Bayesian Constraints on Pre-Equilibrium Jet Quenching and Predictions for Oxygen Collisions

This paper employs a Bayesian analysis of a semi-analytic jet quenching framework coupled with hydrodynamics and pre-equilibrium energy loss to constrain early-time quenching mechanisms in large systems and predict significant jet and hadron suppression in future oxygen-oxygen collisions.

The Gist

Imagine you are trying to understand how a car engine works. Usually, you'd take a big, powerful truck (a heavy nucleus) and smash it into another truck. The crash creates a massive, hot cloud of dust and debris (the Quark-Gluon Plasma, or QGP). By watching how the engine parts (jets of particles) get slowed down or destroyed in this cloud, physicists learn how the engine works.

But what if you want to know how a tiny, efficient motorcycle engine behaves? You can't just smash two motorcycles together and expect the same results. The physics gets messy, the crash is too short, and it's hard to tell if the engine is actually breaking down or just vibrating differently.

This paper is about a team of physicists trying to solve that exact puzzle using a new, super-precise "crash test" involving Oxygen-Oxygen collisions.

Here is the breakdown of their work using simple analogies:

1. The Mystery: The "Ghost" Energy Loss

In big crashes (like Lead-Lead), we know for a fact that the "engine parts" (high-energy jets) lose a lot of energy as they fly through the hot cloud. It's like running through a thick swamp; you get tired fast.

However, in smaller crashes (like Proton-Lead), the jets should lose energy too, but the path through the swamp is so short that we can't measure it. Yet, strangely, the jets still seem to move in a specific pattern (like a dance). This is confusing: How can they be dancing if they aren't losing energy?

2. The New Tool: The "Hydrodynamic Attractor"

To solve this, the authors built a new computer model. Think of their model as a simulator for a car crash.

• The Old Way: The simulator only started counting time after the crash was fully formed and the dust cloud was stable. It ignored the split second before the cloud formed.
• The New Way: This paper says, "Wait! The most important energy loss might happen in that split second before the cloud fully forms."

They introduced a concept called the "Hydrodynamic Attractor." Imagine a magnet that pulls everything into a specific shape. Even before the dust cloud is fully formed, the physics of the crash is already being "pulled" toward a specific behavior. The authors used this "magnet" to calculate how much energy the jets lose during those very first, chaotic moments.

3. The Detective Work: Bayesian Inference

How do they know their new model is right? They used a method called Bayesian Inference.

Think of this as a detective trying to solve a crime with two clues:

1. Clue A (The Suppression): How much energy did the jet lose? (The "Swamp" effect).
2. Clue B (The Flow): How much did the jet dance in a specific pattern? (The "Elliptic Flow").

In the past, detectives tried to solve the crime using only Clue A. But that left too many suspects (the model parameters could be anything). By adding Clue B, the detective can narrow it down.

The authors ran their simulation against thousands of real data points from giant particle colliders (LHC and RHIC). They tweaked their "magnet" (the pre-equilibrium physics) until the simulation matched the real-world clues perfectly.

The Result: They found that the jets do start losing energy almost immediately—within 0.2 femtoseconds (a time so short it's hard to imagine). This early energy loss explains why the jets dance the way they do, even in smaller systems.

4. The Prediction: The Oxygen Crash Test

Now that they have a calibrated, super-accurate simulator, they used it to predict what would happen in a specific, upcoming experiment: Oxygen-Oxygen collisions.

Oxygen is the "Goldilocks" system. It's bigger than a proton but smaller than Lead. It's the perfect size to test if their theory holds up.

Their Prediction:

• The Jet: When Oxygen nuclei smash together, the jets will lose a significant amount of energy, even though the collision is small.
• The Dance: The jets will show a clear "dance pattern" (elliptic flow).
• The Surprise: Because the Oxygen collision is so small, the jets behave like a single, coherent unit (like a solid arrow) rather than a messy spray of parts. This means the energy loss for the jet and the individual particles inside it will be very similar.

Why Does This Matter?

