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arxiv: 2603.09686 · v2 · pith:NHBSX73Lnew · submitted 2026-03-10 · ✦ hep-ph

Probing GPDs in exclusive electroproduction of dijets

Trambak Jyoti Chall , Marta {\L}uszczak , Wolfgang Sch\"afer , Antoni Szczurek This is my paper

Pith reviewed 2026-05-21 11:45 UTC · model grok-4.3

classification ✦ hep-ph
keywords generalized parton distributionsexclusive dijet productioncollinear factorizationvalence quarksdouble distributionElectron Ion Colliderdijet electroproductionazimuthal modulation
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The pith

Valence quark GPD contributions show distinct behavior in exclusive dijet production at large x_P.

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

The authors compute the cross section for exclusive dijet production in electron-proton scattering using collinear QCD factorization with generalized parton distributions modeled by the double distribution approach. They include leading order contributions from gluons, sea quarks, and valence quarks for light and heavy quark pairs. The gluon and sea contributions have similar shapes in differential distributions, but the valence contribution differs and stands out at large x_P. This region is new territory beyond HERA kinematics and may be reached at the Electron Ion Collider. They also calculate the azimuthal modulation and find reasonable agreement with ZEUS data for beta at or above 0.4.

Core claim

Using the double distribution representation of GPDs in collinear QCD factorization, the calculation of exclusive electroproduction of dijets reveals that valence quark exchanges, although relatively small, exhibit markedly different behavior from gluon and sea contributions, becoming particularly noticeable at large x_P.

What carries the argument

Collinear QCD factorization for the hard subprocess combined with the double distribution model for the soft GPD input.

If this is right

  • Valence contributions become noticeable at large x_P in the phase space.
  • The kinematic region at large x_P is potentially accessible in future EIC measurements.
  • Azimuthal angle modulations between leptonic and dijet planes are predicted for general and specific ZEUS kinematics.
  • Agreement with existing ZEUS data holds for diffractive DIS parameter beta greater than or equal to 0.4.

Where Pith is reading between the lines

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

  • These calculations could help design experiments to extract valence GPD information at high momentum fractions.
  • Similar approaches might be applied to other exclusive processes to map out the full GPD structure.
  • Feasibility studies at the EIC would test if the predicted valence signal is observable above backgrounds.

Load-bearing premise

The double distribution approach accurately models the GPDs and collinear QCD factorization holds for exclusive dijet production even at large x_P.

What would settle it

Data from the Electron Ion Collider on dijet production rates and distributions at large x_P that do not show the predicted distinct valence quark contribution.

Figures

Figures reproduced from arXiv: 2603.09686 by Antoni Szczurek, Marta {\L}uszczak, Trambak Jyoti Chall, Wolfgang Sch\"afer.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_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_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the distribution in dijet invariant mass in the left panel and jet transverse momentum (identical for both jets in collinear approximation) in the right panel. The sea quark contribution becomes comparable to the gluon contribution at small M and small p⊥. The azimuthal correlations between the leptonic and hadronic planes shown in [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_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
read the original abstract

We summarize the formalism for calculating the exclusive dijet production in $e p \to e^{\prime} jj p$ in collinear QCD factorization, using generalized parton distributions as the soft hadronic input modeled in the double distribution approach. We include all leading-order contributions coming from light sea and valence quark exchanges, and gluon exchanges for both light quark-antiquark ($q\bar{q}$) production and also the heavy $c\bar{c}$ final state. We present results for several differential distributions for the cross section evaluated over a broad region of phase space, covering a wide range of inelasticity and photon virtuality. The gluon and sea contributions exhibit similar shapes, whereas the valence contribution, though relatively small, shows a markedly different behavior. The latter becomes particularly noticeable at large $x_{\mathbb{P}}$, a kinematic region not explored at HERA, but potentially accessible in future measurements at the Electron Ion Collider. This requires further feasibility studies. We also present the azimuthal angle modulation between the leptonic and the outgoing dijet planes for the general case, as well as for the ZEUS kinematic region where we see reasonable agreement with the data for diffractive deep inelastic scattering parameter $\beta \gtrsim 0.4$.

