Collective effects in O-O and Ne-Ne collisions at $\sqrt{s_{\mathrm{NN}}}$=5.36 TeV from a hybrid approach

This study employs a hybrid approach alongside pure hadronic and string models to predict collective effects in upcoming O-O and Ne-Ne collisions at the LHC, aiming to determine the onset of quark-gluon plasma formation in small collision systems by comparing hydrodynamic and non-hydrodynamic evolutions.

The Gist

The Big Picture: Smashing Tiny Balls to Find the "Perfect Fluid"

Imagine you are a scientist trying to recreate the very first moments of the universe, just a split second after the Big Bang. To do this, you smash heavy atoms together at nearly the speed of light. Usually, scientists smash giant atoms like Lead or Gold. But recently, they found signs that even tiny collisions (like smashing two protons) might create a "perfect fluid" called Quark-Gluon Plasma (QGP).

This paper asks a specific question: If we smash medium-sized atoms (Oxygen and Neon) together, will we see this perfect fluid behavior?

The authors are trying to predict what will happen when the Large Hadron Collider (LHC) runs these specific collisions in July 2025. They want to know: Is the fluid real, or is it just a trick of the math?

The Three "Simulators" (The Models)

To answer this, the team didn't just guess; they ran three different computer simulations (models) to see how the particles behave. Think of these as three different ways to predict the outcome of a chaotic party:

1. The "Hybrid" Model (SMASH-vHLLE): This is the "Goldilocks" model. It assumes that right after the crash, the particles melt into a hot, sticky soup (the fluid) that flows together. Later, as the soup cools down, it turns back into individual particles. This model predicts strong collective behavior (everyone moving together like a dance troupe).
2. The "Pure Transport" Model (SMASH): This model treats the collision like a giant game of billiards or pinball. The particles bounce off each other, but they never melt into a soup. They just bounce around randomly. This model predicts weak or no collective flow.
3. The "Angantyr" Model: This is the "baseline" or the "control group." It assumes the particles are completely independent. It's like a crowd of strangers in a room who bump into each other but have no idea the others exist. It predicts zero collective flow.

The Key Experiments

The researchers looked at two main things to see if the "fluid" was actually forming:

1. The "Nuclear Modification Factor" (The Traffic Jam Test)

Imagine driving on a highway.

• Normal traffic (Angantyr/No Fluid): Cars drive at their own speed.
• Traffic jam (Fluid): If a massive wave of traffic moves together, it pushes slower cars forward and slows down fast cars.

In the simulation, the Hybrid model showed a clear "traffic jam" effect. The heavy particles (baryons) were pushed forward more than the light ones (mesons), creating a specific pattern in their speeds. The Angantyr model showed no such pattern; it was flat and boring. The Pure Transport model showed a tiny bit of slowing down, but nothing like the fluid model.

The Clue: The Hybrid model also noticed something interesting about the shape of the atoms. Oxygen and Neon aren't perfect spheres; they have "clusters" (like little groups of helium atoms stuck together). The Hybrid model showed that these clusters made the "traffic jam" even stronger, suggesting the fluid was denser.

2. The "Anisotropic Flow" (The Ellipse Test)

When you smash two round atoms together, the resulting explosion isn't a perfect circle; it's usually an oval (like a rugby ball).

• Fluid Theory: If a fluid forms, the pressure inside pushes the particles out harder along the short side of the oval than the long side. This creates a specific "flow" pattern.
• Random Theory: If there is no fluid, the particles just fly out randomly. Any oval shape is just a fluke or a result of a few particles bumping into each other by chance.

The Results:

• Hybrid Model: Showed a strong, clear oval flow pattern. The more central the crash, the stronger the flow.
• Angantyr & Pure Transport: Surprisingly, they showed some flow, but the pattern was backwards. In these models, the flow got stronger in "peripheral" (glancing) crashes and weaker in central ones. This proved that the flow they saw wasn't a fluid; it was just random noise (called "nonflow") from particles bumping into each other by chance.

The "Alpha-Cluster" Twist

Oxygen-16 and Neon-20 are special because their protons and neutrons like to group together in little triangles or bowling-pin shapes (called alpha-clusters).

• The paper found that if you use these "clustered" shapes in the Hybrid (fluid) simulation, the flow gets even stronger.
• However, in the Angantyr (random) simulation, the shape didn't matter at all.
• Conclusion: If the LHC sees a strong difference between Oxygen and Neon based on their shapes, it will be a "smoking gun" that a fluid is forming. If the shapes don't matter, it's just random noise.

The Verdict

The paper concludes that:

1. Hydrodynamics (Fluid Theory) works best for the most central (head-on) Oxygen and Neon collisions.
2. Pure randomness (Angantyr) cannot explain the strong flow patterns seen in the Hybrid model.
3. The "Nonflow" trap: In small collisions, it's very easy to mistake random bumps for fluid flow. The researchers showed that you need to look at the shape of the flow and the mass of the particles to tell the difference.

In short: If the LHC sees the specific "mass ordering" and "shape sensitivity" predicted by the Hybrid model in July 2025, it will confirm that even tiny Oxygen and Neon collisions can create a tiny drop of the perfect fluid that existed at the birth of the universe. If they don't, the "fluid" might just be an illusion caused by random particle bumps.

