⚛️ phenomenology

Transport of hard probes in the glasma

This thesis investigates the transport of jets and heavy quarks through the pre-equilibrium glasma phase of heavy-ion collisions using classical and quantum methods, revealing that the glasma induces significantly larger and anisotropic transport coefficients and measurable azimuthal decorrelation, thereby highlighting the necessity of accounting for this stage to avoid biases in extracting QGP properties.

Original authors: Dana Avramescu

Published 2026-10-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dana Avramescu

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

In the most extreme conditions imaginable, where matter is crushed and heated beyond the point of any solid, liquid, or gas, a new state of existence emerges. This is the quark-gluon plasma, a super-hot soup of the fundamental building blocks of the universe. Scientists recreate this state for fleeting moments by smashing heavy atomic nuclei together at nearly the speed of light in massive particle accelerators. When these collisions occur, they do not produce a smooth, uniform fireball immediately. Instead, they create a chaotic, turbulent prelude known as the "glasma." Think of the glasma as a storm of invisible, powerful magnetic and electric tubes stretching between the colliding nuclei, existing for a fraction of a second before the system settles into the hot plasma. Understanding how this stormy beginning affects the particles flying through it is crucial, because it changes how we interpret the data from these high-energy experiments.

For decades, physicists have studied how "hard probes"—specifically heavy quarks and jets, which are sprays of particles—travel through the resulting hot plasma. These probes act like messengers, carrying information about the medium they traverse. However, a significant gap in our understanding has been the very first moments of the collision, the glasma stage. Most previous studies simply ignored this early phase, assuming the probes only began interacting once the hot plasma had formed. This simplification might have been hiding important details about how these particles lose energy and change direction. Dana Avramescu's doctoral research at the University of Jyväskylä tackles this missing piece, investigating exactly how the turbulent glasma fields influence the journey of these hard probes before they even reach the hot plasma.

The research uses powerful computer simulations to model the glasma as a complex, evolving field of color forces. They then sent virtual heavy quarks and jets through this simulated environment to see how they would react. The results were striking. The study found that the glasma is far more aggressive than previously thought. As these particles move through the glasma, they experience a massive and rapid change in their momentum, far greater than what they would encounter later in the hot plasma. This "momentum broadening" is not uniform; it is highly directional. The particles are pushed much harder in the direction of the collision than they are sideways, creating a distinct anisotropy. The strength of this effect is so intense that the transport coefficients, which measure how easily particles move through the medium, are significantly larger in the glasma than in the established hot plasma.

One of the most compelling findings concerns pairs of heavy quarks produced back-to-back in the initial collision. In a calm environment, these pairs would fly apart in opposite directions, maintaining a straight line. However, the simulations showed that the glasma fields act like a violent wind, deflecting these pairs and scrambling their alignment. The angle between them becomes decorrelated very quickly, within a tiny fraction of a second. This suggests that the glasma leaves a unique fingerprint on the final state of these particles. While the hot plasma also scrambles these pairs, the glasma does so with a different signature, offering a potential way for experimentalists to distinguish the early storm from the later fireball. The research indicates that measuring the angular correlation of heavy quark pairs could provide a direct window into this fleeting, pre-equilibrium stage.

The study also addressed a subtle but critical technical challenge: how to define momentum in a system governed by complex quantum rules. The researchers had to carefully distinguish between the physical momentum of a particle and the mathematical "canonical" momentum used in calculations, which can be distorted by the choice of coordinate system. By applying a specific mathematical adjustment known as the Coulomb gauge, they were able to remove these artificial distortions. This allowed them to confirm that their classical simulations, which treat particles as tiny billiard balls, produce results that align perfectly with more complex quantum calculations. This agreement is vital because it validates the use of simpler models to study these incredibly fast and dense environments.

Ultimately, this work does not claim to have solved the entire puzzle of heavy-ion collisions, but it has illuminated a dark corner of the timeline. The simulations show that the glasma is not a passive backdrop but an active participant that significantly alters the trajectory and energy of hard probes. While the effect on the overall energy loss of a single particle is moderate compared to other factors, the impact on the directional correlation of particle pairs is substantial. By proving that the glasma leaves a measurable mark, the research provides a new tool for physicists. It suggests that by looking closely at how heavy quark pairs are scattered, we can finally see the ghost of the glasma, the turbulent first breath of the universe's most extreme matter, before it settles into the hot plasma we have studied for so long.

Technical Summary: Transport of Hard Probes in the Glasma

Problem Statement
Relativistic heavy-ion collisions at RHIC and LHC produce a Quark-Gluon Plasma (QGP) that thermalizes from an initial state of strong classical gluon fields known as the "glasma." Hard probes, specifically jets and heavy quarks, are generated in the initial scatterings and traverse the medium from its earliest moments. Historically, phenomenological studies of these probes have neglected the glasma stage, assuming interactions begin only once the QGP is formed. This thesis addresses the gap in understanding how hard probes interact with these pre-equilibrium color fields. The central questions are: How significantly do glasma fields alter the transport of jets and heavy quarks? What are the resulting signatures on experimental observables? And how can one consistently describe this interaction using both classical and quantum frameworks?

