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arxiv: 2503.07382 · v2 · submitted 2025-03-10 · ✦ hep-ph

Relativistic energy-momentum tensor distributions in a polarized nucleon

Ho-Yeon Won , C\'edric Lorc\'e This is my paper

Pith reviewed 2026-05-23 00:44 UTC · model grok-4.3

classification ✦ hep-ph
keywords energy-momentum tensorpolarized nucleonlight-front distributionsinfinite-momentum framequantum phase-spaceBreit frameLorentz boosts
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0 comments X

The pith

Including nucleon polarization allows relativistic energy-momentum distributions to recover both good and bad light-front components in the infinite-momentum frame.

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

The paper examines distributions of energy, longitudinal momentum, energy flux and thrust inside nucleons using a quantum phase-space formalism that incorporates the nucleon's polarization. It shows that polarization is required for these distributions to transform correctly under longitudinal Lorentz boosts from the Breit frame. In the infinite-momentum frame the polarized distributions recover the complete light-front energy-momentum tensor, including its bad components that are otherwise inaccessible. A sympathetic reader would care because this supplies a concrete bridge between different frames used to picture nucleon structure. The result clarifies how spin affects the internal flow of energy and momentum at relativistic speeds.

Core claim

The relativistic distributions of energy, longitudinal momentum, longitudinal energy flux, and longitudinal thrust inside nucleons are derived from the quantum phase-space formalism with polarization effects included. These distributions transform properly under longitudinal Lorentz boosts, and in the infinite-momentum frame they allow recovery of not only the good but also the bad components of the light-front energy-momentum tensor distributions.

What carries the argument

Quantum phase-space distributions of energy-momentum tensor components that incorporate nucleon polarization to ensure correct transformation under longitudinal boosts.

If this is right

  • Breit-frame distributions transform correctly under boosts only when polarization is included.
  • The infinite-momentum frame yields the full light-front energy-momentum tensor including its bad components.
  • Polarization effects are essential for understanding how energy and momentum flow inside nucleons changes with reference frame.
  • The same polarization requirement found for the electromagnetic current applies to the energy-momentum tensor.

Where Pith is reading between the lines

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

  • The method may be applied to other tensor operators such as those for angular momentum to obtain their bad components as well.
  • It offers a route to compute quantities that are difficult to access directly in light-front calculations.
  • High-energy experiments sensitive to nucleon spin could test whether the recovered bad components affect observable asymmetries.

Load-bearing premise

The quantum phase-space formalism correctly incorporates nucleon polarization and yields distributions that transform properly under longitudinal Lorentz boosts.

What would settle it

An explicit calculation in the infinite-momentum frame that shows the bad components of the light-front energy-momentum tensor are not recovered when polarization is omitted from the phase-space distributions.

Figures

Figures reproduced from arXiv: 2503.07382 by C\'edric Lorc\'e, Ho-Yeon Won.

Figure 1
Figure 1. Figure 1: FIG. 1: Radial EF energy distributions in an unpolarized nucleon for different values of the nucleon momentum. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: EF energy distributions at [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Total EF energy distributions in the transverse plane of a nucleon polarized along the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Total EF frame distributions of longitudinal momentum and longitudinal energy flux in the transverse plane [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Total EF frame distributions of axial momentum flux in the transverse plane of a nucleon polarized along [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Dependence of the quark OAM FF on the quark axial singlet dipole mass Λ [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Evolution of the BF distribution of longitudinal momentum in the transverse plane for different values of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Radial EF distributions of longitudinal momentum in an unpolarized nucleon for different values of the [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Radial EF distributions of axial momentum flux in an unpolarized nucleon for different values of the [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: EF distributions of longitudinal momentum at [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: EF distributions of axial momentum flux at [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
read the original abstract

We study in detail the relativistic distributions of energy, longitudinal momentum, longitudinal energy flux, and longitudinal thrust inside nucleons based on the quantum phase-space formalism. Similar to recent studies on the electromagnetic current, we include the effects of the nucleon polarization and show that the latter are essential for understanding how the Breit frame distributions transform under a longitudinal Lorentz boost. We also explicitly demonstrate that, in the infinite-momentum frame, these distributions allow one to recover not only the ``good'' but also the ``bad'' components of the light-front energy-momentum tensor distributions.

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

0 major / 0 minor

Summary. The paper studies in detail the relativistic distributions of energy, longitudinal momentum, longitudinal energy flux, and longitudinal thrust inside nucleons based on the quantum phase-space formalism. It includes the effects of the nucleon polarization and shows that the latter are essential for understanding how the Breit frame distributions transform under a longitudinal Lorentz boost. The authors explicitly demonstrate that, in the infinite-momentum frame, these distributions allow one to recover not only the ``good'' but also the ``bad'' components of the light-front energy-momentum tensor distributions.

Significance. If the derivations hold, the work advances understanding of frame-dependent EMT distributions in nucleons by showing polarization is required for correct boost transformations and by recovering both good and bad light-front components explicitly. The reliance on standard quantum phase-space methods without ad-hoc parameters is a positive feature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the detailed summary of our results on relativistic EMT distributions and the explicit recovery of both good and bad light-front components in the IMF. We appreciate the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper applies the standard quantum phase-space formalism to derive relativistic EMT distributions, explicitly incorporating polarization effects and demonstrating their role in Lorentz boosts and recovery of light-front components in the IMF. All load-bearing steps are explicit derivations from the formalism rather than reductions to fitted parameters, self-definitions, or unverified self-citations. No quoted equations or claims reduce the central results to inputs by construction. This is the expected outcome for a theoretical derivation paper resting on established methods.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are identifiable. Full text would be required to audit the formalism's assumptions.

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Forward citations

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