Measurement of the azimuthal anisotropy of charged particles in $\sqrt{s_{\mathrm{NN}}}=5.36$ TeV $^{16}$O$+^{16}$O and $^{20}$Ne$+^{20}$Ne collisions with the ATLAS detector

This paper presents the first measurements of charged-particle azimuthal anisotropy coefficients ($v_2$–$v_4$) in $\sqrt{s_{\mathrm{NN}}}=5.36$ TeV $^{16}$O$+^{16}$O and $^{20}$Ne$+^{20}$Ne collisions using the ATLAS detector, revealing a clear $v_2 > v_3 > v_4$ hierarchy and an enhanced elliptic flow in central neon collisions that provides new constraints on nuclear deformation and hydrodynamic response in light-ion systems.

The Gist

The Big Picture: Smashing Light Bulbs to Find Shapes

Imagine you have two different types of light bulbs. One is perfectly round like a beach ball (Oxygen-16), and the other is slightly stretched out like a rugby ball (Neon-20).

Scientists at the Large Hadron Collider (LHC) took these "light bulbs" (which are actually atomic nuclei) and smashed them together at nearly the speed of light. The goal wasn't just to break them, but to see how the debris flies out.

When these tiny nuclei collide, they create a super-hot, super-dense drop of liquid called a Quark-Gluon Plasma (QGP). Think of this like a tiny, fleeting fireball. As this fireball expands and cools, it pushes particles outward. The way these particles fly out tells the scientists about the shape of the original light bulbs before they smashed.

The Main Discovery: The "Rugby Ball" Effect

The paper reports on the very first measurements of this specific type of collision using Oxygen and Neon nuclei.

• The Oxygen Collision: Oxygen nuclei are predicted to be shaped like a slightly squashed sphere (tetrahedral). When they collide, the debris flies out in a fairly balanced pattern.
• The Neon Collision: Neon nuclei are predicted to be shaped like a rugby ball (prolate/deformed). When two rugby balls collide, they create a more elongated, oval-shaped fireball.

The Result: The scientists found that in the most violent (central) collisions, the Neon collisions produced a much stronger "oval" push than the Oxygen collisions. This confirms that the Neon nuclei really do have that stretched-out, rugby-ball shape, while Oxygen is more round.

How They Measured It: The "Crowd Dance"

To measure this, the scientists looked at the Azimuthal Anisotropy. That's a fancy way of saying: "Do the particles fly out in a circle, or do they prefer to fly out in a specific direction?"

They used two main methods to figure this out, which can be compared to analyzing a crowded dance floor:

1. The Two-Person Dance (Two-Particle Correlation):
   Imagine watching pairs of dancers. If you see many pairs moving in the same direction, it suggests a general flow. However, sometimes two people might just bump into each other by accident (like a jet or a random collision) and move together. This is called "non-flow" noise.

   • The Fix: The scientists used a "template" method. They looked at the "bumping" patterns in very quiet, low-energy collisions (where no big fireball forms) and subtracted that pattern from the loud, high-energy collisions. This left them with the pure "dance flow."

2. The Group Dance (Four-Particle Cumulants):
   To be extra sure, they looked at groups of four dancers at a time. It is very unlikely for four people to bump into each other by pure accident and move in a coordinated way. If four people are moving together, it's almost certainly because the whole floor is tilting in a specific direction. This method is very sensitive to the true shape of the initial collision.

The Key Findings in Simple Terms

• The Hierarchy of Flow: The particles didn't just fly out randomly. They followed a pattern:

  • Elliptic Flow ($v_2$): The strongest signal. Particles preferred to fly out in an oval shape (like a rugby ball).
  • Triangular Flow ($v_3$): A weaker signal where particles formed a triangle shape.
  • Quadrangular Flow ($v_4$): An even weaker signal forming a four-sided shape.
  • Analogy: If the collision was a perfect circle, there would be no preferred direction. Because the nuclei are lumpy or stretched, the fireball pushes harder in some directions, creating these shapes.

• The Neon Advantage: When they compared the two systems, the Neon collisions showed a much stronger "oval" push (elliptic flow) than the Oxygen collisions, especially in the most energetic crashes. This matches the theory that Neon is a rugby ball and Oxygen is a sphere.

