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Two-particle number and transverse momentum balance function with event topology in pp collisions at $\sqrt{s}=13$ TeV

This paper presents the first study of charge-dependent two-particle number and transverse momentum balance functions in pp collisions at $\sqrt{s}=13$ TeV, revealing that balance functions narrow with increasing multiplicity and are wider in isotropic than jet-like events, while comparing PYTHIA8 and EPOS-LHC models to isolate hydrodynamic radial-flow effects on charge conservation.

Original authors: Subash Chandra Behera, Arvind Khuntia

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Subash Chandra Behera, Arvind Khuntia

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 subatomic world, matter is not a solid, unchanging thing but a seething soup of fundamental particles. When physicists smash protons together at nearly the speed of light, they create a fleeting, incredibly hot environment where these particles are born, interact, and then fly apart. For decades, scientists have studied these collisions in massive, heavy nuclei to create a state of matter called a quark-gluon plasma, a liquid-like soup where particles move collectively, flowing together like water in a river. However, a surprising discovery has emerged: even when smashing tiny, single protons together, the debris sometimes behaves as if it is part of this same flowing liquid. This raises a profound question: how can such a small system, with so few particles, exhibit the same collective behavior as a giant collision? To answer this, researchers must look at how the electric charge of the particles is balanced. In nature, charge is conserved; if a positive particle is created, a negative one must appear nearby to balance it. By measuring how far apart these balancing pairs are when they finally stop moving, scientists can determine whether they were born together in a tight, local burst or if they were pushed apart by a collective flow, like two people on a crowded dance floor being swept in different directions by a current.

A team of researchers has taken a fresh look at this problem by analyzing results from model calculations of proton-proton collisions at an energy of 13 TeV, a record-breaking level achieved at the Large Hadron Collider. Instead of just counting particles, they sorted these simulated collisions based on their shape, or "event topology." Imagine looking at the spray of debris from a collision: some events look like two distinct jets shooting out in opposite directions, while others look like a uniform, spherical cloud of particles spreading out in all directions. The researchers used a specific measure called transverse spherocity to separate these two types of events. They then examined the "balance function," a tool that maps the distance between positive and negative particle pairs in both their direction of travel and their angle around the collision point. By comparing these measurements across different numbers of particles produced and different event shapes, they aimed to distinguish between simple, independent particle creation and the complex, collective motion seen in larger systems.

To understand what they were seeing, the team relied on two powerful computer simulations. The first, known as pythia8, models collisions where particles are created through a process of string breaking and fragmentation, similar to how a stretched rubber band snaps into smaller pieces. In this model, particles are produced locally, and any collective behavior is minimal. The second model, epos-lhc, is more complex; it includes a "core" that behaves like a fluid, expanding and pushing particles outward, surrounded by a "corona" of particles that behave more like the simple strings in the first model. By running these simulations with and without the fluid-like core, the researchers could isolate the specific effects of this collective flow on how charge-balancing pairs are distributed.

The results revealed a clear pattern that depends heavily on the shape of the event. In collisions that looked like back-to-back jets, the balancing charges were found to be very close together, both in their forward-backward direction and their side-to-side angle. This suggests that in these high-energy, jet-dominated events, the positive and negative particles are created almost instantly next to each other and do not travel far before stopping. However, in the isotropic, cloud-like events, the balancing charges were found much further apart. This wider separation indicates that in these softer, more chaotic events, the particles are not just created locally but are likely being pushed apart by a collective expansion, much like the flow of a fluid. The study found that as the number of particles in a collision increased, the distance between balancing charges generally decreased, meaning the pairs were becoming more localized. Yet, the shape of the event remained the deciding factor: even in high-multiplicity collisions, the isotropic events kept their charges more separated than the jet-like events.

When the researchers compared the two computer models, the difference became even more distinct. The simulation that included the fluid-like core produced a much sharper narrowing of the distance between charges in the side-to-side direction as the number of particles increased. This narrowing is a signature of radial flow, where the expanding medium pushes particles in a coordinated way, tightening the correlation between balancing pairs. In contrast, the simulation without the fluid core showed a much flatter response, with the distance between charges changing very little regardless of how many particles were produced. This suggests that the collective flow is a mechanism that can be modeled and detected in these simulations, setting the stage for future experimental tests to confirm if it is a real physical phenomenon in these tiny proton collisions. The study concludes that by sorting collisions based on their shape, scientists can effectively separate the effects of simple particle production from the more complex, fluid-like behaviors. This approach provides a new way to probe the fundamental mechanisms of how matter forms and moves in the smallest, most energetic environments, offering a clearer picture of how collective behavior can emerge even when the system is too small to be considered a traditional liquid.

