Pith. sign in

REVIEW 3 major objections 7 minor 74 references

Resumming all even-spin gluon exchanges shows the spin-2 model used to extract proton GFFs near threshold is only an effective description, not a controlled expansion.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-31 01:13 UTC pith:DSXWYTTG

load-bearing objection Solid holographic unification of threshold GFFs and the BPST pomeron, but Fig. 2’s separately normalized truncations do not actually quantify the GFF-extraction correction the abstract advertises. the 3 major comments →

arxiv 2607.25099 v1 pith:DSXWYTTG submitted 2026-07-27 hep-ph hep-thnucl-th

Spin resummation of heavy quarkonium photoproduction: from the gluonic gravitational form factors to the holographic pomeron

Kiminad A. Mamo , Kemal Tezgin , Christian Weiss This is my paper
classification hep-ph hep-thnucl-th
keywords heavy quarkonium photoproductiongravitational form factorsholographic pomeronspin resummationMellin-Barnes integralBPST cutgluon GPDJ/ψ
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.

Heavy quarkonium photoproduction is one process from threshold to collider energies, yet theorists usually treat those regimes separately: fixed spin-2 exchange (gravitational form factors) near threshold, and a reggeized pomeron at high energy. This paper builds a single holographic amplitude that resums every even spin-j gluonic exchange, with the spin-2 piece fixed by lattice QCD, and shows that one Mellin–Barnes integral describes the J/ψ cross section from JLab through HERA. The same calculation demonstrates that truncating to j=2 (or 2+4, 2+4+6) does not systematically approach the resummed answer; higher fixed spins overshoot, while the full sum grows with a milder power set by a branch cut. A sympathetic reader cares because near-threshold J/ψ data are being used to extract the proton’s gluonic mass and force distributions—if the spin-2 model is only effective, those extractions need a different error estimate based on the resummed amplitude.

Core claim

With lattice-fixed spin-2 input, a holographic complex-j amplitude that resums all even gluonic exchanges unifies J/ψ photoproduction from threshold to HERA, and shows that the popular spin-2 exchange model is an effective description whose success is not evidence of a controlled finite-spin expansion.

What carries the argument

The even-signature Mellin–Barnes integral over complex spin j: the same analytic integrand yields either a fixed-spin pole sum or the reggeized amplitude according to contour choice, with strong-coupling reggeization entering through the BPST square-root branch point.

Load-bearing premise

The soft-wall holographic formulas for the impact factor, proton coupling, and skewness factor must correctly continue the real QCD even-spin exchanges off the integers into the whole complex-j plane used by the integral.

What would settle it

Measure near-threshold Υ photoproduction (or a full set of J/ψ differential cross sections) and check whether the same proton-side exchanges and λ fixed by the J/ψ total-cross-section fit reproduce the energy and t dependence once only the new channel normalization is allowed.

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

If this is right

  • Corrections to GFF extraction from near-threshold J/ψ should be estimated with the full spin-resummed amplitude, not by adding a few higher integer spins.
  • The same logic applies to large-skewness GPD expansions and to near-threshold ϕ electroproduction: higher moments cannot be organized term-by-term.
  • Ultra-high-energy LHCb points lying below the single-cut curve indicate the onset of multi-pomeron/unitarity corrections beyond the present amplitude.
  • The framework extends directly to electroproduction (Q², L/T) and other exclusive meson channels once the impact factor is updated.

Where Pith is reading between the lines

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

  • If the holographic j-plane integrand is only qualitatively right, the qualitative lesson (fixed-spin truncations are not controlled) may still hold in any analytic continuation that places a leading singularity near j≈1.3 rather than at j=2.
  • EIC near-threshold Υ data would cleanly separate channel normalization from the universal proton-side resummation claimed here.
  • A next practical step is a global refit that floats experiment-dependent normalizations so residual χ² can be attributed to dynamics rather than data tension.

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 / 7 minor

Summary. The manuscript constructs a single amplitude for exclusive J/ψ and Υ photoproduction in the complex angular momentum plane: an even-signature Mellin–Barnes integral (Eq. (1)) with soft-wall holographic residues continued off integer spin, and the BPST spin–dimension relation (Eq. (2)) generating a square-root cut at j0 = 2 − 2/√λ. The spin-2 proton input A_g(t,2), D_g(t,2) is fixed beforehand from lattice QCD; only λ and the J/ψ impact-factor normalization are fitted to world threshold-to-HERA total cross-section data, giving λ ≃ 8.13 (j0 ≃ 1.30) at χ²/d.o.f. ≃ 2.27. The differential t-dependence is then predicted without new parameters and compared to GlueX/CLAS bins; Υ is described with the same exchanges and a refitted normalization. The second, conceptual claim is that the spin-2 exchange model used for near-threshold GFF extraction is an effective description rather than the first term of a controlled finite-spin expansion, argued via Fig. 2 (resummed curve versus j = 2, 2+4, 2+4+6 truncations, each separately normalized to GlueX) and the nonuniformity of fixed-spin truncations (SM Eq. (S14)).

