Pith. sign in

REVIEW 3 major objections 5 minor 34 references

Higher angular moments of the jet wake encode non-hydrodynamic modes that hydrodynamics cannot produce.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-30 19:12 UTC pith:54IUU3OD

load-bearing objection Clean multipole filter that makes ℓ≥3 jet-wake moments a genuine hydro-null observable at k→0; the brick idealization is the real soft spot, not the algebra. the 3 major comments →

arxiv 2607.26851 v1 pith:54IUU3OD submitted 2026-07-29 hep-ph nucl-th

Imaging non-hydrodynamic modes with jet wakes

Aleksi Kurkela , Ian Moult , Alexander Soloviev , Urs Achim Wiedemann This is my paper
classification hep-ph nucl-th
keywords jet wakenon-hydrodynamic modesquark-gluon plasmakinetic theoryangular momentsheavy-ion collisionsshear viscositymedium response
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Heavy-ion collisions have firmly established that the quark-gluon plasma behaves like a fluid, but they have not yet isolated the non-hydrodynamic excitations that every relativistic plasma must also support. This paper argues that the angular pattern of the negative jet wake—the depletion of energy flow opposite a hard jet—supplies that missing probe. In the long-wavelength limit, hydrodynamics can only shape the lowest angular moments (ℓ ≤ 2) of the late-time energy flux; moments with ℓ ≥ 3 live entirely outside hydrodynamics and track the relaxation spectrum of the medium’s collision operator. A general kinetic-theory relation maps those higher moments onto the eigenmodes of the collision kernel. Across several simple models that share the same shear viscosity, the higher harmonics differ, showing that the wake image is sensitive to microscopic equilibration physics. The practical upshot is a call for precision measurements of the ℓ ≥ 3 moments of the negative jet wake: a nonzero signal would be unambiguous evidence that the plasma is more than a hydrodynamic fluid.

Core claim

In the long-wavelength (k → 0) limit, hydrodynamics contributes only to the angular moments ℓ ≤ 2 of the detector image of the jet wake, while moments with ℓ ≥ 3 lie entirely outside the hydrodynamic sector and directly encode the non-hydrodynamic relaxation spectrum of the collision operator. Any nonzero measured ℓ ≥ 3 harmonic would therefore constitute unambiguous evidence that the quark-gluon plasma supports non-hydrodynamic modes.

What carries the argument

The spectral decomposition of the linearized collision operator in angular-momentum channels, combined with the detector moments of the late-time energy flux: δE_ℓ = Σ_n τ_nℓ (1 − e^(−t*/τ_nℓ)) ⟨I_ℓ|ϕ_nℓ⟩⟨ϕ_nℓ|S⟩. This identity relates each angular moment of the jet-wake image to the relaxation times of the corresponding eigenmodes.

Load-bearing premise

That a simplified static medium, instantaneous freeze-out, and an idealized eikonal jet source still leave the higher angular moments free of fake signals from realistic flow, jet evolution, or hadronization.

What would settle it

A precision measurement of the charged-particle or energy-flow distribution in the negative jet wake that extracts a statistically significant nonzero ℓ = 3 (or higher) spherical-harmonic moment after subtraction of the proton-proton baseline; vanishing higher moments at the precision needed to resolve the models would falsify the claim that the wake is an exclusive non-hydro probe under present conditions.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Any confirmed nonzero ℓ ≥ 3 moment of the negative jet wake is direct evidence that the QGP is not a pure hydrodynamic fluid.
  • The hierarchy and magnitudes of higher moments become spectroscopic data on the relaxation spectrum of the medium’s collision operator.
  • Precision jet-wake angular analyses should be prioritized alongside traditional soft-flow measurements of transport coefficients.
  • Theoretical modeling must move from static-brick kinetics to expanding media and realistic jet sources to turn qualitative signals into quantitative mode spectroscopy.

