Pith. sign in

REVIEW 2 major objections 5 minor 2 cited by

Near-threshold charmonium scattering maps the proton’s chromoelectric energy-momentum response onto two light-front transverse profiles, not a static mass radius.

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

2026-07-13 07:35 UTC pith:DJBWCXTT

load-bearing objection Clean clarifying note that turns the established LF EMT density machinery into two normalized chromoelectric profiles for near-threshold quarkonium, with the integrated ratio fixed by an external concurrent-paper input. the 2 major comments →

arxiv 2606.14304 v3 pith:DJBWCXTT submitted 2026-06-12 hep-ph

Light-front transverse profiles of scalar and spin-two chromoelectric EMT responses in near-threshold charmonium probes

Arkadiy I. Syamtomov This is my paper
classification hep-ph
keywords light-front transverse profileschromoelectric EMTgravitational form factorsnear-threshold charmoniumscalar trace anomalyDrell-Yan frameimpact-parameter distributions
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.

Near-threshold production of compact charmonium is a controlled probe of the proton’s gluonic energy-momentum tensor, but the measured slope is often read as a three-dimensional mass radius. This paper shows that the process instead selects a chromoelectric projection that splits cleanly into a scalar-trace response and a non-scalar gravitational combination. In the Drell–Yan frame those two amplitudes become normalized light-front transverse profiles whose integrated ratio is fixed by an external threshold strength of about 15 percent, while their shapes at finite impact parameter still depend on the relative slopes of the form factors. The construction therefore supplies a spatial language for the probe without converting a single measured slope into a model-independent geometric size of the proton. A sympathetic reader cares because it replaces a common over-interpretation with two well-defined, separately normalizable transverse responses that can be tested against future near-threshold data.

Core claim

Compact-charmonium probes of the proton select a chromoelectric energy-momentum-tensor projection that separates into a scalar-trace (anomaly/sigma) amplitude and a non-scalar combination involving A_g, D_g and C-bar_g. In the Drell–Yan frame these two amplitudes define light-front transverse profiles whose integrated ratio equals the externally fixed forward strength R_int_LF ≃ 0.15, while the finite-b behaviour remains sensitive to the relative scalar and gravitational slopes. The result is a spatial representation of the chromoelectric projection that does not equate a measured near-threshold slope with a static three-dimensional mass radius.

What carries the argument

Shape–strength separation: the forward chromoelectric strength N_nt(0)/N_θ(0) ≃ 0.15 is fixed externally by the threshold theorem, while the transverse profiles are the Fourier–Bessel transforms of the normalized off-forward shapes of the scalar trace and of the kinematic combination G_LF_nt(t;ω,ζ).

Load-bearing premise

The absolute normalizations and the precise weights that define the non-scalar combination are imported from a concurrent threshold theorem; if that theorem or the multipole reduction is revised, both the 15 percent ratio and the relative importance of each form factor change.

What would settle it

A high-precision near-threshold dσ/dt measurement (or a helicity-asymmetry or Υ-versus-J/ψ comparison) that cannot be reproduced by two separately normalized transverse profiles whose integrated ratio remains near 0.15 would falsify the claimed projection.

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

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

2 major / 5 minor

Summary. The manuscript applies the established Drell–Yan-frame light-front EMT/GFF density framework to the gluonic response selected by compact-quarkonium chromoelectric scattering. It separates a scalar-trace profile ρ_θ(b) from a non-scalar combination G_LF_nt(t;ω,ζ) built from A_g(t), D_g(t) and C̄_g(t), with forward normalizations fixed externally by the threshold ratio R_int_LF ≃ 0.15 taken from the author’s concurrent work. Normalized Fourier–Bessel transforms define transverse profiles whose integrated ratio recovers R_int_LF by construction, while finite-b localization is controlled by the relative off-forward slopes. Simple dipole/tripole models and a cumulative ratio R_LF(B) are used to illustrate that scalar and non-scalar responses can differ in transverse localization, and that near-threshold quarkonium production probes a chromoelectric EMT projection rather than a single GFF slope or a static three-dimensional mass radius.