Significance. If the construction holds, this is the first single amplitude connecting threshold GFF physics with the BPST pomeron, directly relevant to the JLab 12-GeV and EIC gluonic-GFF programs. Genuine strengths: the spin-2 proton input is fixed externally from lattice QCD before the photoproduction fit, which is real independent grounding; the Mellin–Barnes integral is evaluated numerically rather than approximated by the cut, with documented convergence diagnostics (SM Figs. S5–S7, including a Jordan-type arc check); the t-dependence is a true post-fit prediction agreeing with representative GlueX/CLAS bins; the Υ channel reuses all exchange dynamics with only a normalization refit; and the model yields a falsifiable prediction for near-threshold Υ at the EIC. The fixed-spin versus resummed comparison addresses a question of practical consequence for ongoing GFF extractions, which makes the gap identified in the major comments consequential.

major comments (3)
  1. [Fig. 2 / SM Eq. (S14)] The headline implication — that the spin-2 exchange model is "an effective description, not the first term of a controlled finite-spin expansion" — is not quantified by the comparison shown. Each truncation is separately renormalized to GlueX (SM: "not successive common-normalization partial sums"), so Fig. 2 shows only that renormalized s^2, s^4, s^6 laws fail to extrapolate, not the size of j≥4 contamination of a threshold j=2 fit. The decisive quantity exists within the model: β_{V,j}=I_V(j)d̂_jA_g(t,j) is fixed by the same integrand, so common-normalization partial sums M^(2), M^(2+4),… and the ratio |M_resum|/|M^(2)| over Eγ=8.2–12 GeV measure exactly the bias a spin-2 GFF fit would absorb. With s/κ_N²≈10² at threshold and weak d̂_j damping (SM (S46)–(S47)), the outcome could strengthen or qualify the claim; please show it.
  2. [Eq. (6) / SM Eqs. (S48)–(S49)] λ is the only fitted dynamical parameter and sets j0≃1.30, which anchors both the unified fit and the argument that the j=2 model's success is accidental proximity of j0 to 2. Yet χ²/d.o.f.≃2.27 is driven by mutually inconsistent near-threshold data sets, and the SM notes the curve "follows one of the coexisting determinations" in overlap regions; the HERA-only fit of Ref. [19] gave λ=11.243, i.e. j0≈1.40. Please (i) report the stability of λ under data-set selection (leave-one-experiment-out or normalization nuisance parameters), (ii) state whether the uncertainty in λ≃8.13(6) is statistical-only or rescaled, with the λ–N² correlation, and (iii) discuss the robustness of the j0≈2 narrative over the resulting range.
  3. [Eqs. (1)–(3) / SM §§II–IV] Two stacked extrapolations carry the QCD meaning of both the fit and the fixed-spin comparison: (i) the AdS5/BPST relation Δ(j) is used at λ=8.13 and continued through j≈2, though parametric validity requires λ sin²(πj/2)≫1 (marginal: ≈8 at j=2); (ii) the soft-wall forms I_V(j), A_g(t,j), d̂_j(η,t) — including the off-integer extension of d̂_j with its apparent half-integer poles (SM (S19)–(S21)) — are one particular analytic continuation of the even-spin residues, which is not unique absent a stated growth condition. This is a correctness-risk, not a consensus, concern: please state explicitly that the j-plane integrand is a model of the continuation and add one sensitivity check within the model class (e.g., varying κ_V or the continuation prescription) showing that j0, the fit quality, and the Fig. 2 conclusion are not artifacts of the specific ansatz.
minor comments (7)
  1. [Implications for GFF extraction] "It can be shown that corrections to the second-moment approximation involve the full set of higher moments of the GPDs and cannot be organized by individual moments" is asserted and deferred to future work; since this directly addresses the GPD-based extraction framework, either sketch the argument in the SM or temper it to a conjecture.
  2. [Fig. 1 caption] State explicitly in the caption that the LHCb (and Υ CERN/CMS) points are displayed but excluded from the fit; this is currently only in the SM text.
  3. [Fig. 2] Specify whether the curves are t-integrated or at fixed t, which GlueX data set is used for the normalization fits, and give the numerical normalization factor applied to each truncation.
  4. [SM Eq. (S7) / main text] The convention t_max ≤ t_min ≤ 0 with t_min the forward point is opposite to common usage; a one-line warning in the main text (it is defined in SM Eq. (S7)) would prevent misreading.
  5. [SM Table S1 / Eq. (S30)] κ_V = 1.038 GeV and τ = 3 appear only in SM Table S1; since κ_V enters the threshold normalization through (κ_V/κ_N)^{j+10−3Δ} (SM Eq. (S30)), quote its value and origin (Ref. [19]) in the main text.
  6. [SM §VI] For reproducibility, state the production values of c and ν_max used in the global fit (SM gives c = 1.6 only for the convergence tests) and whether the integration code will be made available.
  7. [Global fit paragraph] "A very satisfactory uniform description is achieved" is subjective; replace with the quantitative statement (χ²/d.o.f. = 2.27 over the stated number of points spanning threshold to HERA).