This paper is a bridge. It connects our understanding of massive, chaotic explosions (Lead-Lead) with the tiny, fleeting interactions of smaller particles.

By proving that energy loss starts immediately (in the pre-equilibrium phase), they are telling us that the "swamp" forms faster than we thought. This helps us understand the fundamental rules of how matter behaves at the highest energies in the universe.

In a nutshell: They built a better crash simulator that accounts for the split-second before the crash fully happens. They tuned it using real data, and now they are using it to predict exactly what will happen when we smash two Oxygen atoms together, revealing that even in tiny collisions, the universe still plays by the rules of a hot, dense fluid.

Technical Summary

1. Problem Statement

The paper addresses a significant tension in the understanding of jet quenching in heavy-ion collisions:

• The Small System Puzzle: While hydrodynamic models successfully describe collective flow in small systems (proton-proton and proton-nucleus collisions), the observation of high-momentum flow coefficients ($v_2$) in these systems contradicts the lack of measurable jet energy loss. In large nucleus-nucleus (AA) collisions, $v_2$ is explained by path-length dependent energy loss, but in small systems, the path lengths are too short for traditional energy loss models to produce significant suppression.
• The Pre-Equilibrium Gap: Traditional jet quenching models typically assume energy loss begins only after the system thermalizes into a Quark-Gluon Plasma (QGP) at a hydrodynamic start time ($\tau_{hyd} \approx 0.4$ fm). However, theoretical studies suggest that the pre-equilibrium phase (Glasma/kinetic theory) exhibits strong anisotropies and high energy density, potentially allowing for significant energy loss earlier than previously modeled.
• The Need for Intermediate Systems: Recent LHC runs with Oxygen-Oxygen (OO) and Neon-Neon (NeNe) collisions offer a unique "bridge" between small (pA) and large (AA) systems. These intermediate-sized collisions reduce uncertainties related to path lengths and centrality determination, providing a critical testbed for system-size dependence.

2. Methodology

The authors extend a semi-analytic jet quenching framework to incorporate state-of-the-art hydrodynamics and pre-equilibrium dynamics.

A. Theoretical Framework:

• Jet Production: Starts with vacuum jet cross-sections calculated at NLO+LL accuracy using MadGraph+Pythia. Nuclear PDF (nPDF) effects are included via EPPS21.
• Energy Loss Mechanism:
  • Uses the Improved Opacity Expansion for medium-induced emissions, capturing single hard and multiple soft scatterings.
  • Includes coherent energy loss effects (color coherence and resolution) where the medium cannot resolve individual partons below a critical angle $\theta_c$.
  • Accounts for elastic energy loss constrained by the Einstein relation.
  • Incorporates medium response (hydrodynamic wakes) by assuming thermalized energy distributes uniformly around the jet hemisphere.
• Hydrodynamic Background: The framework is coupled to event-by-event 2+1D hydrodynamics using the IP-Glasma+JIMWLK+MUSIC+UrQMD multi-stage model. This provides realistic, fluctuating medium profiles.
• Pre-Equilibrium Extension (Key Innovation):
  • For times $\tau < \tau_{hyd}$, the authors do not neglect energy loss. Instead, they use the hydrodynamic attractor from QCD kinetic theory (EKT) to extrapolate the effective local temperature and flow velocity.
  • The effective temperature is scaled using the attractor function $E(\tilde{\omega})$.
  • Transverse flow velocity is scaled linearly with time ($v_{eff} \propto \tau$) based on universal pre-flow solutions.
  • A second parameter, $\tau_{min}$, defines the onset of quenching in the pre-equilibrium phase.

B. Bayesian Analysis:

• Parameters: The model constrains two key parameters:
  1. $g_{med}$: The jet-medium strong coupling constant.
  2. $\tau_{min}$: The initial time for quenching (pre-equilibrium onset).
• Data Used: The inference utilizes a broad dataset of jet suppression ($R_{AA}^{jet}$) and jet elliptic flow ($v_2^{jet}$) from RHIC (AuAu) and LHC (PbPb) across various centralities, jet cone sizes, and transverse momenta.
• Tool: Bayesian parameter estimation is performed using the JETSCAPE/STAT toolkit with Gaussian Process Emulators.

