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The paper argues that generalized parton distributions have moved from model-driven exploration to precision science, with DVCS data now yielding an empirical quark pressure profile inside the proton.

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 →

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2026-08-03 15:54 UTC pith:2VYPKKWB

load-bearing objection A solid community white paper that maps the GPD program's claims and its own fault lines; worth a serious referee, but read it as an agenda, not a result. the 4 major comments →

arxiv 2512.15064 v5 pith:2VYPKKWB submitted 2025-12-17 hep-ph hep-exhep-latnucl-exnucl-th

Three-dimensional imaging of hadrons with hard exclusive reactions: advances in experiment, theory, phenomenology, and lattice QCD

M. Bo\"er , A. Camsonne , M. Constantinou , H.S. Jo , K. Joo , K. Semenov-Tian-Shansky , H.-D. Son , P. Sznajder
show 32 more authors
C. Van Hulse E. Voutier J. Wagner A. Afanasev J.S. Alvarado S. Bhattacharya D. Biswas Xu Cao H.-M. Choi K. Cichy N. Crnkovi\'c W. Hamdi M. Hoballah G.M. Huber P. T. P. Hutauruk A. Jentsch C.-R. Ji H.-Ch. Kim B. Kriesten Huey-Wen Lin P.-J. Lin V. Mart\'inez-Fern\'andez M. Mazouz Z.-E. Meziani M. Nefedov K. Passek-K. B. Pire P. Rossi O. Teryaev A. W. Thomas N. Tomida Z.W. Zhao
This is my paper
classification hep-ph hep-exhep-latnucl-exnucl-th
keywords generalized parton distributionsdeeply virtual Compton scatteringgravitational form factorsD-termhadron tomographyenergy-momentum tensorJ/psi photoproductionlattice QCD
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 tries to establish that generalized parton distributions (GPDs) now provide a working framework for three-dimensional imaging of hadrons: hard exclusive reactions factorize into perturbative coefficients and universal GPDs, and data on deeply virtual Compton scattering (DVCS) already allow extraction of the proton's internal pressure via the D-term form factor. A sympathetic reader would care because this would turn femtometer-scale pictures of quark and gluon distributions, and mechanical properties like pressure and mass radius, into measured quantities rather than model predictions. The paper surveys experiment, theory, phenomenology, and lattice QCD to argue that the next generation of facilities will make these extractions precise rather than exploratory.

Core claim

The central claim is that the GPD framework has matured to the point where hadron tomography is becoming a precision science. On the paper's own terms, recent analyses of DVCS data have enabled the first empirical extraction of the quark pressure profile inside the proton, and near-threshold J/psi photoproduction data, combined with lattice QCD quark contributions, yield gluon gravitational form factors and a proton mass radius smaller than the charge radius, with a scalar radius larger. These extractions rest on the QCD energy-momentum tensor form factors being Mellin moments of GPDs, and on leading-twist collinear factorization relating the measured cross sections to those GPDs.

What carries the argument

The central object is the generalized parton distribution (GPD), a light-cone matrix element of quark and gluon operators whose first Mellin moments give the QCD energy-momentum tensor form factors (mass, spin, and D-term). The D-term form factor is the load-bearing link: it is accessed through the subtraction constant of fixed-t dispersion relations for DVCS Compton form factors and carries the pressure and shear-force distributions of the nucleon. Factorization theorems for DVCS and deeply virtual meson production are the mechanism that converts measured exclusive cross sections into these distributions.

Load-bearing premise

The claim stands or falls on leading-twist collinear QCD factorization holding in the kinematic regions where extraction data live—|t|/Q² small and Q² large enough, and for the gluon extraction additionally skewness ξ > 0.5 in the GPD-based variant; the paper itself notes transverse cross-section dominance suggesting the scaling onset may be delayed at current energies.

