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REVIEW 3 major objections 4 minor 43 references

The gluonic contribution that dominates proton mass can be rebuilt from three measurable form factors.

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2026-07-10 14:32 UTC pith:75O62YT6

load-bearing objection Clean operator identity that isolates the gluonic trace form factor; the numerical reconstruction is still model-dependent through holographic J/ψ extraction. the 3 major comments →

arxiv 2607.07969 v1 pith:75O62YT6 submitted 2026-07-08 hep-ph nucl-ex

Experimental access to the gluonic origin of the proton mass

Zein-Eddine Meziani , Ismail Zahed This is my paper
classification hep-ph nucl-ex
keywords proton masstrace anomalygravitational form factorsscalar gluonic form factornear-threshold quarkoniumDVCSsigma terminstanton liquid
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.

Most of the proton’s mass is not from the Higgs mechanism but from the gluonic trace anomaly in QCD. This paper shows that the scalar gluonic form factor encoding that anomaly can be reconstructed from three experimentally accessible pieces: the quark scalar gravitational form factor from deeply virtual Compton scattering, the gluon scalar gravitational form factor from near-threshold heavy quarkonium production, and the nucleon sigma-term form factor. The reconstructed quantity is shown to agree with independent lattice-QCD determinations and with the interacting instanton liquid model at low momentum transfer. If the reconstruction holds, laboratory measurements of those three quantities give a direct experimental window onto the gluonic origin of visible mass.

Core claim

The scalar gluonic trace form factor of the proton, which governs the dominant gluonic contribution to the proton mass, is experimentally reconstructible as GN(t) = Gs,g(t) + Gs,q(t) − σ(t)/M, where the three terms on the right are the gluon and quark scalar gravitational form factors and the nucleon sigma-term form factor. This identity follows from the anomalous Ward identity for the energy-momentum tensor together with the standard decomposition into quark and gluon pieces.

What carries the argument

The reconstruction identity GN(t) = Gs,g(t) + Gs,q(t) − σ(t)/M (Eqs. 14 and 17), obtained by combining the trace of the quark and gluon energy-momentum tensors with the anomalous Ward identity that isolates the gluonic trace anomaly.

Load-bearing premise

That the gluon scalar gravitational form factor extracted from near-threshold J/ψ production can be treated as a reliable experimental input free of large model systematics.

What would settle it

A direct lattice or independent experimental determination of the full set of scalar gravitational form factors that yields a GN(t) inconsistent with the paper’s reconstructed band over −t ≲ 1 GeV².

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

If this is right

  • Precision DVCS, near-threshold quarkonium production, and sigma-term measurements can be combined into a single experimental determination of the trace-anomaly form factor.
  • The long-distance scalar gluonic structure of the proton can be compared quantitatively with lattice QCD and with semiclassical instanton-liquid expectations.
  • At low momentum transfer the dominant gluonic contribution to proton mass is accessible without relying solely on non-experimental models.
  • The same framework supplies a concrete experimental path for quantifying how the proton polarizes the surrounding topological QCD vacuum.

Where Pith is reading between the lines

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

  • If the reconstruction is confirmed, future electron-ion collider data on DVCS and exclusive quarkonium production become central inputs to a mass-budget program rather than isolated structure measurements.
  • Disagreement between the reconstructed GN(t) and lattice results at larger |t| would isolate the short-distance gluonic dynamics that the instanton liquid does not capture.
  • The same combination of form factors could be applied to other light hadrons once their quark and gluon gravitational form factors become measurable.

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 / 4 minor

Summary. The paper argues that the dominant gluonic contribution to the proton mass, encoded in the QCD trace anomaly, is experimentally accessible through scalar gravitational form factors. Starting from the anomalous Ward identity for the energy-momentum tensor and the standard quark/gluon EMT decomposition, the authors derive that the scalar gluonic trace form factor GN(t) equals Gs,g(t)+Gs,q(t)−σ(t)/M (Eqs. 14 and 17). They identify three inputs: the quark scalar GFF (DVCS), the gluon scalar GFF (near-threshold heavy-quarkonium production), and the nucleon sigma-term form factor. A numerical reconstruction of GN(t) is then compared with lattice QCD gravitational form factors and with the interacting instanton liquid model, with claimed fair agreement at low momentum transfer (−t≲1 GeV²).

