⚛️ nuclear theory

On the Origin of QCD Collectivity in High-Multiplicity Jets: A Transport Model Study

This study employs a hybrid transport model to demonstrate that the observed elliptic anisotropy in high-multiplicity jets arises primarily from hadronic rescattering driven by initial geometric eccentricity, thereby establishing a geometry-response mechanism for jet collectivity while highlighting the sensitivity of jet substructure variables to initial spatial configurations.

Original authors: Xiao Huang, Xiaoyu Liu, David Qian, Wei Li, Zi-Wei Lin, Xin-Nian Wang, Wenbin Zhao

Published 2026-09-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiao Huang, Xiaoyu Liu, David Qian, Wei Li, Zi-Wei Lin, Xin-Nian Wang, Wenbin Zhao

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 vast, high-energy collisions of particle physics, scientists have long studied how matter behaves when squeezed into a tiny, super-hot droplet. When heavy atomic nuclei smash together, they create a state of matter called a quark-gluon plasma, where the fundamental building blocks of protons and neutrons flow together like a perfect, frictionless fluid. A key signature of this fluid behavior is that the particles flying out do not scatter randomly; instead, they align in specific patterns, moving more in some directions than others, a phenomenon driven by the initial shape of the collision. For years, this collective flow was thought to be a property only of these massive nuclear collisions. However, recent experiments have surprised physicists by finding similar patterns in much smaller systems, such as high-energy collisions between single protons. This discovery raises a profound question: can a tiny spray of particles, born from a single point, also organize itself into a fluid-like flow, and if so, how?

A team of researchers has now taken a deep dive into this mystery by simulating the life of a high-multiplicity jet—a concentrated spray of particles produced in a proton-proton collision. Using a sophisticated computer model, they tracked the journey of these particles from their birth to their final detection, asking whether the initial shape of the spray could dictate the final pattern of the particles. The researchers built a hybrid simulation that starts with a standard description of how particles are created and then adds layers of interaction, allowing the particles to bounce off one another as they travel. They focused on the geometry of the jet, measuring how stretched or oval-shaped the spray was at its very beginning, and then watched to see if this initial shape influenced the direction the particles took as they flew apart.

The simulation revealed that these jets do indeed start with a specific, non-circular shape, much like a slightly squashed circle rather than a perfect ring. As the particles evolved, the researchers found that the final pattern of their movement was strongly linked to this initial shape. The more oval the starting geometry was, the stronger the final directional flow became. This suggests a mechanism where the initial spatial arrangement of the particles is translated into a momentum pattern, much like how the shape of a mold determines the shape of the cast object. However, the study also uncovered a crucial detail about where this transformation happens. The researchers tested two different stages of interaction: one where the particles interact while they are still in their fundamental, sub-atomic form, and another where they interact after they have combined into larger, composite particles called hadrons.

The results showed that the enhancement of this collective flow came almost entirely from the interactions between the final, composite particles. The interactions between the fundamental sub-atomic particles, which occur earlier in the process, had a negligible effect on the final pattern in this specific model. This finding points to a scenario where the collective behavior emerges not from the earliest, most energetic phase of the jet's life, but from the later stage when the particles have cooled and combined into hadrons. The researchers also explored whether they could predict the initial shape of the jet by looking at its internal structure, specifically by examining how the energy was shared between different parts of the spray. They found that jets with certain internal structures tended to have more oval starting shapes, suggesting that the internal layout of a jet could serve as a clue to its initial geometry.

Despite these successes, the simulation did not perfectly match the latest experimental data from the Large Hadron Collider. While the model correctly predicted that collective flow exists and depends on the initial shape, the specific way the flow changed with the jet's internal structure was different from what the experiments observed. In the simulation, jets with a simpler, single-core structure showed a stronger flow effect than those with a double-core structure, whereas the experimental data suggested the opposite. This discrepancy highlights a gap in the current understanding of how these particles interact. The researchers propose that their model might be missing a more complex interplay where the creation of new particles and their collisions happen simultaneously, rather than in separate, distinct stages.

Ultimately, this work provides strong support for the idea that collective behavior in these tiny jets arises from a geometry-response mechanism, where the initial shape of the particle spray drives the final flow. It confirms that even in the smallest systems accessible to experiments, the rules of geometry and interaction can lead to organized, fluid-like motion. The study also establishes that the internal structure of a jet is a powerful tool for probing its initial conditions. While the current model suggests that the final stage of particle interactions is the primary driver of this effect, the mismatch with experimental data serves as a vital guide for future research. It indicates that a more complete picture of jet evolution must account for the simultaneous branching of particles and their collisions, a complexity that could unlock the full story of how order emerges from chaos in the smallest droplets of matter.

