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Exposing the parton-hadron transition within jets with energy-energy correlators in pp collisions at $\sqrt{\textit s}=5.02$ TeV

This paper presents a fully-corrected measurement of the energy-energy correlator (EEC) within jets in pp collisions at $\sqrt{s}=5.02$ TeV, revealing a distinct transition region that marks the onset of hadronization and identifies a common energy scale for this process, while demonstrating good agreement with perturbative QCD calculations in the large-angle regime and providing constraints for Monte Carlo event generators.

Original authors: ALICE Collaboration

Published 2026-09-29

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CC BY 4.0

Original authors: ALICE Collaboration

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

Inside the heart of a particle accelerator, where protons smash together at nearly the speed of light, nature performs a violent transformation. When these tiny packets of energy collide, they shatter into a spray of even smaller fragments called quarks and gluons. These fragments are the fundamental building blocks of matter, but they cannot exist in isolation for long. Almost instantly, they begin to radiate energy and split apart, creating a cascading shower of new particles. As this shower expands, the energy of the original fragments spreads out until the particles are forced to bind together into stable, composite objects known as hadrons, such as protons and pions. This final step, where free-floating energy locks itself into solid matter, is a process called hadronization. It is a crucial moment in the life of a particle collision, yet it remains one of the most difficult to understand because the forces involved are so complex that standard mathematical tools often fail to describe them.

Scientists have long sought a way to watch this transition happen in real time, to see exactly where the smooth, predictable splitting of particles gives way to the chaotic binding of hadrons. To do this, researchers at the Large Hadron Collider turned their attention to a specific measurement called the energy-energy correlator. Instead of looking at individual particles, this method tracks how the energy of two particles relates to the angle between them. By measuring this relationship across a jet of particles, scientists can map the flow of energy from the initial high-speed split down to the final, slow-moving clump of matter. It is a way of tracing the path of energy as it moves from the realm of high-speed physics into the realm where particles stick together.

In a recent study, the ALICE collaboration at CERN used this method to examine jets produced in proton-proton collisions at an energy of 5.02 trillion electron volts. The team focused on jets containing charged particles with a specific range of momentum, looking closely at how the energy correlation changed as the angle between particle pairs varied. They found that the behavior of these jets changes dramatically depending on the distance between the particles. When the particles are far apart, the energy correlation follows a predictable pattern that matches calculations based on the known laws of particle physics. This region represents the early stage of the jet, where particles are still splitting apart freely. However, as the researchers looked at particles that were very close together, the pattern shifted. In this tight space, the correlation grew in a straight, linear line, a signature that the particles were no longer acting as free fragments but were instead being shaped by the forces that bind them into hadrons.

Between these two distinct behaviors lies a transition zone, a narrow window where the physics of the jet changes from one mode to the other. The researchers identified a clear peak in the data that marks this turning point. Remarkably, when they adjusted for the total energy of the jet, this peak appeared at the exact same location for all the different energy levels they tested. This consistency suggests that there is a universal scale for the moment when the free-flowing energy stops splitting and begins to lock into matter. The peak occurred at an angular distance that corresponds to a specific energy scale of about 2.43 GeV/c divided by the jet's momentum. This finding implies that the process of hadronization happens at a characteristic energy threshold, regardless of how much energy the original jet started with.

To ensure these observations were real and not just an artifact of the detector, the team compared their results with sophisticated computer simulations that model how particles should behave. They tested different versions of these simulations, each using different assumptions about how particles break apart and stick together. While the simulations generally matched the data, they showed subtle differences in exactly where the transition peak appeared. Some models placed the peak at slightly different angles, revealing that the details of the hadronization process are still sensitive to the specific rules used in the computer models. This mismatch provides a powerful new tool for physicists: by measuring exactly where the transition happens in the real world, they can now fine-tune their theories to better describe how nature builds matter from energy.

The study represents a significant step forward because it is the first time this specific measurement has been fully corrected for the limitations of the detector in such a low-energy regime at the Large Hadron Collider. Previous measurements often focused on higher energies or left some detector effects uncorrected, which can blur the fine details of the transition. By carefully accounting for how the detector sees the particles, the ALICE team was able to reveal the clean, underlying shape of the energy flow. The results confirm that the transition from free particles to bound matter is not a gradual blur but a distinct event with a predictable location. This clarity allows scientists to probe the fundamental forces of the universe with greater precision, offering a new window into the moment when the invisible becomes visible.

Problem and Motivation
Jets serve as powerful probes for studying Quantum Chromodynamics (QCD), encoding information about both the perturbative parton shower and the non-perturbative hadronization process. While various jet substructure observables have been studied to unravel these dynamics, the Energy-Energy Correlator (EEC) offers a distinct approach. The EEC focuses on the correlation function of energy flow inside jets as a function of angular distance. It is infrared-collinear (IRC) safe, allowing for high-precision perturbative QCD (pQCD) calculations, while simultaneously being sensitive to non-perturbative effects like confinement at small angular scales. Previous measurements of EECs have been performed in $e^+e^-$ collisions and by the CMS experiment in $pp$ collisions at higher jet transverse momenta ( $p_T$ ). However, a fully corrected measurement of jet EECs in the low- $p_T$ regime at the Large Hadron Collider (LHC) was lacking. This regime is crucial for examining the transition between perturbative parton splitting and non-perturbative hadronization, as the accessible angular range extends from the perturbative to the non-perturbative domain.

