Measurement of the Muon Flux at the Sanford Underground Research Facility with the LUX-ZEPLIN Dark Matter Detector

Using 366.4 days of data from the LUX-ZEPLIN detector, researchers measured the cosmic-ray muon flux at the Sanford Underground Research Facility's Davis Cavern to be $(5.09\pm0.08_\textrm{stat.}\pm0.10_\textrm{sys.})\times10^{-9}~\textrm{cm}^{-2}\textrm{s}^{-1}$, providing critical background information for dark matter and rare decay searches.

The Gist

The Deep Earth Muon Count: A Story of Invisible Rain and Underground Shields

Imagine you are trying to listen to a single, tiny whisper in a room that is constantly being bombarded by a heavy rainstorm. That is essentially what the LUX-ZEPLIN (LZ) experiment is doing. It is a massive, ultra-sensitive detector buried deep underground in the Sanford Underground Research Facility (SURF) in South Dakota. Its job is to catch "WIMPs" (Weakly Interacting Massive Particles), which are ghostly particles that might make up Dark Matter.

But there's a problem: The "rain" isn't water; it's cosmic-ray muons. These are high-energy particles from space that constantly rain down on Earth. Even though the LZ detector is buried under a mountain of rock (about 1.5 kilometers or 4,850 feet deep), some of these muons still punch through. When they hit the detector, they create a loud "crash" that can look exactly like the "whisper" of a Dark Matter particle.

This paper is the story of how the LZ team decided to count the raindrops to make sure they aren't accidentally mistaking a storm for a whisper.

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1. The Setup: A Three-Layered Onion

Think of the LZ detector as a giant, high-tech onion with three layers:

• The Core (TPC): The innermost layer is filled with liquid xenon. This is where the "whisper" (Dark Matter) is hoped to be heard.
• The Skin: A middle layer of liquid xenon that acts as a buffer.
• The Outer Shell (OD): The outermost layer is filled with a special liquid scintillator (a glowing liquid) loaded with gadolinium.

When a muon (a cosmic raindrop) hits the detector, it doesn't just stop at the door. It smashes through the Outer Shell, the Skin, and often the Core. Because it hits all three layers almost instantly, the detectors see a "triple coincidence"—a signal in all three places at the same time. This is the detector's way of saying, "Hey! That's a muon, not a Dark Matter whisper!"

2. The Mission: Counting the Rain

The scientists wanted to know exactly how many muons are hitting their detector every day. Why? Because if they know the "background noise" (the muons) perfectly, they can subtract it from their data and be much more confident when they find a real Dark Matter signal.

They used data collected over 366 days (a full year). They set up a filter:

• If a muon hits the outer shell with at least 8 MeV of energy (a measure of how hard it hit).
• And if it hits the inner core with at least 20 MeV of energy.
• And if the timing is perfect (all three layers light up within a billionth of a second).

The Result: They counted 10.94 muons per day.

3. The Surprise: The Rain was Lighter Than Expected

Before this experiment, the scientists had a "weather forecast" (a computer simulation) that predicted how many muons should be hitting them. They used a model based on the density of the rock above the lab.

• The Prediction: The computer said, "Expect about 12.8 muons a day."
• The Reality: The detector actually saw only 10.94 muons a day.

The real world was about 15% quieter than the computer predicted.

4. The Detective Work: Why the Difference?

Why was the rain lighter than the forecast? The scientists realized the "weather forecast" was based on an assumption about the density of the rock above them.

Imagine you are trying to stop a bowling ball by throwing a blanket at it.

• If the blanket is thin and light (low density rock), the ball punches right through.
• If the blanket is thick and heavy (high density rock), the ball slows down or stops.

The scientists' computer model assumed the rock above the lab was a certain weight (density). But because fewer muons got through than expected, it meant the "blanket" (the rock) was actually heavier and denser than they thought.

By doing some math, they recalculated the density of the rock. They found it was about 2.76 grams per cubic centimeter, which is about 2.5% denser than their original guess. This is a big deal because knowing the exact density of the rock helps all future experiments at this site predict their background noise more accurately.

5. The Takeaway

This paper is like a meteorologist going outside with a rain gauge, checking the actual rainfall, and then realizing, "Oh, my weather model was slightly off because I underestimated how thick the clouds were."

• What they did: They counted the cosmic muons hitting the LZ detector for a year.
• What they found: There were fewer muons than the computer predicted.
• What it means: The rock above the lab is denser than we thought.
• Why it matters: Now that they have a more accurate "count" of the background noise and a better understanding of the rock, they can tune their detectors to be even more sensitive to the elusive Dark Matter particles they are hunting for.

In short, they didn't find Dark Matter in this specific paper, but they found the perfect map of the noise so they can hear the signal much clearer next time.

Technical Summary

1. Problem Statement

High-energy cosmic-ray muons penetrating deep underground laboratories pose a significant background threat to rare-event search experiments, such as those searching for Weakly Interacting Massive Particles (WIMPs) or neutrinos. Muons can induce nuclear recoils via elastic scattering or generate secondary neutrons through inelastic scattering and capture, mimicking dark matter signals.