Significance. If the reconstruction can be made with controlled systematics, the result would give a concrete experimental path to the gluonic origin of visible mass—an important and timely goal for Jefferson Lab and future EIC programs. The operator identity itself is clean, standard, and useful: it cleanly isolates the anomaly contribution in terms of quantities that are in principle measurable. The connection to topological vacuum structure via the instanton liquid model is physically interesting and falsifiable at low |t|. The manuscript therefore has clear conceptual value even if the present numerical illustration remains model-dependent.

major comments (3)
  1. [Scalar gluonic form factor; Fig. 1; Eqs. (14),(17)] Eqs. (14) and (17) and the abstract claim that Gs,g(t) is a measurable experimental quantity on the same footing as the DVCS quark GFF and the sigma term. In the manuscript, however, the blue band of Fig. 1 is obtained exclusively from a global analysis of near-threshold J/ψ data performed inside the holographic QCD model of Ref. [33] (one of the authors). No alternative extraction, no variation of holographic parameters, and no quantified model systematic are provided. The claimed quantitative consistency with lattice QCD therefore tests the holographic mapping at least as much as the data. The central numerical claim requires either (i) a documented estimate of holographic systematics or (ii) explicit language that separates the model-independent operator identity from a model-dependent illustration.
  2. [Abstract; Fig. 1 caption; Scalar gravitational form factors] The quark contribution to the reconstruction is not taken from DVCS data as advertised in the abstract and introduction, but from lattice dipole/tripole fits to Aq(t)/Cq(t) that are then renormalized by hand so that Aq(0) matches a phenomenological value 0.576±0.011. The abstract’s three-way experimental path is therefore not realized in the figure: one input is holographic, one is lattice-plus-phenomenology, and the sigma-term form factor is not shown with a measured t-dependence in the reconstruction. The paper should either supply a DVCS-based Gs,q(t) (or a clear roadmap with current uncertainties) or restate the numerical exercise as a hybrid consistency check rather than an experimental reconstruction.
  3. [Eq. (17); Fig. 1; Pion-nucleon scalar FF appendix] The sigma-term form factor σ(t) enters Eq. (17) at every t, yet the manuscript does not specify which measured or modeled σ(t) is used in the blue band of Fig. 1, nor does it propagate its uncertainty. Appendix material gives an ILM monopole form with mσ=683 MeV, but it is unclear whether that form (or a data-driven alternative) is actually folded into the reconstruction. Because GN(t) is defined as the difference of three terms, an unquantified σ(t) is a load-bearing gap for the claimed experimental access.
minor comments (4)
  1. [Fig. 1; Fig. 2] Fig. 1 and Fig. 2 axis labels and legends use truncated or garbled text (e.g., “J/ Expt.”, “m = 170 MeV”, “ILM* ( =0.313 fm)”). These should be cleaned for publication quality.
  2. [Scalar gluonic form factor] Notation for the scalar gluonic form factor switches between GN(t), GN(Q²), and the combination Gs,g+Gs,q−σ/M without a single defining sentence that equates them for all t. A short clarifying sentence after Eq. (17) would help.
  3. [Vacuum Compressibility] The vacuum-compressibility appendix (Eqs. 23–25) is interesting but is not used in the main reconstruction or figures; either connect it quantitatively to Fig. 2 or move it to a brief remark to avoid diluting the central result.
  4. [References] Reference list and text contain a few incomplete or future-dated entries (e.g., private communication [35], arXiv items dated 2026). Ensure all citations are complete and publicly available where possible.

Circularity Check

1 steps flagged

Core reconstruction formula (Eqs. 14/17) is a non-circular operator identity; mild self-reference only in the holographic extraction of Gs,g used for the numerical comparison.

specific steps
  1. self citation load bearing [Fig. 1 caption and surrounding text (p. 2)]
    "The gluon contribution is extracted from the global analysis of the near-threshold J/ψ production from the proton experiments [8–11] at Jefferson Lab using holographic QCD [33]."

