Equilibrated fraction of QCD matter in high-energy oxygen--oxygen collisions

This study demonstrates that in high-energy oxygen-oxygen collisions at 5.36 TeV, the produced QCD matter only partially reaches local equilibrium, necessitating a core-corona framework rather than a purely hydrodynamic approach to accurately describe the dynamics, particularly the incomplete chemical equilibrium observed in strange baryon yields.

The Gist

Imagine you are trying to understand what happens when two tiny, high-speed trains crash into each other. In the world of physics, these "trains" are atomic nuclei (specifically Oxygen nuclei), and the crash happens at nearly the speed of light. When they collide, they create a super-hot, super-dense soup of energy and particles called Quark-Gluon Plasma (QGP).

For decades, scientists have studied these crashes using massive trains (like Gold or Lead nuclei). They found that when these big trains crash, the soup behaves like a perfect, flowing liquid. This is called hydrodynamics.

But what happens when you crash smaller trains, like Oxygen? Does the soup still flow like a liquid, or does it just scatter like a bunch of individual marbles? This is the big question the paper tries to answer.

Here is the story of their findings, explained simply.

The "Core" and the "Corona": A Party Analogy

To understand the collision, the scientists used a clever idea called the Core-Corona Picture. Imagine a wild party:

• The Core (The Dance Floor): In the very center of the crash, things are so crowded and chaotic that everyone is bumping into each other constantly. They lose their individual identity and move together as a single, flowing group. This is the Core. It's like a dance floor where everyone is synchronized, moving in a fluid wave. This is the "liquid" part that physicists love to study.
• The Corona (The Periphery): On the edges of the crash, or in less crowded areas, particles don't have enough time to bump into each other. They zip past each other like individual runners on a track. They don't form a liquid; they just fly off in straight lines. This is the Corona. It's the "gas" or "particle" part.

The Big Discovery: It's Never Just One or the Other

The main goal of this paper was to figure out: In an Oxygen-Oxygen crash, how much of the mess is the "liquid" (Core) and how much is the "gas" (Corona)?

Here is what they found:

1. The Tipping Point: They discovered that if the collision produces about 20 particles in the middle, the "liquid" (Core) starts to take over. Below that number, the "gas" (Corona) dominates.
2. The Surprise: Even in the most violent, head-on crashes (the "central" collisions), the "gas" (Corona) never disappears completely. Even in the best-case scenario, about 30% of the particles are still just individual runners (Corona) and not part of the flowing liquid (Core).

Why does this matter?
For a long time, scientists thought that if you had a big enough crash, you could ignore the "gas" and just use math for "liquids" (hydrodynamics) to describe everything. This paper says: No, that's wrong for Oxygen. You cannot ignore the "gas" part. If you try to describe an Oxygen crash using only liquid math, you will get the wrong answer. You need a model that includes both the dance floor and the runners.

The "Strange" Evidence

How do they know the "liquid" is actually forming? They looked at specific particles called Strange Baryons (particles containing "strange" quarks).

• The Analogy: Imagine the "liquid" (Core) is a factory that is very good at making strange toys. The "gas" (Corona) is a small workshop that makes them poorly.
• The Result: As the collisions get more violent (more central), the "factory" (Core) gets bigger. Consequently, the number of strange toys produced goes up.
• The Catch: Even in the biggest crashes, the number of strange toys is lower than if the whole system were a perfect factory. This proves that the "workshop" (Corona) is still there, diluting the results.

The "Heavy" Particles

They also looked at how heavy particles (like Protons) behave compared to light ones (like Pions).

• The Analogy: Imagine the "liquid" (Core) is a giant conveyor belt moving outward.
• The Result: Because the conveyor belt is moving so fast, it gives a bigger boost to the heavy boxes (Protons) than the light boxes (Pions). The scientists saw that Protons stayed in the "liquid" zone longer than Pions did. This proves that the "liquid" is indeed flowing and pushing things around, even in these small Oxygen crashes.

The Bottom Line

This paper is like a reality check for physicists. It tells us that when we smash Oxygen nuclei together:

1. We do create a tiny bit of that perfect, flowing "liquid" (QGP).
2. But a huge chunk of the result is still just a messy spray of individual particles.
3. To understand these collisions, we can't just use the "liquid" math. We need a two-part model that accounts for both the flowing liquid and the scattered particles.

This helps scientists understand the very limits of where "liquid" behavior begins in the universe, bridging the gap between tiny proton crashes and massive heavy-ion crashes. It's a crucial step in mapping out how the universe behaves at its most extreme temperatures.

Technical Summary

1. Problem Statement

High-energy nuclear collisions are used to study the Quark-Gluon Plasma (QGP). While QGP formation is well-established in large systems (e.g., Au+Au, Pb+Pb), its production in small and intermediate systems (e.g., p+p, p+Pb, O+O) remains a subject of intense investigation.

• The Core Question: To what degree does the QCD matter created in high-energy Oxygen-Oxygen (O+O) collisions achieve local thermal equilibrium?
• The Challenge: If the system reaches local equilibrium, its evolution can be described by relativistic hydrodynamics. If not, or if only partially equilibrated, a purely hydrodynamic approach is insufficient. O+O collisions (mass number $A=16$) represent an intermediate regime between protons and heavy ions, offering a unique opportunity to probe the system-size dependence of QGP formation and the potential $\alpha$-cluster structure of oxygen nuclei.
• The Gap: Previous models often assume either full equilibrium or purely string fragmentation. A quantitative framework to separate and measure the contributions of equilibrated matter ("core") versus non-equilibrium particles ("corona") in O+O collisions is needed to interpret experimental data from the LHC.