What would settle it

A falsifying observation would be a precise measurement at a single (x_B, Q², t) point of both DVCS and TCS on the proton, giving Compton form factors whose imaginary parts disagree by more than the combined uncertainty, since universality of GPDs across channels is a core prediction. Alternatively, a lattice QCD calculation of A_g(t) and D_g(t) at the physical pion mass disagreeing with the values extracted from near-threshold J/psi photoproduction would indicate the extraction method fails.

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

If this is right

  • DVCS and deeply virtual meson production amplitudes at reachable kinematics are described by a universal set of GPDs, so a single extraction must simultaneously describe proton and neutron DVCS, meson production, and TCS.
  • The D-term form factor, extracted through dispersion-relation subtraction constants, gives the pressure and shear-force distributions inside the proton, and the von Laue stability condition constrains them.
  • Near-threshold J/psi photoproduction, combined with lattice QCD quark contributions, yields gluon gravitational form factors and a proton mass radius smaller than the charge radius, with the scalar radius larger.
  • With next-generation high-luminosity measurements, these extractions become precision determinations, enabling flavor decomposition and tests of GPD universality across channels.

Where Pith is reading between the lines

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

  • Editorially: if DVCS and TCS extractions agree, the GPD formalism could replace model-dependent form-factor approaches for proton structure; the TCS data are the first direct universality test.
  • Editorially: inclusion of kinematic twist corrections will shift current Compton form factor extractions; reanalysing existing data without the |t|/Q² < 0.2 cut is a direct way to quantify how much of the reported precision depends on that cut.
  • Editorially: the same pressure and radius technology could be applied to transition GPDs for excited states, making mechanical properties of resonances such as the Roper experimentally accessible.

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

4 major / 6 minor

Summary. This is a white paper, based on two 2024 workshops (Incheon and Trento), that surveys the current status and future prospects of GPD-based hadron tomography. It covers experimental results (CLAS12 nDVCS, NPS, SoLID, COMPASS, JLab 12/22 GeV, EIC/EicC), theoretical developments (kinematic twist corrections, DVMP, quarkonium photoproduction factorization, chiral and light-front models, chiral quark-soliton model GFFs, the equivalence principle, GTMDs), and recent lattice QCD calculations. Its central thesis is that GPD studies are 'gradually transforming from model-driven exploration into a precision science' (§1), supported by the claims that DVCS data have enabled 'the empirical extraction of the quark pressure profile inside the proton' (Abstract, §2.2) and that near-threshold J/ψ photoproduction has led to extractions of the gluon gravitational form factors A_g(t), D_g(t) and, in combination with lattice quark inputs, to a mass radius smaller than the charge radius (§3.3, Fig. 12).

Significance. If its central claims hold, the paper is a valuable community roadmap that synthesizes an enormous body of work and makes concrete projections for the next generation of facilities. Its strengths include an unusually honest self-assessment: §4.4 explicitly reports that the NLO collinear-factorization correction to J/ψ photoproduction has a 'catastrophically large' scale sensitivity that 'calls into question the very applicability of the CF approach'; §3.6–3.7 document transverse-cross-section dominance and the 'delayed' onset of scaling in pion and vector-meson electroproduction; and §2.2 candidly lists published criticisms of the mechanical pressure interpretation. These self-flagged tensions are exactly the points that a critical reader would raise, and their presence is a credit to the authors. However, the manuscript's headline claims are more assertive than these admissions support: the 'empirical extraction' and 'precision science' language is not accompanied by a quantitative treatment of the factorization-framework and model dependence that the paper itself documents. The paper is therefore useful as a status report, but it needs revision before the precision claim can be a