    The sole experimental input for Gs,g(t) that enters the reconstructed blue band of GN(t) is obtained exclusively inside the holographic model of Ref. [33] (Mamo & Zahed). While the operator identity itself does not depend on this model, the paper’s claim that the reconstruction is “experimental” and “quantitatively consistent with lattice QCD” therefore partially tests the coauthor’s prior model rather than pure data; the self-citation is load-bearing for the numerical demonstration though not for the formal accessibility argument.

full rationale

The central claim is the experimental accessibility of the scalar gluonic trace form factor via GN(t) = Gs,g(t) + Gs,q(t) − σ(t)/M. This follows directly from the symmetric EMT decomposition (Eq. 3), conservation (Eqs. 4–5, 7), the definition of scalar GFFs (Eqs. 8–9), the trace of the quark EMT (Eq. 10), and the anomalous Ward identity (Eq. 1) that equates it to the sigma-term matrix element (Eq. 11). The algebra yielding Eqs. 12–14 and 17 is therefore definitional from standard QCD operators and contains no free parameters or fitted inputs that force the result. The subsequent numerical reconstruction in Fig. 1 inserts a model-dependent Gs,g extracted from JLab J/ψ data inside the holographic framework of Ref. [33] (coauthored by Zahed) together with lattice-normalized quark GFFs; the comparison to independent lattice GFFs and to the ILM is presented only as a consistency check, not as a prediction forced by construction. No uniqueness theorem is imported, no ansatz is smuggled as a theorem, and no fitted parameter is renamed a prediction of a closely related observable. The self-citation is therefore present but not load-bearing for the operator identity itself, warranting only a low score.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The central claim rests on the standard QCD EMT decomposition and anomalous Ward identity (domain assumptions), plus the practical assumption that holographic QCD reliably converts near-threshold J/ψ cross sections into Gs,g(t). Free parameters enter only in the numerical illustration (Aq(0) normalization, dipole/tripole masses, ILM parameters), not in the reconstruction formula itself. No new entities are postulated.

free parameters (3)
  • Aq(0) phenomenological normalization = 0.576 ± 0.011
    Quark EMT is normalized so that Aq(0) = 0.576 ± 0.011 from global PDF analyses; this sets the absolute scale of the lattice quark GFF contribution used in the reconstruction.
  • dipole/tripole masses for lattice quark GFFs
    Private-communication dipole-tripole fit parameters for Aq(t) and Cq(t) control the t-dependence of Gs,q(t).
  • ILM sigma-mass parameter mσ = 683 MeV
    Used only for the ILM comparison curve of the sigma-term form factor; mσ = 683 MeV in the zero-size approximation.
axioms (3)
  • domain assumption Symmetric gauge-invariant decomposition of the QCD EMT into quark and gluon pieces whose traces satisfy the anomalous Ward identity (Eq. 1).
    Standard in the GFF literature; invoked from the Introduction through Eq. (14).
  • domain assumption Near-threshold heavy-quarkonium production is dominated by the gluon scalar gravitational form factor and can be inverted via holographic QCD to yield Gs,g(t).
    Load-bearing for treating the J/ψ global analysis as an experimental input; stated in the paragraph preceding Fig. 1 and Refs. [8–11,33].
  • standard math Energy-momentum conservation implies C̄q(t) = −C̄g(t).
    Direct consequence of ∂μTμν = 0; used to obtain Eq. (12).

pith-pipeline@v1.1.0-grok45 · 11776 in / 2770 out tokens · 31219 ms · 2026-07-10T14:32:48.126394+00:00 · methodology

0 comments
read the original abstract

Most of the proton mass originates not from the Higgs mechanism but from the quantum structure of the QCD vacuum. The dominant contribution arises from the gluonic trace anomaly associated with the breaking of conformal symmetry in quantum chromodynamics. We show that this anomaly contribution is experimentally accessible through scalar gravitational form factors. The key observable is the scalar gluonic trace form factor of the proton, which can be reconstructed from three measurable quantities: the quark scalar gravitational form factor accessible in deeply virtual Compton scattering, the gluon scalar gravitational form factor measurable in near-threshold heavy quarkonium production, and the nucleon sigma-term form factor. We also show that the scalar gluonic form factor extracted from the trace anomaly is quantitatively consistent with lattice QCD and the instanton liquid model over hadronic distance scales. These results provide a direct experimental path to probing the gluonic origin of visible mass.

Figures

Figures reproduced from arXiv: 2607.07969 by Ismail Zahed, Zein-Eddine Meziani.

Figure 1
Figure 1. Figure 1: FIG. 1. Scalar gluonic form factor of the proton, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of the scalar gluonic form factor ob [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Reference graph

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