Jet quenching in out-of-equilibrium QCD matter

This paper presents the first study of jet substructure modifications during the bottom-up evolution of out-of-equilibrium QCD matter, demonstrating that the early stages of bulk matter evolution in heavy-ion collisions leave a sizable imprint on jet radiation patterns and establishing a foundation for incorporating pre-equilibrium dynamics into realistic jet quenching models.

The Gist

Imagine a high-energy heavy-ion collision (like smashing two gold nuclei together) not as a single event, but as a chaotic, evolving storm. For a long time, scientists have studied what happens to "jets" (streams of particles) as they fly through the hot, dense, and settled part of this storm, known as the Quark-Gluon Plasma (QGP).

However, this new paper asks a different question: What happens to these jets during the very first, messy moments of the storm, before it settles down?

Here is a breakdown of their findings using simple analogies:

1. The Setting: The "Storm" vs. The "Ocean"

Usually, physicists imagine the medium a jet travels through as a calm, uniform ocean (thermal equilibrium). But in reality, right after a collision, the medium is a churning, turbulent storm. It starts out incredibly crowded with particles (over-occupied), then thins out, and eventually settles into a calm liquid.

The authors wanted to see how a jet behaves while flying through this turbulent, pre-storm phase, rather than just the calm ocean phase.

2. The Tool: The "Improved Flashlight"

To study this, the team used a sophisticated mathematical tool called the Improved Opacity Expansion (IOE).

• The Analogy: Imagine trying to see how a flashlight beam is scattered by fog.
  • Old methods assumed the fog was either very thin (single hits) or very thick (many tiny hits).
  • The IOE is like a "smart flashlight" that can handle both at the same time. It accounts for the jet getting hit by many gentle puffs of air (soft interactions) and occasional hard punches (single hard interactions) as it moves through the changing fog.

3. The Experiment: Simulating the "Pre-Storm"

The researchers didn't just guess; they used computer simulations (Effective Kinetic Theory) to model how the "fog" (the QCD matter) changes over time. They looked at three scenarios:

• The Under-occupied Room: A room that starts with too few people and slowly fills up.
• The Over-occupied Room: A room that starts packed tight and slowly empties out.
• The Expanding Room: A room that is packed, then rapidly expands and cools down (this is the most realistic model for heavy-ion collisions).

They tracked a specific property called $\hat{q}$ (jet quenching parameter). Think of this as the "drag coefficient" or the "roughness" of the road the jet is driving on. In a calm ocean, this road is smooth and consistent. In the pre-storm, the road is bumpy, changing from rough to smooth in real-time.

4. The Key Discovery: The "First Impression" Matters

The most important finding is that the early stages leave a permanent mark.

• The Analogy: Imagine two runners starting a race.
  • Runner A runs on a track that is muddy and bumpy for the first 10 seconds, then becomes smooth.
  • Runner B runs on a track that is perfectly smooth from the start.
  • Even if both tracks become identical after 10 seconds, Runner A will have a different stride, different fatigue, and a different final position than Runner B.

The paper shows that jets traveling through the "muddy" early phase of the collision emerge with a different internal structure (substructure) than jets that only traveled through the "smooth" later phase.

5. The Surprising Result: "Late" Doesn't Erase "Early"

The team compared their complex, changing "storm" model against two simpler models:

1. Static Brick: A frozen, unchanging block of matter.
2. Thermal Match: A calm ocean with the same average energy as the storm.

They found that even when the storm eventually settles down to look like the calm ocean, the jet remembers the turbulence it experienced at the start.

• If you only looked at the end of the race, you might think the tracks were the same.
• But if you look at the pattern of the runner's footprints (the jet's substructure), you can tell they started on a bumpy road.

6. Why This Changes Things

Previously, many scientists assumed that the first split-second of a collision was too short or too chaotic to matter, so they ignored it (setting the "drag" to zero).

This paper proves that ignoring the beginning is a mistake. The early, non-equilibrium phase is actually very "rough" (high drag) and leaves a distinct fingerprint on the jets.

In summary:
Just as a car driving through a sudden hailstorm before hitting a highway will have a different ride quality than a car that only drove on the highway, a jet of particles traveling through the chaotic early moments of a heavy-ion collision carries a unique signature of that chaos. This allows scientists to use jets as "tomographic probes"—like an X-ray—to see the very first, invisible moments of the universe's creation in these collisions.

Technical Summary

Technical Summary: Jet Quenching in Out-of-Equilibrium QCD Matter

Problem Statement
High-energy heavy-ion collisions (HICs) produce a quark-gluon plasma (QGP) that undergoes a complex evolution from a far-from-equilibrium state to a thermalized liquid. While the late-stage hydrodynamic expansion is well-studied, the early pre-equilibrium stages remain poorly constrained experimentally because these non-equilibrium states do not reach detectors directly. Conventional jet quenching phenomenology often assumes the jet transport coefficient $\hat{q}$ is zero during the earliest times ($\tau \lesssim 1$ fm/c) or relies on static, thermalized media approximations. However, theoretical frameworks like the Bottom-Up thermalization scenario and Effective Kinetic Theory (EKT) suggest that the medium is highly occupied and anisotropic during these early stages, potentially generating significant jet quenching effects. The central problem addressed is whether the specific dynamics of this pre-equilibrium evolution leave a measurable imprint on the substructure of jets, specifically the medium-induced gluon radiation spectrum.

