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arxiv: 2509.10743 · v3 · submitted 2025-09-12 · ✦ hep-ph · nucl-ex· nucl-th

Glauber quark and gluon contributions to quark energy loss at next-to-leading order and next-to-leading twist

Amit Kumar , Gojko Vujanovic This is my paper

Pith reviewed 2026-05-18 16:53 UTC · model grok-4.3

classification ✦ hep-ph nucl-exnucl-th
keywords quark energy losshigher-twist formalismGlauber interactionsmedium-induced emissionjet quenchingheavy quark massnuclear mediumsingle scattering kernels
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The pith

An incoming quark in nuclear matter loses energy through four distinct single-scattering kernels that incorporate both Glauber quarks and gluons at next-to-leading order and twist.

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

This paper applies the higher-twist formalism at order alpha_s squared to derive the complete set of medium-induced emission kernels for a virtual quark traversing a nucleus. It includes interactions with both in-medium Glauber gluons and quarks, heavy-quark mass corrections in initial and final states, and coherence effects, while retaining the factorization procedure established in the authors' earlier photon-production study. The calculation produces explicit kernels for final states q plus gluon, gluon plus gluon, q plus qbar prime, and q plus q prime, each containing full phase factors plus first-order longitudinal and second-order transverse momentum derivatives. A sympathetic reader would care because these kernels supply the microscopic ingredients needed to compute parton energy loss rates that feed into models of jet quenching in heavy-ion collisions. If the derivation holds, the resulting expressions allow direct inclusion of quark scattering channels and mass dependence that were previously omitted or treated at lower order.

Core claim

Using the higher-twist formalism at O(alpha_s squared), the authors obtain four scattering kernels K_i for incoming quark energy loss with final states (i) q+g, (ii) g+g, (iii) q+qbar' (flavor possibly different), and (iv) q+q' (flavor possibly different). Each kernel incorporates full phase factors from all contributing diagrams, the first-order derivative in k^- and second-order derivative in k_perp within the gradient expansion, and hard transverse-momentum dependence inside the in-medium parton distribution functions and jet transport coefficients. Heavy-quark mass effects appear in both initial and final states, Glauber quark interactions are added to the gluon channels, and coherence (

What carries the argument

Higher-twist single-scattering emission kernels for medium-induced quark energy loss, extended to include Glauber quark and gluon contributions together with heavy-quark mass corrections.

If this is right

  • The four kernels supply the full set of single-scattering contributions needed to integrate for the total medium-induced energy loss of a quark.
  • Hard transverse-momentum dependence inside the in-medium PDFs and transport coefficients enters the phase space of each kernel.
  • Heavy-quark mass corrections modify both the initial virtuality and the final-state kinematics in every channel.
  • The kernels can be inserted into existing jet-quenching calculations to obtain updated suppression factors that include quark scattering.

Where Pith is reading between the lines

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

  • Consistency between these energy-loss kernels and the authors' prior photon-production results would test whether the same factorization applies uniformly across electromagnetic and strong probes.
  • The explicit inclusion of q + q' and q + qbar' channels opens a route to flavor-dependent energy loss that could be contrasted with gluon-only calculations in Monte Carlo simulations.
  • The second-order transverse-momentum derivatives suggest a natural next step of examining the corresponding diffusion coefficients in the transport equation for the jet.

Load-bearing premise

The factorization procedure previously used for medium-induced photon production in electron-nucleus deep-inelastic scattering continues to hold when Glauber quark interactions and heavy-quark mass effects are introduced for quark energy loss.

What would settle it

A numerical evaluation of the transverse-momentum-broadened energy-loss spectrum or the resulting nuclear modification factor for charm quarks that differs measurably from the spectrum obtained with only gluon-induced kernels at the same order.

Figures

Figures reproduced from arXiv: 2509.10743 by Amit Kumar, Gojko Vujanovic.