3. Key Contributions

1. First Realistic Pre-Equilibrium Quenching: This is the first implementation of pre-equilibrium energy loss in a realistic jet quenching model that couples to event-by-event hydrodynamics, utilizing the hydrodynamic attractor to bridge the gap between kinetic theory and hydrodynamics.
2. Joint Constraints on $R_{AA}$ and $v_2$: The authors demonstrate that fitting only jet suppression ($R_{AA}$) leaves the onset time ($\tau_{min}$) unconstrained. However, the simultaneous description of $R_{AA}$ and $v_2$ provides a strong constraint on the early-time dynamics.
3. Resolution of the "Hadron $v_2$ Puzzle": Previous models often required delaying quenching to $\sim 1$ fm to fit hadron $v_2$, which was deemed unphysical. By including pre-equilibrium loss, this model achieves a simultaneous description of jet $R_{AA}$ and $v_2$ without unphysical delays, though it still underestimates hadron $v_2$ at low $p_T$ (suggesting missing medium effects for hadrons).

4. Key Results

A. Bayesian Constraints:

• Onset Time: The joint fit of $R_{AA}^{jet}$ and $v_2^{jet}$ constrains the quenching onset time to $\tau_{min} \approx 0.24$ fm. This confirms that significant energy loss occurs deep in the pre-equilibrium phase.
• Coupling: The extracted bare jet transport coefficient is $\hat{q}_0/T^3 \approx 1.7$, which becomes $\hat{q}/T^3 \approx 7$ after logarithmic corrections. This is consistent with other JETSCAPE extractions.
• Tension: While the model fits jet data well, it underestimates charged hadron $v_2$ at low $p_T$, indicating that the current energy loss formalism (focused on jets) may need refinement for hadronization or medium response at lower momenta.

B. Predictions for Oxygen-Oxygen (OO) Collisions:
Using the constrained parameters, the authors predict observables for OO collisions at $\sqrt{s_{NN}} = 5.36$ TeV:

• Jet Suppression ($R_{AA}$): Predicts sizable energy loss for both jets and charged hadrons, significantly exceeding the "no-quenching" baseline (nPDF effects only).
  • Central collisions (0-30%) show stronger suppression than peripheral (30-100%).
  • Suppression is visible down to $p_T \approx 30$ GeV for hadrons and $50$ GeV for jets.
• Elliptic Flow ($v_2$):
  • Unlike large systems where $v_2$ decreases with centrality, in OO collisions, $v_2$ increases with centrality (from central to peripheral).
  • Reasoning: In small systems, initial state geometric fluctuations dominate over the average almond shape. Peripheral collisions have larger relative fluctuations, leading to higher $v_2$.
• Coherence Effects: Due to the small path length in OO, the coherence angle $\theta_c$ is large ($\approx 0.5$). Consequently, $R=0.4$ jets are fully coherent (unresolved substructure) and lose energy as single color charges. This leads to similar suppression patterns for jets and hadrons (modulo fragmentation shifts), unlike in PbPb where resolved substructure plays a larger role.

5. Significance

• Validation of Early-Time Dynamics: The study provides strong evidence that jet quenching is not a purely hydrodynamic phenomenon but begins in the pre-equilibrium phase, with an onset time of $\sim 0.2$ fm.
• Benchmark for Light Ion Runs: The predictions for OO collisions serve as a crucial benchmark for upcoming LHC data. The specific prediction that jets and hadrons will show similar suppression due to coherence effects offers a distinct signature to test against experimental results.
• Methodological Advance: The successful integration of the hydrodynamic attractor into a jet quenching framework sets a new standard for modeling the earliest stages of heavy-ion collisions, moving beyond the assumption that quenching starts only at $\tau_{hyd}$.
• Future Directions: The paper highlights that while the model works well for jets, the discrepancy in low-$p_T$ hadron $v_2$ points to the need for improved modeling of medium response and hadronization in the pre-equilibrium phase.