arxiv: 2605.12791 · v1 · submitted 2026-05-12 · ✦ hep-ph · hep-th· nucl-th

Recognition: unknown

Jet Momentum Broadening in Viscous QCD Matter: A Moment Expansion Approach

Isabella Danhoni , Nicki Mullins , Jorge Noronha

Authors on Pith no claims yet

Pith reviewed 2026-05-14 19:55 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th

keywords jet momentum broadeningviscous QCD mattermoment expansionshear-stress tensoreffective kinetic theoryheavy-ion collisions14-moment approximationjet quenching

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The pith

The leading near-equilibrium contribution to the jet broadening tensor is controlled by the medium shear-stress tensor in the 14-moment approximation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies a moment expansion to the medium distribution function in QCD effective kinetic theory to describe jet momentum broadening away from equilibrium. It calculates the leading viscous correction to the spatial jet broadening tensor and shows that this correction is set by the shear-stress tensor of the surrounding medium. This creates an explicit link that lets viscous hydrodynamic codes translate local shear fields into direction-dependent adjustments to how jets lose momentum. Readers care because it turns abstract transport coefficients into quantities that can be inserted directly into event-by-event simulations of the quark-gluon plasma.

Core claim

Out-of-equilibrium jet momentum broadening in QCD effective kinetic theory is formulated through a moment expansion of the medium distribution function. The leading near-equilibrium contribution to the spatial jet broadening tensor qhat^ij is computed explicitly within the 14-moment approximation and shown to be controlled by the medium shear-stress tensor. This supplies a direct map from kinetic theory to event-by-event viscous hydrodynamic simulations that converts local shear-stress fields into anisotropic corrections to jet broadening.

What carries the argument

Moment expansion of the medium distribution function in the 14-moment approximation, which isolates the shear-stress tensor contribution to the jet broadening tensor qhat^ij.

If this is right

Local shear-stress fields from viscous hydrodynamics translate directly into anisotropic corrections to jet momentum broadening.
Event-by-event simulations of heavy-ion collisions can incorporate these viscous effects on jets without additional free parameters.
The jet broadening tensor is no longer an independent input but is determined by the same shear tensor that governs hydrodynamic flow.
Near-equilibrium jet transport receives explicit viscous corrections that respect the symmetries of the underlying kinetic theory.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same moment-expansion technique could be applied to other jet observables such as energy loss or angular broadening once the corresponding integrals are evaluated.
Combining the derived correction with realistic hydrodynamic profiles from specific collision events would produce testable predictions for jet anisotropy patterns.
Far-from-equilibrium regimes would require higher moments, so the current result sets a baseline for when the shear-stress term ceases to dominate.

Load-bearing premise

The 14-moment truncation of the distribution function captures the leading viscous correction to jet broadening near equilibrium.

What would settle it

A calculation of qhat^ij that retains higher moments or solves the full Boltzmann equation and finds the shear-stress term is not the dominant viscous correction.

Figures

Figures reproduced from arXiv: 2605.12791 by Isabella Danhoni, Jorge Noronha, Nicki Mullins.

**Figure 1.** Figure 1: shows the coefficients α, β, and γ as functions of Λ⊥, for two values of the screening mass in a purely gluonic medium with screened t-channel exchange. The same formalism applies to quark scattering, with the corresponding changes in statistical factors, color degeneracies, and scattering matrix elements. We find that increasing mD suppresses the magnitude of all three coefficients over the range shown… view at source ↗

read the original abstract

We formulate out-of-equilibrium jet momentum broadening in QCD effective kinetic theory through a moment expansion of the medium distribution function, a method traditionally used to derive relativistic viscous hydrodynamics from kinetic theory. We explicitly compute the leading near-equilibrium contribution to the spatial jet broadening tensor $\hat q^{ij}$ within the 14-moment approximation, and show that it is controlled by the medium shear-stress tensor. This provides a direct map from QCD effective kinetic theory to event-by-event viscous hydrodynamic simulations, converting local shear-stress fields into anisotropic corrections to jet broadening in heavy-ion collisions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives an explicit leading viscous correction to jet broadening in terms of shear stress via the 14-moment expansion, but the truncation needs checks for the hard-probe integral.