Technical Summary: Two-particle number and transverse momentum balance function with event topology in pp collisions at $\sqrt{s} = 13$ TeV

Problem and Motivation
Recent observations of collective phenomena in high-multiplicity proton-proton (pp) and proton-lead (p–Pb) collisions have challenged the distinction between small and large collision systems, raising questions about the applicability of hydrodynamic models to small systems. A central open question is whether collective behavior in these small systems arises from mechanisms such as color reconnection, initial momentum correlations, or hadronization effects, or if it requires a deconfined medium. Charge-sensitive observables, specifically the balance function ( $B$ ), offer a probe into these underlying physics mechanisms. The width of the balance function reflects an interplay between the spatial separation of balancing charges (which broadens the function) and collective radial flow (which narrows it by imparting a momentum boost). While previous studies have analyzed $B$ as a function of charged-particle multiplicity, the sensitivity of these correlations to event topology—specifically distinguishing between back-to-back jet-like structures and isotropic events—remains less explored. This study addresses the need to disentangle medium-driven effects from jet-dominated dynamics by analyzing charge-dependent correlations as a function of transverse spherocity.

Methodology
The authors perform a differential analysis of the charge-dependent two-particle number balance function ( $B$ ) and the momentum balance function ( $P^{CD}_2$ ) using Monte Carlo simulations of pp collisions at $\sqrt{s} = 13$ TeV. The analysis utilizes two distinct event generators:

PYTHIA8 (CP5 tune): Models hadronization via string fragmentation, conserving charge locally. It includes multiparton interactions (MPI) and color reconnection (CR) to mimic dense partonic environments but lacks hydrodynamic evolution.
EPOS-LHC: Employs a core-corona model where a dense core undergoes hydrodynamic evolution (generating radial flow), while a dilute corona hadronizes via string fragmentation. The study compares EPOS-LHC configurations with the hydrodynamic core enabled ("core on") and disabled ("core off") to isolate the specific contribution of radial flow.

Events are classified using transverse spherocity ( $S_0$ ), an event-shape variable that discriminates between soft (bulk-dominated, isotropic) and hard (jet-dominated, jet-like) QCD dynamics. The analysis selects events in low (jet-like, bottom 20% of $S_0$ ) and high (isotropic, top 20% of $S_0$ ) spherocity classes across various charged-particle multiplicity ( $N_{ch}$ ) intervals. The observables are measured for charged particles within $|\eta| < 2.4$ and $0.2 < p_T < 2.0$ GeV. The balance functions are constructed as functions of relative pseudorapidity ( $\Delta\eta$ ) and relative azimuthal angle ( $\Delta\phi$ ), with widths calculated using the root-mean-square (RMS) of the distributions.

Key Contributions and Results

Event Topology Dependence: The study reports the first differential analysis of balance functions with respect to transverse spherocity. It finds that isotropic events exhibit significantly wider balance functions in both $\Delta\eta$ and $\Delta\phi$ compared to jet-like events. This suggests that charge-balancing pairs are more spatially separated in soft-dominated, isotropic topologies, whereas jet-like events show more localized charge conservation.
Multiplicity Dependence: A narrowing of the balance function width is observed in both $\Delta\eta$ and $\Delta\phi$ as charged-particle multiplicity increases. In PYTHIA8, this narrowing is driven by MPI and CR, which increase the density of soft partons and reshuffle string topologies.
Model Comparison and Radial Flow:
- PYTHIA8 vs. EPOS-LHC: EPOS-LHC (with core) produces narrower balance functions in $\Delta\eta$ compared to PYTHIA8, indicating stronger localization of charge-balancing pairs due to hydrodynamic flow. However, in $\Delta\phi$ , EPOS-LHC generally yields larger widths than PYTHIA8, though the core-enabled configuration shows a stronger multiplicity dependence than the no-core configuration.
- Core vs. No-Core: The comparison between EPOS-LHC with and without the hydrodynamic core reveals that the inclusion of radial flow leads to a pronounced narrowing of the $\Delta\phi$ width at high multiplicities. In contrast, the "no-core" scenario exhibits nearly flat widths with multiplicity, suggesting that the observed narrowing in the full EPOS-LHC model is a quantitative handle on radial-flow-induced localization.
Momentum Correlations ( $P^{CD}_2$ ): Unlike the number balance function, the momentum balance function $P^{CD}_2$ shows a mild decrease in width with increasing charged-particle multiplicity in PYTHIA8. In EPOS-LHC, the topology dependence is more pronounced when the core is enabled, with jet-like events showing narrower widths than isotropic events. The $P^{CD}_2$ observable is noted to be particularly sensitive to short-range correlations (jets, resonance decays) and filters out long-range contributions that lack strong $p_T$ covariance.

Significance and Claims
The paper claims that this differential study provides crucial insights into hadronization dynamics and the mechanisms driving charge correlations in small collision systems. By utilizing spherocity to separate jet-like and isotropic topologies, the authors demonstrate that:

$\Delta\eta$ narrowing is primarily sensitive to longitudinal charge conservation and MPI-driven particle production.
$\Delta\phi$ narrowing serves as a probe for radial-flow-like dynamics induced by either color reconnection (in PYTHIA8) or hydrodynamic evolution (in EPOS-LHC).

The work establishes that the balance function, when analyzed across event-shape classes, can disentangle the microscopic mechanisms of hadronization from collective effects. The contrasting behaviors observed between PYTHIA8 and the core-enabled/disabled EPOS-LHC configurations highlight the sensitivity of these observables to the presence of a hydrodynamic medium. The authors conclude that these findings set the stage for future high-precision measurements with LHC Run 3 data to experimentally test these theoretical scenarios and refine the understanding of QCD dynamics, color reconnection, and the potential emergence of collectivity in small systems.

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