major comments (4)
  1. [§4.4 vs §3.3] The paper states in §4.4 that the NLO collinear-factorization correction to J/ψ photoproduction produces a 'catastrophically large' scale sensitivity (Eq. 60) and that this 'calls into question the very applicability of the CF approach to this process.' Section 3.3 nevertheless presents the extraction of A_g(t) and D_g(t) from near-threshold J/ψ photoproduction using the hQCD model (Eq. 31) and a GPD model that requires ξ>0.5, which 'filters out most of the world data' and is described as less stable; only the hQCD fit is shown. No systematic uncertainty is assigned to the choice of reaction model or to the documented NLO instability. This is load-bearing because the mass-radius and scalar-radius conclusions (Fig. 12) rest on these fits. Please provide a quantitative model/systematic uncertainty, or explicitly limit the claim to 'model-dependent extraction within the hQCD framework' and
  2. [§3.3, Fig. 12] The hybrid mass-density procedure combines gluon GFFs from the hQCD fit with lattice quark GFFs without renormalizing A_q(0): the text notes A_q(0)[lattice]=0.51±0.025 while A_q(0)[experiment]≃0.6, and says agreement would improve if A_q(0) were set to ≃0.6. This ad hoc normalization choice is not propagated as an uncertainty into the quoted mass radius, so the conclusion 'the proton mass root-mean-square radius is smaller than the charge' is not established at the claimed precision. Please propagate the normalization uncertainty and show the sensitivity of the radius to this choice.
  3. [Abstract and §2.2] The abstract asserts that 'recent analyses of DVCS data have enabled the empirical extraction of the quark pressure profile inside the proton.' Section 2.2 itself reports that the pressure interpretation has been criticized (Ref. [83]) and that the D-term extraction is model-dependent (Ref. [29]). The paper does not reconcile these statements. A claim of 'empirical extraction' requires that both the leading-twist factorization and the mechanical-density interpretation are accepted; the manuscript documents that both are under debate. Please either add the caveats to the abstract and conclusions or define precisely in what restricted sense 'empirical' is being used.
  4. [§3.6, §3.7, §4.2] The paper documents that in exclusive pion and vector-meson electroproduction the transverse cross section remains comparable to or larger than the longitudinal piece at JLab/COMPASS kinematics, 'suggest[ing] that the onset of the QCD scaling regime, where collinear factorization is expected to apply, may be delayed at current energies.' Yet §7 projects precision GPD extraction from these channels. This is not internally inconsistent, but the paper should state explicitly which conclusions are conditional on the validity of collinear factorization and which are projections, and identify observables (e.g., certain asymmetries) that may be factorization-safe even when unpolarized cross sections are not.
minor comments (6)
  1. [Abstract / §3.2 / §3.4] The paper is described as a white paper/review, but it also contains first-person presentations of unpublished results (e.g., the CLAS12 nDVCS BSA and NPS performance). Please clarify which results are new, which collaboration produces them, and their publication status.
  2. [Eq. (31)] The notation A_g(0) is used both as a form-factor value and, implicitly, as a normalization constant in the hQCD cross-section formula. Please make the normalization explicit and check dimensions.
  3. [Fig. 12] The axis labels in Fig. 12 are garbled ('E o.oa', '{!) 0.06', '0.02' with no units). Please replace with a clean plot and readable axis labels.
  4. [§3.3, first paragraph] The sentence beginning 'If one considers the total contribution of quark and gluons together ¯C q+g = 0. And only three form factors...' is ungrammatical and should be rewritten.
  5. [§4.8] The 'ExEP' (Extended Equivalence Principle / Exact EquiPartition) is introduced as a principle without being labeled as a conjecture or working hypothesis. Please state explicitly whether it is derived, assumed, or proposed, since it is not a standard result in the GPD literature.
  6. [§4.9] The text refers to 'our current work [425]' and presents detailed results from it. If this is an unpublished manuscript, please cite it as 'in preparation' or provide a preprint number so the community can verify the derivation.

