Measurement of charged-particle production in $\sqrt{s_\text{NN}}=9.62$ TeV proton-oxygen collisions as a probe of cosmic-ray air showers with the ATLAS detector

Using the ATLAS detector, this study presents a high-precision measurement of prompt charged-particle production in proton-oxygen collisions at $\sqrt{s_\text{NN}}=9.62$ TeV, providing data that significantly improves the modeling of cosmic-ray air showers for astroparticle physics.

The Gist

The Cosmic Ray Detective: How ATLAS Cracked the Case of the Missing Air Shower

Imagine you are a detective trying to solve a crime that happens high above your head, in the atmosphere, but you can't go up there to see it. You only have the "footprints" left behind on the ground. This is the daily challenge for scientists studying cosmic rays—high-energy particles from deep space that smash into Earth's atmosphere.

When these cosmic rays hit the air, they create a massive cascade, or "shower," of billions of smaller particles. To understand what the original cosmic ray was made of (was it a proton? a heavy nucleus?) and where it came from, scientists need to know exactly how these showers behave. But to predict the shower, they need to know the rules of the game: how particles interact when they crash into each other at incredible speeds.

For decades, the rules of these high-speed crashes were fuzzy. Scientists had to guess, using computer models that were like "best guesses" based on old data. This paper from the ATLAS Collaboration at CERN is like finding a brand-new, high-definition rulebook.

The Experiment: A "Cosmic" Collision Course

Usually, the Large Hadron Collider (LHC) smashes protons into other protons. But to understand cosmic rays hitting the atmosphere, scientists needed to smash a proton into something that looks like the air we breathe.

The Analogy: Imagine you are trying to understand how a car crash happens when a car hits a tree. You could crash two cars together, but that doesn't tell you much about hitting a tree. So, the ATLAS team set up a special experiment where they fired a beam of protons (the "cars") into a beam of oxygen (the "tree," since oxygen is a major part of our air).

They did this at an energy level of 9.62 TeV. To put that in perspective, this is equivalent to a cosmic ray hitting the atmosphere with the energy of a 49 PeV particle. That is roughly 50 times more energy than the most powerful particle accelerator on Earth usually produces in a single collision. It's like smashing two cars together at 100 mph, but the "cars" are subatomic particles.

The Discovery: The Models Were Wrong (or at least, Incomplete)

The team measured exactly how many particles were created, how fast they were moving, and in which directions they flew. They then compared their real-world data to the predictions made by the top computer models used by astrophysicists (like EPOS, QGSJET, and Sibyll).

The Result: The models were off by a lot.

• The "Order of Magnitude" Difference: In some cases, the computer models predicted 10 times more particles than what actually happened. In others, they predicted 10 times fewer.
• The "Tuning" Problem: It's like if you tried to bake a cake using a recipe that said "add 10 cups of flour," but when you actually baked it, you only needed 1 cup. The models had the wrong ingredients for this specific type of collision.

The paper found that the EPOS and HIJING models were the closest to the truth, while others overestimated the chaos of the crash significantly.

Why This Matters: Fixing the "Cosmic Ray Telescope"

Why should you care if a computer model gets a particle count wrong?

1. Unlocking the Secrets of the Universe: Cosmic rays are the only messengers we have from the most violent events in the universe (like black holes and supernovas). But to read the message, we need to know how the "envelope" (the atmosphere) reacts when the message arrives. If our models of the envelope are wrong, we misinterpret the message. We might think a cosmic ray is heavy when it's actually light, or vice versa.
2. The "Muon Puzzle": One of the biggest mysteries in astroparticle physics is that cosmic ray showers seem to produce more "muons" (a type of heavy electron) than our models predict. This new data helps scientists tune their models to see if they can finally solve why there are so many muons.
3. Better Safety and Science: Understanding these showers helps us understand radiation levels for astronauts and satellites, and it refines the data from massive observatories like the Pierre Auger Observatory.