Significance. If the external multipole coefficients and threshold normalization are accepted, the paper supplies a clean shape–strength separation that clarifies what near-threshold J/ψ data can and cannot constrain. The construction correctly emphasizes that measured slopes should not be read as model-independent static 3D mass radii, and it organizes the scalar versus non-scalar content into two light-front profiles with externally fixed integrated strengths. The cumulative diagnostic R_LF(B) and the profile-robustness scans are useful pedagogical tools. The work is incremental rather than foundational: the light-front density machinery is prior art, and the load-bearing normalizations and kinematic coefficients are imported from a concurrent paper. Its main value is interpretive clarity for the ongoing discussion of gluonic gravitational form factors in near-threshold charmonium production.

major comments (2)
  1. The central numerical claim R_int_LF ≃ 0.15 and the kinematic coefficients c_A, c_D, c_C that define G_LF_nt (Eqs. (7)–(12) and Table I) are taken verbatim from the concurrent arXiv:2606.08835. Because lim_B→∞ R_LF(B) = R_int_LF holds by definition once those inputs are inserted (Eq. (16)), the integrated-ratio result is not an independent prediction of the present manuscript. The paper should state more explicitly which statements are new here versus which rest entirely on the concurrent threshold theorem, and should indicate how the profiles would change if that theorem or the multipole reduction is revised.
  2. There is a mismatch between the abstract and the body. The abstract states that the spin-two branch contains the gravitational combination 3B_i(t)−D_i(t)=6J_i(t)−3A_i(t)−D_i(t), yet Sec. III and Eq. (7) omit J_g structures and work with a combination of A_g, D_g and C̄_g only, with the text asserting that angular-momentum structures do not contribute to the leading unpolarized threshold projection. Either the abstract should be aligned with the body, or the body should derive the claimed B/J combination and show how it reduces to the coefficients used in Eq. (7).
minor comments (5)
  1. The abstract uses first-person singular (“I construct”) while the body uses “we”; unify the voice.
  2. Several figure captions and axis labels contain truncated or missing symbols (e.g., “g A(b), = Ag(0) = 0.421”, “d2b nt = Nnt(0)”), which reduces readability; restore the full LaTeX symbols.
  3. Table I lists “Raw off-forward forward value G_LF_nt(0;1,0) = 0.892” next to the physical strength N_nt(0) = 0.1499; a one-sentence reminder in the table note that the inequality is intentional (shape vs. strength) would help readers who land on the table first.
  4. The slope-convention conversion R_b = √(2/3) R_3D is correctly flagged as non-geometric, but a brief cross-reference to Miller (2019) or Petrov (2026) already in the bibliography would strengthen the caution for non-specialist readers.
  5. In Sec. IV the D_g(0) scan is called “illustrative” and lattice values are not used as physical-point input; stating the scanned numerical window for D_g(0) in the text (not only in Table I) would make the robustness claim easier to assess.

Circularity Check

2 steps flagged

Integrated ratio R_LF(B o∞) equals the external R_int_LF by construction once the concurrent-paper threshold strength is inserted; finite-b profiles remain model-driven.

specific steps
  1. self citation load bearing [Sec. III, Eqs. (7)–(12) and Table I]
    "Let G_LF_nt(t;ω,ζ)=c_A A_g(t)+c_D D_g(t)+c_C C̄_g(t) … The values of c_A, c_D, c_C and the operator chain leading to Eq. (7) are taken from Ref. [18]. … The forward chromoelectric strength N_nt(0) is the previously derived integrated threshold normalization [18], R_int_LF ≡ N_nt(0)/N_θ(0)=3α_s β_0 A_g(0)/[8π(1−b_m)]≃0.15 … Non-scalar external strength N_nt(0) 0.1499 = R_int_LF ≃0.15, Eq. (12)"

    The kinematic coefficients that define the non-scalar combination and the absolute forward strength N_nt(0) that normalizes ρ_g,ψ_nt are imported wholesale from the author’s concurrent paper. Without that external input the integrated ratio has no numerical content; the present work supplies only the Fourier–Bessel shape.

