Effects of hadronic reinteraction on jet fragmentation from small to large systems

Using the X-SCAPE event generator coupled with the SMASH afterburner, this study demonstrates that hadronic rescattering significantly modifies jet fragmentation observables even in small systems like $e^++e^-$ collisions, highlighting the critical role of the hadronic phase in jet quenching across different collision environments.

The Gist

Imagine you are watching a high-speed fireworks display. When a firework explodes, it sends out a tight, focused stream of sparks. In the world of particle physics, this is similar to what happens when particles smash together: a "jet" of new particles shoots out in a specific direction.

For a long time, scientists have been trying to understand exactly how these jets behave. A big question has been: Does the "crowd" of other particles around the jet change how the jet spreads out?

This paper, written by Hendrik Roch and the JETSCAPE team, investigates this question. They used a powerful computer simulation to see what happens when these high-speed particles crash into each other and then have to navigate through a "traffic jam" of other particles before they stop moving.

Here is a simple breakdown of what they did and what they found:

The Setup: A Digital Traffic Jam

The researchers used a sophisticated software toolkit called X-SCAPE. Think of this toolkit as a video game engine designed specifically for physics.

1. The Explosion: They started by simulating a clean collision (specifically, an electron and a positron smashing together). This created a high-energy jet of particles, much like a single firework exploding.
2. The "Afterburner": Usually, simulations stop once the particles are created. But this team added a special extra step called SMASH. Imagine this as a "traffic simulator" that runs after the explosion. It lets the newly created particles drive around and bump into each other before the simulation ends.
3. The Test: They ran three versions of the same collision:
   • Version A: The particles fly out and just decay (break apart) without hitting anything else.
   • Version B & C: The particles fly out, wait a tiny fraction of a second (like 0.1 or 1.0 femtoseconds—imagine a blink of an eye that is a billion times faster), and then start bumping into each other in the SMASH traffic simulator.

The Findings: The "Crowd" Changes the Shape

Even though they were simulating a very small, clean system (just two particles colliding, not a massive heavy-ion collision), the results were surprising.

1. The Jet Gets "Fatter"
When the particles were allowed to bump into each other (rescattering), the jet didn't stay as tight.

• Analogy: Imagine a group of runners starting a race in a perfect line. If they run alone, they stay in a straight line. But if they have to weave through a crowd of people, they get pushed to the sides. The line becomes wider and messier.
• The Result: The "thrust" of the event (how pencil-like the explosion looks) became less sharp. The particles spread out more, making the event look "fatter" in momentum space.

2. Energy Gets Shared
The high-speed particles (the "leaders" of the jet) lost some of their speed when they hit other particles.

• Analogy: Think of a fast runner passing a baton to a slower runner. The fast runner slows down, and the slow runner speeds up.
• The Result: The high-momentum particles lost energy, and that energy was transferred to slower particles. This caused a "diffusion" where the energy spread from the fast core of the jet to the slower edges.

3. The Core Gets Empty
The center of the jet, which usually has the most particles, became less crowded.

• Analogy: If you shake a box of marbles, the marbles in the very center might get pushed toward the edges.
• The Result: The "jet shape" showed that particles were being scattered away from the very center of the jet to larger distances.

Why This Matters

The most important takeaway is that even in the smallest, cleanest systems, the interactions between particles after they are created matter.

Previously, scientists might have thought, "Oh, this is just a small collision; the particles won't bump into each other much." This paper proves that wrong. Even in a simple electron-positron collision, if you let the particles interact with each other (like a crowd at a concert), it measurably changes the final picture.

The Bottom Line

The authors conclude that we cannot ignore these "traffic jams" of particles. To get the most accurate picture of how the universe works at the smallest scales, we must simulate not just the explosion, but also the chaotic dance that happens immediately afterward.

This study acts as a foundation. Now that they know this "afterburner" effect works in simple systems, they plan to use the same tools to study more complex, messy collisions (like those in heavy-ion experiments) to better understand the fundamental forces of nature.

