⚛️ nuclear theory

Imaging non-hydrodynamic modes with jet wakes

This paper proposes that the higher angular moments of a jet wake's energy flux serve as a unique spectroscopic probe for detecting non-hydrodynamic modes in the quark-gluon plasma, offering a direct link between microscopic non-equilibrium dynamics and observable detector images.

Original authors: Aleksi Kurkela, Ian Moult, Alexander Soloviev, Urs Achim Wiedemann

Published 2026-07-30

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Aleksi Kurkela, Ian Moult, Alexander Soloviev, Urs Achim Wiedemann

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 the universe as a giant, invisible soup. When scientists smash heavy atoms together at nearly the speed of light, they create a tiny, super-hot drop of this soup called a quark-gluon plasma (QGP). It's the hottest, densest stuff in the universe, a state of matter that existed just microseconds after the Big Bang. For a long time, physicists have studied this soup by watching how it flows like a liquid. They've learned a lot about its "hydrodynamics"—how it ripples, swirls, and spreads out, much like water in a bathtub. But there's a catch: liquids are just the surface level. Deep down, this soup is made of tiny, frantic particles (quarks and gluons) that don't always behave like a smooth fluid. They have their own secret, microscopic dances that happen too fast or too small for the "liquid" rules to describe. Scientists have been trying to catch a glimpse of these hidden, non-fluid movements, but they've been like trying to hear a whisper in a hurricane. The question is: Can we see the tiny, chaotic details of the soup's particles, or are we stuck only seeing the big, smooth waves?

This paper proposes a clever new way to listen to that whisper. The authors suggest using a "jet"—a high-speed particle that punches through the plasma like a bullet through water. As this jet flies through, it leaves a trail, or a "wake," behind it. Think of it like a speedboat cutting through a lake; the water rushes away from the boat, creating a wake. In the plasma, this wake isn't just a simple ripple; it has a complex shape. The researchers realized that if you look at the shape of this wake from different angles, you can separate the "liquid" behavior from the "microscopic particle" behavior.

Here is the magic trick: The smooth, liquid-like flow of the plasma only creates simple, low-angle shapes in the wake (like a simple dip or a gentle bump). However, the chaotic, microscopic particles create more complex, jagged shapes that show up at higher angles. The paper shows that by measuring these higher, more complex angles in the wake, scientists can directly "see" the non-hydrodynamic modes—the secret, microscopic dances of the particles. In their simulations, they found that these complex shapes are distinct and measurable. They argue that if we can measure these higher angles precisely enough, we will finally have proof that the quark-gluon plasma is more than just a simple fluid; it's a complex quantum system with its own hidden layers of behavior.

The authors don't just guess this; they built a mathematical framework to prove it. They used a "sourced Boltzmann equation," which is a fancy way of describing how particles move and bump into each other when a jet hits them. They tested this idea using three different models of how the plasma might behave: one where particles relax quickly (RTA), one where they diffuse slowly (Diffusion), and one based on the actual rules of particle physics (QCD). In all three models, they found that the "liquid" parts of the wake only affect the simplest angles (0, 1, and 2), while the complex, non-liquid parts show up in angles 3 and higher.

Crucially, the paper points out that the "negative jet wake"—the area where particles are actually missing because the jet pushed them away—is the best place to look. They compared their simulations to real data from the CMS experiment at CERN. While the current data is good enough to see the simple "liquid" wake, it's not quite sharp enough yet to clearly see the complex, high-angle patterns that would prove the existence of these microscopic modes. The authors suggest that with better, more precise measurements, we could finally distinguish between different theories of how the plasma works. They aren't claiming to have found the answer yet, but they have handed the experimentalists a new map and a new tool: look at the high-angle details of the jet's wake, and you might just hear the secret language of the universe's smallest building blocks.

Technical Summary: Imaging Non-Hydrodynamic Modes with Jet Wakes

Problem Statement
While ultra-relativistic heavy-ion collisions have firmly established that the quark–gluon plasma (QGP) exhibits hydrodynamic behavior, direct experimental signatures of non-hydrodynamic modes have remained elusive. Hydrodynamic modes (sound, shear, heat, and charge diffusion) govern long-wavelength, late-time dynamics and are universal consequences of conservation laws. In contrast, non-hydrodynamic excitations—ranging from quasi-normal modes in strongly coupled theories to quasi-particle excitations in weakly coupled theories—encode the microscopic structure of the plasma and its approach to thermal equilibrium. Current experimental constraints on the non-hydrodynamic sector are absent. Existing approaches to access these modes, such as studying early-time dynamics in large systems or small collision systems, are limited by the erasure of early-time sensitivity by subsequent hydrodynamic evolution or by uncertainties in initial states and hadronization, respectively. Consequently, no observable is currently known to be exclusively sensitive to non-hydrodynamic modes.

