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arxiv: 2510.24171 · v2 · submitted 2025-10-28 · ✦ hep-ph · nucl-th

Diffractive deep inelastic scattering in the dipole picture: the qbar{q}g contribution in exact kinematics

Abhiram Kaushik , Heikki M\"antysaari , Jani Penttala This is my paper

Pith reviewed 2026-05-18 03:31 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords diffractive deep inelastic scatteringdipole pictureq qbar g contributionnext-to-leading orderdiffractive structure functionssoft gluonsoft quarkhigh-energy QCD
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The pith

The full q qbar g contribution to diffractive structure functions requires exact kinematics rather than soft gluon approximations.

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

The paper computes the contribution of the quark-antiquark-gluon configuration to diffractive structure functions in high-energy deep inelastic scattering within the dipole picture. This provides a finite part of the next-to-leading-order term in the diffractive cross section. Numerical evaluations show that earlier approximations restricted to high Q squared or high M X squared with soft gluons do not accurately represent the complete result. The analysis further reveals that soft quark contributions are as important as soft gluon ones at high Q squared.

Core claim

We compute the q qbar g contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high-Q2 or high-MX2 limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full q qbar g contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high Q2.

What carries the argument

Exact kinematic evaluation of the q qbar g Fock state contribution in the dipole model across the full phase space for diffractive DIS.

If this is right

  • Accurate next-to-leading order predictions for diffractive structure functions require the full q qbar g term instead of limited approximations.
  • Soft gluon estimates at high Q2 or high MX2 produce noticeable inaccuracies in the computed cross sections.
  • Soft quark contributions must be retained alongside soft gluon ones for reliable results at high Q2.
  • Phenomenological studies of diffraction need to adopt this exact result for better agreement with data.

Where Pith is reading between the lines

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

  • This computation could be folded into global analyses of diffractive parton distributions to reduce theoretical uncertainties.
  • Similar exact treatments may prove necessary for other Fock states or related high-energy processes such as vector meson production.
  • Event generators for diffractive events at colliders could be updated with these full contributions for improved simulations.

Load-bearing premise

The dipole picture remains valid and the high-energy approximations hold across the full kinematic range where the exact q qbar g contribution is evaluated, allowing isolation of this term without additional corrections from other NLO pieces.

What would settle it

A numerical comparison across moderate Q2 values around 10 GeV squared and MX2 not much larger than Q2 showing that the exact q qbar g contribution differs by tens of percent from the soft-gluon high-Q2 or high-MX2 approximations.

Figures

Figures reproduced from arXiv: 2510.24171 by Abhiram Kaushik, Heikki M\"antysaari, Jani Penttala.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: The longitudinal contribution vanishes at Q2 = 0, and does not have a log Q2 enhancement at high Q2 unlike the transverse one. As such the longitudinal￾to-transverse ratio vanishes both at very low and large Q2 . Although the transverse component dominates at high Q2 , in realistic EIC kinematics the longitudinal pho￾ton contribution should be included in order to achieve the percent-level precision alread… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
read the original abstract

We compute the $q\bar{q}g$ contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high-$Q^2$ or high-$M_X^2$ limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full $q\bar{q}g$ contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high $Q^2$.

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 computes the q qbar g contribution to the diffractive structure functions in high-energy deep inelastic scattering within the dipole picture, evaluating the amplitude in exact kinematics with full phase-space integration over the gluon momentum fraction and transverse momentum. The result is presented as a finite part of the next-to-leading-order (NLO) contribution to the diffractive cross section. The authors numerically demonstrate that prior phenomenological approximations restricted to high-Q² or high-M_X² limits for a soft gluon do not accurately capture the full contribution, and that a soft quark contribution is comparably important at high Q².

Significance. If the central extraction holds, this provides a more complete and exact-kinematics treatment of an NLO term in the dipole framework for diffractive DIS, serving as a benchmark that can refine phenomenological predictions for processes at the EIC. The direct computation of the contribution (rather than reduction to fitted parameters) is a positive feature of the work.

major comments (1)
  1. [Numerical results and discussion of approximations] The numerical claim that high-Q² or high-M_X² soft-gluon limits are poor approximations (and that the soft-quark piece is comparably important) is load-bearing for the paper's main phenomenological message. This claim depends on the isolated q qbar g term remaining a well-defined finite NLO piece without contamination. The manuscript should explicitly verify or bound the validity of the high-energy eikonal and dipole-factorization assumptions across the full integration domain, including at moderate x and lower Q² where saturation or other NLO real/virtual corrections could become relevant.
minor comments (2)
  1. [Calculation of the amplitude] Clarify the precise definition of the 'finite part' extracted from the NLO expression and how infrared/collinear divergences are handled in the exact-kinematics integration.
  2. [Numerical results] Add a brief table or plot comparing the exact result to the two limiting approximations over a representative kinematic grid to make the numerical demonstration more quantitative.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive summary and the detailed major comment. We address the point below and have revised the manuscript to strengthen the discussion of the model's domain of applicability.

read point-by-point responses

  1. Referee: The numerical claim that high-Q² or high-M_X² soft-gluon limits are poor approximations (and that the soft-quark piece is comparably important) is load-bearing for the paper's main phenomenological message. This claim depends on the isolated q qbar g term remaining a well-defined finite NLO piece without contamination. The manuscript should explicitly verify or bound the validity of the high-energy eikonal and dipole-factorization assumptions across the full integration domain, including at moderate x and lower Q² where saturation or other NLO real/virtual corrections could become relevant.

    Authors: We agree that the domain of validity of the underlying approximations must be stated clearly, as our numerical demonstration of the inadequacy of prior limits relies on working within a consistent framework. Our calculation is performed entirely inside the dipole factorization and high-energy eikonal approximation, which define the dipole picture itself; the exact kinematics refers only to the unrestricted integration over gluon momentum fraction and transverse momentum. To address the referee's request, we have added an explicit paragraph in the introduction and a new subsection in the results section that bounds the applicability of the results to x ≲ 0.05 and Q² ≳ 5 GeV², the regime where the dipole model is standardly applied and where saturation corrections remain sub-dominant according to existing literature. We note that a complete NLO treatment would indeed require virtual diagrams and additional real emissions, but the isolated real q qbar g contribution remains finite and well-defined within the present framework. This revision makes the limitations transparent without changing the central conclusions. revision: partial

Circularity Check

0 steps flagged

Direct computation of finite q qbar g NLO piece in dipole model

full rationale

The paper performs an explicit evaluation of the q qbar g contribution to diffractive structure functions by integrating the dipole-model amplitude over the full gluon phase space in exact kinematics. This follows standard high-energy eikonal and dipole-factorization steps that are taken as established inputs from the broader literature rather than derived or fitted inside the present work. No equation reduces a prediction to a prior fit, no self-citation supplies a uniqueness theorem that forces the result, and the numerical comparisons to soft-gluon limits are external benchmarks, not internal tautologies. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; ledger populated with standard field assumptions only. No free parameters, invented entities, or ad-hoc axioms are identifiable from the abstract.

axioms (1)
  • domain assumption The dipole picture is applicable to diffractive deep inelastic scattering in the high-energy limit.
    This is the modeling framework invoked for the entire calculation.

pith-pipeline@v0.9.0 · 5662 in / 1360 out tokens · 49388 ms · 2026-05-18T03:31:59.529417+00:00 · methodology

discussion (0)

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