Figure 1
Figure 1. Figure 1: FIG. 1: Scattering diagrams with one emission and one scattering for a quark initiating jet. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: A schematic diagram of deep-inelastic scattering between an electron and a nucleon inside the nucleus. The [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Forward scattering diagrams of leading order gluon production from the quark. The cut-line (i.e., dashed [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Diagrams for scattering kernel-1. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: A forward scattering diagram in kernel-1. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Diagrams for scattering kernel-2. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Diagrams for scattering kernel-3. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Diagrams for scattering kernel-4. [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The mass dependence of [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The mass dependence of [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Interference diagrams in which the radiated gluon undergoes double-gluon scattering, contributing to [PITH_FULL_IMAGE:figures/full_fig_p032_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Scattering diagrams with gluon in-medium scattering, contributing to kernel-1. (a) Gluon scattering with [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Scattering diagrams contributing to kernel-1. (a) The right-cut gives an interference between pre-emission [PITH_FULL_IMAGE:figures/full_fig_p037_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: A forward scattering diagram contributing to kernel-1. [PITH_FULL_IMAGE:figures/full_fig_p040_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: A forward scattering diagram contributing to kernel-1. [PITH_FULL_IMAGE:figures/full_fig_p043_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: A forward scattering diagram contributing to kernel-1 with a gluon emission post two successive gluon [PITH_FULL_IMAGE:figures/full_fig_p046_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: A forward scattering diagram contributing to kernel-2. [PITH_FULL_IMAGE:figures/full_fig_p048_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: A forward scattering diagram contributing to kernel-2. [PITH_FULL_IMAGE:figures/full_fig_p050_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: An interference diagram contributing to kernel-2. The cut-line (i.e., dashed line) represents the final state. [PITH_FULL_IMAGE:figures/full_fig_p053_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: A forward scattering diagram contributing to kernel-3. [PITH_FULL_IMAGE:figures/full_fig_p055_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: A forward scattering diagram contributing to kernel-3. [PITH_FULL_IMAGE:figures/full_fig_p057_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23: A forward scattering diagram contributing to kernel-4. [PITH_FULL_IMAGE:figures/full_fig_p059_23.png] view at source ↗
read the original abstract

The higher-twist formalism is used at $O(\alpha^2_s)$ to compute all possible medium-induced single-scattering emission kernels for an incoming highly energetic and virtual quark traversing the nuclear environment. The effects of the heavy-quark mass scale are taken into account [Phys. Rev. C 94, 054902 (2016)] both in the initial state as well as in the final state, along with interactions involving both in-medium Glauber gluons and quarks [Nucl. Phys. A 793, 128 (2007)], as well as coherence effects [Phys. Rev. C 105, 024908 (2022)]. As this study is a continuation of our work on medium-induced photon production [Phys. Rev. C 112, 025204 (2025)], the general factorization procedure for $e$-$A$ deep-inelastic scattering is still used. An incoming quark energy loss in the nuclear medium yields four possible scattering kernels $K_i$ with the following final states: (i) $q+g$, (ii) $g+g$, (iii) $q+\bar{q}'$, where the quark $q$ may have a flavor different from the antiquark $\bar{q}'$, and (iv) $q+q'$, where, again, $q$ may have a flavor different from $q'$. The collisional kernels include full phase factors from all non-vanishing diagrams and complete first-order derivative in the longitudinal direction ($k^-$) as well as second-order derivative in the transverse momentum ($k_{\perp}$) gradient expansion. Furthermore, in-medium parton distribution functions and the related jet transport coefficients have a hard transverse-momentum dependence (of the emitted quark or gluon) present within the phase factor.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript applies the higher-twist formalism at O(α_s²) to compute all medium-induced single-scattering emission kernels for an incoming highly energetic virtual quark in a nuclear medium. It incorporates heavy-quark mass effects in both initial and final states, interactions with in-medium Glauber gluons and quarks, and coherence effects. Building directly on the authors' prior photon-production calculation, the work reuses the same general factorization procedure for e-A deep-inelastic scattering and derives four scattering kernels K_i corresponding to final states (i) q+g, (ii) g+g, (iii) q+ qbar', and (iv) q+q', each including full phase factors, first-order k^- derivatives, second-order k_perp gradient expansions, and hard transverse-momentum dependence in the in-medium PDFs and jet transport coefficients.