• The "Speed Limit" of Flow: The scientists noticed that this flow effect gets stronger as the particles move faster, peaks around a specific speed (2 GeV), and then drops off. This is similar to what they see in much larger collisions (like Lead-Lead), suggesting that even these tiny "light-ion" collisions create a fluid that behaves like the big ones.

Why This Matters

This paper is like a new chapter in a detective story. For a long time, scientists thought this "fluid" behavior only happened in huge collisions (like Lead-Lead). Now, they have proven it happens in tiny collisions too.

By comparing Oxygen and Neon, they have a unique way to test our understanding of nuclear structure. It's like having two different puzzle pieces (Oxygen and Neon) that are almost the same size but have different internal shapes. By seeing how they break apart, the scientists can confirm if our theories about the shape of atomic nuclei are correct.

In summary: The ATLAS detector smashed light nuclei together, found that Neon acts like a rugby ball and Oxygen acts like a sphere, and proved that even these tiny collisions create a fluid-like state of matter that flows in predictable patterns.

Technical Summary

1. Problem and Motivation

The primary goal of this research is to probe the initial-state geometry and nuclear structure of light nuclei by studying the collective behavior of the Quark-Gluon Plasma (QGP) in small collision systems.

• Context: While collective flow (anisotropic flow, $v_n$) is a well-established signature of QGP formation in heavy-ion collisions (e.g., Pb+Pb), its observation in smaller systems ($pp$, $p$+Pb) has raised questions about the nature of the medium and the role of initial-state fluctuations.
• Specific Challenge: To disentangle the effects of initial-state geometry from final-state hydrodynamic evolution, it is necessary to compare collision systems with similar mass numbers but distinct internal nucleon arrangements.
• Target Systems: The paper focuses on $^{16}$O (Oxygen) and $^{20}$Ne (Neon).
  • $^{16}$O: Theoretically predicted to have a near-spherical, tetrahedral $\alpha$-cluster structure.
  • $^{20}$Ne: Predicted to have a prolate deformation, often modeled as an $\alpha$-cluster orbiting a $^{16}$O core.
• Objective: Measure the azimuthal anisotropy coefficients ($v_n$ for $n=2,3,4$) to test theoretical predictions that the prolate deformation of Neon should lead to enhanced elliptic flow ($v_2$) in central collisions compared to Oxygen, while both systems should exhibit similar hydrodynamic responses driven by event-by-event (EbE) fluctuations.

2. Methodology

The analysis utilizes data collected by the ATLAS detector at the LHC in July 2025.

• Datasets:

  • Collision Energy: $\sqrt{s_{NN}} = 5.36$ TeV.
  • Integrated Luminosity: $2 \text{ nb}^{-1}$ for O+O and $0.5 \text{ nb}^{-1}$ for Ne+Ne.
  • Event Selection: Minimum-bias events selected via TRT (Transition Radiation Tracker) triggers and High-Level Trigger (HLT) requirements on track multiplicity. Pileup suppression was applied, leaving a residual pileup of $\le 0.2\%$.
  • Centrality: Defined using the forward calorimeter transverse energy ($\Sigma E_{FCal}^T$) and mapped to collision centrality percentiles (0–80%) using a Glauber model.

• Particle Selection:

  • Charged particles with $p_T > 0.5$ GeV and $|\eta| < 2.5$.
  • Strict track quality criteria (pixel and SCT hits, impact parameter cuts) to minimize fake tracks and secondary particles.
  • Efficiency corrections and fake-track removal were applied using Monte Carlo (HIJING + afterburner) simulations.

• Flow Measurement Techniques:
  Two complementary methods were employed to extract $v_n$:

  1. Two-Particle Correlations (2PC) with Template Fit:
     • Correlations between particle pairs are analyzed as a function of $\Delta\eta$ and $\Delta\phi$.
     • Non-flow suppression: A template fit is used where the non-flow component (jets, resonance decays) is estimated from peripheral events (80–100% centrality) and subtracted from central events. This isolates the long-range "ridge" correlation associated with collective flow.
  2. Four-Particle Subevent Cumulants:
     • Uses a subevent technique (dividing the detector into non-overlapping $\eta$ regions) to construct 4-particle correlations.
     • Advantage: Intrinsically suppresses non-flow effects (which typically involve fewer particles) and provides sensitivity to event-by-event flow fluctuations.
     • The 4-particle cumulant ($v_n\{4\}$) isolates the average geometry-driven component, whereas the 2-particle cumulant ($v_n\{2\}$) includes both average geometry and fluctuations.