read the letter

The punchline here is that the authors have worked out an explicit leading-order viscous correction to the spatial jet broadening tensor, expressed in terms of the medium's shear-stress tensor, all within the 14-moment approximation of QCD effective kinetic theory. They take the moment expansion technique that's standard for getting viscous hydro from kinetic theory and apply it to the jet momentum broadening. The result is a direct way to turn local shear fields from hydro simulations into corrections for how jets broaden in the medium. That's the new piece, and it looks like it could be plugged into event-by-event calculations without introducing new parameters. The derivation starts from the effective kinetic theory and uses the standard 14 moments, so the setup is solid on that front. It avoids circularity and gives something falsifiable in principle. The soft spot is the truncation. Because the broadening tensor comes from integrating the collision kernel against the jet momentum, the correction depends on the distribution function at scales set by the jet. The 14 moments are chosen to match hydrodynamics for soft modes, but it's not automatic that they get the leading viscous term right for this integral. Higher moments could contribute at the same order, and the paper would need to show why they don't or provide some cross-checks against known limits or full solutions. This is for researchers in heavy-ion collisions who model jet quenching and want to include realistic viscous effects from hydro. Someone who knows the moment method and the basics of jet broadening will get the most from it and can judge if the approximation holds. I would send this to peer review. The idea is worth the time to check the integrals and any supporting calculations they have.

Referee Report

2 major / 2 minor

Summary. The paper formulates jet momentum broadening in QCD effective kinetic theory via a moment expansion of the medium distribution function. It computes the leading near-equilibrium viscous correction to the spatial jet broadening tensor qhat^ij in the 14-moment approximation and shows that this correction is controlled by the medium shear-stress tensor, thereby providing a direct map from effective kinetic theory to event-by-event viscous hydrodynamic simulations for anisotropic jet broadening in heavy-ion collisions.

Significance. If the central result holds, the work is significant because it supplies an explicit, parameter-free bridge between the microscopic QCD effective kinetic theory description of the medium and the macroscopic viscous hydrodynamics employed in heavy-ion collision modeling. This enables incorporation of local shear-stress fields into jet quenching calculations without full kinetic simulations, which is a practical advance for phenomenology. The explicit computation of the leading correction within the standard 14-moment framework is a clear technical strength.

major comments (2)

[moment-expansion derivation] The central claim that the leading O(viscous) correction to qhat^ij is fully captured by the shear-stress tensor within the 14-moment truncation (as stated in the abstract and derived in the moment-expansion section) rests on the assumption that omitted higher moments do not contribute at the same order in the hard-probe collision integral. No explicit estimate or bound on residual higher-moment contributions is provided, even though the integral samples medium momenta up to the jet scale where the 14-moment closure (optimized for soft modes) may be insufficient.
[results and discussion] No validation against the equilibrium limit (where the viscous correction must vanish) or against known isotropic qhat results is reported. Such a check would be required to confirm that the truncation does not introduce uncontrolled artifacts into the claimed shear-stress dependence.

minor comments (2)

[introduction] The notation for the jet broadening tensor qhat^ij and its relation to the standard qhat parameter should be introduced more explicitly in the introduction for clarity.
[abstract] The abstract would benefit from a brief statement of the validity range of the near-equilibrium expansion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. We appreciate the recognition of the significance of providing a bridge between effective kinetic theory and viscous hydrodynamics. Below, we address each major comment in detail.

read point-by-point responses

Referee: [moment-expansion derivation] The central claim that the leading O(viscous) correction to qhat^ij is fully captured by the shear-stress tensor within the 14-moment truncation (as stated in the abstract and derived in the moment-expansion section) rests on the assumption that omitted higher moments do not contribute at the same order in the hard-probe collision integral. No explicit estimate or bound on residual higher-moment contributions is provided, even though the integral samples medium momenta up to the jet scale where the 14-moment closure (optimized for soft modes) may be insufficient.

Authors: We agree that providing an explicit estimate or bound on the contributions from higher moments would further solidify the validity of the 14-moment truncation in this context. While the 14-moment approximation is designed to capture the leading dissipative effects through the shear-stress tensor in the gradient expansion, and higher moments are expected to contribute at higher orders, the hard-probe nature of the jet broadening integral does warrant careful consideration. In the revised manuscript, we will include an additional paragraph in the moment-expansion section discussing the potential residual contributions, including a rough estimate based on the scaling of higher moments with the Knudsen number and the jet momentum scale. This will demonstrate that such contributions remain suppressed for the relevant parameter regime in heavy-ion collisions. revision: yes
Referee: [results and discussion] No validation against the equilibrium limit (where the viscous correction must vanish) or against known isotropic qhat results is reported. Such a check would be required to confirm that the truncation does not introduce uncontrolled artifacts into the claimed shear-stress dependence.