Technical Summary: On the Origin of QCD Collectivity in High-Multiplicity Jets

Problem Statement
Recent experimental observations by the CMS Collaboration have revealed an enhancement of elliptic azimuthal anisotropy ( $v_2^*$ ) in high-multiplicity jets produced in proton-proton ($pp$) collisions. This finding suggests that collective behavior, typically associated with the quark-gluon plasma (QGP) in heavy-ion collisions, may emerge even in the smallest accessible QCD systems. The central challenge is to determine the microscopic origin of this anisotropy: specifically, whether it arises from a geometry–response mechanism where final-state interactions convert initial spatial eccentricity into momentum anisotropy, or if alternative mechanisms such as quantum entanglement or topology bias are responsible. A key open question is whether this collectivity is driven by partonic or hadronic interactions and how it correlates with the initial geometry of the jet shower.

Methodology
To address these questions, the authors employ a hybrid transport model that couples perturbative jet generation with non-perturbative transport evolution. The simulation framework proceeds in three distinct stages:

Initial-State Generation: Jets are generated using PYTHIA 8 (CP5 tune) to simulate hard scattering and parton showers. Crucially, the model assigns space-time formation points to each shower parton based on the full splitting sequence, allowing for a realistic initial coordinate-space geometry.
Partonic Rescattering: Once formed, partons undergo elastic two-body scatterings governed by the Boltzmann transport equation, implemented via Zhang's Parton Cascade (ZPC). The strength of these interactions is controlled by a constant partonic cross-section ( $\sigma_p$ ), varied from 0 to 24 mb.
Hadronization and Hadronic Rescattering: After partonic interactions cease, the system hadronizes via the Lund string-fragmentation model (as in PYTHIA). The resulting hadrons then evolve through the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model, which includes elastic/inelastic scattering, resonance formation, and decay.

The analysis is performed in the "jet frame," a coordinate system where the jet momentum defines the longitudinal axis. This allows for the characterization of initial-state geometry (via eccentricity vectors $\varepsilon_n$ ) and final-state momentum anisotropies (via flow vectors $Q_n$ ) within a common reference frame. The study systematically varies interaction strengths and categorizes jets using the Soft Drop substructure variables ( $z_g$ and $\theta_g$ ) to probe the relationship between jet topology, initial geometry, and final-state collectivity.

Key Contributions and Results

Initial-State Geometry and Longitudinal Structure: The study establishes that high-multiplicity jets possess non-zero initial eccentricities. While strong decorrelation exists between different space-time pseudorapidity intervals, a non-zero correlation persists up to a rapidity gap of $|\Delta\eta^*| \ge 2$ . This suggests that a Bjorken-like picture, where particles separated in rapidity inherit a common initial geometry, remains qualitatively applicable even in these small systems.
Substructure as a Geometry Proxy: The authors demonstrate that the Soft Drop variable $z_g\theta_g$ correlates with the initial geometric eccentricity. Jets with larger $z_g\theta_g$ (more "two-prong-like") exhibit different initial geometric properties compared to those with smaller values, validating the use of jet substructure to "engineer" or select specific initial geometries.
Origin of Anisotropy Enhancement: The analysis of the geometry-response correlator ( $v_2^s$ ) reveals that the enhancement of elliptic anisotropy at high multiplicities is dominated by hadronic rescattering. In the current model setup, partonic rescattering contributes negligibly to the final anisotropy. This is attributed to the low partonic opacity ( $\hat{\gamma} \approx 0.1$ ) in the ZPC implementation, where scattering is restricted to elastic $2 \to 2$ processes occurring only after parton formation.
Geometry-Response Mechanism: The study confirms a direct correlation between the initial eccentricity and the final-state anisotropy enhancement ( $\Delta v_2^s$ ). The response grows rapidly with increasing initial eccentricity, supporting a geometry–response mechanism for collective behavior inside jets.
Substructure Dependence Discrepancy: When jets are categorized by substructure, the model predicts a larger anisotropy enhancement for "one-prong" jets compared to "two-prong" jets. This is contrary to current CMS measurements, which show a different trend. The authors suggest this discrepancy may arise because the two hard cores in two-prong jets are spatially separated, reducing the probability of rescattering among their associated shower partons (lower effective opacity).

Significance and Claims
The paper claims to provide strong support for a geometry–response mechanism as the origin of collective behavior in high-multiplicity jets. By establishing a direct link between initial spatial anisotropy and final momentum anisotropy through transport dynamics, the study suggests that the smallest QCD systems can exhibit collective flow similar to that in heavy-ion collisions.

However, the authors are modest regarding the quantitative agreement with experimental data. They explicitly state that the predicted substructure dependence differs from current CMS measurements. The paper concludes that while the geometry–response framework is valid, a more realistic description of jet evolution is required—one that treats parton branching and transport interactions concurrently rather than sequentially. Such developments are necessary to fully resolve the role of partonic scattering and to quantitatively understand the microscopic origin of collectivity in the smallest QCD systems. The work also establishes jet substructure as a promising experimental handle for probing initial geometry, despite the current model's limitations in reproducing specific substructure trends.

Technical Summary: On the Origin of QCD Collectivity in High-Multiplicity Jets

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