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arxiv: 2605.31030 · v1 · pith:KQ7GHMPAnew · submitted 2026-05-29 · ✦ hep-ph

Nuclear matter and proton parton distributions in a light-front Hamiltonian framework

Xiaoyi Wu , Sreeraj Nair , Satvir Kaur , Chandan Mondal , Jiangshan Lan , Xingbo Zhao , J. P. B. C. de Melo , Tobias Frederico This is my paper

Pith reviewed 2026-06-28 22:08 UTC · model grok-4.3

classification ✦ hep-ph
keywords nuclear matterlight-front quantizationquark-meson couplingparton distribution functionsmedium effectssaturation densitygluon probabilityvalence quarks
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The pith

At nuclear saturation density the nucleon gains slight gluon probability while valence probability and quark momentum fraction drop, with quark and gluon distributions enhanced at large x.

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

The paper develops a light-front Hamiltonian formulation of symmetric nuclear matter inside the quark-meson coupling model and solves the in-medium nucleon eigenvalue problem with Basis Light-Front Quantization. The Hamiltonian includes confinement in the valence sector and is limited to at most one dynamical gluon; medium effects enter through density-dependent scalar and vector mean fields that produce a self-consistent effective quark mass. This setup reproduces empirical values for energy per nucleon, pressure, and incompressibility at the saturation point. The calculation then extracts shifts in the nucleon wave-function probabilities and the resulting unpolarized parton distributions.

Core claim

Within this light-front framework, at nuclear saturation density the gluon probability in the nucleon wave function increases slightly while the valence probability and quark momentum fraction decrease. The unpolarized quark and gluon distributions exhibit a noticeable enhancement at large momentum fraction x ≳ 0.4 when evolved to Q² = 10 GeV².

What carries the argument

Basis Light-Front Quantization of the in-medium nucleon eigenvalue problem inside the quark-meson coupling model with mean-field scalar and vector fields and truncation to one dynamical gluon

If this is right

  • Energy per nucleon, pressure, and incompressibility remain consistent with empirical constraints at saturation density.
  • Gluon probability in the nucleon wave function rises slightly at saturation density.
  • Valence probability and quark momentum fraction decrease at the same density.
  • Unpolarized quark and gluon distributions are enhanced at x ≳ 0.4 at the evolved scale Q² = 10 GeV².

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 used to compute nuclear modification factors for deep-inelastic scattering at high x.
  • Extending the gluon truncation beyond one dynamical gluon would test the robustness of the large-x enhancement.
  • The density-dependent mass shift could be applied to other observables such as the EMC effect in different nuclei.

Load-bearing premise

The truncation of the Hamiltonian to at most one dynamical gluon together with the mean-field treatment of medium effects.

What would settle it

A measurement showing no enhancement in nuclear quark or gluon distributions at x ≳ 0.4 when evolved to Q² = 10 GeV² would contradict the predicted medium-induced changes.

Figures

Figures reproduced from arXiv: 2605.31030 by Chandan Mondal, Jiangshan Lan, J. P. B. C. de Melo, Satvir Kaur, Sreeraj Nair, Tobias Frederico, Xiaoyi Wu, Xingbo Zhao.

Figure 1
Figure 1. Figure 1: Top. Quark masses as a function of ρ/ρ0 for the QMC-BLFQ model compared with the QMC model [28], where the u and d quarks are degen￾erate. Bottom. Ratio M∗ N /MN as a function of ρ/ρ0 for the QMC-BLFQ model, compared with the Walecka model (LHS) [29], medium-modified holo￾graphic hadron dynamics (MHD) [30], the modified quark–meson coupling model (MQMC) [26], and relativistic mean-field parametrizations BK… view at source ↗
Figure 2
Figure 2. Figure 2: Energy per nucleon and pressure vs. ρ/ρ0 for the present QMC-BLFQ model and other models/parametrizations: LHS [29], MHD [30], BKA20 [31], BSR10 [32] and IU-FSU [33]. Bands: data extracted from [34–36] (top left), [37] (top right), [38] (bottom left), [34] and references therein (bottom right). is obtained simultaneously with the self-consistent solution of Eq. (15) for the scalar mean field. The advantage… view at source ↗
Figure 4
Figure 4. Figure 4: presents the ratio of down to up quark PDFs in the proton, f d ρ/ρ0 (x)/ f u ρ/ρ0 (x), as a function of x. The results are obtained within the QMC-BLFQ framework at three nuclear densities: ρ/ρ0 = 0 (vacuum), ρ/ρ0 = 0.662 (moderate), and ρ/ρ0 = 1.583 (high). Calculations are shown both at the ini￾tial model scale, µ 2 0 = 0.291 GeV2 , and after QCD evolution x 0 0.2 0.4 0.6 0.8 1 (x) 0 ρ / u ρ (x)/f 0 ρ / … view at source ↗
Figure 3
Figure 3. Figure 3: PDFs of the proton obtained within the QMC-BLFQ framework at the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

We develop a light-front Hamiltonian formulation of symmetric nuclear matter within the quark-meson coupling model, using Basis Light-Front Quantization to solve the in-medium nucleon eigenvalue problem. The Hamiltonian incorporates confinement in the valence sector and is truncated to include up to one dynamical gluon. Medium effects are introduced via scalar and vector mean fields, yielding a self-consistent, density-dependent effective quark mass and modified nucleon structure. The resulting energy per nucleon, pressure, and incompressibility are consistent with empirical constraints at the saturation point. At nuclear saturation density, the gluon probability in the nucleon wave function increases slightly, while the valence probability and quark momentum fraction decrease. The unpolarized quark and gluon distributions show a noticeable enhancement at large momentum fraction ($x \gtrsim 0.4$), illustrated at an evolved scale of $Q^{2} = 10 \mathrm{GeV}^{2}$.

