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Mapping jet substructure in heavy-ion collisions with track functions

This paper investigates how track functions, which encode the flow of energy from partons to charged hadrons, are modified by the quark-gluon plasma in heavy-ion collisions, demonstrating that their non-linear evolution and higher moments can discriminate between different jet quenching models and provide a direct test of quantum field theory predictions within the medium.

Original authors: João Barata, Yeonju Go, Daniel Pablos

Published 2026-06-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: João Barata, Yeonju Go, Daniel Pablos

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

Imagine you are trying to understand how a complex machine works by watching a single, high-speed explosion. In the world of particle physics, this "explosion" is a jet—a spray of particles created when two heavy atomic nuclei smash together at nearly the speed of light.

This paper is like a detective story about what happens to these jets when they fly through a super-hot, super-dense soup of energy called a Quark-Gluon Plasma (QGP). This soup is created in the collision and is so hot that it melts the protons and neutrons into their fundamental building blocks.

Here is the breakdown of the paper's story, using simple analogies:

1. The Problem: How do we see the "Invisible" changes?

When a jet flies through this hot soup, it loses energy and changes shape. Scientists have been trying to figure out exactly how the jet breaks apart inside this soup.

Usually, scientists look at "fragmentation functions." Think of these like counting only the red marbles that come out of a broken jar. It tells you something about the red marbles, but it ignores the blue and green ones. It gives a partial picture.

2. The New Tool: "Track Functions"

The authors introduce a new tool called Track Functions.

The Analogy: Instead of counting just the red marbles, imagine you have a magical net that catches every single marble (red, blue, green, and transparent) that flies out of the jar.
Why it's better: Because this tool tracks all the charged particles, it sees the entire story of how the jet broke apart. It doesn't just look at one piece; it looks at the whole family tree of the explosion.

3. The Experiment: Two Different Stories

The researchers used two different computer simulations (think of them as two different video game engines) to model what happens to these jets in the hot soup:

Model A (Hybrid): A mix of different physics theories.
Model B (Jewel): A model based on standard particle collision rules.

They ran the simulations for two scenarios:

Vacuum: The jet flies through empty space (like a jet in a normal lab).
Soup: The jet flies through the hot Quark-Gluon Plasma.

4. The Findings: What Changed?

When they looked at the "Track Functions" (the total collection of marbles), they found some fascinating things:

The Shape Shifted: In the hot soup, the way the energy was distributed among the particles changed. It wasn't just that the jet lost energy; the pattern of how it broke apart was different.
The "Fingerprint" of the Soup: The changes were most obvious when looking at the "tails" of the distribution (the rare, extreme events). It's like if you usually get a mix of small and medium marbles, but in the soup, you suddenly start getting a few giant marbles and many tiny dust specks. The "Track Function" caught this shift perfectly.
The Models Disagreed: Here is the twist. While both models agreed that the soup changed the jet, they disagreed on how much it changed.
- Model A said the change was moderate.
- Model B said the change was huge.
- The Takeaway: This means "Track Functions" are powerful enough to tell us which computer model is actually closer to reality. They can act as a referee to decide which theory of the soup is correct.

5. The Deep Physics: The "Flow" of Time

The paper also looked at how these patterns change as the energy of the jet gets higher (like zooming in with a microscope).

The Discovery: Even though the soup changes the starting point of the jet, the rules governing how the jet evolves as it travels seem to stay the same as they do in empty space.
The Analogy: Imagine a river flowing through a canyon. The canyon (the soup) might change where the river starts or how wide it is, but the water still flows downhill following the same laws of gravity. The paper suggests that inside the hot soup, the "laws of the river" (the quantum rules of particle branching) remain surprisingly similar to empty space, even though the scenery is totally different.

6. Can We Actually Measure This?

The authors checked if real-world experiments could do this.

The Challenge: It's hard to separate the "jet marbles" from the background noise of the explosion.
The Solution: They found that if you look at narrow jets (a tight cone of particles), the background noise is less of a problem.
The Verdict: Yes, this is something experiments at places like the Large Hadron Collider (LHC) could potentially measure. It requires looking at the details of the charged particles, which modern detectors can do.

Summary

This paper proposes a new way to look at particle jets. Instead of just counting one type of particle, they suggest counting all charged particles to see the full picture of how jets break apart in a hot, dense environment.

They found that:

The hot soup definitely changes how jets break apart.
Different theories predict different amounts of change, so this new method can help scientists pick the right theory.
Surprisingly, the fundamental rules of how the jet evolves seem to stay the same, even inside the soup.

It's a new lens for looking at the universe's most extreme environments, helping us understand the "rules of the game" when matter is melted down to its most basic form.

