⚛️ nuclear theory

Particle Correlations in Jets

This paper proposes a method to study particle correlations in high-energy jets by comparing measured energy-energy correlators with those constructed from individual energy flows, revealing that genuine correlations stem from correlated splitting at moderate to large angles and exhibit a unique energy-dependent pattern at small angles that can be used to probe jet energy loss in heavy-ion collisions.

Original authors: Wenbin Zhao, Volker Koch, Feng Yuan

Published 2026-09-29

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Wenbin Zhao, Volker Koch, Feng Yuan

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

High-energy physics seeks to understand the fundamental building blocks of matter and the forces that bind them together. At the heart of this quest is the study of jets, which are narrow sprays of particles created when subatomic particles collide at tremendous speeds. These collisions act like microscopic particle accelerators, smashing protons together so violently that they shatter into streams of debris. Scientists have long used a specific tool called an energy-energy correlator to map out how the energy in these sprays is distributed. Think of this tool as a way to measure how much energy two particles share based on how far apart they are flying from the center of the spray. While this method has been successful for decades, it measures the total energy flow, which includes both random, unconnected particles and pairs that are genuinely linked because they came from the same source. To truly understand the complex physics happening inside these jets, researchers need to separate the signal of true connections from the background noise of random chance.

A team of physicists has developed a new way to isolate these genuine connections within high-energy jets. Instead of just looking at the total energy distribution, they devised a method to compare the actual measurements against a theoretical baseline where no connections exist. They did this by taking the energy flow of individual particles and mathematically combining them as if they were completely unrelated, creating a "disconnected" version of the data. By subtracting this disconnected version from the real measurements, they were able to strip away the random noise and reveal the true correlations between particles. This approach allows them to see exactly where particles are influencing each other, distinguishing between pairs that are merely flying in the same direction by chance and those that are physically linked because they were born from the same splitting event.

Using computer simulations of particle collisions, the researchers found that these genuine correlations are strongest at moderate to large angles across all jet energies. This pattern indicates that the particles are coming from correlated splitting events, where a single particle breaks apart into two. However, the behavior changes at very small angles. Here, the strength of the correlation increases as the energy of the jet increases, revealing a specific pattern that had not been clearly isolated before. The study identified three distinct regions within the jet's angular distribution. At the smallest angles, the data suggests a region of free hadrons where particles are emitted without significant modification. As the angle increases to a moderate range, the correlations drop, signaling a transition where the processes of particle formation and splitting begin to suppress these connections. Finally, at larger angles, the correlations rise again, driven by the fundamental laws of particle physics that govern how particles split apart.

To ensure their method worked in the real world, the team applied their analysis to actual data from the Large Hadron Collider, specifically using a public dataset from 2011. They reconstructed the jets and calculated the same energy correlations, finding that the real-world data matched their computer simulations in a qualitative sense. The genuine correlations in the real data were positive at small angles, turned negative at intermediate angles, and approached zero at large angles, mirroring the patterns seen in the simulations. This successful test on real data proves that the proposed measurement is feasible and robust, even when accounting for the limitations of real-world detectors. The researchers noted that while the specific transition points between these regions differed slightly between the simulation and the real data, likely due to how particle decays are handled, the overall structure of the findings held up.

The ultimate goal of this work is to provide a unique tool for studying what happens when these jets travel through the dense, hot matter created in heavy-ion collisions, such as when gold or lead nuclei are smashed together. In these extreme environments, jets lose energy as they plow through the nuclear medium, a phenomenon known as jet energy loss. The researchers propose that by comparing the genuine correlations in heavy-ion collisions to those in standard proton-proton collisions, scientists can cancel out many of the confusing background effects. Because the method focuses on the ratio of correlated to uncorrelated energy, it naturally filters out the single-particle effects that often obscure the physics. This means that at small angles, the measurement could directly reveal how much energy the jet lost, while at large angles, it could show how the medium modifies the way particles split apart. This approach offers a cleaner path to understanding the properties of the nuclear matter that fills the universe in its earliest moments.

Technical Summary: Particle Correlations in Jets

Problem Statement
Energy-Energy Correlators (EECs) have long served as a precision tool for testing Quantum Chromodynamics (QCD) and studying jet substructure in $e^+e^-$ , proton-proton ($pp$), and heavy-ion ( $AA$ ) collisions. However, the standard EEC observable, defined as an energy-weighted sum of all particle pairs within a jet, inherently includes contributions from uncorrelated particle pairs. Consequently, the measured EEC does not vanish even in the absence of genuine physical correlations between particles. This limitation obscures the extraction of true two-particle correlations, which are essential for understanding specific QCD mechanisms such as parton splitting, hadronization, and medium-induced modifications in heavy-ion collisions. The authors aim to disentangle these "genuine" correlations from the background of uncorrelated energy flows to reveal the underlying physics driving jet substructure.