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 / 0 minor

Summary. The paper develops a light-front Hamiltonian formulation of symmetric nuclear matter in the quark-meson coupling model, solved via Basis Light-Front Quantization (BLFQ). The Hamiltonian includes confinement in the valence sector and is truncated to at most one dynamical gluon; medium effects enter through self-consistent, density-dependent scalar and vector mean fields that modify the effective quark mass and nucleon structure. At saturation density the calculation yields a slight increase in gluon probability, a decrease in valence probability and quark momentum fraction, and an enhancement of unpolarized quark and gluon distributions at x ≳ 0.4 (shown at Q² = 10 GeV²), while the energy per nucleon, pressure, and incompressibility remain consistent with empirical constraints.

Significance. If the reported medium-induced shifts in parton distributions survive beyond the one-gluon truncation, the work supplies a Hamiltonian-based route from nuclear saturation properties to modifications of nucleon PDFs. The self-consistent mean-field treatment combined with BLFQ offers a technically novel framework that could be extended to polarized distributions or finite nuclei. The strength of the approach lies in its explicit light-front dynamics and the direct link between bulk nuclear observables and parton-level quantities.

major comments (2)
  1. [Abstract] Abstract (and the description of the Hamiltonian truncation): the central claims of a slight increase in gluon probability and a noticeable large-x enhancement rest on a Fock-space cutoff limited to valence plus at most one dynamical gluon. Because the gluon sector cannot accommodate additional emission or absorption channels, the medium-induced redistribution of momentum between quarks and gluons is computed in a restricted Hilbert space whose response may not be representative of the full theory.
  2. [Abstract] Abstract: the self-consistent solution at saturation density employs free parameters (confinement strength and quark-meson coupling constants) that are adjusted to nuclear data. It is therefore unclear whether the reported changes in valence probability, gluon probability, and large-x distributions constitute independent predictions or are largely shaped by those fits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, clarifying the scope of our approximations and the predictive nature of the parton-distribution results within the model. We propose targeted revisions to the abstract and text to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the description of the Hamiltonian truncation): the central claims of a slight increase in gluon probability and a noticeable large-x enhancement rest on a Fock-space cutoff limited to valence plus at most one dynamical gluon. Because the gluon sector cannot accommodate additional emission or absorption channels, the medium-induced redistribution of momentum between quarks and gluons is computed in a restricted Hilbert space whose response may not be representative of the full theory.

    Authors: We agree that the Fock-space truncation to valence quarks plus at most one dynamical gluon restricts the gluon dynamics and that the reported medium-induced shifts are obtained within this limited Hilbert space. The manuscript already states the truncation explicitly in the Hamiltonian section and notes that higher Fock components are omitted. The results therefore constitute a controlled first exploration rather than a claim about the complete theory. We will revise the abstract to emphasize that all quantitative statements refer to the one-gluon truncation and will add a brief remark on the expected direction of future extensions. revision: yes

  2. Referee: [Abstract] Abstract: the self-consistent solution at saturation density employs free parameters (confinement strength and quark-meson coupling constants) that are adjusted to nuclear data. It is therefore unclear whether the reported changes in valence probability, gluon probability, and large-x distributions constitute independent predictions or are largely shaped by those fits.

    Authors: The confinement strength and quark-meson couplings are fixed once by reproducing the empirical saturation point (binding energy per nucleon and saturation density). With these parameters held fixed, the density-dependent mean fields are solved self-consistently and the resulting light-front wave functions determine the parton distributions. The modifications to valence and gluon probabilities and to the large-x distributions are therefore genuine predictions of the model at the parton level, given the nuclear-matter constraints. We will insert a clarifying sentence in the abstract and introduction to make this separation explicit. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained; no circular reductions identified

full rationale

The paper constructs the in-medium nucleon wave function by solving the light-front Hamiltonian eigenvalue problem in BLFQ under a Fock-space truncation (valence plus at most one dynamical gluon) with density-dependent scalar and vector mean fields taken from the quark-meson coupling model. The resulting probabilities, momentum fractions, and evolved distributions at saturation density are direct outputs of that solution; the reported consistency of energy per nucleon, pressure, and incompressibility with empirical values is presented as a validation check rather than an input that forces the parton-distribution shifts. No equations are shown that define a quantity in terms of itself, rename a fit as a prediction, or reduce the central claim to a self-citation chain. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard light-front QCD assumptions plus the quark-meson coupling mean-field treatment; several parameters are expected to be fixed by fitting to nucleon and nuclear data.

free parameters (2)
  • confinement strength
    Standard parameter in light-front valence-sector Hamiltonian, fitted to free-nucleon properties
  • quark-meson coupling constants
    Adjusted to reproduce nuclear saturation density and binding energy
axioms (2)
  • domain assumption Hamiltonian truncated to at most one dynamical gluon
    Explicitly stated in abstract as the truncation level used
  • domain assumption Medium effects captured entirely by uniform scalar and vector mean fields
    Core modeling choice of the quark-meson coupling approach

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discussion (0)

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Reference graph

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