Investigating Production of TeV-scale Muons in Extensive Air Shower at 2400 Meters Underground

Using 1,338.6 live days of data from a one-ton prototype detector at the 2,400-meter-deep China Jinping Underground Laboratory, researchers measured a TeV-scale underground muon flux that deviates by approximately 40% from leading hadronic interaction models, offering new constraints on air shower physics and suggesting a lighter cosmic-ray mass composition in the tens of TeV to PeV energy range.

The Gist

Imagine the universe is constantly raining invisible, high-speed bullets called cosmic rays. Most of these bullets are just protons (hydrogen nuclei) or helium nuclei, but some are heavy elements like iron. When these cosmic rays hit the Earth's atmosphere, they don't just stop; they crash into air molecules and trigger a massive chain reaction, like a giant cosmic billiard game. This creates a shower of billions of secondary particles, known as an Extensive Air Shower (EAS).

Most of these particles are like confetti—they are light, low-energy, and get stopped by just a few meters of rock or water. But a tiny fraction of them are "super-bullets": muons with enormous energy (TeV scale). These are so powerful that they can punch through kilometers of solid mountain rock.

The Experiment: A Deep-Sea Cave Detector

Scientists built a special detector inside the China Jinping Underground Laboratory (CJPL), which is buried under 2,400 meters (about 1.5 miles) of solid rock. Think of this rock as a giant, natural filter.

• The Filter: The rock acts like a sieve. It stops all the weak, low-energy particles.
• The Target: Only the strongest, most energetic muons can survive the journey to the bottom.
• The Device: Inside this deep cave, the team used a one-ton prototype detector (a large sphere filled with a special glowing liquid called scintillator). When a high-energy muon zips through, it makes the liquid glow, and cameras (photomultiplier tubes) catch the light.

They watched this detector for over 1,300 days, counting how many of these "super-bullets" arrived.

The Big Surprise: The "Missing" Muons

The scientists had a very clear expectation of how many muons should arrive. They used the best computer models available (like a weather forecast for particle physics) to predict the numbers. These models are based on how we think particles smash into each other at the highest energies.

The Result: The detector found 40% more muons than the models predicted.

To put this in perspective: If you ordered a pizza expecting 10 slices, but 14 slices showed up, you'd know something is wrong with the recipe. In this case, the "recipe" is our understanding of how particles interact. The fact that there are so many extra muons suggests our current models of particle physics are missing a key ingredient.

Why Does This Matter? Two Possible Explanations

The paper offers two creative ways to explain this "extra slice" of muons:

1. The "Harder Kick" Theory (New Physics in the Crash)
When the cosmic ray hits the atmosphere, it's the first collision that matters most. The scientists think this first crash might be "harder" or more energetic than we thought.

• Analogy: Imagine two cars crashing. Our current models say the crash scatters the parts gently. But the data suggests the crash was much more violent, sending heavy, fast-moving pieces (charged Kaons and pions) flying forward. These heavy pieces decay into the high-energy muons we see underground.
• Significance: This would solve a long-standing mystery called the "Muon Puzzle," where ground-based observatories have also seen too many muons. It suggests our understanding of particle collisions at extreme energies needs an update.

2. The "Lighter Bullet" Theory (Different Cosmic Ray Ingredients)
If the physics of the crash is correct, maybe the "bullet" hitting the atmosphere was different.

• Analogy: Imagine throwing a bowling ball vs. a baseball at a wall. A heavy bowling ball (heavy cosmic rays like iron) tends to break apart into many small, slow pieces. A lighter baseball (light cosmic rays like protons) might keep its speed better and punch through deeper.
• Significance: The data suggests that in the energy range of 10 TeV to 1 PeV, the cosmic rays hitting Earth might be lighter (more protons/helium) than we previously believed. This helps us understand what these cosmic rays are made of and where they come from.

The Bottom Line

This study is like looking through a very specific, high-powered telescope that only sees the "elite" particles that survive a 2,400-meter rock tunnel. By counting these survivors, the scientists found a gap between reality and our computer simulations.

Whether the gap is caused by new rules of particle physics (the crash is harder than we thought) or different ingredients (the cosmic rays are lighter than we thought), this discovery is a major clue. It helps us solve the mystery of where cosmic rays come from and how they behave when they hit our atmosphere, bridging the gap between what we see in particle accelerators (like the Large Hadron Collider) and what happens in the vastness of space.

Technical Summary

1. Problem Statement

The paper addresses two interconnected challenges in high-energy astrophysics and particle physics:

• The Muon Puzzle: Ground-based observatories (e.g., Pierre Auger) have observed a persistent excess of muons in Extensive Air Showers (EAS) at EeV scales compared to predictions from leading hadronic interaction models. The origin of this discrepancy is unclear, potentially stemming from inaccuracies in modeling hadronic interactions in the extreme forward phase space or the chemical composition of primary cosmic rays (CRs).
• Lack of Constraints in the TeV–PeV Regime: While space-based experiments measure CRs up to ~100 TeV and ground arrays measure EeV events, the energy range between tens of TeV and PeV remains poorly constrained, particularly regarding the mass composition of CRs and the details of the first hadronic interactions.
• Limitations of Existing Underground Data: Previous underground measurements often suffer from low statistics or are dominated by lower-energy muons where information about the primary interaction is obscured by subsequent shower development.