Circularity Check

3 steps flagged

Lattice spin-2 GFFs are external, but the headline “not a controlled spin expansion” is shown with separately refit truncations whose high-s failure is forced by construction (SM S14); the J/ψ total-cross-section “unified description” is a two-parameter fit to the same data.

specific steps
  1. fitted input called prediction [Main text ‘Global fit…’; SM V.B Eqs. (S48)–(S49); Fig. 1]
    "Only the coupling λ and the overall normalization of the amplitude (contained in the impact factor IV) are fitted to the J/ψ photoproduction data, giving λ≃8.13 … Figure 1 shows the resulting fit of the cross section data … A very satisfactory uniform description is achieved in this minimal framework. The model describes both the near-threshold and the high-energy regime, clearly showing the power of the j-resummation."

    λ and NJ/ψ are determined by χ² minimization on the same full threshold-to-HERA J/ψ total-cross-section compilation that Fig. 1 then presents as successfully “described” in a unified way. The totals curve is the fit output, not an independent prediction; the rhetorical step treats agreement with the training observable as evidence that spin resummation is validated. (Differentials and the Υ shape are cleaner and are not this step.)

  2. self definitional [Main text ‘Fixed-spin vs. resummed exchanges’ + Fig. 2; SM II.A Eqs. (S12)–(S14)]
    "For each fixed-spin model the normalization is separately fitted to the near-threshold JLab GlueX data; the curves are therefore not successive terms with a common normalization. … Thus every finite fixed-spin model in this holographic QCD construction is nonuniform in energy and is eventually dominated by its highest retained power. Adding j = 4, 6, . . . does not define a systematically improving global approximation. The separately normalized curves in main-text Fig. 2 are therefore effective fixed-spin models, not successive common-normalization partial sums."

    The headline claim that spin-2 is “not the first term of a controlled finite-spin expansion” is illustrated by Fig. 2. But with each truncation’s residue refit independently, SM (S14) already implies M^(J)∼s^J at large s, so j=2+4 and j=2+4+6 must overshoot any data set whose energy dependence is softer than s^4/s^6 once the range extends past GlueX. The failure of those curves is therefore built into the separate-normalization protocol plus the definition of the truncated sum, not a measurement of how large the common-normalization j≥4 contamination of a threshold GFF extraction actually is.

  3. fitted input called prediction [Main text ‘From J/ψ to Υ’; Fig. 1 dashed; SM Table S1]
    "Here the model input is the same as in the J/ψ analysis, and λ is taken as determined by the fit to the J/ψ data, Eq. (6); only the overall normalization (contained in the impact factor) is fitted to the HERA Υ data [53, 59]. The Υ comparison therefore does not test a parameter-free prediction; rather, it tests whether the dynamics with the same exchanges and proton couplings as in the J/ψ can accommodate the Υ data once the new channel normalization is specified."

    Milder instance: NΥ is fit to the HERA Υ points that the dashed curve is then said to describe. The paper correctly disclaims a parameter-free prediction, but the remaining test is only whether one free norm can match the Υ normalization/level given λ from J/ψ—not an independent confirmation of the j-plane dynamics on that channel.

full rationale

The proton-side spin-2 input is fixed from lattice QCD before any photoproduction fit (Ag(0), κN, mS from [63]/Fig. S3), and the t-dependent differential cross section is a genuine out-of-sample check once λ and NJ/ψ are fixed on totals. That is real independent content. Circularity is partial and concentrated on two load-bearing rhetorical moves. First, λ and the J/ψ impact-factor normalization are minimized on the full threshold-to-HERA J/ψ total-cross-section set (SM S48–S49), after which Fig. 1 is presented as the framework describing those same totals “in a unified manner”—a successful fit renamed as structural validation of j-resummation. Second, and more central to the GFF-extraction claim, Fig. 2 compares the resummed amplitude to j=2, 2+4, 2+4+6 models each with its own normalization refit to GlueX; the paper itself states these are “not successive terms with a common normalization” and SM (S14) proves every finite truncation is eventually dominated by its highest retained power. Thus the visual that higher spins “do not lead to an improved approximation” is largely forced by the separate-normalization protocol plus power counting, not a demonstration of the size of j≥4 corrections to a common-normalization spin-2 GFF extraction at threshold. The practically important payload (“corrections … should be estimated with the resummed-j amplitude”) is therefore not established by the figure used to support it. Self-citation to prior Mamo–Zahed holographic work supplies the soft-wall integrand but is not a uniqueness theorem and is not scored as load-bearing circularity. Overall score 5: one clear by-construction step on the central claim plus routine fit-as-description, with independent lattice and differential content remaining.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central claims rest on soft-wall holographic QCD plus BPST strong-coupling reggeization as the model of the complex-j integrand, lattice QCD for the j=2 proton residue, and a two-parameter fit (λ, NJ/ψ) to world J/ψ totals. No new particles are postulated; the ‘holographic pomeron’ and BPST cut are imported from prior gauge/string work. Load-bearing model assumptions dominate over free parameters.