Technical Summary

Technical Summary: Effects of Hadronic Reinteraction on Jet Fragmentation from Small to Large Systems

Problem Statement
The impact of the hadronic phase on jet quenching in nuclear collider experiments remains an open question in heavy-ion physics. While previous studies utilizing simplified setups suggested that hadronic interactions could significantly alter high-momentum hadron dynamics, a systematic analysis within a comprehensive event generator framework was lacking. Specifically, the extent to which hadronic rescattering modifies final-state hadronic and jet observables in small systems, such as $e^+ + e^-$ collisions, required quantification.

Methodology
This study utilizes the JETSCAPE event generator framework, specifically the upcoming X-SCAPE 1.2 version, to simulate $e^+ + e^-$ collisions at a center-of-mass energy of $\sqrt{s} = 91.2$ GeV. The simulation chain employs the following components:

• Hard Scattering and Showering: Hard scattering is generated using PYTHIA 8.3. The resulting hard parton system undergoes showering via the MATTER module until the parton virtuality drops below a cutoff scale $Q_0$.
• Hybrid Hadronization: Partons below $Q_0$ are hadronized using a novel Hybrid Hadronization module. This module interpolates between quark recombination (in dense phase-space regions) and Lund string fragmentation (in dilute regions). It utilizes a Wigner function formalism to calculate recombination probabilities based on the overlap of parton wave functions, accounting for spin and color states. Crucially, it allows shower partons to recombine with thermal partons from a background medium if present, though in this specific study, the focus is on vacuum systems.
• Hadronic Afterburner: The hadrons produced by Hybrid Hadronization are fed into SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). SMASH solves the Boltzmann equation to simulate non-equilibrium hadronic dynamics, including decays and elastic/inelastic rescattering.

To isolate the effects of hadronic reinteraction, three simulation scenarios were compared:

1. Baseline: Hadrons undergo only decays in SMASH (no rescattering).
2. Rescattering (0.1 fm): A short free-streaming period of 0.1 fm is applied before rescattering begins.
3. Rescattering (1.0 fm): A free-streaming period of 1.0 fm is applied before rescattering begins.

A total of $1.5 \times 10^6$ events were simulated for each setup using a preliminary parameter set. Events containing heavy-flavor hadrons were excluded as SMASH does not yet implement their decay channels.

Key Results
The analysis focused on event shape variables, hadronic spectra, and jet observables, comparing simulation outputs with ALEPH experimental data.

• Event Shapes: The inclusion of hadronic rescattering broadens events. The thrust variable ($\tau = 1 - T$) and total jet broadening ($B_T$) both show increased values when rescattering is active, indicating that hadrons are scattered away from the thrust axis. The variation in free-streaming time (0.1 fm vs. 1.0 fm) did not significantly impact these results. While the thrust distribution did not perfectly match experimental data at large $\tau$ (attributed to untuned generator settings), the inclusion of final-state interactions improved the description of total jet broadening data.
• Hadronic Spectra: Rescattering leads to a diffusion of momentum from high to low values. The hadronic $x_p$ spectrum ($x_p \equiv 2|\vec{p}|/\sqrt{s}$) shows a depletion of large-momentum hadrons and a corresponding enhancement at lower momenta. A similar shift is observed in the transverse momentum spectrum of reconstructed jets, where high-$p_T$ jets shift toward lower $p_T$.
• Jet Fragmentation and Shape: The jet fragmentation function $D(z)$ (where $z = p_{ch}^T / p_{jet}^T$) demonstrates that high-momentum hadrons transfer momentum to lower-momentum particles within the jet. Furthermore, the jet shape $P(\Delta r)$ reveals that rescattering shifts hadrons from the jet core to larger radii, effectively broadening the jet profile.

Significance and Claims
The paper claims to demonstrate that hadronic rescattering significantly affects event shapes, hadronic spectra, and jet observables even in the most dilute collider systems, specifically $e^+ + e^-$ collisions. The study establishes that the hadronic phase can transfer momentum from high-energy hadrons to softer ones, broadening event shapes and scattering hadrons away from the jet or thrust axis.

The authors position this work as a foundational step for future investigations. They intend to apply this framework to systems with underlying events, such as $p+p$ and heavy-ion ($A+A$) collisions. Additionally, they aim to explore higher-energy $e^+ + e^-$ collisions to address significant two-particle correlations observed in high-multiplicity events that current generators fail to describe, suggesting that momentum reshuffling in the afterburner phase may help bridge the gap between theory and experiment in these regimes.