Significance. If the factorization extension is valid and the kernels are correctly derived, the results would supply a more complete set of O(α_s²) medium-induced contributions to quark energy loss, explicitly including Glauber quark scatterers and mass effects that were previously omitted. This extension is relevant for phenomenological modeling of heavy-flavor suppression and jet quenching in heavy-ion collisions, where both gluon and quark interactions in the medium matter.

major comments (1)
  1. [Factorization procedure and kernel derivation] The central claim that the general factorization procedure developed for medium-induced photon production remains valid after inserting Glauber quark interactions and heavy-quark mass terms into initial and final states is load-bearing for the derivation of all four kernels K_i. The manuscript states that the procedure is still used but does not isolate or demonstrate the steps confirming that these insertions preserve the original power counting, do not generate new leading-power contributions, and leave the first-order k^- and second-order k_perp derivative expansions intact. This verification is required to support the explicit inclusion of full phase factors and hard-p_T dependence in the kernels.
minor comments (2)
  1. The abstract and summary describe the computational framework and list the four kernels but do not present explicit analytic expressions, numerical evaluations, or cross-checks against the gluon-only limit; these should be added to allow independent verification of the results.
  2. Notation for the four kernels K_i and the in-medium PDFs/jet transport coefficients could be clarified with a summary table or explicit definitions early in the text to improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and for identifying the need for explicit verification of the factorization procedure. We address the major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Factorization procedure and kernel derivation] The central claim that the general factorization procedure developed for medium-induced photon production remains valid after inserting Glauber quark interactions and heavy-quark mass terms into initial and final states is load-bearing for the derivation of all four kernels K_i. The manuscript states that the procedure is still used but does not isolate or demonstrate the steps confirming that these insertions preserve the original power counting, do not generate new leading-power contributions, and leave the first-order k^- and second-order k_perp derivative expansions intact. This verification is required to support the explicit inclusion of full phase factors and hard-p_T dependence in the kernels.

    Authors: We agree that an explicit verification of the power counting is necessary to support the central claim. The present work extends the general factorization procedure established in our prior photon-production calculation (Phys. Rev. C 112, 025204 (2025)) by incorporating Glauber quark scatterers and heavy-quark mass terms in the initial and final states, following the higher-twist formalism of Refs. [Phys. Rev. C 94, 054902 (2016)] and [Nucl. Phys. A 793, 128 (2007)]. These insertions are introduced through the same set of diagrams and do not alter the leading-power structure: the Glauber quark contributions enter at the same twist as the gluon terms, while mass corrections appear as subleading modifications to the propagators that preserve the first-order k^- derivative and second-order k_perp gradient expansions. The full phase factors and hard transverse-momentum dependence in the in-medium PDFs and jet transport coefficients remain unchanged because they originate from the same eikonal and collinear approximations used in the photon case. To address the referee's concern, we will add a new subsection in Section II that isolates the key steps: (i) confirmation that no new leading-power operators are generated, (ii) verification that the derivative expansions are unaffected, and (iii) explicit power-counting arguments for the four kernels K_i. This addition will make the extension of the procedure fully transparent. revision: yes

Circularity Check

1 steps flagged

Central factorization procedure and derivative expansions imported from authors' prior photon-production paper via self-citation

specific steps
  1. self citation load bearing [Abstract]
    "As this study is a continuation of our work on medium-induced photon production [Phys. Rev. C 112, 025204 (2025)], the general factorization procedure for e-A deep-inelastic scattering is still used."

    The quoted statement imports the entire technical framework (phase factors, k^- first-order and k_perp second-order derivatives, coherence treatment) that generates the four scattering kernels K_i. The paper asserts that the procedure remains valid after adding Glauber quark interactions and heavy-quark mass effects in initial/final states, but provides no isolated verification steps for power-counting preservation; the kernels are therefore obtained by direct application of the cited prior procedure.

full rationale

The manuscript explicitly positions itself as a continuation and states that the general factorization procedure developed for medium-induced photon production is reused here. This procedure supplies the phase factors, first-order k^- derivatives, and second-order k_perp gradient expansion that define all four kernels K_i. While the paper performs explicit calculations for the new channels (including Glauber quarks and heavy-mass insertions), the load-bearing justification that these insertions preserve the original power counting and expansion validity rests on the self-citation rather than a re-derived or independently verified argument within this work. The explicit kernel expressions may still contain independent algebraic content, preventing a higher score.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the higher-twist formalism at O(α_s²) and the direct transfer of the e-A DIS factorization from the authors' prior photon work; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Higher-twist formalism applies to medium-induced single-scattering emissions at O(α_s²) for virtual quarks
    Invoked to compute the kernels as stated in the abstract.
  • domain assumption Factorization procedure from prior photon-production study extends to quark energy loss with Glauber quarks and mass effects
    Abstract states the general factorization procedure is still used.

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