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Charmonium-nucleon femtoscopy as a possible probe of the nucleon gravitational form factor

T0 review · 2 major / 2 minor · reviewed 2026-07-03 · grok-4.3

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Pith's one-line read The J/ψ-N and ψ(2S)-N correlation functions exhibit sensitivity to the nucleon D-form factor.

desk verdict The paper sketches a model linking charmonium-nucleon femtoscopy to the D-form factor but leaves the key approximation untested. read the letter →

arxiv 2607.00650 v2 pith:OMHDVWEN submitted 2026-07-01 hep-ph

Ren Ejima , Daisuke Fujii , Mamiya Kawaguchi This is my paper · ORCID
classification hep-ph
keywords charmonium-nucleoninteractiongravitationalformfactorsfemtoscopycorrelationfunctionQCDmultipoleexpansionD-formfactorlatticeHALpotential
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper investigates the charmonium-nucleon interaction and its link to the nucleon's gravitational form factors. An effective potential is built from the QCD multipole expansion in the chromoelectric dipole approximation, using energy and pressure distributions from gravitational form factors fitted to lattice data. Parameters are fixed by matching to the HAL QCD potential at larger distances and to scattering phase shifts. The computed correlation functions for J/ψ-N and ψ(2S)-N are then shown to depend on the D-form factor. A reader would care because this suggests a new experimental method to access the mechanical structure of the nucleon through correlation measurements.

What carries the argument

Effective potential from the leading chromoelectric dipole term in the QCD multipole expansion, expressed in terms of nucleon energy and pressure distributions from gravitational form factors.

What would settle it

A direct measurement of the J/ψ-N correlation function in an experiment that differs significantly from the one predicted by varying the D-form factor in the potential would falsify the sensitivity.

Watch

Extended reading notes

Core claim

The J/ψ-N and ψ(2S)-N correlation functions exhibit sensitivity to the nucleon D-form factor, allowing femtoscopy to serve as a probe of the gravitational form factors. The effective potential is expressed in terms of the energy and pressure distributions inside the nucleon, constructed from the gravitational form factors fitted to lattice-QCD data, with remaining parameters fixed by reproducing the HAL QCD potential outside the short-distance region and the scattering phase shift.

Load-bearing premise

The effective potential constructed from the leading chromoelectric dipole term accurately represents the charmonium-nucleon interaction at the distances relevant for the correlation function.

Editorial extensions

If this is right

  • The correlation function for the J/ψ-N system can be evaluated using the constructed potential.
  • The ψ(2S)-N correlation function can be similarly computed and shows sensitivity to the D-form factor.
  • Femtoscopy of these systems can serve as a probe of the nucleon gravitational form factors.
  • The potential reproduces the HAL QCD results outside short distances when parameters are fixed accordingly.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Experimental data on these correlation functions could provide constraints on the D-form factor independent of lattice calculations.
  • The approach might be generalized to other heavy mesons interacting with nucleons to study similar structure properties.
  • Confirmation would require dedicated measurements in high-energy collisions where such pairs are produced.
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Signed reviews

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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 / 2 minor

Summary. The manuscript constructs an effective charmonium-nucleon potential from the leading chromoelectric dipole term of the QCD multipole expansion, with the nucleon's energy and pressure distributions obtained from gravitational form factors (GFFs) fitted to lattice QCD. Model parameters are fixed by matching the resulting J/ψ-N potential to the HAL QCD potential for r larger than a short-distance cutoff and to the associated phase shift. The J/ψ-N and ψ(2S)-N correlation functions are then computed and shown to exhibit sensitivity to the D-form factor, leading to the claim that femtoscopy can serve as a probe of nucleon GFFs.

Significance. If the leading-dipole approximation and parameter-fixing procedure remain valid in the distance window controlling the correlation functions, the work supplies a concrete, falsifiable link between lattice GFFs and a measurable femtoscopic observable, offering an independent route to the D-term that complements existing lattice and phenomenological approaches.

major comments (2)
  1. [effective potential construction] The central sensitivity claim rests on the assertion that the leading chromoelectric dipole potential accurately represents the interaction at distances 0.5–2 fm. No explicit estimate or bound is provided on the size of higher-multipole corrections in this interval (see the section constructing the effective potential from the multipole expansion and the subsequent comparison with HAL QCD data).
  2. [correlation function results] The correlation functions are evaluated after fixing parameters to reproduce the HAL QCD potential outside a short-distance cutoff. The manuscript does not report a quantitative propagation of the lattice GFF fit uncertainties or of the cutoff choice into the final C(q) curves, leaving the statistical significance of the reported D-form factor dependence unquantified (see the results section on J/ψ-N and ψ(2S)-N correlation functions).
minor comments (2)
  1. [GFF definitions] The notation for the energy and pressure distributions extracted from the GFFs should be defined explicitly with reference to the standard decomposition of the energy-momentum tensor matrix element.
  2. [figures] Figure captions for the correlation functions should state the momentum range over which C(q) is plotted and whether the curves include Coulomb or other long-range corrections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the positive overall assessment. We address each major comment below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [effective potential construction] The central sensitivity claim rests on the assertion that the leading chromoelectric dipole potential accurately represents the interaction at distances 0.5–2 fm. No explicit estimate or bound is provided on the size of higher-multipole corrections in this interval (see the section constructing the effective potential from the multipole expansion and the subsequent comparison with HAL QCD data).