  2. self definitional [Sec. V, Eqs. (15)–(16) and Table II]
    "A natural model-level diagnostic … is the cumulative ratio R_LF(B)=∫_0^B 2πb db ρ_g,ψ_nt(b)/∫_0^B 2πb db ρ_θ(b). … lim_B o∞ R_LF(B)=R_int_LF=0.1499, independently of the assumed scalar profile. … The B=5 fm column shows uniform convergence to R_int_LF=0.1499"

    By the definitions ρ_g,ψ_nt = N_nt(0) F_⊥[bG_nt] and ρ_θ = N_θ(0) F_⊥[bG_θ] the cumulative ratio is forced to equal N_nt(0)/N_θ(0) once the integration domain covers the whole plane. The numerical “result” R_LF(∞)=0.1499 is therefore identical to the external input inserted in Eq. (12); it is not an independent prediction.

full rationale

The paper’s central numerical claim is the shape–strength separation: two Drell–Yan Fourier–Bessel profiles whose integrated ratio is fixed at R_int_LF ≃ 0.15 while finite-b localization is controlled by the normalized off-forward combination G_LF_nt. That integrated limit is definitional once N_nt(0) and N_θ(0) are taken from the author’s concurrent arXiv:2606.08835 (Eqs. (7)–(12) and Table I). The finite-B shape dependence, pole-order scans, and stress-kernel illustrations are independent model content and are not circular. No uniqueness theorem is smuggled in, no data fit is re-labeled as a prediction, and the light-front density framework itself is standard. The circularity is therefore partial and confined to the load-bearing forward-strength anchor; score 6 reflects that the headline integrated-ratio “result” reduces by construction while the rest of the construction does not.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 2 invented entities

The paper’s central numerical claim rests on an external forward strength and an operator reduction taken from the author’s concurrent work, plus a set of illustrative pole parameters chosen by hand. The light-front density formalism itself is standard; the multipole expansion for compact quarkonium is a domain assumption whose validity sets the whole framework. No new dynamical entities are postulated beyond the defined response profiles.

free parameters (5)
  • A_g dipole mass m_A = 1.13 GeV
    Set by hand to 1.13 GeV to match the baseline of Ref. [18]; controls the transverse width of the A_g contribution.
  • scalar-trace pole mass m_θ = 1.021 GeV (baseline)
    Baseline 1.021 GeV (tripole); scanned via R_m = 0.55–0.85 fm to vary the scalar profile.
  • D_g(0) = –1.10
    Illustrative value –1.10 chosen to explore stress kernels; not taken from a physical-point lattice determination.
  • pole orders n_D, n_θ = n_D=2 (baseline), n_θ=3 (baseline)
    Dipole/tripole variants scanned by hand to test profile robustness.
  • R_int_LF = 0.1499
    Imported numerical value ≃0.15 that fixes the absolute non-scalar normalization; ultimately depends on α_s, A_g(0) and b_m of the prior paper.
axioms (4)
  • standard math Drell–Yan-frame light-front transverse densities are obtained by the Fourier–Bessel transform of GFF shapes (Eq. (5)).
    Standard result of Burkardt, Diehl and subsequent EMT literature; invoked throughout Sec. II–IV.
  • domain assumption Compact-quarkonium multipole expansion reduces the interaction to a second-order chromoelectric operator whose proton matrix element is the linear combination G_LF_nt of A_g, D_g and C-bar_g.
    Taken from Peskin/Bhanot–Peskin and Kharzeev–Satz–Syamtomov–Zinovjev; coefficients imported from Ref. [18].
  • ad hoc to paper The forward chromoelectric strength equals the threshold ratio R_int_LF ≃ 0.15 derived in the author’s concurrent paper.
    External anchor of Sec. III; without it the absolute normalizations of the profiles are undefined.
  • domain assumption Angular-momentum structures proportional to J_g(t) do not contribute to the leading unpolarized threshold projection.
    Stated in Sec. III and VI; required to drop J_g from the combination.
invented entities (2)
  • quarkonium-projected non-scalar LF distribution ρ_g,ψ_nt(b) no independent evidence
    purpose: Spatial representation of the chromoelectric non-scalar EMT combination selected by the compact QQ operator.
    Defined by Eq. (10) as the Fourier–Bessel transform of the normalized G_LF_nt shape times the external strength N_nt(0). No independent experimental handle is given beyond the construction itself.
  • cumulative response ratio R_LF(B) no independent evidence
    purpose: Diagnostic of how the non-scalar strength accumulates relative to the scalar strength as a function of transverse radius.
    Defined by Eq. (15); its large-B limit is tautological once N_nt and N_θ are fixed.