Technical Summary

Technical Summary: Collective Effects in O-O and Ne-Ne Collisions at $\sqrt{s_{NN}}=5.36$ TeV from a Hybrid Approach

Problem Statement
While hybrid approaches combining viscous hydrodynamics (for the hot, dense Quark-Gluon Plasma phase) and hadronic transport (for the dilute stage) successfully describe collective phenomena in large collision systems (e.g., Au-Au, Pb-Pb), the onset of Quark-Gluon Plasma (QGP) formation in smaller systems remains an open question. Recent observations of long-range correlations and anisotropic flow in proton-proton ($p$-$p$) and proton-lead ($p$-Pb) collisions challenge the assumption that collectivity is exclusive to large nuclei. This study aims to investigate the applicability of hybrid approaches in intermediate small systems—specifically Oxygen-Oxygen (O-O) and Neon-Neon (Ne-Ne) collisions—scheduled for the CERN Large Hadron Collider (LHC) in July 2025. The goal is to distinguish between genuine collective effects driven by hydrodynamic expansion and "nonflow" correlations arising from other mechanisms.

Methodology
The authors employ a comparative simulation framework using three distinct models to generate O-O and Ne-Ne collisions at $\sqrt{s_{NN}}=5.36$ TeV:

1. SMASH-vHLLE Hybrid: A hybrid approach coupling the hadronic transport code SMASH with the 3+1-dimensional viscous hydrodynamics code vHLLE. The initial state is derived from the hadronic evolution of SMASH, switching to hydrodynamics at a proper time $\tau_{sw}$ and back to transport at a switching energy density $\epsilon_{sw}$. Two viscosity scenarios are tested: a temperature-dependent shear viscosity over entropy ratio ($\eta/s$) inferred from Bayesian analysis of larger systems, and a constant $\eta/s = 0.08$.
2. SMASH (Pure Transport): A pure hadronic transport simulation using SMASH without the hydrodynamic phase, serving as a baseline to test the necessity of hydrodynamics for observed collectivity.
3. Angantyr: A Pythia-based extension for heavy-ion collisions that treats sub-collisions as independent, thereby generating no collective flow. This serves as a baseline for "no collective effects."

Initial State and Nuclear Structure
The simulations utilize two types of nuclear configurations:

• Woods-Saxon: Standard spherical distributions.
• $\alpha$-Clustered: Configurations derived from Nuclear Lattice Effective Field Theory (NLEFT), where $^{16}$O is modeled as a tetrahedron and $^{20}$Ne as a bowling-pin shape.
  The study assesses the applicability of hydrodynamics via the opacity parameter $\hat{\gamma}$, finding that hydrodynamic descriptions are reliable ($\hat{\gamma} > 3$) in the top 10% most central events but degrade in peripheral collisions.

Key Results

• Multiplicity and Centrality: The hybrid model produces the highest final-state charged multiplicity due to entropy generation in the viscous hydrodynamic phase. The pure transport model produces fewer particles, and Angantyr produces the fewest, lacking hadronic rescatterings. Centrality bins are defined individually for each model based on charged multiplicity in $|y| < 2.5$.
• Nuclear Modification Factor ($R_{AA}$):
  • The Hybrid model exhibits a significant enhancement in $R_{AA}$ for intermediate transverse momentum ($p_T \approx 2\text{--}5$ GeV), with baryons showing a larger enhancement than mesons. This mass ordering is attributed to radial flow pushing particles to higher $p_T$. The $\alpha$-clustered configuration yields a slightly higher enhancement, suggesting a denser medium.
  • The Pure Transport model shows a modest enhancement at low $p_T$ and constant suppression at high $p_T$, attributed to hadronic rescattering and stopping.
  • Angantyr shows approximately constant $R_{AA} < 1$, indicating a lack of medium-induced modifications and potential normalization issues relative to binary collisions.
• Anisotropic Flow ($v_n$):
  • Hybrid Model: Exhibits the largest elliptic ($v_2$) and triangular ($v_3$) flow in central to mid-central collisions. The flow decreases as collisions become more peripheral, consistent with decreasing system size. The $\alpha$-clustered configurations generally enhance flow compared to Woods-Saxon, with the Ne bowling-pin shape showing a distinct increase in $v_2$.
  • Pure Transport and Angantyr: Both models show an opposite trend, where flow coefficients increase in more peripheral collisions. The authors attribute this to the dominance of "nonflow" contributions (scaling as $1/(N-1)$), which become more significant as the final-state multiplicity decreases in peripheral events.
  • Cumulant Analysis: Four-particle cumulants ($c_n\{4\}$) for the transport and Angantyr models are close to zero, confirming their flow signals are dominated by nonflow. The hybrid model yields negative $c_n\{4\}$, allowing for the extraction of unbiased flow coefficients ($\langle v_n \rangle$) and flow fluctuations ($\sigma_{v_n}$).
• Differential Flow: The hybrid model displays a mass ordering in differential $v_2(p_T)$ (heavier particles gaining more $p_T$), consistent with radial flow. No significant baryon-meson splitting is observed at high $p_T$ due to the absence of parton coalescence in the model.

Significance and Conclusions
The paper concludes that if a fluid-like QGP forms in O-O and Ne-Ne collisions, it would manifest as a significant enhancement of $v_2$ and $v_3$ in central collisions and a distinct dependence on nuclear structure (e.g., $\alpha$-clustering) only when collective dynamics are present. The study highlights that pure hadronic transport and independent sub-collision models (Angantyr) fail to reproduce the characteristic centrality dependence of flow observed in hybrid models, instead showing trends driven by nonflow correlations.

The authors emphasize the critical importance of using higher-order cumulants and subevent methods to suppress nonflow contributions when analyzing small collision systems. The results provide theoretical predictions for the upcoming LHC light-ion run, offering a framework to interpret experimental data regarding the onset of collectivity and the validity of hydrodynamic descriptions in small systems. The paper notes that while the absolute magnitude of flow in the hybrid model is parameter-dependent, the qualitative behavior (decreasing flow with centrality) is robust.