Where Pith is reading between the lines

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

  • Energy-energy correlators built on the same late-time energy flux may offer a cleaner experimental path to the same higher multipoles with reduced hadronization systematics.
  • If expanding-flow backgrounds can be shown not to feed ℓ ≥ 3, small-system collisions could become complementary laboratories for the same non-hydro modes.
  • A null result at current precision would still leave open whether the modes exist but are diluted by realistic jet evolution, motivating differential measurements tagged on jet energy loss or path length.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper argues that the angular structure of the jet-induced medium response (the jet wake) provides a spectroscopic probe of non-hydrodynamic modes in the QGP. Within linearized kinetic theory, the late-time, spatially integrated energy-flux image is expanded in spherical harmonics. Conserved (hydrodynamic) modes live only in ℓ=0,1; the shear channel sits in ℓ=2; and at k→0 the hydrodynamic constitutive relations contain no content for ℓ≥3. Consequently the detector moments δE_ℓ for ℓ≥3 are sourced only by the non-conserved eigenmodes of the collision operator (Eqs. 14–17, 21). Three simple collision kernels (RTA, angular diffusion, leading-log QCD) with a common η/s produce visibly different higher moments, motivating precision measurements of the negative wake. An eikonal two-gluon-exchange source and an idealized static brick with instantaneous freeze-out are used throughout.

Significance. If the exclusivity of ℓ≥3 survives under more realistic conditions, the work supplies a qualitatively new, conservation-law-based observable that is null in pure hydrodynamics and nonzero once non-hydrodynamic relaxation is present—something the field has lacked. The spectral decomposition relating detector moments to the relaxation times τ_nℓ of the collision operator (Eq. 17) is clean, model-independent within kinetic theory, and immediately falsifiable: a statistically significant ℓ=3 (or higher) moment in the wake would be direct evidence that the QGP is not a pure hydrodynamic fluid. The transparent analytic link between wake multipoles and the collision spectrum, and the explicit comparison of three kernels at fixed η/s, are genuine strengths.

major comments (3)
  1. [Summary and outlook; Eqs. 2–3, 10–11, 17–22] The central experimental claim—that any nonzero ℓ≥3 harmonic is unambiguous evidence of non-hydrodynamic modes (Summary; also Eqs. 17–22)—rests on the detector image being the pure k→0 spatial integral of a static homogeneous brick with instantaneous freeze-out at fixed t* (Eqs. 2–3, 10–11). On a realistic expanding freeze-out hypersurface the map from fluid variables to asymptotic energy flux mixes multipoles: a pure hydrodynamic velocity or temperature perturbation acquires higher spherical harmonics through the curved surface, Cooper–Frye boost factors, and residual gradients. The Outlook asserts that such effects “do not affect the qualitative conclusion that harmonics with ℓ≥3 vanish identically in hydrodynamics,” but supplies no estimate of leakage. If hydro-only evolution already feeds O(few-percent) strength into ℓ=3—comparable to the kinetic signals in Fig. 2—the “unambiguous” c
  2. [Fig. 2 and surrounding text] Fig. 2 overlays kinetic-theory energy-flow moments δE_ℓ on CMS charged-particle yields versus Δφ. The paper notes that these are “strictly speaking, different experimental observables,” yet still uses the comparison to gauge the precision needed to establish a nonzero ℓ=3 mode. Because the conversion from energy flux to charged-particle flow is species- and p_T-dependent and is not modeled, the figure cannot support quantitative statements about experimental reach. Either a consistent particle-level folding or a clear separation of the two observables (with the data comparison demoted to purely qualitative) is needed.
  3. [Jet wake and its image; Appendix] The source is an eikonal color charge with free-gluon two-gluon exchange, retained only in the k→0 sector (Appendix, Eqs. 27–66). Realistic jets broaden, split, and partially thermalize; the medium has longitudinal and transverse flow. While the Outlook correctly states that these change amplitudes, the paper does not show that they preserve the angular selection rules that keep hydro out of ℓ≥3. A short argument or numerical check that the leading hydrodynamic response of a dynamical jet still projects only onto ℓ≤2 at the detector would strengthen the load-bearing claim.
minor comments (5)
  1. [The detector state] Notation for the detector state ⟨I_ℓm| mixes bra-ket and integral definitions; a single consistent convention would help (Eqs. 11–12).
  2. [Eq. (17)] In Eq. (17) the factor τ_nℓ(1−e^{−t*/τ_nℓ}) is written without the overall source strength; the normalization convention relative to Eq. (15) should be stated explicitly.
  3. [Fig. 1] Fig. 1 caption fixes η/s=0.12 and v_jet=1 but does not state the value of T t* used for the curves; adding it would aid reproducibility.
  4. [References] The CMS reference is given as Phys. Lett. B 874, 140120 (2026); confirm the bibliographic details once the published version is final.
  5. [Throughout] Typographical: “quasi-normal” is hyphenated inconsistently; “leading-log” vs “leading-logarithmic” likewise.