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

2 major / 2 minor

Summary. The manuscript computes exclusive dijet electroproduction (ep → e' jj p) in collinear QCD factorization, modeling GPDs via the double-distribution representation. All leading-order channels are included: light sea and valence quark exchanges plus gluons, for both light q q-bar and c c-bar final states. Differential cross-section distributions are presented over wide ranges of inelasticity and Q^2; the valence component is shown to exhibit distinct kinematic dependence that becomes visible at large x_P. Azimuthal modulations between lepton and dijet planes are also given, with reasonable agreement reported to ZEUS diffractive DIS data for β ≳ 0.4.

Significance. If the double-distribution parametrization and collinear factorization remain valid in the unexplored large-x_P domain, the work supplies concrete, falsifiable predictions for valence-GPD sensitivity at the EIC. The explicit inclusion of all LO channels and the direct comparison to existing HERA data in the β ≳ 0.4 region constitute clear strengths.

major comments (2)
  1. [Results section] Results section (around the large-x_P distributions): the claim that valence contributions become 'particularly noticeable' at large x_P rests on the double-distribution model without any sensitivity study varying its free parameters (e.g., the profile function or skewness parameter). No uncertainty bands or alternative GPD representations (dual parametrization, etc.) are shown, so the distinct valence behavior is an unquantified extrapolation rather than a robust prediction.
  2. [Abstract and results] Abstract and results: agreement with ZEUS data is stated for β ≳ 0.4, yet no numerical error estimates, full parameter documentation, or χ² values are provided, making it impossible to judge how well the LO calculation actually describes the data or to assess extrapolation reliability to large x_P.
minor comments (2)
  1. Notation for x_P and β should be defined explicitly on first use and kept consistent with standard diffractive DIS conventions.
  2. A short table listing the numerical values of all double-distribution parameters employed would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below, indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Results section] Results section (around the large-x_P distributions): the claim that valence contributions become 'particularly noticeable' at large x_P rests on the double-distribution model without any sensitivity study varying its free parameters (e.g., the profile function or skewness parameter). No uncertainty bands or alternative GPD representations (dual parametrization, etc.) are shown, so the distinct valence behavior is an unquantified extrapolation rather than a robust prediction.

    Authors: We agree that the analysis is performed within the double-distribution representation and that varying the profile function or skewness parameter, or comparing to alternative representations such as the dual parametrization, would provide additional context. The distinct kinematic dependence of the valence contribution follows from the support properties and x-dependence inherent to valence GPDs in this standard framework, which differ from those of sea quarks and gluons. Standard parameter choices from the literature are employed. In the revised manuscript we will add a dedicated paragraph discussing these choices, the model dependence of the results, and the rationale for focusing on this representation, while noting that a full sensitivity analysis lies beyond the present scope. revision: partial

  2. Referee: [Abstract and results] Abstract and results: agreement with ZEUS data is stated for β ≳ 0.4, yet no numerical error estimates, full parameter documentation, or χ² values are provided, making it impossible to judge how well the LO calculation actually describes the data or to assess extrapolation reliability to large x_P.

    Authors: The parameters of the double-distribution model are documented in the manuscript together with references to the original determinations. As the calculation is strictly leading order, it does not incorporate higher-order corrections or associated theoretical uncertainties. The comparison with ZEUS data is presented as a qualitative check of shapes and magnitudes in the β ≳ 0.4 region. We will revise the abstract and relevant results paragraphs to state the parameter values more explicitly and to clarify that the agreement is visual and qualitative rather than a statistical fit, thereby better indicating the reliability of the extrapolation to large x_P. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model inputs yield independent predictions for unexplored kinematics

full rationale

The paper takes the double distribution representation of GPDs and collinear factorization as external inputs, then computes differential cross sections for exclusive dijet production. The reported valence contribution at large x_P is the direct numerical output of this calculation applied to a new kinematic region, not a redefinition or statistical fit to the same data. Agreement with ZEUS data is shown only for β ≳ 0.4, while the large-x_P claim is an extrapolation whose content is independent of the input parametrization. No equation reduces to its own input by construction, and no self-citation chain is invoked to force uniqueness or to rename a fitted result as a prediction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The results rest on the double distribution parametrization of GPDs (whose parameters are fitted elsewhere) and the assumption that collinear factorization applies to this exclusive process.

free parameters (1)
  • double distribution model parameters
    GPDs are modeled via double distributions whose functional form and parameters are taken from prior fits to other data.
axioms (1)
  • domain assumption Collinear QCD factorization holds for exclusive dijet production in the considered kinematics
    Invoked as the theoretical framework allowing GPDs to be the sole non-perturbative input.

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