Authors: This is a valid point, and we apologize for the oversight. In the revised manuscript, we will add explicit checks in the results section: first, verifying that when the shear-stress tensor is set to zero (equilibrium limit), the correction to qhat^ij vanishes as required; second, comparing our leading-order isotropic qhat to established results from equilibrium QCD kinetic theory calculations in the literature. These validations will confirm the consistency of our truncation scheme and ensure no artifacts are introduced. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation follows directly from kinetic theory moment expansion

full rationale

The paper derives the leading viscous correction to qhat^ij by inserting the standard 14-moment expansion of the medium distribution (from QCD effective kinetic theory) into the jet broadening integral. This produces an explicit map to the shear-stress tensor without any reduction to fitted parameters, self-definitions, or load-bearing self-citations. The 14-moment truncation is an input approximation whose validity is an external question of correctness, not a circularity issue in the algebra itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of QCD effective kinetic theory for the medium and the sufficiency of the 14-moment truncation for the leading viscous correction.

axioms (2)

domain assumption QCD effective kinetic theory accurately describes the medium distribution function near equilibrium
Standard starting point for deriving viscous hydrodynamics from kinetic theory in the quark-gluon plasma context.
domain assumption The 14-moment approximation captures the leading near-equilibrium correction to jet broadening
The paper invokes the same truncation used in standard derivations of relativistic viscous hydrodynamics.

pith-pipeline@v0.9.0 · 5390 in / 1290 out tokens · 43046 ms · 2026-05-14T19:55:30.427878+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages · 42 internal anchors

[1]

Review of Jet Measurements in Heavy Ion Collisions

M. Connors, C. Nattrass, R. Reed, and S. Salur, Jet mea- surements in heavy ion physics, Rev. Mod. Phys.90, 025005 (2018), arXiv:1705.01974 [nucl-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[2]

Gyulassy and M

M. Gyulassy and M. Plumer, Jet Quenching in Dense Matter, Phys. Lett. B243, 432 (1990)

work page 1990
[3]

Energy loss in perturbative QCD

R. Baier, D. Schiff, and B. G. Zakharov, Energy loss in perturbative QCD, Ann. Rev. Nucl. Part. Sci.50, 37 (2000), arXiv:hep-ph/0002198

work page internal anchor Pith review Pith/arXiv arXiv 2000
[4]

Jet Quenching and Radiative Energy Loss in Dense Nuclear Matter

M. Gyulassy, I. Vitev, X.-N. Wang, and B.-W. Zhang, Jet quenching and radiative energy loss in dense nuclear matter, inQuark Gluon Plasma 3, edited by R. C. Hwa and X.-N. Wang (World Scientific, 2004) pp. 123–191, arXiv:nucl-th/0302077

work page internal anchor Pith review Pith/arXiv arXiv 2004
[5]

Jet quenching in high-energy heavy-ion collisions

G.-Y. Qin and X.-N. Wang, Jet quenching in high-energy heavy-ion collisions, Int. J. Mod. Phys. E24, 1530014 (2015), arXiv:1511.00790 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[6]

Jet physics in heavy-ion collisions

Y. Mehtar-Tani, J. G. Milhano, and K. Tywoniuk, Jet physics in heavy-ion collisions, Int. J. Mod. Phys. A28, 1340013 (2013), arXiv:1302.2579 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[7]

U. A. Wiedemann, Jet quenching in heavy ion collisions, inRelativistic Heavy Ion Physics, Landolt-B¨ ornstein, Vol. 23, edited by R. Stock (Springer, 2010) pp. 521–562, arXiv:0908.2306 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[8]

Approach to equilibrium in weakly coupled nonabelian plasmas

A. Kurkela and E. Lu, Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas, Phys. Rev. Lett. 113, 182301 (2014), arXiv:1405.6318 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[9]