free parameters (4)
  • λ ('t Hooft coupling) = ≃8.13
    Controls BPST branch point j0=2-2/√λ and thus the energy dependence of the resummed amplitude; fitted by χ² minimization to the global J/ψ total cross section.
  • N²_J/ψ (J/ψ impact-factor normalization) = 5.27×10^{-5} GeV² nb
    Overall amplitude normalization absorbed in IV(j); fitted jointly with λ to the same global J/ψ total-cross-section set.
  • N²_Υ (Υ impact-factor normalization) = 9.98×10^{-8} GeV² nb
    Independent channel normalization fit to HERA Υ data after freezing J/ψ-determined Regge/proton parameters; not used in the J/ψ claim but enters the Υ curve.
  • κV (heavy-meson soft-wall scale) = 1.038 GeV
    Taken from prior holographic electroproduction work and set equal for J/ψ and Υ by a universality approximation; residual channel dependence absorbed into normalizations.
axioms (6)
  • domain assumption Soft-wall holographic QCD overlap integrals analytically continued in j give the correct residues IV(j) and Ag(t,j) for real QCD gluonic exchanges.
    Entire integrand of Eq. (1) is built from SM §§III soft-wall expressions; without this, lattice-fixed j=2 does not determine the resummed amplitude.
  • domain assumption BPST spin-dimension relation Δ(j)=2+√(2/√λ (j-j0)) with j0=2-2/√λ governs strong-coupling reggeization and the leading j-plane cut.
    Main text Eq. (2); sets high-energy growth and the contour deformation target.
  • domain assumption Polynomiality of GPD moments extends to complex j via the hypergeometric factor d̂j(η,t), reducing at j=2 to the standard D-term structure.
    Main text Eq. (3) and SM §IV; implements skewness and suppresses large real j.
  • domain assumption Lattice MS gluon EMT form factors at μ=2 GeV fix Ag(t,2) and Dg(t,2) (hence Ag(0), κN, mS) as the physical spin-2 proton input.
    SM Fig. S3 and Table S1; external benchmark that anchors the j=2 residue.
  • ad hoc to paper Single BPST-cut (single-exchange) resummation is adequate from threshold through HERA; multi-Pomeron/eikonal effects only matter at LHCb UPC energies.
    Stated in ‘Onset of unitarity corrections’; LHCb points are excluded from the fit on this basis.
  • standard math Even-signature Sommerfeld–Watson / Mellin–Barnes transform correctly resums the discrete even-spin exchange sum into the contour integral Eq. (1).
    SM §II; standard complex angular momentum method with stated contour orientation.

pith-pipeline@v1.2.0-grok45-kimik3 · 23741 in / 4182 out tokens · 73646 ms · 2026-07-31T01:13:38.115718+00:00 · methodology

0 comments
read the original abstract

Exclusive heavy quarkonium photoproduction probes the proton's gluonic structure from near-threshold (fixed-spin exchanges, gravitational form factors) to high energies (reggeized dynamics). We construct a holographic QCD amplitude that resums the even spin-$j$ gluonic exchanges, with the spin-2 input fixed by lattice QCD GFFs. The new framework describes the $J/\psi$ cross section from JLab to HERA energies in a unified manner. It explains why the spin-2 exchange model for GFF extraction near threshold is not a controlled approximation and suggests how to improve it.

Figures

Figures reproduced from arXiv: 2607.25099 by Christian Weiss, Kemal Tezgin, Kiminad A. Mamo.

Figure 1
Figure 1. Figure 1: FIG. 1. Total cross section of exclusive heavy quarkonium photoproduction ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Resummed vs. fixed-spin models of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 50 linked inside Pith

  1. [1]

    M. G. Ryskin, Diffractive J/ψ electroproduction in LLA QCD, Z. Phys. C57, 89 (1993)

    1993

  2. [2]

    does not lead to an improved approx- imation

    However, this should not be regarded as evidence of a controlled expansion in spin, as the addition of higher terms j = 4, 6, . . .does not lead to an improved approx- imation. More basically, there is no model-independent connection between the strength of the BPST-cut and the residue of thej= 2 pole in this representation. 4 Implications for GFF extract...

  3. [3]

    J. C. Collins, L. Frankfurt, and M. Strikman, Factor- ization for hard exclusive electroproduction of mesons in QCD, Phys. Rev. D56, 2982 (1997), arXiv:hep- ph/9611433 [hep-ph]

    arXiv 1997

  4. [4]

    D. Y. Ivanov, A. Schafer, L. Szymanowski, and G. Kras- nikov, Exclusive photoproduction of a heavy vector me- son in QCD, Eur. Phys. J. C34, 297 (2004), [Erratum: Eur.Phys.J.C 75, 75 (2015)], arXiv:hep-ph/0401131

    Pith/arXiv arXiv 2004

  5. [5]

    Diehl, Generalized parton distributions, Phys

    M. Diehl, Generalized parton distributions, Phys. Rept. 388, 41 (2003), arXiv:hep-ph/0307382 [hep-ph]

    Pith/arXiv arXiv 2003

  6. [6]

    A. V. Radyushkin, Nonforward parton distributions, Phys. Lett. B385, 333 (1996), arXiv:hep-ph/9605431 [hep-ph]

    Pith/arXiv arXiv 1996

  7. [7]

    E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, The Pomer- anchuk singularity in nonabelian gauge theories, Sov. Phys. JETP45, 199 (1977), [Zh. Eksp. Teor. Fiz. 72, 377 (1977)]