Methodology
The authors combine two theoretical frameworks to compute the differential gluon radiation spectrum $dI/d\omega d^2k$ for a hard parton traversing a dynamically evolving medium:

1. Improved Opacity Expansion (IOE): To calculate the radiation spectrum, the authors employ the IOE formalism. This approach treats the scattering potential $v(x)$ as a sum of a harmonic oscillator (HO) term (resumming multiple soft exchanges) and a perturbative correction $\delta v$ (accounting for single hard Coulomb-like exchanges). This allows for an analytic treatment that captures both the multiple soft scattering regime and the large-momentum sector, overcoming limitations of pure HO or pure opacity expansions. The spectrum is expressed in terms of time-dependent functions derived from the jet quenching parameter $\hat{q}(t)$ and a screening mass $\mu^*(t)$.
2. Effective Kinetic Theory (EKT) Simulations: To provide the time-dependent medium properties, the authors utilize EKT simulations based on the Boltzmann equation with elastic and inelastic collision kernels. They extract the bare jet quenching parameter $\hat{q}_0(t)$ and the screening mass $\mu^*(t)$ from these simulations. The relation between the EKT-derived $\hat{q}$ (which depends on a transverse momentum cutoff $\Lambda_\perp$) and the parameters required for the IOE is established by matching the small-distance behavior of the scattering potential.

Simulation Scenarios
The study investigates three distinct bulk evolution scenarios:

• Isotropic Under-Occupied: A system starting with gluon density below equilibrium, evolving toward thermalization.
• Isotropic Over-Occupied: A system starting with high gluon density (scaling solution attractor), evolving toward equilibrium.
• Bjorken Expanding: A longitudinally expanding system mimicking the early stages of HICs, undergoing "bottom-up" thermalization. This includes phases of initial over-occupancy, dilution into an under-occupied anisotropic regime, and eventual isotropization.

For each scenario, the authors compute the radiation spectrum and compare it against two reference cases: a "thermal-matched" system (equilibrium medium with the same instantaneous energy density) and a "static brick" (a static medium with parameters matched to preserve characteristic energy scales).

Key Results

• Non-Convergence to Equilibrium in Expanding Systems: For isotropic, non-expanding systems, the nonequilibrium radiation spectra closely resemble the thermal-matched results, with deviations decreasing as the system size increases. However, for the Bjorken expanding system, the ratio of the nonequilibrium spectrum to the equilibrium spectrum (specifically the ratio of their maxima, $\chi_m$) does not converge to unity at late times.
• Sensitivity to Early-Time Dynamics: The study demonstrates that the radiation pattern is dominated by the early stages of the medium's evolution. Modifications to the time evolution of $\hat{q}_0(\tau)$ and $\mu^*(\tau)$ at early times ($\tau \lesssim 50/Q_s$) significantly alter the resulting spectrum, particularly near the spectral peak. Conversely, modifications at late times have a negligible impact.
• IOE vs. Harmonic Approximation: Comparisons between the full IOE and the leading-order Harmonic Oscillator (HO) approximation show good agreement at low transverse momenta. However, at higher momenta, the IOE exhibits distinct power-law scaling due to the inclusion of single hard interactions (Coulomb tail), which the HO approximation misses.
• Coupling Dependence: The magnitude of the deviations between nonequilibrium and equilibrium scenarios depends on the coupling strength $\lambda$. In the expanding case, the nonequilibrium values of $\hat{q}_0$ and $\mu^*$ deviate from their thermal counterparts for most of the evolution, leading to persistent differences in the jet substructure.

Significance and Claims
The paper claims to present the first study of jet substructure modifications specifically during the bottom-up evolution of heavy-ion collisions. The primary significance lies in establishing that:

1. Pre-equilibrium Imprints: The early, out-of-equilibrium stages of bulk matter evolution in HICs leave a "sizable imprint" on the radiation pattern inside jets. This challenges the conventional assumption that early-time jet quenching is negligible or that static/thermal approximations are sufficient for describing the full evolution.
2. Jet Tomography: Jets serve as sensitive tomographic probes of the medium's early-time dynamics. The persistent deviation of ratio observables from unity indicates that jets retain a "memory" of the medium's initial non-equilibrium state, even after the medium has thermalized.
3. Theoretical Foundation: The work provides a self-consistent framework for incorporating pre-equilibrium dynamics into realistic descriptions of jet quenching. It establishes a basis for moving beyond static or purely thermal models in phenomenological studies of jet suppression and substructure.

The authors conclude that while their current framework neglects anisotropic plasma instabilities (a limitation shared with the underlying EKT and BDMPS-Z assumptions), the results robustly demonstrate the importance of bulk expansion and early-time non-equilibrium dynamics in shaping final-state jet observables. They suggest these findings could motivate future studies of jet substructure in small collisional systems (e.g., proton-nucleus or light-ion collisions) where pre-equilibrium dynamics may dominate.