A. Ipp, D. I. M¨ uller, and D. Schuh, Jet momentum broad- ening in the pre-equilibrium Glasma, Phys. Lett. B810, 135810 (2020), arXiv:2009.14206 [hep-ph]

work page arXiv 2020
[10]

Jet quenching as a probe of the initial stages in heavy-ion collisions

C. Andres, N. Armesto, H. Niemi, R. Paatelainen, and C. A. Salgado, Jet quenching as a probe of the initial stages in heavy-ion collisions, Phys. Lett. B803, 135318 (2020), arXiv:1902.03231 [hep-ph]

work page arXiv 2020
[11]

Andres, F

C. Andres, F. Dominguez, A. V. Sadofyev, and C. A. Sal- gado, Jet broadening in flowing matter: Resummation, Phys. Rev. D106, 074023 (2022), arXiv:2207.07141 [hep- ph]

work page arXiv 2022
[12]

Fluctuating Glasma initial conditions and flow in heavy ion collisions

B. Schenke, P. Tribedy, and R. Venugopalan, Fluctuating Glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett.108, 252301 (2012), arXiv:1202.6646 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[13]

How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions?

H. Niemi and G. S. Denicol, How large is the Knudsen number reached in fluid dynamical simulations of ultra- relativistic heavy ion collisions?, (2014), arXiv:1404.7327 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[14]

Sensitivity of flow harmonics to sub-nucleon scale fluctuations in heavy ion collisions

J. Noronha-Hostler, J. Noronha, and M. Gyulassy, Sensi- tivity of flow harmonics to subnucleon scale fluctuations in heavy ion collisions, Phys. Rev. C93, 024909 (2016), arXiv:1508.02455 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[15]

Jet quenching and medium response in high-energy heavy-ion collisions: a review

S. Cao and X.-N. Wang, Jet quenching and medium response in high-energy heavy-ion collisions: a review, Rept. Prog. Phys.84, 024301 (2021), arXiv:2002.04028 [hep-ph]

work page arXiv 2021
[16]

Mehtar-Tani,The Physics of Jet Quenching in Perturbative QCD,2509.26394

Y. Mehtar-Tani, The Physics of Jet Quenching in Per- turbative QCD, (2025), arXiv:2509.26394 [hep-ph]

work page arXiv 2025
[17]

A simple sum rule for the thermal gluon spectral function and applications

P. Aurenche, F. Gelis, and H. Zaraket, A Simple sum rule for the thermal gluon spectral function and applications, JHEP05, 043, arXiv:hep-ph/0204146. 6

work page internal anchor Pith review Pith/arXiv arXiv
[18]

P. B. Arnold and W. Xiao, High-energy jet quenching in weakly-coupled quark-gluon plasmas, Phys. Rev. D78, 125008 (2008), arXiv:0810.1026 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[19]

O(g) plasma effects in jet quenching

S. Caron-Huot, O(g) plasma effects in jet quenching, Phys. Rev. D79, 065039 (2009), arXiv:0811.1603 [hep- ph]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[20]

Gauge invariant definition of the jet quenching parameter

M. Benzke, N. Brambilla, M. A. Escobedo, and A. Vairo, Gauge invariant definition of the jet quenching parame- ter, JHEP02, 129, arXiv:1208.4253 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv
[21]

Momentum Broadening in Weakly Coupled Quark-Gluon Plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma)

F. D’Eramo, M. Lekaveckas, H. Liu, and K. Rajagopal, Momentum Broadening in Weakly Coupled Quark- Gluon Plasma (with a view to finding the quasiparti- cles within liquid quark-gluon plasma), JHEP05, 031, arXiv:1211.1922 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 1922
[22]

Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions

A. Kurkela, A. Mazeliauskas, J.-F. Paquet, S. Schlicht- ing, and D. Teaney, Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions, Phys. Rev. C99, 034910 (2019), arXiv:1805.00961 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[23]

Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas

J. Ghiglieri and D. Teaney, Parton energy loss and mo- mentum broadening at NLO in high temperature QCD plasmas, Int. J. Mod. Phys. E24, 1530013 (2015), arXiv:1502.03730 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[24]

Schlichting and I

S. Schlichting and I. Soudi, Medium-induced fragmenta- tion and equilibration of highly energetic partons, JHEP 07, 077, arXiv:2008.04928 [hep-ph]

work page arXiv 2008
[26]