The Bottom Line

Think of the ATLAS detector as a super-precise camera taking a snapshot of a cosmic crash that usually happens 20 miles up in the sky. By recreating this crash in a controlled lab setting with oxygen, they provided the first high-precision "ground truth."

They handed this new data to the astrophysicists, saying, "Here are the real rules. Update your simulations." This is a massive step forward in understanding the origins of the most energetic particles in the universe, turning a blurry, guesswork-heavy picture into a sharp, clear image of how our universe works at its most extreme levels.

Technical Summary

1. Problem Statement and Motivation

The origin and composition of ultra-high-energy cosmic rays (UHECRs) remain central open questions in astroparticle physics. Direct measurement of cosmic rays above PeV energies is impossible from space due to low flux; instead, they are studied indirectly via extensive air showers (EAS) produced when cosmic rays interact with Earth's atmosphere.

• The Challenge: Reconstructing the properties of primary cosmic rays (mass, energy) from air showers relies heavily on Monte Carlo simulations of hadronic interactions at TeV center-of-mass energies. These interactions are governed by non-perturbative Quantum Chromodynamics (QCD), which cannot be calculated from first principles.
• The Gap: Existing phenomenological hadronic interaction models (e.g., EPOS, QGSJET, Sibyll) are tuned to accelerator data, primarily from proton-proton ($pp$) and heavy-ion ($PbPb$, $XeXe$) collisions. However, the primary interaction of a cosmic ray proton with an atmospheric nucleus (mostly Nitrogen and Oxygen) differs significantly from $pp$ collisions. The lack of direct experimental data on proton-oxygen ($pO$) and proton-nitrogen ($pN$) interactions at TeV scales introduces large systematic uncertainties in air shower simulations, affecting the interpretation of UHECR data.

2. Methodology

The ATLAS Collaboration performed the first measurement of prompt charged-particle production in $pO$ collisions at the Large Hadron Collider (LHC).

• Data Source: Data collected in July 2025 during a special LHC run with a 3.4 TeV per-nucleon Oxygen-16 beam colliding with a 6.8 TeV proton beam.
  • Center-of-Mass Energy: $\sqrt{s_{NN}} = 9.62$ TeV.
  • Integrated Luminosity: $634 \, \mu\text{b}^{-1}$.
  • Event Sample: 246 million selected events with at least one reconstructed track.
• Detector: The ATLAS detector, utilizing the Inner Detector (Pixel, SCT, TRT) for tracking.
• Event Selection:
  • Primary Vertex: Events must have one primary vertex (PV) with $\ge 2$ tracks ($p_T > 100$ MeV).
  • Track Selection: Tracks must have $p_T > 500$ MeV and $|\eta| < 2.5$.
  • Quality Cuts: Requirements on silicon hits (Pixel $\ge 1$, SCT $\ge 6$), impact parameters ($|d_0| < 1.5$ mm, $|z_0 \sin\theta| < 1.5$ mm), and track fit probability.
  • Pileup Suppression: Veto on events with a second vertex containing $\ge 5$ tracks.
• Background Estimation:
  • Secondary particles (from decays, conversions, hadronic interactions) were estimated by fitting the transverse impact parameter ($d_0$) distribution in a sideband region ($4 < |d_0| < 9.5$ mm).
  • Background fraction determined: $f_{sec} = (2.5 \pm 0.4)\%$.
  • Strange baryon contributions and fake tracks were estimated to be negligible or small ($< 3\%$).
• Corrections and Unfolding:
  • Efficiency Corrections: Trigger, vertex, and track reconstruction efficiencies were determined using data-driven methods and simulation (HIJING, Pythia 8 Angantyr).
  • Unfolding: Bayesian unfolding was applied to correct for detector resolution and acceptance effects, mapping observed track distributions to true charged-particle distributions.
  • Systematics: Dominant uncertainties arise from track reconstruction efficiency (passive material modeling) and the dependence of the unfolding procedure on the generator model used.