pith-pipeline@v1.1.0-grok45 · 13412 in / 3459 out tokens · 38969 ms · 2026-07-13T07:35:14.916474+00:00 · methodology

0 comments
read the original abstract

I construct light-front transverse profile functions for the scalar and spin-two chromoelectric energy-momentum-tensor responses selected by compact-charmonium probes of the proton. The scalar branch is the anomaly and sigma amplitude, while the spin-two branch contains the gravitational combination $3B_i(t)-D_i(t)=6J_i(t)-3A_i(t)-D_i(t)$ rather than $A_i(t)$ alone. In the Drell-Yan frame, these two amplitudes define normalized transverse response profiles whose integrated ratio reproduces the forward light-front spin-two/scalar strength, while the finite transverse-distance behavior is sensitive to the relative scalar and gravitational slopes. The construction gives a spatial representation of the chromoelectric EMT projection without interpreting a measured near-threshold slope as a model-independent static three-dimensional mass radius.

Figures

Figures reproduced from arXiv: 2606.14304 by Arkadiy I. Syamtomov.

Figure 1
Figure 1. Figure 1: FIG. 1. Normalized form-factor shapes for [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Non-derivative model LF transverse distributions [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Derivative-weighted stress kernels [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Scalar trace distribution [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Pointwise (top) and cumulative (bottom) response ratios. The pointwise ratio is shape-dependent and not a forward [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Profile sensitivity of the cumulative response ratio. Three values of the slope-convention radius [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sub-eikonal stress and model dependence of the small-$x$ gluon D-term

    hep-ph 2026-07 unverdicted novelty 7.0

    The gluon D-term at small x is a next-to-eikonal stress observable whose sign is not determined by the dipole or saturation profile.

  2. Sub-eikonal stress and model dependence of the small-$x$ gluon D-term

    hep-ph 2026-07 conditional novelty 6.0

    The small-x gluon D-term is a next-to-eikonal stress probe and is not fixed by the leading-eikonal dipole or saturation profile alone.

Reference graph

Works this paper leans on

19 extracted references · 15 linked inside Pith · cited by 1 Pith paper

  1. [1]

    A QCD analysis of the mass structure of the nucleon,

    X.-D. Ji, “A QCD analysis of the mass structure of the nucleon,” Phys. Rev. Lett.74, 1071 (1995), arXiv:hep-ph/9410274. 8 0 1 2 3 4 5 B [fm] 0.0 0.1 0.2 0.3 0.4 0.5RLF(B) Profile scan changes transverse shape and saturation rate, but not Rint LF = Nnt(0)/N (0) = 0.1499. Scalar profile sensitivity: Nnt(0) and N (0) held fixed Rm = 0.65 fm, dipole Rm = 0.75...

    Pith/arXiv arXiv 1995

  2. [2]

    Short-distance analysis for heavy quark systems. I. Diagrammatics,

    M. E. Peskin, “Short-distance analysis for heavy quark systems. I. Diagrammatics,” Nucl. Phys. B156, 365 (1979)

    1979

  3. [3]

    Short-distance analysis for heavy quark systems. II. Applications,

    G. Bhanot and M. E. Peskin, “Short-distance analysis for heavy quark systems. II. Applications,” Nucl. Phys. B156, 391 (1979)

    1979

  4. [4]