Methodology
The authors propose the angular structure of the jet wake as a spectroscopic probe for the medium's non-hydrodynamic sector. The study employs a general kinetic-theory framework that extends beyond hydrodynamics to describe the collective QGP dynamics coupled to jets.

Theoretical Framework: The authors utilize a sourced Boltzmann equation for the phase distribution function $f(x, p)$ , where a collision operator $\hat{C}$ encodes microscopic interactions and a source term $S$ accounts for jet-medium interactions. The system is linearized around a local equilibrium distribution.
Spectral Decomposition: The collision operator is decomposed into an orthonormal basis of eigenmodes $|\phi_a\rangle$ with eigenvalues $1/\tau_a$ representing relaxation rates. Hydrodynamic modes correspond to conserved perturbations (null space of $\hat{C}$ ), while non-hydrodynamic modes correspond to non-conserved excitations with finite relaxation times.
Detector Image: The observable is defined as the asymptotic particle flow (detector image) at late times, specifically the jet-induced energy flux integrated over space. This is expanded into spherical harmonic moments $\delta E_{\ell m}$ .
Angular Moment Analysis: The authors analyze the sensitivity of different angular moments ( $\ell$ $ℓ$ ) to the relaxation spectrum:
- $\ell = 0, 1$ (Monopole/Dipole): These moments are orthogonal to all non-conserved excitations and are determined solely by the energy and momentum deposited by the jet.
- $\ell = 2$ (Quadrupole): This sector receives contributions from the full spectrum of non-conserved excitations and is closely related to shear viscosity.
- $\ell > 2$ : In the long-wavelength limit ( $k \to 0$ ), hydrodynamic descriptions contain angular structure only up to $\ell = 2$ . Therefore, moments with $\ell > 2$ lie entirely outside the hydrodynamic sector and directly probe non-hydrodynamic excitations.
Model Comparison: To demonstrate sensitivity, the authors calculate the jet wake image using three distinct kinetic theories:
- Relaxation-Time Approximation (RTA) with a common relaxation time $\tau_R$ .
- Diffusive dynamics governed by the angular Laplacian.
- Leading-log (LL) perturbative QCD, which possesses a richer spectrum of non-hydrodynamic excitations.
  All models are tuned to reproduce the same shear viscosity ( $\eta/s = 0.12$ ) to isolate differences in the non-hydrodynamic relaxation spectrum.

Key Contributions and Results

Spectroscopic Probe: The paper establishes that the negative jet wake (the depletion of energy flow opposite to the jet direction) serves as a spectroscopic probe. While low-order moments ( $\ell \le 2$ ) are dominated by hydrodynamic or conserved quantities, higher angular moments ( $\ell \ge 3$ ) are exclusively sensitive to non-hydrodynamic modes.
Distinct Imprints: Calculations across the three kinetic models show that while the overall shape of the negative jet wake (dominated by $\ell=1$ ) is similar, the higher angular moments exhibit distinct signatures. Specifically, the $\ell > 2$ harmonics are non-vanishing in all models but differ in amplitude and structure depending on the underlying microscopic dynamics (e.g., RTA vs. LLQCD).
Experimental Feasibility: The authors overlay their theoretical calculations with existing CMS data on charged particle yields. They find that while current data describes the negative jet wake well, establishing a non-vanishing $\ell=3$ harmonic and distinguishing between microscopic models requires improved experimental precision. The $\ell=3$ mode is identified as the most promising candidate for a clean experimental probe, as it is independent of hydrodynamic modes and less sensitive to the poorly controlled forward jet fragmentation region than higher moments.

Significance and Claims
The paper claims that the detection of non-zero higher angular moments ( $\ell \ge 3$ ) in the jet wake would provide unambiguous evidence that the QGP is more than a hydrodynamic fluid. This conclusion is presented as generic and independent of model-dependent assumptions; it relies on the fundamental property that hydrodynamics cannot generate angular structure beyond the viscous quadrupole ( $\ell=2$ ).

The authors emphasize that their proposal does not require greater theoretical predictive power to detect the presence of non-hydrodynamic modes, but rather sufficient experimental precision to measure these higher moments. While the simplified kinetic models used here lack the quantitative predictive power to distinguish between specific classes of non-hydrodynamic scenarios (e.g., RTA quasi-particles vs. other classes), they successfully establish a transparent analytical connection between the jet wake and the non-hydrodynamic relaxation spectrum. The paper concludes that precision measurements of the higher angular moments of the negative jet wake should become a target for the heavy-ion program to develop refined techniques for detecting these elusive modes.

More like this