3. Key Contributions

• First Measurements: This is the first comprehensive measurement of $v_n$ ($n=2$–4) in O+O and Ne+Ne collisions at the LHC.
• Nuclear Structure Probe: It provides the first experimental evidence linking light-ion flow harmonics directly to specific nuclear shape predictions (spherical/tetrahedral vs. prolate) using ab initio nuclear structure models (PGCM).
• Methodological Rigor: The paper demonstrates the efficacy of template-fit subtraction and subevent cumulants in light-ion systems where multiplicity is low and non-flow contamination is significant.
• Systematic Comparison: It offers a direct comparison between O+O and Ne+Ne, isolating the impact of nuclear deformation by holding the collision energy and system size (mass number) relatively constant.

4. Key Results

• Flow Hierarchy: A clear hierarchy $v_2 > v_3 > v_4$ is observed in both systems, consistent with hydrodynamic expectations.
• $p_T$ Dependence: $v_2$ exhibits a non-monotonic dependence on transverse momentum, rising linearly at low $p_T$, peaking around 2 GeV, and decreasing at higher $p_T$. This behavior mirrors trends seen in heavy-ion collisions.
• Centrality and Multiplicity Dependence:
  • $v_2$ Enhancement in Neon: In central collisions (0–10%), Ne+Ne shows a significant enhancement in $v_2$ compared to O+O. This is most pronounced in the four-particle cumulant ($v_2\{4\}$) measurement, which is sensitive to the average geometry.
  • Interpretation: This enhancement aligns with theoretical predictions that the prolate (elongated) shape of the $^{20}$Ne nucleus creates a larger initial spatial eccentricity ($\epsilon_2$) than the near-spherical $^{16}$O.
  • $v_3$ Similarity: The triangular flow ($v_3$) shows remarkable similarity between O+O and Ne+Ne as a function of charged-particle multiplicity ($N_{ch}$). This suggests that $v_3$ is driven primarily by event-by-event geometric fluctuations (which depend on particle density) rather than the average nuclear shape.
• Model Comparison:
  • The data is compared to Hydro+IPGlasma+PGCM and Hydro+Trento+PGCM models.
  • The Hydro+Trento+PGCM model (using PGCM for nuclear configurations) successfully reproduces the enhanced $v_2$ ratio in central Ne+Ne collisions, confirming the link between nuclear deformation and flow.
  • The Hydro+IPGlasma+PGCM model fails to capture the centrality dependence of the $v_2$ ratio, suggesting limitations in its treatment of initial-state multiplicity fluctuations or the correlation between centrality and impact parameter.

5. Significance

• Validation of Nuclear Structure Models: The results provide strong experimental support for ab initio nuclear structure theories (specifically the PGCM model) that predict the prolate deformation of $^{20}$Ne and the tetrahedral nature of $^{16}$O.
• Constraints on QGP Properties: By isolating the initial geometry effects, these measurements allow for more precise extraction of QGP transport properties, such as the shear viscosity to entropy density ratio ($\eta/s$), in small systems.
• Understanding Small Systems: The study confirms that collective flow in light-ion collisions is driven by a combination of average nuclear geometry (dominating $v_2$ in central collisions) and event-by-event fluctuations (dominating $v_3$ and peripheral collisions).
• Future Physics: These measurements set a benchmark for future high-precision studies of nuclear structure using relativistic heavy-ion collisions, potentially offering new insights into $\alpha$-clustering and the pre-hydrodynamic evolution of the QGP.

In summary, this paper establishes that the shape of the atomic nucleus is a critical determinant of the collective flow observed in high-energy collisions, successfully using the ATLAS detector to distinguish between the flow signatures of spherical and deformed light nuclei.