Methodology
The authors propose a method to isolate genuine particle correlations by constructing a "disconnected" EEC baseline and comparing it against the measured "full" EEC.

Definitions:
- Full EEC ( $\langle \text{EEC} \rangle_{\text{full}}$ ): The standard observable defined in Eq. (1), representing the energy-weighted distribution of all particle pairs $(i, j)$ in a jet $J$ with relative angle $\theta$ .
- Disconnected EEC ( $\langle \text{EEC} \rangle_{\text{Disc.}}$ ): A constructed baseline representing the expectation if particles were uncorrelated. This is derived from the product of single-particle energy distributions (Eq. 6). The authors define this via an integral over two independent energy flows (Eq. 7) or alternatively via a "mixed-event" technique (Eq. 8), where particles are randomly sampled from different jets to destroy genuine correlations while preserving single-particle kinematics.
- Normalization: A normalization factor ( $N_{\text{Disc.}}$ or $C_{\text{mix}}$ ) is introduced to account for the fact that the integral of the full EEC is not unity, ensuring the disconnected baseline is properly scaled.
Extraction of Genuine Correlations:
- Difference: The genuine correlation is extracted as the difference: $\langle \text{EEC}(\theta) \rangle_C = \langle \text{EEC}(\theta) \rangle_{\text{full}} - \langle \text{EEC}(\theta) \rangle_{\text{Disc.}}$ (Eq. 9).
- Ratio: A ratio observable, $R_{\text{EEC}}(\theta)$ , is defined as the quotient of the full and disconnected EECs (Eq. 10). This ratio is highlighted as a robust tool for visualizing correlation strength across different angular regions.
Validation:
- Theoretical predictions are generated using the PYTHIA8.306 event generator for $pp$ collisions at LHC energies.
- A proof-of-principle analysis is performed using CMS 2011 Open Data ($pp$ collisions at $\sqrt{s}=7$ TeV), reconstructing jets with the anti- $k_T$ algorithm ( $R=0.5$ ) and utilizing Particle Flow Candidates (PFCs).

Key Results
The analysis reveals distinct behaviors in the genuine correlations across three angular regions:

Small Angles ( $\theta \to 0$ ):
- The genuine correlation increases with jet energy.
- The ratio $R_{\text{EEC}}$ is essentially flat, indicating a "Free Hadron Region" where emissions are dominated by non-perturbative Transverse Momentum Dependent (TMD) fragmentation.
- In the CMS Open Data analysis, $\langle \text{EEC} \rangle_C$ is positive at small angles.
Moderate Angles:
- The ratio $R_{\text{EEC}}$ decreases, signaling a "Transition Region."
- This region reflects the onset of collinear dynamics and hadronization processes that suppress two-particle correlations relative to the uncorrelated baseline.
- Lower jet energies show ratios closer to unity, implying the measured EEC is dominated by uncorrelated contributions in this regime.
Large Angles (toward jet boundary):
- The ratio $R_{\text{EEC}}$ rises again, driven by perturbative-QCD collinear splittings which enhance genuine correlations.
- The difference $\langle \text{EEC} \rangle_C$ decreases toward zero as both the full and disconnected terms vanish near the jet boundary.

Significance and Claims
The paper claims that this method provides a unique tool to disentangle different physical mechanisms in jet substructure:

Disentangling Physics: By comparing the genuine correlations (via the difference or ratio) between heavy-ion ( $AA$ ) and proton-proton ($pp$) collisions, one can isolate specific nuclear effects.
Jet Energy Loss: The authors propose that the double ratio (comparing $AA$ to $pp$ genuine correlations) at small angles can directly inform the fraction of jet energy loss. Since the correlation ratio is proportional to jet energy, deviations in $AA$ collisions can be attributed to energy loss mechanisms.
Medium Modification of Splitting: At large angles, the double ratio is expected to reveal medium modifications of parton splitting.
Cancellation of Systematics: The authors argue that medium response effects (which lack specific angular dependence) will largely cancel out in the ratio of genuine correlations, unlike in standard EEC measurements where they might be misinterpreted as splitting modifications.
Feasibility: The qualitative agreement between the PYTHIA8 simulation and the CMS 2011 Open Data analysis demonstrates that the proposed observables are robust and extractable from real collider data, despite detector limitations. The authors emphasize that while the study uses Open Data as a proof of principle, modern LHC datasets will allow for higher-precision measurements.

The paper concludes that this approach, applicable to $pp$, $pA$ , and $AA$ collisions, offers a pathway to quantify cold and hot nuclear matter effects and could be extended to multi-point energy correlators and $e^+e^-$ collisions for cleaner benchmarks.

Technical Summary: Particle Correlations in Jets

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