Circularity Check

1 steps flagged

No quantity presented as a prediction reduces to a fitted input by construction; the only in-manuscript derivation is the §3.3 gluon-GFF fit, whose mass/scalar radius conclusions are produced by a single holographic ansatz imported by citation ([216]) while the alternative GPD model is set aside. External data anchors (GlueX, JLab, lattice, CTEQ18) keep the central claims partially independent, so

specific steps
  1. ansatz smuggled in via citation [§3.3 (fit of Eqs. 31–32; conclusions of Fig. 12; echoed in Abstract)]
    "First, we used the QCD holographic model developed in Ref. [216] to perform a two-dimensional fit of the differential cross sections. This model effectively captures the non-perturbative interaction between the J/ψ dipole and the nucleon, interpreting the exchange as a coherent sum of a graviton-like tensor glueball (2++) and a dilaton-like scalar glueball (0++). ... It is clear from Fig. 12 that the proton mass root-square-mean radius is smaller than the charge. We also find that the scalar energy density root-square-mean radius is larger than the charge radius and seems to define the size of"

    The gluon GFFs Ag(t), Dg(t) driving the §3.3 conclusions are not measured; they are parameters of the holographic ansatz (Eqs. 31–32) adopted from Ref. [216] (2++ graviton-like + 0++ dilaton-like glueball exchange; dipole/tripole FFs), with Ag(0) fixed from CTEQ18. The alternative GPD model is dropped ('we will show results only for the QCD holographic model') because its ξ>0.5 convergence cut 'filters out most of the world data.' The radius-ordering claims (mass radius < charge radius; scalar radius > charge radius) are outputs of that single cited ansatz, and the paper itself concedes 'all extractions rely on specific modeling frameworks (holographic or GPD-based).' Reporting these fit outputs as established findings ('It is clear from Fig. 12...') imports the cited model's shapes into t

full rationale

This is a workshop white paper, not a derivation chain, so the circularity pass looks for load-bearing steps that reduce to their own inputs. The only in-manuscript analysis is the §3.3 two-dimensional fit of near-threshold J/ψ photoproduction data: the quoted mass/scalar radius ordering is a fit output of the holographic model of Ref. [216] (Eq. 31), with the alternative GPD-based extraction (Eq. 33) suppressed because the ξ>0.5 condition 'filters out most of the world data.' That is a framework-adopted-by-citation situation (step above), and the paper's own sentence 'all extractions rely on specific modeling frameworks' confirms the dependence; however, the fit is anchored to external GlueX/Hall-C data, to external lattice quark GFFs [219], and to CTEQ18 for Ag(0), so the central claim retains independent content. I also weighed, per the reviewing rule, three other passages. (i) §2.2 delegates the rebuttal of the pressure-interpretation criticisms (Ref. [83]) to a single sentence: 'These concerns were recently addressed in some detail in Ref. [33]...'; this is the load-bearing support for the Abstract's strongest claim ('empirical extraction of the quark pressure profile') and is an in-family adjudication if [33] shares authors, but authorship cannot be verified from the manuscript text, so I did not count it as a hard self-citation step. (ii) §3.2 presents the authors' own nDVCS BSA (figures 'taken from Ref. [185]') as the basis for the ImE flavor-separation claim; this is self-presentation, but it is a real external-falsifiable data analysis. (iii) The skeptic's main attack — §4.4's NLO collinear-factorization instability ('calls into question the very applicability of the CF approach to this process') and §3.6's transverse-cross-section dominance suggesting delayed onset of the scaling regime — concerns the validity of factorization in the used kinematics, i.e., an external correctness condition, not a circular reduction; per the rules those concerns belong to correctness risk. I therefore find no step where a prediction equals a fitted input by construction, no uniqueness theorem imported from the authors, and no renaming of a known result; the moderate score reflects the in-family, citation-imported model framework that carries the gluon-GFF and pressure claims while remaining externally anchored.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 2 invented entities

Free parameters cluster in the §3.3 gluon-GFF fit (mA, mC, Cg(0)); the §3.2 VGG interpretation scans J_u, J_d in a grid against the nDVCS data, i.e., fitting inside a model. A_g(0)=0.414 from CTEQ18 and lattice A_q(0)=0.51 are adopted inputs from prior literature. Axioms: leading-twist collinear factorization (§2.1/§4.1), the Breit-frame pressure interpretation (§2.2/§4.8), NRQCD v² expansion (§4.4), the hQCD cross-section formula used for the gluon-FF extraction (§3.3, Eq. 31), the VGG model (§3.2), the χQSM instanton-vacuum suppression of gluons (§4.7), and the ExEP requirement (§4.8). All but the last two are standard domain assumptions of the field; ExEP is stated as a requirement, not a derivation.

