beam line.

Experimental Apparatus

• Beam: Negative muons with a momentum of $\sim 38$ MeV/c were selected to maximize the stopping rate in the target.
• Target: Approximately 2 g of selenium powder enriched to 99.68% $^{76}$Se.
• Muon Tagging System: A set of plastic scintillator counters (C0–C3) equipped with Photomultiplier Tubes (PMTs) identified muons that stopped in the target (no signal in veto counters C0/C3, coincident signals in C1/C2).
• Spectroscopy: An array of eight High-Purity Germanium (HPGe) detectors surrounded the target to detect subsequent $\gamma$-rays and muonic X-rays ($\mu$X-rays).
  • 2 Broad Energy Germanium (BEGe) detectors (high energy resolution).
  • 6 Coaxial (COAX) detectors (high efficiency and timing).
• Data Acquisition (DAQ): Two independent systems were used to ensure robust cross-validation:
  1. MIDAS: Triggered independently per channel; recorded online energy/timing. Prone to dead-time issues where true coincidences might be missed.
  2. ALPACA: Triggered by HPGe detectors; recorded full waveforms for offline reconstruction, allowing for better handling of pile-up and timing.

Analysis Strategy

The muon lifetime ($\tau$) was extracted from the time difference between the muon stopping signal and the emission of $\gamma$-rays from the excited daughter nucleus ($^{76}$As).

1. Time Profile Extraction:
   • Constructed 2D histograms of Energy vs. Time.
   • ALPACA: Used a combined maximum likelihood fit of all time slices (32 ns bins) with shared shape parameters for Full Energy Peaks (FEP) but individual backgrounds.
   • MIDAS: Used binned $\chi^2$ fits, analyzing the tail of the time distribution where prompt effects had settled.
2. Lifetime Fit:
   • The time profile of $\gamma$-rays was modeled as a convolution of a prompt timing response (derived from $\mu$X-rays, which have negligible delay) and an exponential decay representing the muon lifetime.
   • ALPACA: Combined fits of $\gamma$ and $\mu$X-ray lines using cubic spline interpolation for the prompt response.
   • MIDAS: Fits started at late times ($>200$ ns) where the signal is purely exponential decay on a constant random background.

Systematic Uncertainty Control

The authors rigorously addressed systematic effects that plagued previous work:

• Charge Collection Effects: Events with longer drift times (reconstructed later) showed energy deficits. This was modeled by allowing FEP parameters to vary per time slice with "pull terms."
• Background Modeling: Linear background assumptions were tested against higher-order polynomials.
• Prompt Response Energy Dependence: The timing resolution varies with energy; this was corrected by transforming the prompt response from $\mu$X-rays to $\gamma$-rays.
• Cross-Validation: The use of two independent DAQ systems and analysis chains (ALPACA vs. MIDAS) allowed for the identification and correction of method-specific biases.

3. Key Contributions

1. Correction of Previous Data: The paper definitively corrects the previously reported muon lifetime in $^{76}$Se from $148.5 \pm 0.1$ ns to $135.1 \pm 0.5$ ns.
2. Methodological Robustness: It demonstrates the necessity of using independent DAQ systems and analysis chains to uncover hidden systematic errors (specifically related to timing reconstruction and charge collection) in muon capture experiments.
3. Comprehensive Systematic Budget: The study provides a detailed breakdown of systematic uncertainties, showing that they dominate over statistical uncertainties (statistical error $< 0.1$ ns vs. total error $0.5$ ns).

4. Results

• Final Value: The combined muon lifetime in $^{76}$Se is determined to be $\tau = 135.1 \pm 0.5$ ns.
• Consistency:
  • ALPACA result: $134.8 \pm 0.7$ ns.
  • MIDAS result: $135.4 \pm 0.7$ ns.
  • The agreement between the two independent methods validates the result.
• Theoretical Comparison:
  • The result is in excellent agreement with QRPA calculations that use an unquenched axial-vector coupling constant ($g_A = 1.27$).
  • It contradicts calculations using a strongly quenched $g_A$ ($g_A = 0.8$), which predict a much shorter lifetime ($\sim 59$ ns).
  • It also aligns well with semi-empirical models (Primakoff and Goulard-Primakoff formalisms).

5. Significance

• Benchmarking Nuclear Models: The result provides a critical experimental constraint for nuclear models used in $0\nu\beta\beta$ decay searches. The agreement with unquenched QRPA calculations suggests that little to no quenching of the axial-vector coupling is required to describe the total muon capture strength in this mass region.
• Impact on $0\nu\beta\beta$ Searches: By validating the theoretical framework (specifically the NMEs) used for $^{76}$Ge, this measurement increases confidence in the sensitivity projections and interpretation of results from major $0\nu\beta\beta$ experiments like LEGEND.
• Future Directions: The paper highlights that while the total capture rate is now well-determined, the partial capture rates (individual transitions to excited states) require further analysis with improved detection efficiency (e.g., Compton suppression) to fully map the nuclear structure.

In conclusion, the MONUMENT collaboration has successfully resolved a discrepancy in muon capture data, providing a precise benchmark that supports the use of unquenched QRPA models for neutrinoless double beta decay nuclear matrix elements.