⚛️ nuclear theory

Event-by-event fluctuations of elliptic flow in ultrarelativistic O+O collisions

This paper utilizes a 3D $\text{McDipper}$ + $\text{MUSIC}$ model to demonstrate that in ultrarelativistic O+O collisions at 5.36 TeV, event-by-event fluctuations in energy deposition drive the initial elliptical eccentricity and elliptic flow ( $v_2$ ), distinguishing their origin from that in heavy nucleus collisions while showing that a small set of fluctuation modes can accurately reproduce the joint probability distribution of these observables.

Original authors: Renata Krupczak, Nicolas Borghini, Hendrik Roch

Published 2026-06-23

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Renata Krupczak, Nicolas Borghini, Hendrik Roch

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine two tiny, fluffy clouds of oxygen atoms smashing into each other at nearly the speed of light inside a giant particle accelerator. Scientists want to know: when these clouds collide, do they behave like a smooth, predictable fluid, or do they act like a chaotic mess of individual particles?

This paper investigates that question by simulating these collisions using a supercomputer. Here is the story of what they found, explained without the heavy math.

The Big Picture: A New Kind of Collision

Usually, scientists smash together huge nuclei (like Lead or Xenon). In those big collisions, the shape of the collision zone is mostly determined by how "off-center" the hit is. If you hit two billiard balls slightly off-center, they create a distinct almond shape. This shape drives the flow of particles afterward.

But oxygen is much smaller. The authors asked: Does a small collision work the same way?

Their answer is a resounding no.

The Analogy: The Smooth Pancake vs. The Studded Boulder

To understand the difference, imagine trying to flatten two objects into a pancake:

Heavy Nuclei (Lead): Imagine two large, smooth, round pancakes. If you press them together slightly off-center, they naturally form a smooth, predictable almond shape. The "fluctuations" (little bumps) are tiny compared to the whole pancake.
Oxygen Nuclei: Imagine two small, bumpy rocks made of only a few large pebbles stuck together. When you smash them, the resulting shape isn't a smooth almond. It's a chaotic mess of "hot spots" (the pebbles). Sometimes the pebbles line up to make a circle; other times, they line up to make a weird, lopsided triangle or a jagged oval.

The Key Finding: In oxygen collisions, the final shape is not determined by how off-center the hit was. Instead, it is determined entirely by random chance—specifically, where the few "pebbles" (nucleons) happened to land in that specific split second.

The "Event-by-Event" Surprise

The researchers looked at thousands of these simulated collisions, one by one.

In big collisions: If you take the average shape of 1,000 collisions, it looks very similar to any single collision. The average is a good guess.
In oxygen collisions: The average shape is almost a perfect circle. But almost no single collision looks like that circle. Every single collision is wildly different from the average and from each other.

It's like rolling a die. If you roll a 20-sided die 1,000 times, the average result is 10.5. But you will never actually roll a 10.5. In oxygen collisions, the "average" result is a ghost that never actually happens in reality. The real action is in the wild, random fluctuations.

The "Fluctuation Modes" (The Recipe for Chaos)

The authors developed a clever way to describe this chaos. They realized that even though every collision looks different, they can be built by mixing a few standard "ingredients" (which they call modes).

Think of it like mixing paint:

You have a base color (the average state).
You have a few special brushes (the fluctuation modes) that add swirls, dots, or streaks.

The surprising discovery was that you only need a very small number of these brushes (about 10) to recreate the statistical behavior of the elliptic flow (how the particles fly out in an oval shape). Even though the collisions look chaotic, the underlying rules are surprisingly simple.

However, they also found that if you want to measure something very specific about how the collision looks at different angles (longitudinal decorrelation), you need to add many more "brushes" to the recipe.

The Conclusion: Oxygen is Unique

The paper concludes that oxygen collisions are a unique middle ground. They are too small to be the smooth, predictable fluid of heavy nuclei, but they are still fluid-like enough to show collective behavior.

Heavy Nuclei: Shape is driven by geometry (how you hit them).
Oxygen: Shape is driven by randomness (where the particles happen to be).

This means that to understand oxygen collisions, you cannot just look at the "average" event. You have to look at the individual, chaotic events, because the chaos is the story. The researchers showed that they can predict the outcome of these chaotic events accurately using a simplified model that accounts for these random fluctuations, proving that even in a small, chaotic system, there is an underlying order.

Technical Summary: Event-by-event fluctuations of elliptic flow in ultrarelativistic O+O collisions

Problem Statement
The paper investigates the nature of anisotropic flow, specifically elliptic flow ( $v_2$ ), in oxygen-oxygen (O+O) collisions at $\sqrt{s_{NN}} = 5.36$ TeV. While the prevailing view for large nuclei (e.g., Pb+Pb) is that elliptic flow arises primarily from the geometric asymmetry of the overlap region determined by the impact parameter, the authors posit that O+O collisions may represent a distinct regime. In smaller systems, the limited number of nucleons suggests that event-by-event fluctuations of energy deposition might dominate the initial geometry, potentially making O+O collisions more analogous to small systems (p+p) than to heavy-ion collisions regarding the origin of flow. The study aims to quantify these fluctuations and determine if a reduced set of fluctuation modes can accurately reproduce the statistical properties of elliptic flow.

