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arxiv: 2605.18519 · v1 · pith:7U7N2ANRnew · submitted 2026-05-18 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Quark and gluon tomography of the helium-4 nucleus

V. Mart\'inez-Fern\'andez , B. Pire , P. Sznajder , J. Wagner This is my paper

Pith reviewed 2026-05-20 09:23 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th
keywords helium-4quark gluon tomographygeneralized parton distributionsdeeply virtual Compton scatteringQCD collinear factorizationnuclear structuretransverse spatial distributions
4
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The pith

The helium-4 nucleus has distinct transverse spatial distributions for its quarks and gluons.

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

This paper applies QCD collinear factorization to hard exclusive reactions on helium-4 to perform 3D tomography of its partonic structure. It analyzes elastic form factors and deeply virtual Compton scattering at next-to-leading order, including kinematic twist corrections and full evolution of generalized parton distributions. The result is the first such tomography for a light nucleus, showing that quarks and gluons occupy different positions in the transverse plane. A sympathetic reader would care because this extends our understanding of nuclear structure from the proton to composite nuclei using the same QCD tools.

Core claim

QCD collinear factorization allows coherent hard exclusive reactions to reveal the quark-gluon structure of light nuclei, enabling their 3D tomography. We study elastic form factors and deeply virtual Compton scattering on a helium-4 target, achieving theoretical precision unprecedented even in proton studies. Constraining generalized parton distributions at next-to-leading order in α_s, incorporating kinematic twist corrections, and using full evolution equations, we provide the first tomography of a light nucleus, revealing distinct transverse spatial distributions of quarks and gluons.

What carries the argument

Generalized parton distributions of the helium-4 nucleus extracted via collinear factorization of deeply virtual Compton scattering and elastic form factors.

If this is right

  • Light nuclei can now undergo 3D quark-gluon tomography with theoretical precision matching or exceeding proton studies.
  • Quarks and gluons in helium-4 occupy measurably different transverse spatial distributions.
  • Kinematic twist corrections and full evolution equations are required to control higher-twist effects in nuclear GPDs.
  • The approach demonstrates that coherent hard exclusive reactions can map parton structure inside light nuclei.

Where Pith is reading between the lines

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

  • The same framework could be applied to other light nuclei to isolate nuclear binding effects at the parton level.
  • Future DVCS measurements on nuclear targets would provide direct tests of the predicted quark versus gluon distributions.
  • Differences in transverse distributions may connect to how gluons mediate nuclear forces compared to quarks.

Load-bearing premise

Collinear factorization and the chosen GPD parametrization remain valid for the composite helium-4 nucleus at the kinematics considered.

What would settle it

An experimental measurement of the deeply virtual Compton scattering cross section on helium-4 that deviates significantly from the predicted values based on these GPDs.

Figures

Figures reproduced from arXiv: 2605.18519 by B. Pire, J. Wagner, P. Sznajder, V. Mart\'inez-Fern\'andez.

Figure 1
Figure 1. Figure 1: FIG. 1. Examples of Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fit to helium-4 elastic form factor data. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Fit to the beam spin asymmetry for DVCS, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spatial distributions of quarks, [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Normalized second moments of spatial distributions [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

QCD collinear factorization allows coherent hard exclusive reactions to reveal the quark-gluon structure of light nuclei, enabling their 3D tomography. We study elastic form factors and deeply virtual Compton scattering on a helium-4 target, achieving theoretical precision unprecedented even in proton studies. Constraining generalized parton distributions at next-to-leading order in $\alpha_s$, incorporating kinematic twist corrections, and using full evolution equations, we provide the first tomography of a light nucleus, revealing distinct transverse spatial distributions of quarks and gluons.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper applies QCD collinear factorization to elastic form factors and deeply virtual Compton scattering on helium-4. It constrains generalized parton distributions at NLO in α_s with full evolution equations and kinematic twist corrections, claiming to deliver the first 3D tomography of a light nucleus and to reveal distinct transverse spatial distributions of quarks versus gluons.

