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arxiv: 2604.18355 · v1 · submitted 2026-04-20 · ✦ hep-ph

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Generalized parton distributions of valence, sea, and gluon components of the proton

Yiping Liu , Siqi Xu , Chandan Mondal , Xingbo Zhao , James P. Vary
Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:03 UTC · model grok-4.3

classification ✦ hep-ph
keywords generalized parton distributionslight-front wave functionsbasis light-front quantizationproton structurevalence quarkssea quarksgluonsCompton form factors
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The pith

Light-front wave functions in the BLFQ framework compute the proton's generalized parton distributions for valence quarks, sea quarks, and gluons.

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

The paper aims to establish a method for calculating generalized parton distributions of the proton directly from its light-front wave functions in the BLFQ approach. These wave functions are generated from a light-front QCD Hamiltonian that includes higher Fock components like three-quark-gluon and three-quark-quark-antiquark states, without needing an explicit confining potential. This allows computation of quark GPDs with nonzero skewness in both the DGLAP and ERBL kinematic regions and gluon GPDs in the DGLAP region for the first time in this framework. The results are qualitatively consistent with but smaller than global extractions from data and lattice calculations, and they produce Compton form factors that agree with global analyses. A sympathetic reader would care because this offers a QCD-based, parameter-light way to understand the three-dimensional structure of the nucleon encoded in GPDs.

Core claim

Using light-front wave functions derived within the BLFQ framework from a light-front QCD Hamiltonian truncated to the three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors, we evaluate the GPDs for valence quarks, sea quarks, and gluons in the proton. For the first time in this framework, quark GPDs are computed at nonzero skewness in the DGLAP and ERBL regions, while gluon GPDs are obtained in the DGLAP region. These GPDs exhibit features similar to but smaller in magnitude than the GUMP1.0 global extraction and lead to Compton form factors consistent with global analysis.

What carries the argument

Light-front wave functions in the BLFQ framework obtained from the QCD Hamiltonian in the three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors, which are used to evaluate the GPD matrix elements.

If this is right

  • Quark GPDs can now be evaluated at nonzero skewness in both the DGLAP and ERBL regions for the first time in BLFQ.
  • Gluon GPDs are accessible in the DGLAP region using the same framework.
  • The computed GPDs are qualitatively similar to but smaller than those from the GUMP1.0 global extraction.
  • The associated Compton form factors are consistent with results from global analysis.

Where Pith is reading between the lines

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

  • Evolving these low-scale GPDs to higher energy scales could allow direct comparison with more experimental data.
  • Applying the BLFQ method to other baryons or mesons might reveal patterns in hadron structure.
  • The smaller magnitude compared to global fits suggests that including additional Fock sectors could improve the description.
  • Direct comparisons with lattice QCD calculations at matching resolution scales would test the approach's validity.

Load-bearing premise

The light-front wave functions derived from a light-front QCD Hamiltonian without an explicit confining potential and truncated to three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors provide a realistic description of the nucleon at low resolution scale.

What would settle it

A precise lattice QCD calculation or experimental extraction of proton GPDs or Compton form factors at low resolution scale that shows large quantitative disagreement with the BLFQ predictions would challenge the claim of a realistic description.

Figures

Figures reproduced from arXiv: 2604.18355 by Chandan Mondal, James P. Vary, Siqi Xu, Xingbo Zhao, Yiping Liu.

Figure 1
Figure 1. Figure 1: Quark GPDs H(x, ξ, t) (upper panels) and E(x, ξ, t) (lower panels) shown as functions of x and −t at fixed skewness ξ = 0.1, covering both the DGLAP and ERBL regions. The left (right) panels correspond to the up (down) quark [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: GPDs H(x, ξ, t) and E(x, ξ, t) in DGLAP region for quarks (upper panels) and their antiquarks (lower panels) shown as functions of x and −t at skewness ξ = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Quark GPDs H(x, ξ, t) (upper panels) and E(x, ξ, t) (lower panels) in ERBL region shown as functions of x and −t at skewness ξ = 0.1. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Gluon GPDs H(x, ξ, t) (left panel) and E(x, ξ, t) (right panel) shown as functions of x and −t at skewness ξ = 0.1. negative anomalous magnetic moment of the down quark. For antiquarks, both Eu¯ and Ed¯ are negative. This be￾havior arises because, under SU(3) symmetry, the valence contributions to Eu and Ed have opposite signs, whereas no such constraint exists for sea quarks; moreover, the uu¯ and d ¯d se… view at source ↗
Figure 5
Figure 5. Figure 5: Evolved quark GPDs H(x, ξ, t) (upper panels) and E(x, ξ, t) (lower panels) at different scale µ 2 = 1, 3, 10 GeV2 shown as functions of x at fixed skewness ξ = 0.1 and −t = 1 GeV2 , cov￾ering both the DGLAP and ERBL regions. The left (right) panels correspond to the up (down) quark [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the isovector combination of the quark GPDs obtained in the BLFQ framework (red bands) with the GUMP1.0 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolved gluon GPDs H(x, ξ, t) (left panel) and E(x, ξ, t) (right panel) at different scale µ 2 = 1, 3, 10 GeV2 shown as functions of x at fixed skewness ξ = 0.1 and −t = 1 GeV2 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Imaginary and real parts of the CFF H as function of ξ at Q2 = 4 GeV2 and t = −0.2 GeV2 , compared with a neural￾network–based global analysis [79]. neural-network–based global analysis [79]. As shown in the left panel, our results are consistent with the experi￾mental data in the range 0.03 < ξ < 0.13. For ξ < 0.03, our predictions are larger than those from the global anal￾ysis, while for ξ > 0.13 they b… view at source ↗
read the original abstract