    Authors: We agree that an explicit estimate or bound on higher-multipole corrections would strengthen the presentation. The leading dipole approximation is justified by the multipole expansion and by the matching to HAL QCD data in the relevant range, which constrains the net effect of higher terms. We will add a short discussion of the expected suppression of higher multipoles (scaling with powers of the charmonium size over distance) in the revised manuscript, while noting that a precise numerical bound would require additional higher-order lattice calculations not available here. revision: partial

  2. Referee: [correlation function results] The correlation functions are evaluated after fixing parameters to reproduce the HAL QCD potential outside a short-distance cutoff. The manuscript does not report a quantitative propagation of the lattice GFF fit uncertainties or of the cutoff choice into the final C(q) curves, leaving the statistical significance of the reported D-form factor dependence unquantified (see the results section on J/ψ-N and ψ(2S)-N correlation functions).

    Authors: We accept this point. The revised manuscript will include error bands on the correlation functions propagated from the lattice GFF fit uncertainties and will show results for a range of cutoff values. This will allow a quantitative assessment of the robustness and statistical significance of the D-form factor dependence. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation uses external inputs without self-referential reduction

full rationale

The paper constructs the effective potential from GFFs fitted to independent lattice-QCD data, fixes auxiliary parameters by matching to external HAL QCD results, and then computes correlation functions to illustrate their dependence on the D-form factor. This dependence follows directly from the model construction but does not constitute a 'prediction' that reduces to the inputs by definition or via self-citation; the central claim is a proposal that femtoscopy measurements could constrain the GFFs, which remains falsifiable against future data and does not rely on any of the enumerated circular patterns. No load-bearing self-citation, ansatz smuggling, or fitted-input-renamed-as-prediction is present in the provided text.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the validity of the leading chromoelectric dipole approximation in the multipole expansion, the accuracy of lattice-fitted gravitational form factors for constructing energy and pressure distributions, and the assumption that matching the potential to HAL QCD outside short distances captures the relevant physics for femtoscopy. No new particles or forces are introduced.

free parameters (1)
  • remaining model parameters after GFF input
    Fixed by requiring the J/ψ-N potential to reproduce HAL QCD results outside short-distance region and the estimated scattering phase shift.
assumptions (2)
  • domain assumption QCD multipole expansion in leading chromoelectric dipole approximation accurately describes charmonium-nucleon interaction
    Invoked to express the potential in terms of nucleon energy and pressure distributions.
  • domain assumption Gravitational form factors fitted to lattice-QCD data correctly yield the energy and pressure distributions inside the nucleon
    Used to construct the distributions that enter the effective potential.

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Cite this review

Pith. "Pith review of Charmonium-nucleon femtoscopy as a possible probe of the nucleon gravitational form factor." pith.science (2026). https://pith.science/paper/OMHDVWEN

@misc{pith2026260700650,
  author       = {Pith},
  title        = {Pith review of: Charmonium-nucleon femtoscopy as a possible probe of the nucleon gravitational form factor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OMHDVWEN}},
  note         = {Machine review of arXiv:2607.00650}
}
abstract

We investigate the charmonium-nucleon interaction, focusing on its connection with the internal structure of the nucleon encoded in the gravitational form factors. To describe this interaction, we employ an effective potential based on the QCD multipole expansion within the leading chromoelectric dipole approximation. In this framework, the potential is expressed in terms of the energy and pressure distributions inside the nucleon. We first construct these distributions from the gravitational form factors fitted to lattice-QCD data. The remaining model parameters are then fixed by requiring that the resulting $J/\psi$-$N$ potential reproduce the HAL QCD potential outside the short-distance region, as well as the scattering phase shift estimated from the HAL QCD data. Based on this potential, we evaluate the $J/\psi$-$N$ correlation function and further investigate the $\psi(2S)$-$N$ system. We then examine the sensitivity of these correlation functions to the nucleon $D$-form factor.

Figures

Figures reproduced from arXiv: 2607.00650 by the authors.

Figure 1
Figure 1. FIG. 1. Momentum transfer dependence of the GFFs based [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The radial dependence of the energy distribution [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Response of the charmonium-nucleon correlation [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

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Forward citations

Cited by 1 Pith paper

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

  1. Chromoelectric and chromomagnetic matching to scalar and spin-two nucleon structure

    hep-ph 2026-07 accept novelty 6.0 of 10

    A consistent matching framework shows the chromomagnetic-to-chromoelectric ratio rescales the gluonic spin-two/scalar response by (1+rho)/(1-rho) in aligned quarkonium-nucleon scattering.

Reference graph

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