Significance. If the central results hold, the work would be significant for extending GPD-based tomography from protons to light nuclei at high theoretical precision. The explicit use of NLO, full evolution, and kinematic twist corrections strengthens the theoretical control relative to many proton studies and could provide falsifiable predictions for future nuclear DVCS measurements.

major comments (2)
  1. [§2 and §4] §2 (Formalism) and §4 (Numerical results): the central claim that collinear factorization plus the chosen GPD parametrization yields reliable transverse quark and gluon distributions for ⁴He rests on the unquantified assumption that nuclear binding, Fermi motion, and impulse-approximation corrections remain negligible beyond the included kinematic twist terms; no explicit residual nuclear correction estimate or sensitivity test is provided, which directly affects the robustness of the reported distinct spatial distributions.
  2. [§3] §3 (GPD parametrization): the free parameters of the GPD model are fitted to proton data and then applied to ⁴He without a dedicated nuclear-data constraint or cross-validation; this makes the extracted transverse densities dependent on an external parametrization whose extrapolation to a composite nucleus is not independently verified within the manuscript.
minor comments (2)
  1. [Figure 2] Figure 2: axis labels and legend do not clearly distinguish the quark and gluon contributions at the same kinematics; adding a second panel or explicit line-style key would improve readability.
  2. [§2] Notation: the symbol for the skewness parameter ξ is used inconsistently between the evolution equations and the numerical tables; a single definition in §2 would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments raise important points about the treatment of nuclear effects and the application of the GPD parametrization. We address each major comment below, indicating where we agree and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§2 and §4] §2 (Formalism) and §4 (Numerical results): the central claim that collinear factorization plus the chosen GPD parametrization yields reliable transverse quark and gluon distributions for ⁴He rests on the unquantified assumption that nuclear binding, Fermi motion, and impulse-approximation corrections remain negligible beyond the included kinematic twist terms; no explicit residual nuclear correction estimate or sensitivity test is provided, which directly affects the robustness of the reported distinct spatial distributions.

    Authors: We agree that an explicit discussion of residual nuclear corrections would improve the robustness assessment. Our calculation incorporates kinematic twist corrections within the collinear factorization framework to account for leading higher-twist contributions from nuclear structure. These terms are intended to capture the dominant corrections beyond the strict impulse approximation at the kinematics of interest. To address the referee's concern, we will revise §2 to include a short estimate of the expected size of binding and Fermi-motion effects based on existing nuclear DVCS phenomenology, and we will add a corresponding paragraph in §4 discussing the sensitivity of the extracted transverse densities to these corrections. This addition will quantify the associated uncertainties without changing the central results. revision: yes

  2. Referee: [§3] §3 (GPD parametrization): the free parameters of the GPD model are fitted to proton data and then applied to ⁴He without a dedicated nuclear-data constraint or cross-validation; this makes the extracted transverse densities dependent on an external parametrization whose extrapolation to a composite nucleus is not independently verified within the manuscript.

    Authors: The GPD model parameters are constrained by proton data, as is standard when direct nuclear GPD measurements are unavailable. We adapt the parametrization to ⁴He by incorporating nuclear form factors and assuming the same functional form for the underlying distributions, which allows us to generate the first predictions for nuclear tomography. While a dedicated refit to nuclear data is beyond the scope of this initial study, we will revise §3 to explicitly discuss the extrapolation assumptions, associated model uncertainties, and the rationale for applying the proton-constrained form to the nucleus. We will also add a brief comparison of our computed ⁴He elastic form factors with experimental data to provide partial validation of the nuclear application. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation applies external factorization and GPD frameworks

full rationale

The paper applies established QCD collinear factorization theorems and standard GPD parametrization techniques (NLO in alpha_s, full evolution, kinematic twist corrections) to elastic form factors and DVCS on helium-4. The tomography of transverse quark and gluon distributions follows directly from these external inputs without any quoted reduction of a central result to a fitted parameter renamed as prediction, a self-definitional loop, or a load-bearing self-citation chain. No equations or sections in the provided abstract and context exhibit the patterns of self-definition or imported uniqueness; the work is an extension of proton-style methods to a light nucleus and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The tomography rests on the assumption that collinear factorization applies to helium-4 with controllable higher-twist effects and on a specific parametrization of nuclear GPDs whose parameters are constrained by existing data.

free parameters (1)
  • GPD model parameters
    Parameters in the generalized parton distribution ansatz for helium-4 are adjusted to match form-factor and DVCS data.
axioms (1)
  • domain assumption Collinear factorization holds for hard exclusive processes on light nuclei at the considered kinematics
    Invoked to justify the use of GPDs for helium-4 tomography.

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