Technical Summary: Mapping Jet Substructure in Heavy-Ion Collisions with Track Functions

Problem and Motivation
Jets serve as primary tomographic probes of the quark-gluon plasma (QGP) created in ultrarelativistic heavy-ion collisions. While significant theoretical progress has been made in describing medium-modified virtuality cascades and time-dependent backgrounds, the connection between first-principles QCD dynamics and experimentally accessible jet observables remains incomplete. Standard fragmentation functions, which describe the energy flow to a specific single hadron, satisfy linear Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution and are insufficient for capturing the collective, non-linear dynamics of the entire jet branching process. The authors motivate the use of track functions ( $T_i(x)$ ), non-perturbative objects that measure the energy fraction $x$ carried by all charged hadrons originating from an initiating parton. Unlike standard fragmentation functions, track functions encode the entire branching history and exhibit a highly non-linear renormalization group (RG) evolution. The paper aims to investigate how the presence of a QGP modifies these track functions and their scale evolution, offering a systematic framework to study jet fragmentation that links heavy-ion measurements to fundamental QFT understanding.

Methodology
The study employs a phenomenological approach combining theoretical definitions with Monte-Carlo (MC) simulations.

Theoretical Framework: The authors utilize the operatorial definition of track functions and their known perturbative RG evolution equations. They focus on the evolution of moments ( $T[N]$ ) and cumulants ( $\kappa_n$ ), noting that the RG flow mixes different moments, unlike the linear evolution of single-hadron fragmentation functions. Specifically, they examine the $(\kappa_2, \kappa_4)$ plane, where the evolution of the fourth cumulant receives a source term proportional to $\kappa_2^2$ , representing non-linear mixing.
Monte-Carlo Simulations: The authors extract track functions from two distinct jet quenching models:
- Hybrid Model: A framework combining perturbative DGLAP evolution (via Pythia 8) for high- $Q^2$ splittings with non-perturbative energy loss modeled via gauge/gravity duality for the strongly coupled medium.
- Jewel 2.3: A perturbative QCD-based event generator simulating shower radiation and in-medium re-scattering (bremsstrahlung induced by elastic collisions).
Simulation Setup: Simulations were performed for proton-proton (pp) and lead-lead (PbPb) collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Jets were reconstructed using the anti- $k_T$ algorithm with a radius $R=0.2$ . To isolate modifications to the hard shower from medium response effects (e.g., hydrodynamic wakes or recoil particles), the authors disabled medium response contributions in both models. They analyzed jets with transverse momenta $p_T > 50$ GeV across six hard scales ( $\mu = 100$ to $1000$ GeV), separating quark- and gluon-initiated jets.

Key Results

Medium-Induced Modifications: In both Hybrid and Jewel models, the track function distributions in PbPb collisions are broader than in pp collisions, even when medium response is disabled. This indicates that medium-induced energy loss alters the event-by-event charged energy fraction.
Sensitivity of Higher Moments: The modifications are most pronounced in higher-order moments and cumulants. The ratio of PbPb to pp moments increases with the moment order $N$ . For instance, at $N=10$ , the ratio reaches $\sim 10-25\%$ in Hybrid but $\sim 30-45\%$ in Jewel. This demonstrates that track function moments are sensitive to medium-induced substructure fluctuations rather than just overall energy loss.
Model Discrimination: The quantitative magnitude of the modifications and their dependence on the hard scale $\mu$ differ significantly between the two models. Jewel predicts a stronger reshaping of the charged fraction distribution and a slower convergence to vacuum-like values at high $\mu$ compared to Hybrid. This suggests track functions can discriminate between competing microscopic pictures of jet-medium interactions.
RG Flow Structure: A critical finding is that the RG flow of the cumulants in PbPb collisions follows the same trajectory in the $(\kappa_4, \kappa_2^2)$ plane as in pp collisions, merely shifted by different initial conditions. This implies that the perturbative dynamics governing the scale evolution of the virtuality cascade remain largely vacuum-like in the medium. The medium primarily modifies the effective boundary conditions of the shower rather than the fundamental RG evolution equations.
Experimental Robustness: The observables are found to be robust against realistic tracking thresholds (e.g., $p_T > 0.5$ GeV) and are less sensitive to medium response effects when using narrow jet radii ( $R=0.2$ ).

Significance and Claims
The paper claims to provide the first phenomenological study of track functions in the context of heavy-ion collisions. Its primary significance lies in establishing track functions as a class of observables capable of:

Probing Collective Dynamics: Offering a systematic framework to study the entire fragmentation process and inter-parton correlations, which are inaccessible via standard fragmentation functions.
Testing QFT in Medium: Providing a direct avenue to test RG flows inside a QGP. The observation that the cumulant trajectories remain aligned with vacuum predictions suggests that the in-medium virtuality cascade develops essentially as in vacuum, a hypothesis central to many jet quenching models but previously unquantified.
Discriminating Models: The differing magnitudes and scale dependencies observed between the Hybrid and Jewel models demonstrate that track functions can distinguish between different microscopic descriptions of jet-medium interactions.

The authors conclude that while the quantitative extraction of track functions from experimental data presents challenges, the theoretical framework and MC results provide a clear path for future experimental tests to gauge the differences between in-medium and vacuum virtuality cascades.