Boguslavski, A

K. Boguslavski, A. Kurkela, T. Lappi, F. Lindenbauer, and J. Peuron, Jet momentum broadening during initial stages in heavy-ion collisions, Phys. Lett. B850, 138525 (2024), arXiv:2303.12595 [hep-ph]

work page arXiv 2024
[27]

Barata, K

J. Barata, K. Boguslavski, F. Lindenbauer, and A. V. Sadofyev, Jet quenching in out-of-equilibrium QCD mat- ter, (2025), arXiv:2511.07519 [hep-ph]

work page arXiv 2025
[28]

H. Liu, K. Rajagopal, and U. A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett.97, 182301 (2006), arXiv:hep-ph/0605178

work page internal anchor Pith review Pith/arXiv arXiv 2006
[29]

Gauge/String Duality, Hot QCD and Heavy Ion Collisions

J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. Achim Wiedemann,Gauge/String Duality, Hot QCD and Heavy Ion Collisions(Cambridge University Press, 2014) arXiv:1101.0618 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[30]

Grefa, M

J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Transport co- efficients of the quark-gluon plasma at the critical point and across the first-order line, Phys. Rev. D106, 034024 (2022), arXiv:2203.00139 [nucl-th]

work page arXiv 2022
[31]

M. R. Khan, A. Nascimento, Y. Yang, J. Grefa, M. Hip- pert, J. Noronha, C. Ratti, and R. Rougemont, Uncer- tainty quantification of holographic transport and en- ergy loss for the hot and baryon-dense QGP, (2026), arXiv:2603.20482 [nucl-th]

work page arXiv 2026
[32]

Transverse Momentum Broadening and the Jet Quenching Parameter, Redux

F. D’Eramo, H. Liu, and K. Rajagopal, Transverse Mo- mentum Broadening and the Jet Quenching Parameter, Redux, Phys. Rev. D84, 065015 (2011), arXiv:1006.1367 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[33]

Towards understanding thermal jet quenching via lattice simulations

M. Laine and A. Rothkopf, Towards understanding ther- mal jet quenching via lattice simulations, PoSLA T- TICE2013, 174 (2014), arXiv:1310.2413 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[34]

A lattice study of the jet quenching parameter

M. Panero, K. Rummukainen, and A. Sch¨ afer, Lattice Study of the Jet Quenching Parameter, Phys. Rev. Lett. 112, 162001 (2014), arXiv:1307.5850 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[35]

Kumar, A

A. Kumar, A. Majumder, and J. H. Weber, Jet transport coefficient qˆ in lattice QCD, Phys. Rev. D106, 034505 (2022), arXiv:2010.14463 [hep-lat]

work page arXiv 2022
[36]

K. M. Burkeet al.(JET), Extracting the jet transport co- efficient from jet quenching in high-energy heavy-ion col- lisions, Phys. Rev. C90, 014909 (2014), arXiv:1312.5003 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[37]

J. Xu, J. Liao, and M. Gyulassy, Consistency of Per- fect Fluidity and Jet Quenching in semi-Quark-Gluon Monopole Plasmas, Chin. Phys. Lett.32, 092501 (2015), arXiv:1411.3673 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[38]

Caoet al.(JETSCAPE), Determining the jet trans- port coefficient qˆ from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys

S. Caoet al.(JETSCAPE), Determining the jet trans- port coefficient qˆ from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C104, 024905 (2021), arXiv:2102.11337 [nucl-th]

work page arXiv 2021
[39]

C. A. Salgado and U. A. Wiedemann, Calculating quenching weights, Phys. Rev. D68, 014008 (2003), arXiv:hep-ph/0302184

work page internal anchor Pith review Pith/arXiv arXiv 2003
[40]

QCD Shear Viscosity at (almost) NLO

J. Ghiglieri, G. D. Moore, and D. Teaney, QCD Shear Viscosity at (almost) NLO, JHEP03, 179, arXiv:1802.09535 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv
[41]

Boguslavski, A

K. Boguslavski, A. Kurkela, T. Lappi, F. Lindenbauer, and J. Peuron, Heavy quark diffusion coefficient in heavy- ion collisions via kinetic theory, Phys. Rev. D109, 014025 (2024), arXiv:2303.12520 [hep-ph]

work page arXiv 2024
[42]

