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Improved nonflow control for multiparticle correlators and system-size-dependent evolution from OO to Pb--Pb collisions at the LHC

This paper validates an improved nonflow subtraction framework using the $v_1$ -estimator-based scaling method to reliably extract symmetry plane correlators and symmetric cumulants, enabling a systematic comparison of system-size-dependent evolution from light-ion (OO) to heavy-ion (Pb--Pb) collisions at the LHC.

Original authors: Neelkamal Mallick, Suraj Prasad

Published 2026-10-28

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CC BY 4.0

Original authors: Neelkamal Mallick, Suraj Prasad

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

In the heart of the Large Hadron Collider, where protons and heavy atomic nuclei smash together at nearly the speed of light, physicists are searching for the ghostly remains of the universe's first moments. When these particles collide, they create a fleeting drop of super-hot, super-dense matter known as the quark-gluon plasma. This state of matter behaves less like a gas and more like a perfect fluid, flowing with almost no friction. As this fluid expands and cools, it leaves behind subtle patterns in the directions the particles fly. By studying these patterns, scientists can reconstruct the shape of the collision and understand how the fluid responds to the initial squeeze. However, there is a significant challenge: not every particle that flies out is part of this smooth, collective flow. Some come from unrelated, chaotic sources like the breakup of short-lived particles or jets of debris. These "nonflow" signals act like static on a radio, obscuring the true music of the fluid, especially in smaller collisions where the signal is weaker.

A new study by Neelkamal Mallick and Suraj Prasad tackles this problem by refining the tools used to listen to these tiny signals. The researchers focused on a specific type of measurement that looks at how the flow of particles in different directions is connected. Imagine trying to hear a single instrument in a loud orchestra; if you only listen to the whole room, the noise drowns out the detail. Instead, these scientists developed a method to isolate the specific connections between different flow patterns, known as symmetry plane correlators and symmetric cumulants. These measurements tell us how the shape of the collision influences the final spray of particles and how different flow patterns talk to each other. The team tested their improved method on computer simulations of oxygen-oxygen collisions, a system smaller than the usual lead-lead collisions but large enough to potentially show this collective fluid behavior. Their goal was to strip away the chaotic noise to see if the underlying fluid dynamics were truly present and to compare how these patterns change as the size of the colliding system grows.

The researchers began by creating a controlled environment to test their new subtraction technique. They used a computer model where they knew exactly how much "true" flow existed and how much "noise" was present, allowing them to see if their method could accurately remove the noise without damaging the signal. They compared two different ways of estimating the noise: one based simply on the number of particles produced, and another that also considered the direction of the very first particles. The tests showed that the second method, which accounted for the direction of the initial particles, was far more reliable. It successfully removed the noise without accidentally subtracting the real flow signal, a mistake the simpler method made in the outer, less crowded regions of the collisions. This validation gave them confidence to apply the technique to more complex simulations that included both flow and noise.

Applying this refined method to simulations of oxygen-oxygen collisions at a specific high energy, the team predicted what the flow patterns should look like once the noise was removed. They found that as the collisions became more crowded with particles, the connections between different flow patterns grew stronger, eventually reaching levels similar to those seen in the much larger lead-lead collisions. Specifically, the way the fluid's shape in one direction influenced its shape in another direction increased steadily as the system size grew. However, the relationship between two specific flow patterns remained near zero in the smaller oxygen collisions, only becoming noticeable in the largest, most crowded events. This suggests that the complex interplay between different flow directions requires a certain minimum size of the fluid drop to emerge clearly.

When the researchers compared their cleaned-up oxygen results with existing data from lead-lead collisions, a clear picture of system-size dependence emerged. The oxygen collisions, when viewed through the lens of particle count, fit smoothly onto the curve established by the larger lead collisions. The data suggested that the physics governing the fluid's behavior is consistent across these different sizes, but the strength of the connections depends on how many particles are involved. In the smaller systems, the fluid is just beginning to develop the complex, interconnected behaviors seen in the larger ones. The study confirms that by carefully removing the background noise, scientists can now trace the evolution of this perfect fluid from small, light-ion collisions all the way to the massive heavy-ion crashes. These findings provide a solid baseline for future experiments, helping to distinguish between the true collective behavior of the quark-gluon plasma and the random chatter of unrelated particle interactions.