2. Methodology

The authors employ the Dynamical Core–Corona Initialization (DCCI2) framework, a two-component model that simultaneously describes the evolution of equilibrated fluids and non-equilibrium particles.

• Model Updates (DCCI2):
  • Initial State: Initial partons are generated using PYTHIA 8.315 (upgraded from 8.244) with the Angantyr model for heavy-ion collisions. The GLISSANDO 2 model is used to generate the initial nucleon configurations within the oxygen nuclei.
  • Core Formation: Non-equilibrium partons dynamically deposit energy and momentum into the medium based on local parton density. This acts as a source term for (3+1)-dimensional ideal hydrodynamics, forming the "core" (locally equilibrated QGP).
  • Corona Formation: Partons that do not fully lose their energy/momentum continue to propagate as the "corona" (non-equilibrium component).
  • Hadronization:
    • Core: Converted to hadrons via the iS3D Monte Carlo sampler based on the Cooper-Frye prescription when the fluid temperature drops below the switching temperature ($T_{sw} = 165$ MeV).
    • Corona: Hadronized via Lund string fragmentation within PYTHIA.
  • Final State: Both components are passed to the JAM hadronic transport model. Crucially, hadronic rescatterings are switched off in this study to isolate the fractional contributions of the core and corona without mixing them in the late stage. Only resonance decays are included.
• Simulation Parameters:
  • System: O+O collisions at $\sqrt{s_{NN}} = 5.36$ TeV (LHC energy).
  • Statistics: $10^5$ minimum-bias events.
  • Weighting: Event averages are calculated using PYTHIA-provided weights to ensure correct cross-section and impact-parameter sampling.

3. Key Contributions

1. Quantification of Equilibration: The paper provides the first quantitative breakdown of the fraction of hadrons originating from locally equilibrated matter versus non-equilibrium string fragmentation in O+O collisions.
2. Identification of the Crossover Point: The authors identify a specific multiplicity threshold where the production mechanism transitions from corona-dominated to core-dominated.
3. Mass-Dependent Flow Analysis: The study demonstrates how the radial flow of the core component affects different particle species (pions, kaons, protons) differently, shifting the dominance of the core to higher transverse momenta ($p_T$) for heavier particles.
4. Strangeness Enhancement Mechanism: The paper explains the observed strangeness enhancement in O+O collisions as a natural consequence of the increasing fraction of thermalized core matter, rather than a purely geometric effect.

4. Key Results

A. Multiplicity and Centrality Dependence

• Total Yields: The model reproduces preliminary CMS data for charged-particle multiplicity ($\langle dN_{ch}/d\eta \rangle$) in O+O collisions.
• Core-Corona Crossover:
  • The transition point where the core contribution exceeds the corona contribution occurs at $\langle dN_{ch}/d\eta \rangle|_{|\eta|<0.5} \approx 20$.
  • In central collisions (0–10%), the system is core-dominated, but the corona still contributes ~30% of the total hadron yield.
  • In peripheral collisions (60–90%), the corona dominates.
• Implication: Pure hydrodynamics is insufficient even for central O+O collisions; a two-component approach is essential.

B. Transverse Momentum ($p_T$) Spectra

• Low $p_T$ ($< 1.5$ GeV): The core dominates, reflecting collective flow.
• High $p_T$ ($> 3.7$ GeV): The corona dominates, reflecting hard parton fragmentation.
• Mass Ordering: The crossover point where the core loses dominance to the corona shifts to higher $p_T$ as particle mass increases:
  • Pions: Crossover at $p_T \approx 3.3$ GeV (0–30% centrality).
  • Kaons: Crossover at $p_T \approx 3.8$ GeV.
  • Protons: Crossover at $p_T \approx 5.0$ GeV.
• Significance: This mass-dependent shift confirms the presence of radial flow in the core component of O+O collisions, pushing heavier particles to higher momenta.

C. Strangeness Enhancement

• Observation: The yield ratios of strange baryons ($\Lambda, \Xi, \Omega$) to charged pions increase monotonically with multiplicity.
• Mechanism: In the corona (string fragmentation), strangeness production is suppressed. In the core (thermalized QGP), strangeness is enhanced due to partonic processes. As collisions become more central, the core fraction increases, driving the overall yield ratios up.
• Comparison: The ratios in O+O collisions never reach the values predicted for a purely equilibrated system (100% core), confirming the persistent ~30% corona contribution even in central events.
• Trend: The enhancement is most pronounced for multi-strange baryons (e.g., $\Omega$, $|S|=3$), consistent with ALICE data from p+p to Pb+Pb.

5. Significance and Conclusion

• Theoretical Impact: The study establishes that intermediate-sized systems like O+O cannot be described by pure hydrodynamics. The "core-corona" picture is necessary to accurately model bulk observables, even in the most central collisions.
• Experimental Context: The results provide a robust baseline for interpreting recent and future LHC data (CMS, ALICE, ATLAS) on O+O collisions. The identified crossover multiplicity ($\approx 20$) serves as a critical benchmark for the onset of QGP-like behavior.
• Future Directions: The updated framework (using PYTHIA 8.315) allows for systematic studies of nuclear density profiles. The authors propose applying this model to Neon-Neon (Ne+Ne) collisions to investigate specific nuclear structures, such as $\alpha$-clustering and nuclear deformation, which may leave imprints on the initial state and final observables.

In summary, the paper demonstrates that while O+O collisions at 5.36 TeV produce a significant amount of locally equilibrated matter, a substantial non-equilibrium component persists. This dual nature is crucial for understanding the transition from small to large collision systems and the emergence of collective phenomena.