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REVIEW 3 major objections 5 minor 4 cited by

Jets that pass through the pre-equilibrium stage of a heavy-ion collision retain a durable memory of that early phase: the emission pattern is fixed by what happens to the transport coefficients at early times, and late-time changes barely

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2026-08-03 23:02 UTC pith:MLIYE44W

load-bearing objection First realistic computation of medium-induced gluon spectra in pre-equilibrium EKT backgrounds, with a central non-convergence claim that is plausible but not yet asymptotic-proof. the 3 major comments →

arxiv 2511.07519 v2 pith:MLIYE44W submitted 2025-11-10 hep-ph hep-exnucl-th

Jet quenching in out-of-equilibrium QCD matter

Jo\~ao Barata , Kirill Boguslavski , Florian Lindenbauer , Andrey V. Sadofyev This is my paper
classification hep-ph hep-exnucl-th
keywords jet quenchingpre-equilibrium QCD matterimproved opacity expansionmedium-induced gluon radiationjet substructureeffective kinetic theorybottom-up thermalizationBjorken expansion
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.

The paper asks whether the brief, out-of-equilibrium phase of quark–gluon matter—before it hydrodynamizes—can be seen in the jets that plough through it. It computes the medium-induced gluon radiation spectrum using the Improved Opacity Expansion, fed with the jet transport parameter and screening mass extracted from QCD kinetic theory simulations. For three bulk scenarios (initially under- and over-occupied isotropic plasmas, and a Bjorken-expanding plasma), it compares the nonequilibrium spectrum with thermally matched and static-brick references. The central finding for the expanding case is that altering the transport coefficients at early times changes the emission pattern substantially, while altering them at late times does almost nothing; the ratio observables never converge to unity as the medium length grows. A sympathetic reader would conclude that jets carry a durable imprint of pre-equilibrium dynamics, and that the standard practice of switching on jet quenching only after about one fermi misses part of the signal.

Core claim

For a Bjorken-expanding QCD medium, the soft medium-induced gluon spectrum is controlled by the early-time behavior of the bare jet quenching parameter q̂0(τ) and screening mass μ∗(τ). Modifying them before τ ≲ 50/Qs changes the emission pattern substantially; modifying them later leaves it nearly unchanged. Hence the ratio observables χρ and χm, defined against an equilibrium medium of the same energy density, stay visibly different from unity even as L → ∞ and the medium dilutes. The paper's central claim is that the early out-of-equilibrium evolution fixes the radiation pattern and identical late-time evolution cannot erase it — while in isotropic non-expanding systems the ratios do conve

What carries the argument

The load-bearing object is the pair of time-dependent transport parameters (q̂0(τ), μ∗(τ)) that determine the effective scattering potential v(x, τ) = (q̂0/4) x² log(1/(x² μ∗²)) at leading logarithmic accuracy. q̂0 and μ∗ are extracted from QCD kinetic theory by parametrizing the jet quenching parameter as q̂(Λ⊥) = a(τ) log(Λ⊥/Qs) + b(τ), identifying q̂0 = a/2, and converting b via μ∗² = (1/4) exp(−b/q̂0 + 2γE − 2). These feed the Improved Opacity Expansion, which expands the emission kernel around the harmonic-oscillator potential and treats the logarithmic tail as a correction, thereby including both multiple soft and single hard momentum exchanges. Self-consistency scales Qb and Qr fix th

Load-bearing premise

The calculation assumes that the jet quenching parameter extracted from kinetic theory for the highly anisotropic, expanding plasma can be converted into the two parameters of the isotropic scattering potential using the equilibrium perturbative tail of the collision kernel; if that conversion is off, the screening mass—and with it the radiation spectrum—is off.

What would settle it

Take the same Bjorken-expanding background and compute the radiation spectrum with μ∗(τ) replaced by its thermal value while keeping the nonequilibrium q̂0(τ); if the ratios χm and χρ then converge to unity, the memory effect is an artifact of the μ∗ mapping rather than of early-time transport. Alternatively, extract v(x) directly from the anisotropic kinetic-theory background and compare its short-distance coefficient with the formula used in the paper; any substantial mismatch would invalidate the q̂0, μ∗ input.