Barata, S

J. Barata, S. Hauksson, X. Mayo L´ opez, and A. V. Sadofyev, Jet quenching in the glasma phase: Medium- induced radiation, Phys. Rev. D110, 094055 (2024), arXiv:2406.07615 [hep-ph]

work page arXiv 2024
[43]

Danhoni, N

I. Danhoni, N. Mullins, and J. Noronha, Covariant diffu- sion tensor for jet momentum broadening out of equilib- rium, (2026), arXiv:2603.00844, arXiv:2603.00844 [hep- ph]

work page arXiv 2026
[44]

Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

P. Romatschke and U. Romatschke,Relativistic Fluid Dynamics In and Out of Equilibrium, Cambridge Mono- graphs on Mathematical Physics (Cambridge University Press, 2019) arXiv:1712.05815 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[45]

Parton energy loss in glasma

P. Aurenche and B. G. Zakharov, Parton energy loss in glasma, Phys. Lett. B718, 937 (2013), arXiv:1205.6462 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[46]

M. E. Carrington, A. Czajka, and S. Mrowczynski, Trans- port of hard probes through glasma, Phys. Rev. C105, 064910 (2022), arXiv:2202.00357 [nucl-th]

work page arXiv 2022
[47]

Some Features of the Glasma

T. Lappi and L. McLerran, Some features of the glasma, Nucl. Phys. A772, 200 (2006), arXiv:hep-ph/0602189

work page internal anchor Pith review Pith/arXiv arXiv 2006
[48]

Barata, M

J. Barata, M. V. Kuzmin, X. Mayo L´ opez, A. V. Sado- fyev, and C. A. Salgado, Directional dead-cone effect in QCD matter, (2025), arXiv:2512.11951 [hep-ph]

work page arXiv 2025
[49]

Barata, X

J. Barata, X. Du, and A. V. Sadofyev, Nonlocal high-pt transport in anisotropic QCD matter, Phys. Rev. D111, 114017 (2025), arXiv:2502.13205 [nucl-th]

work page arXiv 2025
[50]

Jet Drift and Collective Flow in Heavy-Ion Collisions

L. Antiporda, J. Bahder, H. Rahman, and M. D. Sievert, Jet drift and collective flow in heavy-ion collisions, Phys. Rev. D105, 054025 (2022), arXiv:2110.03590 [hep-ph]

work page arXiv 2022
[51]

Barata, J

J. Barata, J. G. Milhano, and A. V. Sadofyev, Picturing QCD jets in anisotropic matter: from jet shapes to en- ergy energy correlators, Eur. Phys. J. C84, 174 (2024), arXiv:2308.01294 [hep-ph]

work page arXiv 2024
[52]

Jet quenching in a strongly coupled anisotropic plasma

M. Chernicoff, D. Fernandez, D. Mateos, and D. Tran- canelli, Jet quenching in a strongly coupled anisotropic plasma, JHEP08, 041, arXiv:1203.0561 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv
[53]

M. V. Kuzmin, X. Mayo L´ opez, J. Reiten, and A. V. Sadofyev, Jet quenching in anisotropic flowing matter, 7 Phys. Rev. D109, 014036 (2024), arXiv:2309.00683 [hep- ph]

work page arXiv 2024
[54]

Barata, A

J. Barata, A. V. Sadofyev, and C. A. Salgado, Jet broad- ening in dense inhomogeneous matter, Phys. Rev. D105, 114010 (2022), arXiv:2202.08847 [hep-ph]

work page arXiv 2022
[55]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01, 030, arXiv:hep-ph/0209353

work page internal anchor Pith review Pith/arXiv arXiv
[56]

Boguslavski, A

K. Boguslavski, A. Kurkela, T. Lappi, F. Linden- bauer, and J. Peuron, Jet quenching parameter in QCD kinetic theory, Phys. Rev. D110, 034019 (2024), arXiv:2312.00447 [hep-ph]

work page arXiv 2024
[57]

G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D85, 114047 (2012), [Erratum: Phys.Rev.D 91, 039902 (2015)], arXiv:1202.4551 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[58]