Methodology
The ALICE Collaboration analyzed minimum bias $pp$ collision data collected at a center-of-mass energy of $\sqrt{s} = 5.02$ TeV in 2017, corresponding to an integrated luminosity of $18.0 \pm 0.4$ nb $^{-1}$ . Charged particles were reconstructed using the Inner Tracking System (ITS) and Time Projection Chamber (TPC) within the central barrel ( $|\eta| < 0.9$ ). Jets were reconstructed using the anti- $k_T$ algorithm with a radius parameter $R=0.4$ via the FastJet package.

The EEC observable, $\Sigma_{EEC}(R_L)$ , was defined as an energy-weighted two-particle correlation function dependent on the angular distance $R_L$ between particle pairs within a jet. The measurement was performed for charged-particle jets in three transverse momentum intervals: $20 < p_{T}^{ch\ jet} < 40$ , $40 < p_{T}^{ch\ jet} < 60$ , and $60 < p_{T}^{ch\ jet} < 80$ GeV/ $c$ . To reduce the impact of the underlying event, only charged particle constituents with $p_{T,track} > 1$ GeV/ $c$ were included in the EEC calculation.

Detector effects, including track momentum and angular resolution, efficiency, and the "track-merging" effect (where closely spaced tracks are misreconstructed), were assessed using PYTHIA 8 (Monash tune) simulations propagated through a GEANT3 model of the ALICE detector. Instead of full unfolding, a two-dimensional bin-by-bin correction was applied, comparing generator-level and detector-level information. A Bayesian unfolding cross-check confirmed the robustness of this approach. Systematic uncertainties were evaluated regarding single-track and pair efficiencies, generator dependence, and the correction method, resulting in a total uncertainty of less than 4% for most of the measured $R_L$ range.

Key Results
The fully corrected $\Sigma_{EEC}$ distributions exhibit three distinct regions as a function of $R_L$ :

Perturbative Region (Large $R_L$ ): The data shows a dependence scaling approximately as $1/R_L$ , consistent with next-to-leading-log (NLL) pQCD calculations.
Transition Region: A broad peak structure is observed, marking the crossover where perturbative contributions diminish and hadronization effects begin to dominate.
Non-Perturbative Region (Small $R_L$ ): The data exhibits a linear dependence on $R_L$ , consistent with a spatially uniform population of particles produced from hadronization.

A significant finding is the scaling behavior of the transition peak. When the distributions are normalized and plotted against the scaled variable $\langle p_{T}^{ch\ jet} \rangle R_L$ , the data from different jet $p_T$ bins collapse onto a common curve. The peak of this transition region is located at a common energy scale defined by the relation:
$R_L^{peak} = \frac{2.43 \pm 0.14 \text{ GeV}/c}{\langle p_{T}^{ch\ jet} \rangle}$
This indicates a universal energy scale for the parton-hadron transition, independent of the jet energy. The peak height also follows a specific scaling relation proportional to $\langle p_{T}^{ch\ jet} \rangle / \ln \langle p_{T}^{ch\ jet} \rangle$ .

Comparisons with Monte Carlo event generators (PYTHIA 8, Herwig 7, and Sherpa) show that the models generally describe the data within 20% across the measured range. However, differences in the transition peak position and height are observed between models employing different hadronization mechanisms (e.g., Lund string vs. cluster hadronization). Specifically, the transition region in Herwig 7 (cluster) appears at smaller angles compared to PYTHIA 8 (string), and Sherpa's AHADIC tune (cluster) deviates significantly from data at small angles compared to its Lund tune.

Significance and Claims
The paper claims to present the first fully corrected EEC measurement in jets at the LHC within a low- $p_T$ kinematic regime ($20-80 $GeV/$ c$). The primary significance lies in the experimental observation of the parton-hadron transition region within jets. The identification of a common transition scale, where the peak location is given by $2.43 \pm 0.14$ GeV/ $c$ divided by the average jet $p_T$ , provides a quantitative baseline for the energy scale where QCD radiation ceases and confinement takes over.

The author states that these results provide a new perspective on jet evolution, bridging the gap between perturbative splittings and parton confinement. The measurements serve as a constraint for state-of-the-art Monte Carlo generators, particularly regarding parton shower and hadronization mechanisms. Furthermore, the paper posits that this study establishes a baseline for future investigations into cold and hot nuclear medium effects on jet formation and propagation, which can be explored using EECs in proton-nucleus and nucleus-nucleus collisions. The author modestly notes that while the data constrains models, theoretical predictions based on first principles for the non-perturbative hadronization process remain challenging, and future developments in lattice QCD and quantum computation may be required for further improvements.

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