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Untangling flow-harmonic correlations in OO and Pb--Pb collisions at the LHC using event-shape engineering

This study utilizes EPOS4 simulations to demonstrate how event-shape engineering via reduced flow vector selections ( $q_2, q_3$ ) disentangles linear and nonlinear flow-harmonic correlations in OO and Pb--Pb collisions at 5.36 TeV, revealing distinct correlation mechanisms within $q_n$ classes for light-ion versus heavy-ion systems.

Original author: Suraj Prasad

Published 2026-11-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original author: 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 author. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the heart of the Large Hadron Collider, scientists smash heavy atomic nuclei together at nearly the speed of light. These collisions create a fleeting, super-hot soup of matter known as the quark-gluon plasma, a state of the universe that existed only moments after the Big Bang. Because this plasma vanishes in a fraction of a second, researchers cannot look at it directly. Instead, they study the particles that fly out from the explosion, looking for patterns in how they move. One of the most telling patterns is a collective flow, where the debris moves in coordinated waves rather than randomly. The shape of these waves depends on the initial geometry of the collision; if the nuclei collide off-center, the debris flows in an elliptical pattern, while random fluctuations in the positions of the particles inside the nuclei create triangular and more complex wave shapes. By measuring how these different wave shapes relate to one another, physicists can learn about the internal structure of the nuclei and the fluid-like properties of the plasma itself.

A recent study by Suraj Prasad at the Wigner Research Centre for Physics in Budapest uses advanced computer simulations to investigate how these wave patterns interact in two very different types of collisions: those involving lead nuclei and those involving much lighter oxygen nuclei. The research focuses on a specific technique called event-shape engineering, which acts like a filter to sort collision events based on the strength of their initial flow. The goal is to see if sorting these events helps scientists understand how the different wave shapes are connected. In the heavy lead collisions, this sorting method works well, allowing researchers to separate the influence of one wave shape from another. However, the study reveals that in the lighter oxygen collisions, the method hits a wall. Because oxygen nuclei are smaller, they produce far fewer particles, and the statistical noise from this low number of particles overwhelms the signal. As a result, the sorting technique cannot effectively isolate the specific connections between the wave shapes in oxygen collisions, even though it works beautifully for the heavier lead collisions.

The researchers used a sophisticated computer model called EPOS4 to simulate billions of these collisions at an energy level of 5.36 TeV, matching the conditions of the LHC. They focused on how the elliptical flow, the triangular flow, and higher-order wave shapes fluctuate from one collision to the next. In the heavy lead collisions, the team found that by selecting events with a strong elliptical flow, they could clearly see how this strength influenced the triangular and other wave shapes. They were able to break down the relationship between these waves into two parts: one part driven by the differences between the sorted groups of events, and another part that remained hidden within the groups. In the lead collisions, the sorting method successfully captured a large portion of the connection between the waves, proving that the technique can be used to disentangle complex physical mechanisms.

In contrast, the simulations for the oxygen collisions told a different story. When the researchers applied the same sorting technique to the lighter oxygen data, they found that the vast majority of the connection between the wave shapes remained hidden within the sorted groups. The method simply could not separate the signals effectively because the forward detectors, which measure the initial shape of the collision, did not have enough particles to work with. The statistical fluctuations in the small number of particles were too large, masking the true physical relationship. The study showed that in oxygen collisions, the sorting method changes the overall strength of the waves but fails to reveal how they are linked. This suggests that to study these subtle correlations in light-ion collisions, scientists will need detectors with much higher resolution or different methods to overcome the limitations of low particle counts.

Despite this limitation in the lighter system, the study uncovered a fascinating detail in the central oxygen collisions. When the researchers looked specifically at the events with the weakest elliptical flow, they found that the connection between the elliptical and triangular waves became weaker. This happened because the higher-order waves in these specific events behaved more like a simple, direct response to the initial shape, rather than a complex mix of influences. This observation hints that even with the current limitations, specific subsets of data might still offer unique insights into how the plasma responds to different initial conditions. The work also demonstrated a powerful way to isolate the nonlinear interactions in lead collisions, showing that by sorting events based on different wave shapes, scientists can independently study the factors that drive the complex coupling of these flows.

Ultimately, this research serves as a crucial guide for future experiments. It confirms that while event-shape engineering is a powerful tool for understanding the quark-gluon plasma in heavy collisions, its application to lighter systems like oxygen requires significant improvements in measurement precision. The study does not claim to have solved the mystery of light-ion collisions, but it clearly maps out where the current methods succeed and where they fall short. By simulating these scenarios, the work provides a baseline for what experimentalists should expect when they analyze real data from the LHC. It highlights that the ability to see the fine details of the universe's earliest moments depends not just on the energy of the collision, but on the ability to count the resulting particles with enough precision to see through the noise.

Technical Summary: Untangling flow-harmonic correlations in OO and Pb–Pb collisions at the LHC using event-shape engineering

Problem Statement
Symmetric cumulants, $SC(m, n)$ , quantify the event-by-event correlations between flow harmonics $v_m$ and $v_n$ . For higher-order harmonics ( $v_4, v_5$ ), these correlations are significantly influenced by nonlinear responses to lower-order flows, specifically the elliptic ( $v_2$ ) and triangular ( $v_3$ ) flows. While event-shape engineering (ESE) using the reduced flow vector $q_n$ is a established method to control these contributions in large systems like Pb–Pb collisions, its efficacy in light-ion collisions (such as Oxygen-Oxygen, OO) is uncertain. In light-ion collisions, the forward multiplicity used to measure $q_n$ is an order of magnitude smaller than in Pb–Pb, potentially limiting the resolution of the selection and its ability to isolate specific correlation mechanisms. Prior to this work, it was unknown how much of the correlation between $v_m$ and $v_n$ fluctuations is controlled by $q_n$ selections versus how much remains intrinsic within the selected classes, particularly in light-ion systems.