Methodology
The authors employ a fully three-dimensional numerical framework combining McDipper (initial state), MUSIC (hydrodynamic evolution), and iSS (particlization).

Initial State: Nucleon configurations for the $^{16}$ O nucleus are generated using Nuclear Lattice Effective Field Theory (NLEFT). These configurations are randomly rotated and collided with a random impact parameter. The McDipper code, based on the Color Glass Condensate effective field theory (GBW mode), generates 3D energy density profiles $\Phi(x, y, \eta_s)$ , incorporating subnucleonic hot spots and thickness fluctuations.
Hydrodynamics: The profiles serve as initial conditions for MUSIC, evolving the system with a constant specific shear viscosity ( $\eta/s = 0.16$ ) and temperature-dependent bulk viscosity until a freeze-out temperature of 155 MeV.
Decomposition Framework: A key methodological innovation is the decomposition of the 3D initial state energy density into an average profile $\bar{\Psi}$ and a set of uncorrelated fluctuation modes $\{\Psi_l\}$ with coefficients $c_l$ . This is performed via an eigen-decomposition of the autocorrelation matrix of energy-density fluctuations. This approach is applied here for the first time to non-boost-invariant 3D initial states.
Linear Response: The authors utilize a linear response framework where observables (eccentricity $\varepsilon_2$ and flow $v_2$ ) are approximated as linear functions of the fluctuation modes. They compare "event-by-event" simulations (5000 events per centrality class) against "linearized" observables generated by sampling Gaussian-distributed coefficients for a reduced set of modes.

Key Contributions and Results

Dominance of Fluctuations: The study demonstrates that in O+O collisions, the initial elliptic eccentricity ( $\varepsilon_2$ ) is driven primarily by event-by-event fluctuations of energy deposition rather than the finite impact parameter. Consequently, the average initial state $\bar{\Psi}$ is nearly round-shaped even in non-central collisions (20–30% centrality), with a very small average eccentricity ( $\varepsilon_2 \approx 0.087$ ). This contrasts sharply with heavy-ion collisions where the average state is significantly almond-shaped.
Fluctuation Weights: The relative weight of the average state ( $\bar{w}$ ) in O+O is found to be only $\sim 2\%$ , significantly lower than the $\sim 13\%$ observed in Pb+Pb collisions. This quantitatively confirms that fluctuations are the dominant contribution to the initial geometry in O+O.
Mode Decomposition Accuracy: The authors show that the joint probability distribution of $\vare2$ and $v_2$ can be reproduced with reasonable accuracy using a small set of fluctuation modes (specifically 10 modes). The "linear model" and "analytical Gaussian fluctuation approximation" (G.f.a.) yield results in close agreement with full event-by-event simulations for $\varepsilon_2 \lesssim 0.6$ .
Non-linear Limitations: At large eccentricities ( $\varepsilon_2 > 0.6$ ), the linear approximation deviates from event-by-event data due to non-linear hydrodynamic response (specifically cubic terms in the relation $v_2 \approx \kappa_{2,2}\varepsilon_2 + \kappa_{2,222}\varepsilon_2^3$ ). The linear models fail to capture the "banana" shape of the distribution and the broader tail of $v_2$ caused by these non-linearities.
Longitudinal Decorrelation: The paper notes that while integrated flow can be captured by few modes, observables sensitive to longitudinal structure, such as the longitudinal decorrelation of eccentricity ( $r_2$ ), require a much larger number of modes (hundreds) to reproduce event-by-event results. This is attributed to the importance of rapidity-odd fluctuation modes, which appear at higher orders in the mode spectrum.

Significance and Claims
The paper claims that O+O collisions are not merely a "scaled-down" version of heavy-ion collisions. Instead, the origin of elliptic flow in O+O is fundamentally different, being dominated by initial-state fluctuations rather than the global impact-parameter geometry. This suggests that O+O collisions provide a unique laboratory to study the onset of collective phenomena where fluctuations are the primary driver.

The authors modestly claim that their mode-by-mode decomposition framework is a viable, lower-cost alternative to full event-by-event 3D hydrodynamic simulations for describing the bulk statistical behavior of elliptic flow. They demonstrate that a limited set of fluctuation modes suffices to reproduce the mean values and probability distributions of $v_2$ and $\varepsilon_2$ , provided one accounts for the dominance of fluctuations over the average geometry. However, they acknowledge that the linear approximation has limitations regarding non-linear responses at high eccentricities and that more complex observables (like longitudinal decorrelation) require a significantly larger mode basis.

The Big Picture: A New Kind of Collision

The Analogy: The Smooth Pancake vs. The Studded Boulder

The "Event-by-Event" Surprise

The "Fluctuation Modes" (The Recipe for Chaos)

The Conclusion: Oxygen is Unique

More like this