G. S. Rocha, D. Wagner, G. S. Denicol, J. Noronha, and D. H. Rischke, Theories of Relativistic Dissipative Fluid Dynamics, Entropy26, 189 (2024), arXiv:2311.15063 [nucl-th]

work page arXiv 2024
[59]

Israel and J

W. Israel and J. M. Stewart, Transient relativistic ther- modynamics and kinetic theory, Annals Phys.118, 341 (1979)

work page 1979
[60]

G. S. Denicol, E. Moln´ ar, H. Niemi, and D. H. Rischke, Derivation of fluid dynamics from kinetic theory with the 14-moment approximation, Eur. Phys. J. A48, 170 (2012), arXiv:1206.1554 [nucl-th]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[61]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP05, 051, arXiv:hep-ph/0302165

work page internal anchor Pith review Pith/arXiv arXiv
[62]

Jet-Medium Interactions at NLO in a Weakly-Coupled Quark-Gluon Plasma

J. Ghiglieri, G. D. Moore, and D. Teaney, Jet-Medium Interactions at NLO in a Weakly-Coupled Quark-Gluon Plasma, JHEP03, 095, arXiv:1509.07773 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv
[63]

Chemical Equilibration in Weakly Coupled QCD

A. Kurkela and A. Mazeliauskas, Chemical equilibration in weakly coupled QCD, Phys. Rev. D99, 054018 (2019), arXiv:1811.03068 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[64]

M. C. Abraao York, A. Kurkela, E. Lu, and G. D. Moore, UV cascade in classical Yang-Mills theory via kinetic the- ory, Phys. Rev. D89, 074036 (2014), arXiv:1401.3751 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[65]

D. H. Rischke, The Quark gluon plasma in equilib- rium, Prog. Part. Nucl. Phys.52, 197 (2004), arXiv:nucl- th/0305030

work page arXiv 2004
[66]

M. E. Peskin and D. V. Schroeder,An Introduction to quantum field theory(Addison-Wesley, Reading, USA, 1995)

work page 1995
[67]

P. B. Arnold, G. D. Moore, and L. G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Lead- ing log results, JHEP11, 001, arXiv:hep-ph/0010177

work page internal anchor Pith review Pith/arXiv arXiv
[68]

Analytic solution of the Boltzmann equation in an expanding system

D. Bazow, G. S. Denicol, U. Heinz, M. Martinez, and J. Noronha, Analytic solution of the Boltzmann equation in an expanding system, Phys. Rev. Lett.116, 022301 (2016), arXiv:1507.07834 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[69]

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lema\^itre-Robertson-Walker spacetime

D. Bazow, G. S. Denicol, U. Heinz, M. Martinez, and J. Noronha, Nonlinear dynamics from the rela- tivistic Boltzmann equation in the Friedmann-Lemaˆ ıtre- Robertson-Walker spacetime, Phys. Rev. D94, 125006 (2016), arXiv:1607.05245 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[70]

Mullins, G

N. Mullins, G. S. Denicol, and J. Noronha, Far-from- equilibrium kinetic dynamics ofλϕ4 theory in an ex- panding universe, Phys. Rev. D106, 056024 (2022), arXiv:2207.07786 [hep-ph]

work page arXiv 2022
[71]

Israel and J

W. Israel and J. M. Stewart, Transient relativistic ther- modynamics and kinetic theory, Annals of Physics118, 341 (1979)

work page 1979
[72]

Udey and W

N. Udey and W. Israel, General relativistic radiative transfer: The 14-moment approximation, Monthly No- tices of the Royal Astronomical Society199, 1137 (1982)

work page 1982
[73]

P. B. Arnold, C. Dogan, and G. D. Moore, The Bulk Viscosity of High-Temperature QCD, Phys. Rev. D74, 085021 (2006), arXiv:hep-ph/0608012

work page internal anchor Pith review Pith/arXiv arXiv 2006
[74]

Radiative energy loss and v2 spectra for viscous hydrodynamics

K. Dusling, G. D. Moore, and D. Teaney, Radiative en- ergy loss and v(2) spectra for viscous hydrodynamics, Phys. Rev. C81, 034907 (2010), arXiv:0909.0754 [nucl- th]. 8 Supplemental Material In this Supplementary Material, we present details of the analytical calculation of the covariant jet momen- tum–broadening tensor in equilibrium and its leading non-...

work page internal anchor Pith review Pith/arXiv arXiv 2010