Technical Summary: Improved Nonflow Control for Multiparticle Correlators and System-Size-Dependent Evolution from OO to Pb–Pb Collisions

Problem Statement
Multiparticle correlators, specifically Symmetry Plane Correlators (SPCs) and Symmetric Cumulants (SCs), are essential for constraining the initial conditions and transport properties of the medium formed in heavy-ion collisions. While these observables are robust against nonflow biases in large systems (e.g., Pb–Pb), they are significantly distorted in small and intermediate systems (e.g., OO, Ne–Ne) at low multiplicity. In these regimes, short-range few-body correlations (nonflow)—arising from jets, resonance decays, and quantum statistics—can dominate the signal, mimicking collective flow. Existing suppression techniques, such as subevent methods or pseudorapidity gaps, often compromise statistical precision. Consequently, there is a need for a validated, high-precision nonflow subtraction framework to reliably interpret SPCs and SCs in light-ion collisions and to map the system-size dependence of nonlinear mode coupling from small to large systems.

Methodology
The authors propose and validate an improved nonflow subtraction framework based on two scaling approaches:

Multiplicity Reweighting ( $c_0$ ): Based on the independent-source picture, where nonflow in an $m$ -particle correlator scales as $1/N^{m-1}$ . The subtraction uses a low-multiplicity (LM) template (70–100% centrality class) scaled by the ratio of effective multiplicities.
$v_1$ -Estimator Scaling ( $c_1$ ): A refinement that utilizes a nonflow estimator containing at least one power of the dipole flow ( $v_1$ ). This method accounts for multiplicity selection effects and deviations not captured by pure multiplicity scaling.

The validation process involves three stages:

Toy Model: A controlled generator with known, separable flow and nonflow components to test the recovery of the "flow truth."
Pythia 8 Angantyr: A nonflow-only reference (no collective flow by construction) to quantify residual biases.
AMPT String-Melting Model: A realistic model containing both flow and nonflow, used to generate predictions for O–O collisions at $\sqrt{s_{NN}} = 5.36$ TeV.

The study focuses on SPCs (e.g., $\langle \cos(4\psi_4 - 4\psi_2) \rangle$ ) and Normalized Symmetric Cumulants (NSCs) for harmonic pairs (3,2), (4,2), (4,3), (5,2), and (5,3). The results are compared against published Pb–Pb data from ALICE and AMPT predictions, plotted against the mean charged-particle multiplicity at midrapidity, $\langle N_{ch} \rangle$ , to establish a common system-size axis.

Key Results

Validation: In the toy model, the $c_1$ scaling tracks the flow truth more closely than $c_0$ , which tends to oversubtract correlations in peripheral bins. In the Pythia 8 Angantyr (nonflow-only) test, both methods reduce SPCs to near zero. However, for NSCs, $c_1$ yields residuals consistent with zero, whereas $c_0$ significantly oversubtracts (leaving negative residuals of $\sim$ 20% for NSC(4,2) and NSC(3,2)).
AMPT Predictions: Applying the preferred $c_1$ scaling to AMPT O–O predictions reveals that SPCs and NSC(4,2) rise with multiplicity, approaching the magnitude of peripheral Pb–Pb collisions around $\langle N_{ch} \rangle \sim 200$ . Conversely, NSC(3,2) remains near zero in O–O, only acquiring a modest negative value at the highest multiplicities.
System-Size Evolution: When mapped against $\langle N_{ch} \rangle$ , the AMPT O–O results sit on the rising edge of the system-size dependence observed in Pb–Pb. The data suggests that as the system size increases from O–O to Pb–Pb, the initial geometry becomes more anisotropic, and nonlinear hydrodynamic responses strengthen, leading to the characteristic mid-central maxima in SPCs and the specific evolution of NSCs.

Significance and Claims
The paper claims that the $c_1$ -based nonflow subtraction framework provides a more reliable control of nonflow biases than standard multiplicity reweighting, particularly for normalized symmetric cumulants. By applying this method, the authors provide a concrete baseline for forthcoming measurements of SPCs and NSCs in light-ion collisions (pO, OO, Ne–Ne) at the LHC.

The work demonstrates that placing light- and heavy-ion systems on a common $\langle N_{ch} \rangle$ axis allows for a continuous examination of how initial-state geometry and nonlinear mode coupling evolve across system sizes. The authors assert that comparing future experimental data to these AMPT-based predictions will offer necessary constraints on models of initial-state effects, transport properties, and the onset of collective behavior in small systems. The paper does not claim to definitively prove the existence of flow in light ions via these specific correlators but rather establishes the methodological tools required to interpret such measurements rigorously.

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