While previous measurements of muon flux at the Sanford Underground Research Facility (SURF) exist (e.g., from the Davis solar neutrino experiment and the MAJORANA DEMONSTRATOR), there are discrepancies between these measurements and theoretical models. Specifically:

• Previous vertical intensity measurements suggested a flux higher than the total flux measured by MAJORANA.
• Simulations used for the LUX-ZEPLIN (LZ) experiment initially predicted a total muon flux (~$6.16 \times 10^{-9} \text{ cm}^{-2}\text{s}^{-1}$) that was ~16% higher than recent measurements.
• Accurate knowledge of the muon flux and the overburden rock density is critical for tuning background models and optimizing future large-scale detectors (e.g., DUNE) planned for SURF.

2. Methodology

The study utilized the LUX-ZEPLIN detector, located at the 4850 ft level (approx. 1480 m vertical depth) in the Davis Campus of SURF. The analysis covered 366.4 days of exposure across two operational periods (WS2022 and WS2024).

Detector Configuration:

• TPC (Time Projection Chamber): Dual-phase liquid xenon core.
• Skin: Liquid xenon layer surrounding the TPC.
• OD (Outer Detector): Gadolinium-loaded liquid scintillator surrounding the Skin.
• All three systems act as veto detectors to identify muon events.

Event Selection:
Muons were identified by their distinct signature: large, nearly simultaneous energy deposits across the OD, Skin, and TPC.

• Timing Cuts: Events were selected based on strict time coincidence between the three detectors ($\Delta t < 200\text{--}1200$ ns depending on the pair).
• Energy Thresholds:
  • OD: $> 8$ MeV (2000 phd).
  • TPC: $> 20$ MeV. This threshold was chosen to ensure the muon physically traversed the TPC, minimizing uncertainties from secondary particles produced outside the TPC that might enter it.
• Data Processing: Waveforms were analyzed to distinguish the long S2 pulse tail of a muon track from standard dark matter signals.

Simulation and Modeling:

• MUSIC/MUSUN: Used to simulate muon propagation from the surface through rock to the cavern, generating energy spectra and angular distributions.
• BACCARAT (GEANT4-based): Used to simulate muon interactions within the detector geometry.
• NEST Model: Used to convert detected photon counts (S1+S2) in the TPC to deposited energy.
• Rock Density: Initial simulations assumed an average rock density of $2.70 \text{ g cm}^{-3}$.

3. Key Contributions

• Direct Flux Measurement: Provided a direct, high-precision measurement of the total cosmic-ray muon flux in the Davis cavern using a large-volume, multi-component detector.
• Model Tuning: Identified a discrepancy between the initial simulation predictions and observed data, leading to a refined estimate of the local rock density.
• Systematic Uncertainty Reduction: Improved upon previous measurements by reducing statistical and systematic uncertainties through the use of the LZ detector's high granularity and veto capabilities.
• Multiple Muon Analysis: Quantified the fraction of multiple muons (bundles) at this depth, concluding they constitute $<1\%$ of the total rate and can be neglected for this analysis.

4. Results

Muon Rate:

• The measured muon rate through the detector (with TPC $>20$ MeV and OD $>8$ MeV thresholds) was $10.94 \pm 0.18 \text{ day}^{-1}$.
• This rate was approximately 15–20% lower than the rate predicted by the initial simulation model.

Muon Flux:

• By scaling the simulated flux by the ratio of measured-to-simulated rates, the total muon flux at the top of the Davis cavern was calculated as:
  $$\Phi = (5.09 \pm 0.08_{\text{stat}} \pm 0.10_{\text{sys}}) \times 10^{-9} \text{ cm}^{-2}\text{s}^{-1}$$
• This result is consistent with the MAJORANA DEMONSTRATOR measurement ($5.31 \pm 0.17 \times 10^{-9} \text{ cm}^{-2}\text{s}^{-1}$) but resolves the discrepancy with the older vertical intensity measurements when integrated over all angles.

Rock Density Estimation:

• The lower-than-expected muon rate was attributed to an underestimation of the rock density in the simulation.
• By adjusting the rock density in the simulation to match the measured flux, the authors derived a corrected average rock density above the LZ detector:
  $$\rho = (2.76 \pm 0.01_{\text{stat}} \pm 0.01_{\text{sys}}) \text{ g cm}^{-3}$$
• This is 2.5% higher than the initial assumption ($2.70 \text{ g cm}^{-3}$) and aligns well with other geological surveys of the area.

5. Significance

• Background Suppression: The precise muon flux measurement allows for more accurate modeling of cosmogenic backgrounds (neutrons and isotopes) in the LZ experiment, directly improving the sensitivity of WIMP searches.
• Future Experiments: The derived rock density and flux values are critical inputs for designing and simulating future, larger detectors at SURF, such as the Deep Underground Neutrino Experiment (DUNE).
• Geological Insight: The study provides an independent, physics-based validation of the overburden density at the Davis Campus, confirming that the rock is slightly denser than previously assumed in standard models.
• Validation of Simulation Tools: The work validates the MUSIC/MUSUN and BACCARAT simulation frameworks, provided the rock density parameter is correctly tuned, reinforcing their utility for underground physics.