2. Methodology

The study utilizes data from the China Jinping Underground Laboratory (CJPL), which features a vertical rock overburden of 2,400 meters. This depth acts as a natural filter, blocking all cosmic muons with energies below approximately 3 TeV, leaving only the most energetic muons produced in the earliest stages of EAS.

• Detector: A one-ton prototype detector for the Jinping Neutrino Experiment (JNE).
  • Target: 1 ton of liquid scintillator (LS) in a 1.29 m diameter spherical acrylic vessel.
  • Readout: 30 inward-facing 8-inch photomultiplier tubes (PMTs) detecting scintillation photons.
  • Shielding: Enclosed in a water tank with lead and black acrylic shields to suppress external radiation and radon.
• Data Collection: The analysis covers 1,338.6 live days of data (July 2017 – March 2024), resulting in a sample of 547 selected muon events after rigorous quality cuts (energy > 90 MeV, waveform analysis to remove noise).
• Simulation Framework:
  • Production: Used the Matrix Cascade Equations (MCEq) package to solve coupled cascade equations for EAS development.
  • Interaction Models: Employed three post-LHC hadronic interaction models tuned to collider data: SIBYLL-2.3d, QGSJET-II-04, and EPOS-LHC.
  • Primary CRs: Used the Global Spline Fit (GSF) model for primary CR spectra, which is data-driven and minimizes theoretical assumptions.
  • Propagation: Simulated muon propagation through the mountain using GEANT4, accounting for ionization, radiation, and hadronic interactions in marble rock (density 2.8 g/cm³).
  • Reconstruction: Developed a template-based directional reconstruction method and a "de-saturation" algorithm to handle waveform saturation from high-energy muon deposits (~200 MeV).

3. Key Contributions

• First Differential Measurement: This work presents the first precise measurement of the differential underground muon flux at CJPL, covering energies from 3 TeV to 9 TeV (depending on zenith angle) with an angular resolution of 4.5°.
• Systematic Control: The study provides a comprehensive evaluation of systematic uncertainties, including seasonal atmospheric temperature variations (0.5%), detector position within the mountain (1.6%), and primary CR model uncertainties (11.8%).
• Dual-Perspective Analysis: The authors interpret the data through two complementary lenses:
  1. Hadronic Physics: Assuming standard CR spectra (GSF), they constrain the modeling of the first hadronic interactions.
  2. Cosmic Ray Composition: Assuming standard hadronic models, they infer the mass composition of primary CRs in the TeV–PeV range.

4. Key Results

• Flux Excess: The measured underground muon flux is approximately 40% higher than predictions from all three leading hadronic models (SIBYLL-2.3d, EPOS-LHC, QGSJET-II-04).
  • The discrepancy has a statistical significance of > 2σ (including model uncertainties) and 5.5σ (excluding them).
  • The excess shows no significant dependence on the zenith angle, suggesting a global feature rather than a directional anomaly.
• Hadronic Interaction Interpretation:
  • The excess suggests a hardening of the charged hadron spectrum (specifically pions) in the first interaction of the cascade, or a modest enhancement (~percent level) in charged Kaon (K) production.
  • Enhanced K production is favored because K mesons have a higher probability of decaying into muons than pions at TeV energies. This scenario could also resolve the "muon puzzle" at EeV scales by retaining more energy in the hadronic channel (reducing neutral pion production).
• Cosmic Ray Composition Interpretation:
  • If hadronic models are assumed correct, the data favor a lighter primary composition (more protons/helium, fewer heavy nuclei like iron) in the 10 TeV to PeV energy range compared to the GSF model.
  • Light primaries produce higher average nucleon energies, increasing the probability of generating high-energy mesons that decay into TeV muons.

5. Significance

• New Window into Forward Physics: The study demonstrates that deep underground laboratories provide a unique, complementary probe to accelerator experiments (like LHCf, FASER) for studying charged hadron production in the extreme forward phase space (pseudo-rapidity > 10), a region inaccessible to current colliders.
• Resolving the Muon Puzzle: The results provide direct experimental evidence that current hadronic interaction models may underestimate high-energy muon production in the first interaction stage of air showers. This supports hypotheses involving harder spectra or enhanced strangeness (Kaon) production.
• Constraints on CR Composition: The findings offer new constraints on the chemical composition of cosmic rays in the "knee" region (TeV–PeV), suggesting a lighter composition than previously estimated by some models.
• Future Prospects: The paper advocates for combined analyses of surface and underground data to further refine our understanding of primary CR composition and hadronic interactions, potentially guiding future updates to interaction models (e.g., QGSJET-III, EPOS-LHC-R).

In conclusion, this paper establishes deep underground muon measurements as a critical tool for probing the fundamental physics of cosmic ray interactions, offering a potential solution to long-standing discrepancies in air shower simulations.