Methodology
The study utilizes the EPOS4 event generator (version 4.0.3) to simulate minimum-bias OO and Pb–Pb collisions at $\sqrt{s_{NN}} = 5.36$ TeV. The analysis employs an ATLAS-like acceptance:

Flow Observables: Two-particle flow coefficients $v_n\{2\}$ ( $n=2$ –5) and symmetric cumulants $SC(m, n)$ are calculated for charged primary particles with $|\eta| < 2.5$ and $0.2 < p_T < 5$ GeV/c.
Event-Shape Selection: Events are classified into $q_n$ classes based on the reduced flow vector measured in a forward window ( $3.3 < |\eta| < 4.8$ ), separated from the midrapidity flow measurement by $\Delta\eta > 0.8$ .
Centrality and Binning: Centrality is defined by the forward transverse energy sum. Events within 1% centrality intervals are sorted by $q_2$ or $q_3$ and divided into five equal-statistics classes (0–20% to 80–100%).
Nonflow Subtraction: Nonflow contributions (e.g., jets, resonance decays) are subtracted using a template method based on the low-multiplicity (70–100% centrality) class, scaled by the effective multiplicity ( $c_0$ scaling).
Decomposition: A key methodological contribution is the application of the law of total covariance to decompose the symmetric cumulant of $q_n$ $q_{n}$ -integrated events into two parts:
1. Selected Part ( $SC_{sel}$ ): The correlation arising from the differences in average $v_m$ and $v_n$ between the $q_n$ classes.
2. Residual Part ( $SC_{res}$ ): The correlation remaining within the $q_n$ classes after selection.

Key Results

Flow Coefficient Response:
- In both OO and Pb–Pb collisions, the $q_2$ selection successfully modulates $v_2$ , with the highest $q_2$ class showing increased $v_2$ and the lowest showing decreased $v_2$ . The magnitude of this change is driven primarily by multiplicity rather than the collision system.
- $v_3$ exhibits an anticorrelation with $v_2$ (decreasing in high $q_2$ classes), consistent with initial geometry anticorrelations ( $\epsilon_2$ vs. $\epsilon_3$ ).
- $v_4$ follows $v_2$ due to its nonlinear response ( $v_4 \propto v_2^2$ ). Notably, in central OO collisions, the lowest $q_2$ class shows a significant reduction in $v_4$ , indicating that $v_4$ in these events is closer to its linear response to $\epsilon_4$ .
- The $q_3$ selection has a much weaker effect in OO collisions compared to Pb–Pb, as the statistical fluctuation of $q_3$ in the low-multiplicity forward window dominates the signal.
Symmetric Cumulant Decomposition:
- OO Collisions: The decomposition reveals that $SC_{sel}$ is negligible. Over 90% of the correlations between $v_2$ and $v_3$ (NSC(3,2)) and $v_2$ and $v_4$ (NSC(4,2)) reside in the residual part ( $SC_{res}$ ). This indicates that the $q_2$ selection in OO collisions cannot effectively separate the correlations driven by $v_2$ fluctuations.
- Pb–Pb Collisions: In contrast, $SC_{sel}$ captures a substantial fraction (50–70% for NSC(3,2) and 37–42% for NSC(4,2)) of the total correlation in mid-central collisions. The selection effectively moves the correlation into the differences between classes.
- Nonlinear Coupling Isolation: In Pb–Pb collisions, the $q_2$ and $q_3$ selections act separately on the factors of the nonlinear coupling term $\chi_{523}V_2V_3$ governing $v_5$ . The $q_2$ selection increases the correlation between $v_5$ and $v_3$ (by increasing $v_2$ ) while decreasing the correlation between $v_5$ and $v_2$ . The $q_3$ selection produces the reverse effect. This establishes a method to experimentally isolate these nonlinear factors. In OO collisions, while the trends for NSC(5,2) and NSC(5,3) in the highest $q_2$ class are similar to those in Pb–Pb, the changes induced by the $q_2$ and $q_3$ selections are not statistically significant, preventing the establishment of this separation mechanism in the current OO sample.
Specific Observations in OO:
- While the selection power is limited, the lowest $q_2$ class in central OO collisions (0–10% centrality) shows a statistically significant reduction (22% for NSC(3,2) and 29% for NSC(4,2)) in correlation strength compared to integrated events. This is attributed to the suppression of the nonlinear contribution to $v_4$ and the weakening of the $v_2$ - $v_3$ anticorrelation in events with small $v_2$ .

Significance and Claims
The paper claims that the decomposition of symmetric cumulants into selected and residual parts provides a direct measure of how much a specific event-shape selection controls a given correlation. The study demonstrates that in light-ion collisions (OO), the limited forward multiplicity restricts the power of event-shape engineering; the selection changes the magnitudes of flow harmonics but fails to disentangle their correlations, which remain largely within the selected classes. Conversely, in Pb–Pb collisions, the method successfully isolates the nonlinear coupling mechanisms, particularly for $v_5$ .

The author emphasizes that these findings serve as a model baseline (using EPOS4) and that the observed mechanisms—specifically the dependence of selection power on multiplicity and the ability to isolate nonlinear factors in Pb–Pb—are expected to hold beyond the specific model used. The work concludes that future event-shape engineering in light-ion collisions requires significantly better resolution of $v_2$ than provided by current forward windows to effectively probe correlation structures.

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