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

If this is right

  • Pre-equilibrium dynamics must be included in phenomenological jet-quenching calculations; switching q̂ on only after about 1 fm/c discards the very stage that dominates the spectrum for expanding matter.
  • Jet-substructure observables such as jet shapes and the location or maximum of the gluon spectrum can serve as tomographic probes of the thermalization history, not just of the equilibrated plasma.
  • A static-brick medium is a poor surrogate for an expanding out-of-equilibrium medium; energy-density-matched thermal references reproduce the nonequilibrium spectrum more closely.
  • The main conclusion already appears at the harmonic-oscillator (leading) order of the Improved Opacity Expansion, so the memory effect is not an artifact of the subleading hard-scattering correction.
  • In small collision systems where the medium never fully hydrodynamizes, the same framework applies and the early-stage imprint may be even more pronounced.

Where Pith is reading between the lines

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

  • Beyond the paper: if the non-convergence survives a full anisotropic treatment, measured jet substructure in heavy-ion and small-system collisions could discriminate between different early-time models of the initial Glasma state.
  • Beyond the paper: because late-time changes are subleading, coarse-grained models that reproduce only the early-time q̂0 and μ∗ evolution—for instance a weighted 'early dose'—may suffice for many observables; the static-brick matching used here could be improved by matching to that early dose rather than the full evolution.
  • Beyond the paper: the quantitative size of the memory effect hinges on the μ∗ conversion formula; a direct extraction of v(x) from the expanding anisotropic background would show whether the offset in the ratio observables is over- or under-estimated.

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 presents the first computation of medium-induced gluon emission from jets using the Improved Opacity Expansion (IOE) with time-dependent transport coefficients q̂0(τ) and μ∗(τ) extracted from QCD effective kinetic theory (EKT) simulations. Three bulk scenarios are studied: isotropic under- and over-occupied plasmas, and a longitudinally expanding system initialized from a CGC-like distribution and evolving through the bottom-up thermalization stages. The emission spectra are compared with thermally matched and static-brick baselines through two ratio observables, χρ (jet shape ratio) and χm (peak-spectrum ratio). For the isotropic systems these ratios approach unity at large path length L, as expected. The main claim is that for the Bjorken-expanding system the ratios do not converge to unity as L→∞, implying that early pre-equilibrium stages leave a persistent, sizable imprint on jet substructure. The paper also compares IOE with the harmonic-oscillator approximation and performs a numerical experiment modifying early- versus late-time inputs to support the interpretation.

Significance. If the central claim is correct, the result is significant: it would establish jets as sensitive tomographic probes of the pre-equilibrium phase and challenge the common phenomenological practice of switching on jet quenching only after ~1 fm/c. The paper has clear strengths: the numerical evaluation is careful, with continuum extrapolations and publicly available code; the conclusion is checked for consistency between the HO and IOE truncations; and the modification experiment in Fig. 8 directly addresses the role of early times. The potential impact is high, provided the two load-bearing assumptions—the validity of the μ∗ mapping and the reality of the L→∞ non-convergence—are properly secured.

major comments (3)
  1. [§III.B, Figs. 5–6; §III.D] The central claim that χm and χρ do not tend to 1 as L→∞ is inferred from finite-L runs and from the early/late modification experiment. For the Bjorken thermal tail, Eq. (33a) with Tε∝τ^{−1/3} gives q̂0(τ)∝1/τ, so the integrated broadening in Eq. (12) grows as Q_b^2∼∫dτ q̂0∼log L. A finite early-time difference is then an additive constant inside this logarithm, and a generic smooth dependence of the spectrum on accumulated transport would drive χi→1 as L→∞. The present runs are not manifestly asymptotic: for λ=10 the largest length is QsL=33.5, while for λ=0.5 the largest run has QsL=3×10^4 but remains below the relaxation scale τR. Fig. 8 only modifies inputs up to τ≈150/Qs. Please supply a quantitative asymptotic argument, a scan reaching the late-time thermally matched regime, or an analytic leading-log estimate; without this, 'persistent deviations' is an extrapolation rather than
  2. [§II.B, Eq. (31)] The input μ∗ is obtained from the EKT fit via μ∗²=(1/4) exp[−b/q̂0+2γE−2], with q̂0=a/2, by matching the small-x expansion of the potential using the isotropic perturbative tail of Eq. (26). This is exactly the step that converts the EKT output (a,b) into the time-dependent μ∗ entering q̂r and q̂b in Eqs. (12)–(13). For the anisotropic, expanding backgrounds (initial condition Eq. (19), ξ=10), the EKT simulations use an isotropic/Debye screening prescription, and Eq. (31) is not validated against a direct extraction of v(x) for these settings; the text only cites [84] for the short-distance behavior. Please validate Eq. (31) on the EKT backgrounds or demonstrate that a reasonable uncertainty in μ∗ does not alter the qualitative non-convergence of χi.
  3. [§II.A, footnote 1; §III.C] The quantitative use of the IOE truncated at NLO for time-dependent out-of-equilibrium matter rests on the assertion that leading+NLO already capture the qualitative features of the exact spectrum. Footnote 1 acknowledges that this was originally established for the energy spectrum, and the extension to jet-shape and peak ratios is stated as an expectation. The HO/IOE comparison in §III.C is a useful internal consistency check, but both truncations share the same expansion variable and do not provide a convergence estimate. I ask for a more explicit validity statement—e.g., where the matching scales Qr and Qb have real solutions and where δv in Eq. (5) remains small across the time profile in Fig. 2—or, failing that, a sensitivity study varying the truncation in a simplified time-dependent potential.
minor comments (5)
  1. [§III.A] The text says the jet-shape ratio χρ is 'shown in the central column of Fig. 3'; the correct cross-reference is Fig. 4.
  2. [§III.B] The text states that the triangle marker denotes 'where the pressure anisotropy drops below 2', but the preceding definition is PL/PT=0.5. This wording is confusing and should be corrected.
  3. [§II.A and Appendix A] The notation for the initial time is inconsistent: t0 is used in Eqs. (1)–(14), while the numerical section switches to tmin/tmax. Please unify the notation.
  4. [§II.B] The discussion of the thermal limit for b notes that Table III of [22] parametrizes the cutoff with log(Λ⊥/mD) instead of log(Λ⊥/Qs). This is important and should be stated more prominently, since the reader needs to know which b is actually used in Eq. (22).
  5. [Appendix A] The continuum extrapolation uses exponent n=4 for Simpson's rule but n=1 for the double integral. The text says the four discretizations agree, but a sentence explaining why the n=1 term is nevertheless controlled would be helpful.