Methodology
The thesis employs a multi-faceted approach combining effective field theory, classical numerical simulations, and quantum evolution techniques:

Glasma Generation: The background fields are formulated using the Color Glass Condensate (CGC) effective theory. The initial conditions are derived from the McLerran-Venugopalan (MV) model, where colliding nuclei are treated as sheets of color charge. The classical Yang-Mills (CYM) equations are solved numerically on a real-time lattice in Milne coordinates to generate the boost-invariant glasma fields, characterized by strong longitudinal electric and magnetic flux tubes.
Classical Transport (Articles I–III): Hard probes are modeled as classical colored test particles obeying Wong's equations. A Colored Particle-In-Cell (CPIC) method is developed to couple these particles to the lattice gauge fields. The framework includes a rigorous treatment of SU(3) classical color charges, ensuring they satisfy the correct Casimir invariants and group theory properties to match the quantum limit.
Quantum Transport (Articles IV–V): To address the limitations of the classical approximation, the thesis investigates the distinction between kinetic and canonical momentum. It utilizes the time-dependent Basis Light-Front Quantization (tBLFQ) technique to evolve a high-energy quark state in the classical glasma background. This approach uses the light-front Hamiltonian formalism, expanding the state in a basis of free eigenstates and truncating the Fock space to the single-quark sector ( $|q\rangle$ ).
Gauge Fixing: A systematic analysis of gauge invariance is performed. The thesis demonstrates that while kinetic momentum broadening is gauge-invariant, canonical momentum broadening is gauge-dependent. It establishes that imposing the transverse Coulomb gauge at the initial time significantly reduces gauge artifacts and numerical errors, particularly for eikonal trajectories.

Key Contributions and Results

Transport Coefficients: The study calculates the jet quenching parameter ( $\hat{q}$ ) and the heavy quark momentum diffusion coefficient ( $\kappa$ ) in the glasma. Both coefficients are found to be significantly larger than in the thermalized QGP and exhibit strong anisotropy, with longitudinal broadening exceeding transverse broadening at early times. The coefficients show a sharp peak at very early proper times ( $\tau \sim 0.04$ fm/c) before decaying as the fields dilute.
Heavy Flavor Phenomenology:
- Angular Decorrelation: The glasma induces a rapid and significant decorrelation of back-to-back heavy quark pairs ( $c\bar{c}$ and $b\bar{b}$ ) in azimuthal angle. This decorrelation width ( $\sigma_{\Delta\phi}$ ) scales with the saturation scale $Q_s$ and decreases with increasing initial transverse momentum. The effect is comparable to that induced by the QGP, suggesting that $D\bar{D}$ angular correlations could serve as a measurable signature of the glasma stage.
- Nuclear Modification Factor ( $R_{AA}$ ): The glasma causes a migration of heavy quarks in transverse momentum space, suppressing $R_{AA}$ at low $p_T$ and enhancing it at high $p_T$ . However, the thesis finds this effect to be moderate compared to the suppression caused by nuclear parton distribution functions (nPDFs).
Classical-Quantum Correspondence:
- Momentum Definitions: The thesis clarifies that comparing classical and quantum calculations requires distinguishing between kinetic momentum (physical, gauge-invariant) and canonical momentum (gauge-dependent).
- Validation: The quantum calculation of momentum broadening using tBLFQ yields results consistent with the classical CPIC estimates. This agreement validates the classical framework for momentum broadening in the glasma and lays the groundwork for including quantum radiation effects in future studies.
Casimir Scaling: The study confirms that in the limiting cases (static and eikonal), momentum broadening exhibits Casimir scaling, where the ratio of broadening between adjoint and fundamental representations matches the ratio of their quadratic Casimir invariants. For general dynamical trajectories, deviations from exact scaling are observed.

Significance and Claims
The thesis establishes a systematic framework for describing the transport of hard probes within the glasma stage, while acknowledging that connecting this transport to the subsequent QGP phase remains an open problem requiring future work. Its primary significance lies in:

Quantifying the Pre-Equilibrium Impact: It provides concrete estimates showing that the glasma stage cannot be ignored, as it imparts substantial momentum broadening and decorrelation to hard probes before they enter the thermal medium.
Methodological Bridge: By demonstrating the agreement between classical Wong's equations and quantum light-front evolution (in the absence of radiation), the work validates the use of classical transport for momentum broadening while providing a foundation for extending the framework to include quantum radiation effects in future studies.
Phenomenological Signatures: It identifies azimuthal decorrelation of heavy-flavor pairs as a potentially unique observable sensitive to the glasma stage, distinct from the bulk medium effects.
Gauge Artifacts: It highlights the critical importance of gauge fixing (specifically Coulomb gauge) in numerical simulations to ensure the accuracy of both classical and quantum comparisons, particularly for canonical momentum and gauge potential evolution.

The work concludes that while the glasma modifies observables like $R_{AA}$ , its most distinct signature may be found in differential correlations. The thesis acknowledges that a fully consistent description requires coupling these initial-stage effects to kinetic theory and hydrodynamics, and extending the quantum framework to include the $|qg\rangle$ Fock sector to model medium-induced radiation.

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