    J/ψphotoproduction and the gluon structure of the nucleon,

    D. Kharzeev, H. Satz, A. Syamtomov, and G. Zinovjev, “J/ψphotoproduction and the gluon structure of the nucleon,” Eur. Phys. J. C9, 459 (1999), arXiv:hep-ph/9901375

    Pith/arXiv arXiv 1999

  5. [5]

    Impact parameter dependent parton distributions and off-forward parton distributions forζ→0,

    M. Burkardt, “Impact parameter dependent parton distributions and off-forward parton distributions forζ→0,” Phys. Rev. D62, 071503 (2000), arXiv:hep-ph/0005108

    Pith/arXiv arXiv 2000

  6. [6]

    Generalized parton distributions,

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

    Pith/arXiv arXiv 2003

  7. [7]

    Skewed and double distributions in pion and nucleon,

    M. V. Polyakov and C. Weiss, “Skewed and double distributions in pion and nucleon,” Phys. Rev. D60, 114017 (1999), arXiv:hep-ph/9902451

    Pith/arXiv arXiv 1999

  8. [8]

    Forces inside hadrons: pressure, surface tension, mechanical radius, and all that,

    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

    Pith/arXiv arXiv 2018

  9. [9]

    Forces within hadrons on the light front,

    A. Freese and G. A. Miller, “Forces within hadrons on the light front,” Phys. Rev. D103, 094023 (2021), arXiv:2102.01683

    Pith/arXiv arXiv 2021

  10. [10]

    Light-front synchronization and rest-frame densities of the proton: Electromagnetic densities,

    A. Freese and G. A. Miller, “Light-front synchronization and rest-frame densities of the proton: Electromagnetic densities,” Phys. Rev. D107, 074036 (2023), arXiv:2302.09171

    Pith/arXiv arXiv 2023

  11. [11]

    Revisiting the mechanical properties of the nucleon,

    C. Lorcé, H. Moutarde, and A. P. Trawiński, “Revisiting the mechanical properties of the nucleon,” Eur. Phys. J. C79, 89 (2019), arXiv:1810.09837

    Pith/arXiv arXiv 2019

  12. [12]

    Colloquium: Gravitational Form Factors of the Proton,

    V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorcé, P. Schweitzer, and P. E. Shanahan, “Colloquium: Gravitational Form Factors of the Proton,” Rev. Mod. Phys.95, 041002 (2023), arXiv:2303.08347

    Pith/arXiv arXiv 2023

  13. [13]

    Quark and gluon contributions to the QCD trace anomaly,

    Y. Hatta, A. Rajan, and K. Tanaka, “Quark and gluon contributions to the QCD trace anomaly,” JHEP12, 008 (2018), arXiv:1810.05116

    Pith/arXiv arXiv 2018

  14. [14]

    Gluon gravitational structure of hadrons of different spin,

    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

    Pith/arXiv arXiv 2022

  15. [15]

    Determining the proton’s gluonic gravitational form factors,

    B. Duran et al., “Determining the proton’s gluonic gravitational form factors,” Nature615, 813 (2023), arXiv:2207.05212

    Pith/arXiv arXiv 2023

  16. [16]

    Defining the proton radius: A unified treatment,

    G. A. Miller, “Defining the proton radius: A unified treatment,” Phys. Rev. C99, 035202 (2019), arXiv:1812.02714

    Pith/arXiv arXiv 2019

  17. [17]

    On Sizes of Hadrons,

    V. A. Petrov, “On Sizes of Hadrons,” arXiv:2603.14352 (2026)

    arXiv 2026

  18. [18]

    Trace anomaly and non-scalar gluon EMT contributions in near-threshold quarkonium scattering on the light front,

    A. I. Syamtomov, “Trace anomaly and non-scalar gluon EMT contributions in near-threshold quarkonium scattering on the light front,” arXiv:2606.08835 (2026)

    Pith/arXiv arXiv 2026

  19. [19]

    A two-dimensional model for mesons,

    G. ’t Hooft, “A two-dimensional model for mesons,” Nucl. Phys. B75, 461 (1974)

    1974