Circularity Check

0 steps flagged

No significant circularity: exclusivity of ℓ≥3 follows from conservation laws and k o0 hydro structure, not from fitted inputs or self-citation chains.

full rationale

The load-bearing claim—that in the spatially integrated (k o0) limit hydrodynamics populates only detector moments ℓ≤2 while ℓ≥3 are purely non-hydrodynamic—is derived from the null space of the collision operator (energy/momentum conservation), rotational invariance of the eigenbasis, and the fact that viscous constitutive relations stop at the quadrupole. Equations (17)–(22) make this explicit: 〈I00〉 and 〈I1m〉 coincide with the conserved modes, so non-conserved projections vanish by orthogonality; ℓ=2 mixes with shear; ℓ>2 lies outside hydro. Model comparisons fix a common η/s and compute distinct higher multipoles from different relaxation spectra; that is illustration, not a fit renamed as prediction. The Fig. 2 source normalization is fixed to the measured ℓ=1 mode only for a qualitative overlay of experimental precision, not to manufacture an ℓ≥3 signal claimed as first-principles output. Self-citations supply background on kinetic theory and non-hydro modes but are not used as uniqueness theorems that force the result. The derivation is self-contained against its stated idealizations; limitations (static brick, instantaneous freeze-out) are correctness/robustness issues, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 1 invented entities

The central exclusivity claim rests on standard kinetic theory plus several domain idealizations (static brick, k→0 detector image, instantaneous freeze-out, linearized eikonal source). Illustrative plots add a few hand-set scales. No new physical entities are postulated; ‘detector state’ is a projection, not a new degree of freedom. The hydro-null property of ℓ≥3 is a theorem inside those assumptions, not an extra axiom.

free parameters (4)
  • η/s = 0.12
    Common shear viscosity fixed by hand so RTA, diffusion, and LLQCD share the same hydrodynamic response while non-hydro spectra differ.
  • T t* = 4.5
    Dimensionless freeze-out time chosen for Fig. 2 illustration of wake multipoles.
  • jet source overall normalization = fixed to CMS ℓ=1
    Fixed so the model PbPb−pp difference reproduces the measured ℓ=1 mode in the CMS comparison (Fig. 2 caption).
  • τ_R = τ_D (in units of 1/μ_A) = ≈5×0.461/μ_A
    Relaxation-time and diffusion scales set equal via η/s = T τ_R/5 ≈ 0.12 to match hydrodynamic sector across models.
axioms (7)
  • domain assumption Linearized Boltzmann kinetics with a self-adjoint collision operator fully describes the relevant medium response, including hydro and non-hydro modes.
    Sourced Boltzmann equation and spectral decomposition (Eqs. 1, 5, 8); standard for weakly coupled QGP but not derived from QCD here.
  • domain assumption The calorimetric detector image is the spatially integrated distribution (k→0 only), so only zero-momentum eigenmodes enter δE_ℓm.
    Eqs. 2–3, 10–11; load-bearing for dropping finite-k hydro structure.
  • domain assumption Instantaneous freeze-out at time t* with negligible post-freeze-out interactions for the energy flux.
    Stated under Sourced Boltzmann equation / Jet wake and its image; converts kinetic modes into Eq. 17 weights τ(1−e^{−t*/τ}).
  • domain assumption At k→0, relativistic hydrodynamics supports angular structure only through ℓ≤2 (conserved energy/momentum and shear stress).
    Used to declare ℓ>2 purely non-hydrodynamic (Non-hydrodynamic sector, ℓ>2); standard constitutive counting, assumed without finite-k or nonlinear corrections.
  • domain assumption Jet source is an eikonal color charge with leading color-singlet response from two-gluon exchange (Fokker–Planck force-force correlator), evaluated with free gluon propagators.
    Appendix construction following Neufeld et al.; IR Coulomb log left implicit; controls ⟨ϕ|S⟩ multipole weights.
  • ad hoc to paper Background medium is a static, homogeneous equilibrium brick with azimuthal symmetry about the jet axis until freeze-out.
    Idealized geometry in Jet wake and its image; excludes expansion and flow that real collisions have.
  • standard math Spectral theorem / orthonormal eigenbasis of a self-adjoint collision kernel in the kinetic inner product.
    Eqs. 8–9; underpins the mode sum for δE_ℓ.
invented entities (1)
  • detector state |I_ℓm⟩ independent evidence
    purpose: Projects the phase-space perturbation onto spherical-harmonic moments of the late-time energy flux so δE_ℓm = ⟨I_ℓm|δf⟩.
    Convenient bra in the kinetic inner product (Eqs. 11–12); not a new physical field or particle, only a measurement functional.