    1977

  8. [8]

    A. V. Belitsky and A. V. Radyushkin, Unraveling hadronic structure with generalized parton distributions, Phys. Rept.418, 1 (2005), arXiv:hep-ph/0504030 [hep-ph]

    Pith/arXiv arXiv 2005

  9. [9]

    K. J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low Q2 and its implications on diffraction, Phys. Rev. D59, 014017 (1998), arXiv:hep- ph/9807513

    arXiv 1998

  10. [10]

    I. I. Balitsky and L. N. Lipatov, The Pomeranchuk singu- larity in quantum chromodynamics, Sov. J. Nucl. Phys. 28, 822 (1978), [Yad. Fiz. 28, 1597 (1978)]

    1978

  11. [11]

    Kowalski, L

    H. Kowalski, L. Motyka, and G. Watt, Exclusive diffrac- tive processes at HERA within the dipole picture, Phys. Rev. D74, 074016 (2006), arXiv:hep-ph/0606272

    Pith/arXiv arXiv 2006

  12. [12]

    Kowalski and D

    H. Kowalski and D. Teaney, An Impact parameter dipole saturation model, Phys. Rev. D68, 114005 (2003), arXiv:hep-ph/0304189

    Pith/arXiv arXiv 2003

  13. [13]

    Bautista, A

    I. Bautista, A. Fernandez Tellez, and M. Hentschinski, BFKL evolution and the growth with energy of exclusive J/ψ and Υ photoproduction cross sections, Phys. Rev. D 94, 054002 (2016), arXiv:1607.05203 [hep-ph]

    Pith/arXiv arXiv 2016

  14. [14]

    Watt and H

    G. Watt and H. Kowalski, Impact parameter dependent colour glass condensate dipole model, Phys. Rev. D78, 014016 (2008), arXiv:0712.2670 [hep-ph]

    Pith/arXiv arXiv 2008

  15. [15]

    R. C. Brower, M. J. Strassler, and C.-I. Tan, On the Pomeron at Large ’t Hooft Coupling, JHEP03, 092, arXiv:0710.4378 [hep-th]

    Pith/arXiv arXiv

  16. [16]

    R. C. Brower, J. Polchinski, M. J. Strassler, and C.-I. Tan, The Pomeron and Gauge/String Duality, JHEP12, 005, arXiv:hep-th/0603115 [hep-th]

    Pith/arXiv arXiv

  17. [17]

    Nishio and T

    R. Nishio and T. Watari, Skewness Dependence of GPD / DVCS, Conformal OPE and AdS/CFT Correspondence II: a holographic model of GPD (2014), arXiv:1408.6365 [hep-ph]

    Pith/arXiv arXiv 2014

  18. [18]

    Ballon-Bayona, R

    A. Ballon-Bayona, R. Carcass´ es Quevedo, and M. S. Costa, Unity of pomerons from gauge/string duality, JHEP08, 085, arXiv:1704.08280 [hep-ph]

    Pith/arXiv arXiv

  19. [19]

    obtained a larger coupling, λ = 11 .243. In that analysis the Mellin-Barnes integral was approximated by the contribution of the BPST cut in the high-energy regime, whereas here it is evaluated numerically, and the fit includes the full threshold-to-HERA data set. FIG. 2. Resummed vs. fixed-spin models of J/ψ photopro- duction at near-threshold energies.S...

  20. [20]

    K. A. Mamo and I. Zahed, Diffractive photoproduction of J/ψ and Υ using holographic QCD: gravitational form factors and GPD of gluons in the proton, Phys. Rev. D 101, 086003 (2020), arXiv:1910.04707 [hep-ph]

    Pith/arXiv arXiv 2020

  21. [21]

    K. A. Mamo and I. Zahed, Electroproduction of heavy vector mesons using holographic QCD: From near thresh- old to high energy regimes, Phys. Rev. D104, 066023 (2021), arXiv:2106.00722 [hep-ph]

    Pith/arXiv arXiv 2021

  22. [22]

    K. A. Mamo and I. Zahed, Quark and gluon GPDs at finite skewness from strings in holographic QCD: Evolved and compared with experiment, Phys. Rev. D108, 086026 (2023), arXiv:2206.03813 [hep-ph]

    Pith/arXiv arXiv 2023

  23. [23]

    Hatta and D.-L

    Y. Hatta and D.-L. Yang, Holographic J/ψ production near threshold and the proton mass problem, Phys. Rev. D98, 074003 (2018), arXiv:1808.02163 [hep-ph]

    Pith/arXiv arXiv 2018

  24. [24]

    Hatta, A

    Y. Hatta, A. Rajan, and D.-L. Yang, Near threshold J/ψ and Υ photoproduction at JLab and RHIC, Phys. Rev. D100, 014032 (2019), arXiv:1906.00894 [hep-ph]

    Pith/arXiv arXiv 2019

  25. [25]

    Kharzeev, Quarkonium interactions in QCD, Proc

    D. Kharzeev, Quarkonium interactions in QCD, Proc. Int. Sch. Phys. Fermi130, 105 (1996), arXiv:nucl-th/9601029

    Pith/arXiv arXiv 1996

  26. [26]