free parameters (6)
  • mA (dipole mass of A_g(t)) = not reported in text
    Free fit parameter in Eq. (32) for the gluon mass form factor; fitted to J/psi photoproduction dσ/dt data in §3.3. Value not quoted in the white paper.
  • mC (pole mass of C_g(t)) = not reported
    Free fit parameter in Eq. (32) (dipole n=2 or tripole n=3); fitted to the same data. Value not quoted.
  • C_g(0) = not reported
    Free fit parameter in Eq. (32), the gluon D-term at t=0; fitted. Value not quoted.
  • VGG model J_u, J_d scan = J_d constrained to 0–0.2 (3σ) within the model; J_u unconstrained
    §3.2: J_u and J_d scanned in a grid (step 0.025, range ±1) and χ²-selected against the new nDVCS BSA; a model-scan, i.e., fitting within the VGG double-distribution framework used to interpret the data.
  • hQCD cross-section normalization N_e = 7.768 nb·GeV⁻⁶ (quoted)
    Normalization factor in Eq. (31); presented as a fixed model constant, effectively a calibration of the dipole-nucleon interaction strength from the hQCD framework (Refs [215,216]).
  • Lattice quark A_q(0) input for hybrid mass density = 0.51 (lattice) vs ≈0.6 (experiment)
    Fig. 12 combines lattice quark A_q(0)=0.51 with experimental gluon A_g(0)=0.414 without enforcing A_q(0)+A_g(0)=1; the text concedes the hybrid 'would improve if we set Aq(0)≃0.6'. An input choice, not a fit, but load-bearing for the mass-radius claim.
axioms (7)
  • domain assumption Leading-twist collinear QCD factorization applies to DVCS/DVMP/TCS at the kinematics of the data used (|t|/Q² ≪ 1, Q² ≳ 1–2 GeV²)
    Invoked throughout §2.1 (Eq. 15) and §4.1; the paper itself flags the stress in §4.4 ('calls into question the very applicability of the CF approach') and §3.6 (delayed scaling onset).
  • domain assumption EMT matrix elements in the Breit frame can be interpreted as pressure and shear densities of a continuous medium (Eqs. 26–28), with the von Laue condition as a stability requirement
    Used in §2.2 for the D-term/pressure picture; the paper documents the controversy and rebuts it via Ref [33], an in-family source.
  • domain assumption NRQCD velocity expansion (v² ∼ 0.3 for J/ψ, ∼0.1 for Υ) converges for exclusive quarkonium photoproduction
    Underlies the J/ψ-based gluon-GFF program and the §4.4 scale-stability discussion; the paper notes an unresolved sign disagreement for the O(v²) correction between CF and CGC (§4.4).
  • ad hoc to paper The hQCD cross-section formula (Eq. 31) with tensor and scalar glueball exchange describes near-threshold J/ψ photoproduction
    The basis of the §3.3 gluon-GFF and mass-radius extraction; the alternative GPD model is dropped for instability, so all headline numbers rest on this single model framework.
  • domain assumption VGG double-distribution + Regge parametrization for the (x,ξ,t) dependence of GPDs used to interpret the nDVCS BSA
    Used in §3.2 to convert the measured BSA into the J_d constraint (0 < J_d < 0.2); the paper states the model 'does not reproduce the kinematic dependence' of the data.
  • domain assumption χQSM instanton-vacuum suppression: gluon twist-2 operators vanish (A_g=J_g=0) and flavor-nonsinglet EMT operators are constructed from ordinary derivatives
    Assumed in §4.7 (Eqs. 80–84) for the flavor-decomposed GFFs; the paper concedes the flavor-nonsinglet EMT construction 'is not guaranteed to be consistent with the effective quark-gluon dynamics'.
  • ad hoc to paper ExEP: quark and gluon anomalous gravitomagnetic form factors vanish separately
    Formulated as a requirement in §4.8 (Eq. 104), leading to equal momentum/angular-momentum partition between quarks and gluons; a conjecture of the paper, not derived.
invented entities (2)
  • Graviton-like tensor glueball (2++) and dilaton-like scalar glueball (0++) exchange no independent evidence
    purpose: Non-perturbative interaction mechanism in the hQCD model used to fit J/ψ photoproduction and extract gluon GFFs (§3.3, Eq. 31)
    Model components adopted from Refs [215,216]; as used here they parameterize the amplitude rather than making a falsifiable prediction of this paper. Glueballs are QCD-predicted states, but the 2++/0++ exchange roles are not tested by this fit.
  • ExEP (Exact EquiPartition / Extended Equivalence Principle) no independent evidence
    purpose: Conjectured constraint that quark and gluon anomalous gravitomagnetic form factors vanish separately, Ba(0)=0, implying equal momentum/angular-momentum partition (§4.8, Eq. 104)
    Stated as 'a requirement', not derived; its empirical content (equal quark/gluon momentum partition) is approximately testable via global fits, but the paper presents it as a proposed formulation rather than a result.