pith-pipeline@v1.2.0-daily-grok45 · 16952 in / 4302 out tokens · 97166 ms · 2026-07-30T19:12:18.495948+00:00 · methodology

0 comments
read the original abstract

While studies of ultra-relativistic heavy-ion collisions have established that the quark--gluon plasma exhibits hydrodynamic behavior, direct signatures of non-hydrodynamic modes have remained elusive, and no observable is known to be exclusively sensitive to them. Here, we show that the angular structure of the jet wake provides such a probe. In the long-wavelength limit, hydrodynamics contributes only to the lowest angular moments of the detector image of the jet wake, while higher moments directly encode microscopic non-equilibrium dynamics. The jet wake thus serves as a spectroscopic probe of the medium's non-hydrodynamic sector. We develop a general kinetic-theory framework relating the angular moments of the late-time energy flux generated by a jet to the relaxation spectrum of the collision operator. In all models considered, non-hydrodynamic modes leave distinct imprints on the higher angular moments. Our results motivate precision measurements of the higher angular moments of the negative jet wake.

Figures

Figures reproduced from arXiv: 2607.26851 by Aleksi Kurkela, Alexander Soloviev, Ian Moult, Urs Achim Wiedemann.

Figure 1
Figure 1. Figure 1: FIG. 1. The evolution of the jet-wake image, defined in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Negative jet-wake yield extracted from the kinetic theories defined in Eqs. (23–25), compared with the CMS measure [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Diagram of the two-gluon exchange process giving [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

34 extracted references · 30 linked inside Pith

  1. [1]

    Baier, P

    R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, JHEP04, 100, arXiv:0712.2451 [hep-th]

    Pith/arXiv arXiv

  2. [2]

    P. K. Kovtun and A. O. Starinets, Phys. Rev. D72, 086009 (2005), arXiv:hep-th/0506184

    Pith/arXiv arXiv 2005

  3. [3]

    Romatschke, Eur

    P. Romatschke, Eur. Phys. J. C76, 352 (2016), arXiv:1512.02641 [hep-th]

    Pith/arXiv arXiv 2016

  4. [4]

    Hong and D

    J. Hong and D. Teaney, Phys. Rev. C82, 044908 (2010), arXiv:1003.0699 [nucl-th]

    Pith/arXiv arXiv 2010

  5. [5]

    Kurkela and U

    A. Kurkela and U. A. Wiedemann, Eur. Phys. J. C79, 776 (2019), arXiv:1712.04376 [hep-ph]

    Pith/arXiv arXiv 2019

  6. [6]

    G. D. Moore, JHEP05, 084, arXiv:1803.00736 [hep-ph]

    Pith/arXiv arXiv

  7. [7]

    Grozdanov, P

    S. Grozdanov, P. K. Kovtun, A. O. Starinets, and P. Tadi´ c, JHEP11, 097, arXiv:1904.12862 [hep-th]

    Pith/arXiv arXiv 1904

  8. [8]

    Ochsenfeld and S

    S. Ochsenfeld and S. Schlichting, JHEP09, 186, arXiv:2308.04491 [hep-th]

    Pith/arXiv arXiv

  9. [9]

    Grozdanov and A

    S. Grozdanov and A. Soloviev, arXiv:2501.00099 [hep- th]

    Pith/arXiv arXiv

  10. [10]

    Kurkela, U

    A. Kurkela, U. A. Wiedemann, and B. Wu, Eur. Phys. J. C79, 965 (2019), arXiv:1905.05139 [hep-ph]

    Pith/arXiv arXiv 2019

  11. [11]

    V. E. Ambrus, S. Schlichting, and C. Werthmann, Phys. Rev. D105, 014031 (2022), arXiv:2109.03290 [hep-ph]

    Pith/arXiv arXiv 2022

  12. [12]

    V. E. Ambrus, S. Schlichting, and C. Werthmann, Phys. Rev. D107, 094013 (2023), arXiv:2211.14379 [hep-ph]

    Pith/arXiv arXiv 2023

  13. [13]

    M. P. Heller and M. Spalinski, Phys. Rev. Lett.115, 072501 (2015), arXiv:1503.07514 [hep-th]

    Pith/arXiv arXiv 2015

  14. [14]

    M. P. Heller, A. Kurkela, M. Spali´ nski, and V. Svensson, Phys. Rev. D97, 091503 (2018), arXiv:1609.04803 [nucl- th]

    Pith/arXiv arXiv 2018

  15. [15]