We compute the generalized parton distributions (GPDs) of valence quarks, sea quarks, and gluons in the proton using light-front wave functions obtained within the basis light-front quantization (BLFQ) framework, providing a realistic description of the nucleon at a low resolution scale. The wave functions are derived from a light-front QCD Hamiltonian without an explicit confining potential and include the three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors. For the first time within BLFQ, we evaluate quark GPDs at nonzero skewness in both the DGLAP and ERBL regions, while gluon GPDs are computed in the DGLAP region. The resulting GPDs exhibit qualitative features similar to, but smaller than the GUMP1.0 global extraction of GPDs based on experimental and lattice QCD data at next-to-leading order accuracy. We further compute the associated Compton form factors and obtain results consistent with the global analysis.

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

1 major / 1 minor

Summary. The manuscript computes generalized parton distributions (GPDs) of valence quarks, sea quarks, and gluons in the proton from light-front wave functions obtained in the basis light-front quantization (BLFQ) framework. The wave functions are derived from a light-front QCD Hamiltonian without an explicit confining potential, truncated to the three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors. The work reports the first BLFQ results for quark GPDs at nonzero skewness in both DGLAP and ERBL regions (gluon GPDs in DGLAP only), finds qualitative similarity but smaller magnitudes relative to the GUMP1.0 global extraction, and obtains Compton form factors consistent with global analysis.

Significance. If validated, the calculation supplies a Hamiltonian-derived, low-scale GPD model that incorporates higher Fock components and extends BLFQ to nonzero skewness. This complements global fits by providing an ab initio route constrained by the underlying light-front dynamics rather than direct GPD data fitting. The qualitative agreement with GUMP1.0 is consistent with truncation effects and represents technical progress, though the absence of quantitative benchmarks limits immediate impact on phenomenology or lattice comparisons.

major comments (1)
  1. Abstract: the assertion that the BLFQ wave functions furnish a 'realistic description of the nucleon at a low resolution scale' rests only on qualitative similarity with smaller magnitudes to GUMP1.0; no quantitative comparisons (e.g., values at benchmark (x,ξ,t) points, integrated moments, or goodness-of-fit metrics) or uncertainty estimates from the Hamiltonian parameters and Fock truncation are provided, leaving the central claim of realism unsupported by the reported evidence.
minor comments (1)
  1. Specify the numerical values of the Hamiltonian parameters, the observables used to fix them, and any sensitivity tests performed on the resulting GPDs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the major comment point by point below.

read point-by-point responses

  1. Referee: Abstract: the assertion that the BLFQ wave functions furnish a 'realistic description of the nucleon at a low resolution scale' rests only on qualitative similarity with smaller magnitudes to GUMP1.0; no quantitative comparisons (e.g., values at benchmark (x,ξ,t) points, integrated moments, or goodness-of-fit metrics) or uncertainty estimates from the Hamiltonian parameters and Fock truncation are provided, leaving the central claim of realism unsupported by the reported evidence.

    Authors: We agree that the term 'realistic' in the abstract is not supported by quantitative evidence such as benchmark values, moments, or uncertainty estimates, and that the comparison to GUMP1.0 is qualitative only. The BLFQ results represent a first computation within the truncated Fock space at nonzero skewness, with the observed similarity serving as an initial consistency check rather than a full validation. We will revise the abstract to remove 'realistic' and instead describe the wave functions as providing 'a description of the nucleon at a low resolution scale' based on light-front QCD dynamics. We will also add a brief statement in the conclusions acknowledging the current limitations and the need for future quantitative benchmarks and uncertainty analysis from the Hamiltonian parameters and Fock truncation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from independent Hamiltonian inputs

full rationale

The central computation obtains GPDs by direct evaluation of matrix elements using light-front wave functions solved from the BLFQ Hamiltonian in specified Fock sectors. No GPD data enter the Hamiltonian or the wave-function solution; parameters are fixed externally and results are compared to an independent global fit (GUMP1.0). No self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation appears in the derivation chain. The approach is therefore a genuine first-principles evaluation at the chosen truncation, not a re-expression of its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the BLFQ light-front Hamiltonian and limited Fock-sector truncation; no explicit free parameters or invented entities are named in the abstract.

free parameters (1)
  • Hamiltonian parameters
    Coupling strengths, quark masses, and other constants in the light-front QCD Hamiltonian are expected to be set by fitting to other observables such as masses or form factors.
axioms (2)
  • domain assumption Light-front QCD Hamiltonian without explicit confining potential accurately describes the nucleon at low resolution scale
    Invoked to justify the wave functions used for GPD computation.
  • domain assumption Truncation to three-quark, three-quark-gluon, and three-quark-quark-antiquark Fock sectors is sufficient
    Limits the Hilbert space used to obtain the light-front wave functions.

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Reference graph

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