    Kharzeev, H

    D. Kharzeev, H. Satz, A. Syamtomov, and G. Zinov- jev, J/ψ photoproduction and the gluon structure of the nucleon, Eur. Phys. J. C9, 459 (1999), arXiv:hep- ph/9901375

    arXiv 1999

  27. [27]

    D. E. Kharzeev, Mass radius of the proton, Phys. Rev. D 104, 054015 (2021), arXiv:2102.00110 [hep-ph]

    Pith/arXiv arXiv 2021

  28. [28]

    Y. Guo, X. Ji, and Y. Liu, QCD Analysis of Near- Threshold Photon-Proton Production of Heavy Quarko- nium, Phys. Rev. D103, 096010 (2021), arXiv:2103.11506 [hep-ph]

    Pith/arXiv arXiv 2021

  29. [29]

    K. A. Mamo and I. Zahed, J/ψ near threshold in holo- graphic QCD: A and D gravitational form factors, Phys. Rev. D106, 086004 (2022), arXiv:2204.08857 [hep-ph]

    Pith/arXiv arXiv 2022

  30. [30]

    Y. Guo, X. Ji, Y. Liu, and J. Yang, Updated analysis of near-threshold heavy quarkonium production for probe of proton’s gluonic gravitational form factors, Phys. Rev. D108, 034003 (2023), arXiv:2305.06992 [hep-ph]

    Pith/arXiv arXiv 2023

  31. [31]

    Ji, Deeply virtual Compton scattering, Phys

    X.-D. Ji, Deeply virtual Compton scattering, Phys. Rev. D55, 7114 (1997), arXiv:hep-ph/9609381

    Pith/arXiv arXiv 1997

  32. [32]

    Ji, Gauge-Invariant Decomposition of Nucleon Spin, Phys

    X.-D. Ji, Gauge-Invariant Decomposition of Nucleon Spin, Phys. Rev. Lett.78, 610 (1997), arXiv:hep-ph/9603249

    Pith/arXiv arXiv 1997

  33. [33]

    M. V. Polyakov, Generalized parton distributions and strong forces inside nucleons and nuclei, Phys. Lett. B 555, 57 (2003), arXiv:hep-ph/0210165

    Pith/arXiv arXiv 2003

  34. [34]

    Pasquini, M

    B. Pasquini, M. V. Polyakov, and M. Vanderhaeghen, Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering, Phys. Lett. B739, 133 (2014), arXiv:1407.5960 [hep-ph]

    Pith/arXiv arXiv 2014

  35. [35]

    V. D. Burkert, L. Elouadrhiri, and F. X. Girod, The pressure distribution inside the proton, Nature557, 396 (2018)

    2018

  36. [36]

    M. V. Polyakov and P. Schweitzer, Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, Int. J. Mod. Phys. A33, 1830025 (2018), arXiv:1805.06596 [hep-ph]

    Pith/arXiv arXiv 2018

  37. [37]

    P. E. Shanahan and W. Detmold, Pressure Distribution and Shear Forces inside the Proton, Phys. Rev. Lett.122, 072003 (2019), arXiv:1810.07589 [nucl-th]

    Pith/arXiv arXiv 2019

  38. [38]

    K. A. Mamo and I. Zahed, Nucleon mass radii and dis- tribution: Holographic QCD, Lattice QCD and GlueX data, Phys. Rev. D103, 094010 (2021), arXiv:2103.03186 [hep-ph]

    Pith/arXiv arXiv 2021

  39. [39]

    Cao, F.-K

    X.-H. Cao, F.-K. Guo, Q.-Z. Li, and D.-L. Yao, Disper- sive determination of nucleon gravitational form factors, Nature Commun.16, 6979 (2025), arXiv:2411.13398 [hep- ph]

    Pith/arXiv arXiv 2025

  40. [40]

    Lorc´ e and P

    C. Lorc´ e and P. Schweitzer, Pressure inside hadrons: crit- icism, conjectures, and all that, Acta Phys. Polon. B56, 6 3 (2025), arXiv:2501.04622 [hep-ph]

    Pith/arXiv arXiv 2025

  41. [41]

    Broniowski and E

    W. Broniowski and E. Ruiz Arriola, Gravitational form factors and mechanical properties of the nucleon in a meson dominance approach, Phys. Rev. D112, 054028 (2025), arXiv:2503.09297 [hep-ph]

    arXiv 2025

  42. [42]

    Hechenberger, K

    F. Hechenberger, K. A. Mamo, and I. Zahed, Rapidity- dependent spin decomposition of the nucleon, Phys. Rev. D113, 034027 (2026), arXiv:2507.18615 [hep-ph]

    arXiv 2026

  43. [43]

    Ji and C

    X. Ji and C. Yang, A journey of seeking pressure and forces in the nucleon, Nucl. Phys. B1024, 117342 (2026), arXiv:2508.16727 [hep-ph]

    arXiv 2026

  44. [44]

    Aliet al.(GlueX), First Measurement of Near- Threshold J/ψ Exclusive Photoproduction off the Proton, Phys