3. Key Contributions

1. First $pO$ Cross-Section Measurement: This is the first direct measurement of the fiducial and inelastic cross-sections for proton-oxygen collisions at $\sqrt{s_{NN}} = 9.62$ TeV.
2. Extrapolation to Proton-Air: The results were extrapolated to the full inelastic phase space and converted to the proton-air ($p+\text{air}$) cross-section using a model-dependent scaling factor based on the composition of Earth's atmosphere (78% N, 22% O).
3. High-Precision Differential Distributions: The paper provides measurements of charged-particle multiplicity ($n_{ch}$), transverse momentum ($p_T$), mean $p_T$ vs. multiplicity, and pseudorapidity ($\eta$) distributions with precision an order of magnitude better than the spread between current hadronic interaction models.

4. Key Results

A. Cross-Sections

• Fiducial Cross-Section:
  $$\sigma_{pO}^{\text{fid.}} = 396 \pm 6 \, (\text{exp.}) \pm 9 \, (\text{lumi.}) \, \text{mb}$$
  Measured in the region $p_T > 500$ MeV, $|\eta| < 2.5$.
• Extrapolated Inelastic $pO$ Cross-Section:
  $$\sigma_{pO}^{\text{inel.}} = 438 \pm 6 \, (\text{exp.}) \pm 10 \, (\text{lumi.}) \pm 30 \, (\text{th.}) \, \text{mb}$$
  Theoretical uncertainty is dominated by the model dependence of the extrapolation.
• Proton-Air Inelastic Cross-Section:
  $$\sigma_{p+\text{air}}^{\text{inel.}} = 406 \pm 6 \, (\text{exp.}) \pm 9 \, (\text{lumi.}) \pm 28 \, (\text{th.}) \, \text{mb}$$
  This corresponds to a cosmic-ray proton energy of $\approx 49$ PeV in the target rest frame.

B. Comparison with Models

• Cross-Section: The measured fiducial cross-section is compatible with EPOS LHC-R and HIJING, but is significantly lower (by $>3\sigma$) than predictions from DPMJET III, Pythia 8 (Angantyr), QGSJET II-04/III, and Sibyll 2.3e.
• Distributions:
  • Multiplicity ($n_{ch}$): Data uncertainties (1.5%–28%) are far smaller than model spreads (factors of 2 to $>10$ at high multiplicity). Angantyr and QGSJET III are closest at low $n_{ch}$, but diverge significantly at high $n_{ch}$.
  • $p_T$ Spectrum: Data uncertainties (2.5%–17%) are much smaller than model spreads ($>40\%$). Angantyr describes the data best (within 12%), while DPMJET, HIJING, and Sibyll predict harder spectra, and QGSJET predicts softer spectra.
  • Mean $p_T$ vs. $n_{ch}$: Data uncertainties are $<0.3\%$ (rising to 2.5% at low $n_{ch}$), compared to model spreads of 10–25%.
  • Pseudorapidity ($\eta$): The particle density peaks at $\eta \approx 1.1$. Data uncertainties (1.9%–4.4%) are small compared to the $\sim 50\%$ model spread. The data shape is flatter than EPOS and HIJING predictions.

5. Significance

• Cosmic-Ray Physics: This measurement provides the first direct constraint on hadronic interactions relevant to the primary interaction of cosmic rays with atmospheric nuclei at PeV energies. It reduces the reliance on extrapolations from $pp$ data, which poorly constrain the nuclear effects in $pO$ collisions.
• Model Tuning: The results expose significant tensions between current hadronic interaction models and data, particularly in the high-multiplicity and high-$p_T$ regimes. These discrepancies suggest that models require re-tuning to accurately simulate air showers.
• Astroparticle Impact: Improved modeling of particle multiplicity and kinematics in $pO$ collisions will lead to more accurate simulations of air shower development (e.g., depth of maximum $X_{\text{max}}$ and muon content). This is crucial for determining the mass composition of UHECRs and understanding the transition from galactic to extragalactic sources.
• Collider Physics: It demonstrates the capability of the LHC to serve as a unique "cosmic-ray factory" by colliding light nuclei with protons, bridging the gap between collider physics and astroparticle physics.