    J. E. Bernhard, J. S. Moreland, and S. A. Bass, Nature Phys.15, 1113 (2019)

    2019

  16. [16]

    G. Nijs, W. van der Schee, U. G¨ ursoy, and R. Snellings, Phys. Rev. Lett.126, 202301 (2021), arXiv:2010.15130 [nucl-th]

    Pith/arXiv arXiv 2021

  17. [17]

    Casalderrey-Solana, E

    J. Casalderrey-Solana, E. V. Shuryak, and D. Teaney, J. Phys. Conf. Ser.27, 22 (2005), arXiv:hep-ph/0411315

    Pith/arXiv arXiv 2005

  18. [18]

    R. B. Neufeld, B. Muller, and J. Ruppert, Phys. Rev. C 78, 041901 (2008), arXiv:0802.2254 [hep-ph]

    Pith/arXiv arXiv 2008

  19. [19]

    W. Chen, Z. Yang, Y. He, W. Ke, L. Pang, and X.-N. Wang, Phys. Rev. Lett.127, 082301 (2021), arXiv:2101.05422 [hep-ph]

    Pith/arXiv arXiv 2021

  20. [20]

    Chekhovskyet al.(CMS), Phys

    V. Chekhovskyet al.(CMS), Phys. Lett. B874, 140120 (2026), arXiv:2507.09307 [nucl-ex]

    arXiv 2026

  21. [21]

    Jeon and L

    S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996), arXiv:hep-ph/9512263

    Pith/arXiv arXiv 1996

  22. [22]

    P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP01, 030, arXiv:hep-ph/0209353

    Pith/arXiv arXiv

  23. [23]

    Moult and H

    I. Moult and H. X. Zhu, arXiv:2506.09119 [hep-ph]

    Pith/arXiv arXiv

  24. [24]

    P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP05, 051, arXiv:hep-ph/0302165

    Pith/arXiv arXiv

  25. [25]

    P. B. Arnold, G. D. Moore, and L. G. Yaffe, JHEP11, 001, arXiv:hep-ph/0010177

    Pith/arXiv arXiv

  26. [26]

    M. P. Heller and V. Svensson, Phys. Rev. D98, 054016 (2018), arXiv:1802.08225 [nucl-th]

    Pith/arXiv arXiv 2018

  27. [27]

    Bajec, S

    M. Bajec, S. Grozdanov, and A. Soloviev, JHEP08, 065, arXiv:2403.17769 [hep-th]

    Pith/arXiv arXiv

  28. [28]

    Bajec and A

    M. Bajec and A. Soloviev, Phys. Rev. D112, 065002 (2025), arXiv:2506.15531 [hep-th]

    Pith/arXiv arXiv 2025

  29. [29]

    Landau, Phys

    L. Landau, Phys. Z. Sowjetunion10, 154 (1936)

    1936

  30. [30]

    M. N. Rosenbluth, W. M. MacDonald, and D. L. Judd, Phys. Rev.107, 1 (1957). Vµ jet eikonal jet sourcej µ jet vµ p medium quasiparticle K −K Fa i Fa j FIG. 3. Diagram of the two-gluon exchange process giving rise to the source discussed in the Appendix

    1957

  31. [31]

    Z. Yang, T. Luo, W. Chen, L.-G. Pang, and X.-N. Wang, Phys. Rev. Lett.130, 052301 (2023), arXiv:2203.03683 [hep-ph]

    Pith/arXiv arXiv 2023

  32. [32]

    Casalderrey-Solana, D

    J. Casalderrey-Solana, D. C. Gulhan, J. G. Milhano, D. Pablos, and K. Rajagopal, JHEP10, 019, [Erratum: JHEP 09, 175 (2015)], arXiv:1405.3864 [hep-ph]

    Pith/arXiv arXiv 2015

  33. [33]

    D. M. Hofman and J. Maldacena, JHEP05, 012, arXiv:0803.1467 [hep-th]

    Pith/arXiv arXiv

  34. [34]

    1 + v2 jet −1 vjet L # ,(53) S∥,1 =π

    G. D. Moore and D. Teaney, Phys. Rev. C71, 064904 (2005), arXiv:hep-ph/0412346. Appendix: Details on the jet source In this appendix we review the construction of the jet-induced source term introduced in Ref. [18], adapted to the framework used in this work. A hard color charge propagating through the medium at fixed velocity vjet generates chromoelectri...

    Pith/arXiv arXiv 2005