Circularity Check

0 steps flagged

No significant circularity: the χi ratios are emergent outputs of independent EKT inputs and the IOE calculation.

full rationale

Walk of the derivation chain: the medium parameters q̂0(τ) and μ*(τ) are not chosen to reproduce the radiation observables; they are derived from EKT simulations via the cutoff-dependence of q̂(Λ⊥) (Eqs. 20–31), with the equilibrium baseline set by Landau matching to the same energy density (Eq. 32). The radiation spectrum is then a direct numerical evaluation of the IOE expressions (Eqs. 7 and 14), and χρ, χm are output ratios (Eqs. 40–41). No quantity in those ratios is fitted to them, and no equation defines the input in terms of the output. The author-overlapping citations are to previous EKT-q̂ extraction papers [21,22], the short-distance potential identification [84], and the IOE framework [52–57]; these supply inputs or a method, not the conclusion. The assertion that χi do not approach unity is a numerical finding at finite L, and the claim that early times dominate is supported by an independent modification experiment (Fig. 8). Whether Eq. (31) is quantitatively accurate for anisotropic backgrounds or whether the largest L is sufficiently asymptotic are correctness risks, not circularity. Therefore no circular step can be exhibited.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central computation is layered: the IOE radiation kernel (Eqs. 6–14) is fixed by prior literature [52–56], the medium inputs q̂0(t) and μ∗(t) are fixed by EKT simulation outputs imported from [21,22] and converted by the [84] bridge, and the comparison baselines are fixed by Landau matching and the static-brick matching procedure (Eqs. 35–36). Free parameters are limited to the EKT initial-condition choices and coupling values; no parameter is tuned to reproduce the final spectra or the χ ratios. The main imported physical assumptions — Gaussian/local correlations, the leading-log form of v(x), and NLO-truncation validity — are the standard BDMPS-Z/IOE package, with the truncation validity the least tested for time-dependent media. No new entities are postulated.