    A. Aliet al.(GlueX), First Measurement of Near- Threshold J/ψ Exclusive Photoproduction off the Proton, Phys. Rev. Lett.123, 072001 (2019), arXiv:1905.10811 [nucl-ex]

    Pith/arXiv arXiv 2019

  45. [45]

    Duranet al., Determining the gluonic gravitational form factors of the proton, Nature615, 813 (2023), arXiv:2207.05212 [nucl-ex]

    B. Duranet al., Determining the gluonic gravitational form factors of the proton, Nature615, 813 (2023), arXiv:2207.05212 [nucl-ex]

    Pith/arXiv arXiv 2023

  46. [46]

    Adhikariet al.(GlueX), Measurement of the J/ψ pho- toproduction cross section over the full near-threshold kinematic region, Phys

    S. Adhikariet al.(GlueX), Measurement of the J/ψ pho- toproduction cross section over the full near-threshold kinematic region, Phys. Rev. C108, 025201 (2023), arXiv:2304.03845 [nucl-ex]

    Pith/arXiv arXiv 2023

  47. [47]

    Joostenet al.( J/ψ-007), Near-Threshold J/ψ→µ +µ− Photoproduction and the Gluonic Gravitational Form Factors of the Proton (2026), arXiv:2602.14416 [nucl-ex]

    S. Joostenet al.( J/ψ-007), Near-Threshold J/ψ→µ +µ− Photoproduction and the Gluonic Gravitational Form Factors of the Proton (2026), arXiv:2602.14416 [nucl-ex]

    arXiv 2026

  48. [48]

    Chatagnonet al.(CLAS), Measurement of the near- threshold J/ ψ photoproduction cross section with the CLAS12 experiment, Phys

    P. Chatagnonet al.(CLAS), Measurement of the near- threshold J/ ψ photoproduction cross section with the CLAS12 experiment, Phys. Rev. C113, 065203 (2026), arXiv:2602.22128 [hep-ex]

    Pith/arXiv arXiv 2026

  49. [49]

    V. N. Gribov,The theory of complex angular momenta: Gribov lectures on theoretical physics, Cambridge Mono- graphs on Mathematical Physics (Cambridge University Press, 2007)

    2007

  50. [50]

    Gittelman, K

    B. Gittelman, K. M. Hanson, D. Larson, E. Loh, A. Silver- man, and G. Theodosiou, Photoproduction of the ψ(3100) Meson at 11 GeV, Phys. Rev. Lett.35, 1616 (1975)

    1975

  51. [51]

    Camerini, J

    U. Camerini, J. G. Learned, R. Prepost, C. M. Spencer, D. E. Wiser, W. Ash, R. L. Anderson, D. Ritson, D. Sher- den, and C. K. Sinclair, Photoproduction of the ψ Parti- cles, Phys. Rev. Lett.35, 483 (1975)

    1975

  52. [52]

    Barateet al.(NA14), Measurement of J/ψ and ψ′ Real Photoproduction on 6Li at a Mean Energy of 90 GeV, Z

    R. Barateet al.(NA14), Measurement of J/ψ and ψ′ Real Photoproduction on 6Li at a Mean Energy of 90 GeV, Z. Phys. C33, 505 (1987)

    1987

  53. [53]

    M. E. Binkleyet al., J/ψ Photoproduction from 60-GeV/c to 300-GeV/c, Phys. Rev. Lett.48, 73 (1982)

    1982

  54. [54]

    P. L. Frabettiet al.(E687), A Measurement of Elastic J/ψ Photoproduction Cross Section at Fermilab E687, Phys. Lett. B316, 197 (1993)

    1993

  55. [55]

    Adloffet al.(H1), Elastic photoproduction of J/ψ and Υ mesons at HERA, Phys

    C. Adloffet al.(H1), Elastic photoproduction of J/ψ and Υ mesons at HERA, Phys. Lett. B483, 23 (2000), arXiv:hep-ex/0003020

    Pith/arXiv arXiv 2000

  56. [56]

    Chekanovet al.(ZEUS), Exclusive photoproduction of J/ψ mesons at HERA, Eur

    S. Chekanovet al.(ZEUS), Exclusive photoproduction of J/ψ mesons at HERA, Eur. Phys. J. C24, 345 (2002), arXiv:hep-ex/0201043 [hep-ex]

    Pith/arXiv arXiv 2002

  57. [57]

    Aktaset al.(H1), Elastic J/ψ production at HERA, Eur

    A. Aktaset al.(H1), Elastic J/ψ production at HERA, Eur. Phys. J. C46, 585 (2006), arXiv:hep-ex/0510016 [hep-ex]

    Pith/arXiv arXiv 2006

  58. [58]

    Alexaet al.(H1), Elastic and Proton-Dissociative Photoproduction of J/ψ Mesons at HERA, Eur

    C. Alexaet al.(H1), Elastic and Proton-Dissociative Photoproduction of J/ψ Mesons at HERA, Eur. Phys. J. C73, 2466 (2013), arXiv:1304.5162 [hep-ex]

    Pith/arXiv arXiv 2013

  59. [59]