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0 comments
read the original abstract

Generalized Parton Distributions (GPDs) have emerged as a powerful framework for exploring the internal structure of hadrons in terms of their partonic constituents. Over the past three decades, the field has witnessed significant theoretical and experimental advancements. The interpretation of GPDs in impact parameter space offers a vivid three-dimensional visualization of hadron structure, correlating longitudinal momentum and transverse spatial distributions, thereby enabling tomographic imaging of hadrons. Furthermore, the link between GPDs and the matrix elements of the QCD energy-momentum tensor provides access to fundamental properties of hadrons, including spin decomposition and internal pressure distributions. Notably, recent analyses of Deeply Virtual Compton Scattering (DVCS) data have enabled the empirical extraction of the quark pressure profile inside the proton. Motivated by the rapidly evolving experimental landscape, this white paper provides a timely and focused overview of recent developments in GPD theory, phenomenology, and lattice QCD studies. Its scope is shaped by the needs and opportunities of forthcoming experimental programs, and it highlights advances that are particularly relevant for the next generation of dedicated measurements, including the extended Jefferson Lab 12 GeV program and its potential 22 GeV upgrade, J-PARC, COMPASS/AMBER, LHC ultra-peripheral collisions, and the future electron-ion colliders EIC and EicC.

Figures

Figures reproduced from arXiv: 2512.15064 by A. Afanasev, A. Camsonne, A. Jentsch, A. W. Thomas, B. Kriesten, B. Pire, C.-R. Ji, C. Van Hulse, D. Biswas, E. Voutier, G.M. Huber, H.-Ch. Kim, H.-D. Son, H.-M. Choi, H.S. Jo, Huey-Wen Lin, J.S. Alvarado, J. Wagner, K. Cichy, K. Joo, K. Passek-K., K. Semenov-Tian-Shansky, M. Bo\"er, M. Constantinou, M. Hoballah, M. Mazouz, M. Nefedov, N. Crnkovi\'c, N. Tomida, O. Teryaev, P.-J. Lin, P. Rossi, P. Sznajder, P. T. P. Hutauruk, S. Bhattacharya, V. Mart\'inez-Fern\'andez, W. Hamdi, Xu Cao, Z.-E. Meziani, Z.W. Zhao.

Figure 6
Figure 6. Figure 6: shows the exclusive J=ψ photoproduction cross section σðγ þ p → J=ψ þ pÞ reported in Table III as a function of Wγp, covering the range 27 <Wγp < 57 GeV. Comparisons with previous measurements and with several theoretical models are also shown. Measurements at low Wγp were performed by fixed target experiments, such as those reported by the E401 [66], E516 [67], and E687 [68] Collaborations. Recently, mea￾… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p068_6.png] view at source ↗

discussion (0)

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Forward citations

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