free parameters (5)
  • Under-occupied initial-condition amplitude A (Eq. 17) = set via Q = 50 T
    Defines the starting gluon distribution for the isotropic under-occupied EKT run; controls how far below equilibrium the system starts and hence the early-time q̂0(t), μ∗(t) inputs.
  • Over-occupied attractor initial-condition parameters (Eq. 18) = coefficients 0.22, 2; exponents −4/7, −1/7; Q t0 = 1e−4
    Parametrize the non-thermal attractor initial distribution; sets the early overshoot of q̂0 above its thermal value, which drives the χ > 1 behavior.
  • Expanding/CGC initial-condition parameters (Eq. 19) = ξ = 10, A(ξ) = 5.24171, ⟨p_T⟩ = 1.8 Qs
    Glasma-inspired initial distribution for the Bjorken runs; determines the early overoccupied stage and the entire bottom-up evolution feeding q̂0(t), μ∗(t).
  • Thermal-limit coefficient b for λ ≥ 2 = Table III of ref. [22]
    Used instead of the analytic weak-coupling b of Eq. (33b) to ensure the numerically extracted q̂ approaches the correct thermal limit; a same-group calibration that shapes the thermal-matched baseline.
  • Coupling choices = λ ∈ {0.5, 2, 10}
    Three representative couplings; λ = 10 is the phenomenologically relevant case and the one used for the early-time modification study of Fig. 8.
axioms (6)
  • domain assumption The background fields follow Gaussian statistics with correlations local in space and time and diagonal in color (Eq. 2).
    Standard BDMPS-Z starting point; needed for the P and K evolution equations; not derived for the EKT medium.
  • domain assumption The medium is transversely homogeneous and effectively isotropic; plasma instabilities and anisotropy effects are neglected on both the EKT and IOE sides.
    Explicitly stated in Sec. II and Sec. II.C as a consistency requirement; known to be an approximation in the early, highly anisotropic stage of the Bjorken evolution.
  • domain assumption Leading-log potential v(x) ≈ (q̂0/4) x² log(1/(x² μ∗²)) with an isotropic 1/q⁴ hard tail, keeping only the x² term in the small-x expansion (Eqs. 3, 25–30).
    Underlies the identification of q̂0 and μ∗ from the EKT-extracted a and b; the truncation at order x² and the isotropic tail are uncontrolled for the anisotropic runs.
  • ad hoc to paper The IOE truncation at NLO captures the qualitative features of the exact spectrum for time-dependent media.
    Footnote 1: the extension from the energy spectrum to other observables is 'generally expected'; the paper does not benchmark the NLO-truncated spectrum against exact kernel solutions for the EKT time profiles.
  • domain assumption Weak-coupling AMY kinetic theory describes the pre-equilibrium bulk matter (Eq. 16 with elastic and inelastic kernels).
    Underlies the EKT background; valid at weak coupling and used here up to λ = 10, where its applicability is an extrapolation.
  • ad hoc to paper The mapping from cutoff-dependent q̂(Λ⊥) = a log(Λ⊥/Qs) + b to the BDMPS-Z potential parameters, q̂0 = a/2 and Eq. (31), is valid.
    Taken from same-group preprint [84] (arXiv:2509.03868); converts EKT output into the (q̂0, μ∗) inputs of the IOE; not re-derived or validated here for the anisotropic expanding backgrounds.

pith-pipeline@v1.3.0-alltime-deepseek · 23886 in / 22866 out tokens · 231897 ms · 2026-08-03T23:02:05.626273+00:00 · methodology

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read the original abstract

We present the first study of jet substructure modifications during the bottom-up evolution that describes the early stages of heavy-ion collisions. To this end, we study the bremsstrahlung radiation rate of soft gluons from a hard parton propagating through out-of-equilibrium QCD matter. The gluon spectrum is computed within the Improved Opacity Expansion, which accounts for both multiple soft and single hard momentum exchanges between the hard probe and the medium. The background evolution is obtained from effective kinetic theory simulations that determine the jet quenching parameter, which in turn controls the radiation rate. We compute the radiation rate for initially under- and over-occupied systems, as well as for an expanding system undergoing hydrodynamization, which typically represents the initial stages of heavy-ion collisions. The results for these dynamical backgrounds are compared to static and thermally matched scenarios, allowing to gauge the importance of bulk expansion in the evolution of the jet cascade. Our findings show that the early stages of the bulk matter evolution in heavy-ion collisions leave a sizable imprint on the radiation pattern inside jets. These results establish a basis for incorporating pre-equilibrium dynamics into realistic descriptions of jet quenching and hard-probe evolution.

Figures

Figures reproduced from arXiv: 2511.07519 by Andrey V. Sadofyev, Florian Lindenbauer, Jo\~ao Barata, Kirill Boguslavski.

Figure 1
Figure 1. Figure 1: FIG. 1. Summary of results for single gluon production in the presence of an out-of-equilibrium QCD medium, as illustrated on [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time evolution of the bare jet quenching parameter [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Illustration of the jet shape at leading order in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Medium-induced gluon spectrum (left column) for an isotropic initially underoccupied (top row) and overoccupied [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Medium-induced gluon spectrum (left column) for Bjorken expanding matter. In the middle and right columns, we [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The ratio quantities [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Differences in the spectra obtained using the IOE and [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Time evolution of [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

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