    Aaijet al.(LHCb), Exclusive J/ψ and ψ(2S) produc- tion in pp collisions at √s = 7 TeV, J

    R. Aaijet al.(LHCb), Exclusive J/ψ and ψ(2S) produc- tion in pp collisions at √s = 7 TeV, J. Phys. G40, 045001 (2013), arXiv:1301.7084 [hep-ex]

    Pith/arXiv arXiv 2013

  60. [60]

    Aaijet al.(LHCb), Measurement of exclusive J/ψ and ψ(2S) production at √s = 13 TeV, SciPost Phys.18, 071 (2025), arXiv:2409.03496 [hep-ex]

    R. Aaijet al.(LHCb), Measurement of exclusive J/ψ and ψ(2S) production at √s = 13 TeV, SciPost Phys.18, 071 (2025), arXiv:2409.03496 [hep-ex]

    arXiv 2025

  61. [61]

    Chekanovet al.(ZEUS), Exclusive photoproduction of Υ mesons at HERA, Phys

    S. Chekanovet al.(ZEUS), Exclusive photoproduction of Υ mesons at HERA, Phys. Lett. B680, 4 (2009), arXiv:0903.4205 [hep-ex]

    Pith/arXiv arXiv 2009

  62. [62]

    Aaijet al.(LHCb), Measurement of the exclusive Υ production cross-section in pp collisions at √s = 7 TeV and 8 TeV, JHEP09, 084, arXiv:1505.08139 [hep-ex]

    R. Aaijet al.(LHCb), Measurement of the exclusive Υ production cross-section in pp collisions at √s = 7 TeV and 8 TeV, JHEP09, 084, arXiv:1505.08139 [hep-ex]

    Pith/arXiv arXiv

  63. [63]

    A. M. Sirunyanet al.(CMS), Measurement of exclu- sive Υ photoproduction from protons in pPb collisions at√sNN = 5.02 TeV, Eur. Phys. J. C79, 277 (2019), [Er- ratum: Eur.Phys.J.C 82, 343 (2022)], arXiv:1809.11080 [hep-ex]

    Pith/arXiv arXiv 2019

  64. [64]

    M. V. Polyakov and C. Weiss, Skewed and double distri- butions in pion and nucleon, Phys. Rev. D60, 114017 (1999), arXiv:hep-ph/9902451 [hep-ph]

    Pith/arXiv arXiv 1999

  65. [65]

    D. A. Pefkou, D. C. Hackett, and P. E. Shanahan, Gluon gravitational structure of hadrons of different spin, Phys. Rev. D105, 054509 (2022), arXiv:2107.10368 [hep-lat]

    Pith/arXiv arXiv 2022

  66. [66]

    Hatta and M

    Y. Hatta and M. Strikman, ϕ-meson lepto-production near threshold and the strangeness D-term, Phys. Lett. B817, 136295 (2021), arXiv:2102.12631 [hep-ph]

    Pith/arXiv arXiv 2021

  67. [67]

    Hatta, H

    Y. Hatta, H. T. Klest, K. Passek-K., and J. Schoenleber, Deeply virtual ϕ-meson production near threshold (2025), arXiv:2501.12343 [hep-ph]

    arXiv 2025

  68. [68]

    Joosten and Z

    S. Joosten and Z. E. Meziani, Heavy Quarkonium Produc- tion at Threshold: from JLab to EIC, PoSQCDEV2017, 017 (2018), arXiv:1802.02616 [hep-ex]

    Pith/arXiv arXiv 2018

  69. [69]

    Gryniuk, S

    O. Gryniuk, S. Joosten, Z.-E. Meziani, and M. Van- derhaeghen, Υ photoproduction on the proton at the Electron-Ion Collider, Phys. Rev. D102, 014016 (2020), arXiv:2005.09293 [hep-ph]

    Pith/arXiv arXiv 2020

  70. [70]

    R. C. Brower, M. J. Strassler, and C.-I. Tan, On the eikonal approximation in AdS space, JHEP03, 050, arXiv:0707.2408 [hep-th]

    Pith/arXiv arXiv

  71. [71]

    Cornalba, M

    L. Cornalba, M. S. Costa, and J. Penedones, Eikonal approximation in AdS/CFT: Conformal partial waves and Regge theory, JHEP06, 048, arXiv:0707.0120 [hep- th]

    Pith/arXiv arXiv

  72. [72]

    Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys

    M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev.123, 1053 (1961)

    1961

  73. [73]

    Martin, Unitarity and high-energy behavior of scatter- ing amplitudes, Phys

    A. Martin, Unitarity and high-energy behavior of scatter- ing amplitudes, Phys. Rev.129, 1432 (1963)

    1963

  74. [74]

    K. A. Mamo, Entanglement, trace anomaly, and con- finement in QCD, Phys. Rev. D112, L111506 (2025), arXiv:2507.00176 [hep-ph]. 7 Supplemental Material: Spin resummation of heavy quarkonium photoproduction: from the gluonic gravitational form factors to the holographic pomeron Kiminad A. Mamo, Kemal Tezgin, and Christian Weiss (Dated: July 29, 2026) CONTEN...

    arXiv 2025