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arxiv: 2604.07616 · v1 · submitted 2026-04-08 · ✦ hep-ph · nucl-th

Recognition: unknown

Transverse energy-momentum tensor distributions in polarized nucleons

C\'edric Lorc\'e, Ho-Yeon Won

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:01 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords energy-momentum tensorpolarized nucleonslight-front distributionsphase-space formalismtransverse componentsinfinite-momentum framemultipole structurerelativistic nucleon structure
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The pith

The quantum phase-space formalism reproduces standard light-front distributions of the transverse energy-momentum tensor in polarized nucleons 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.

This paper completes the application of the quantum phase-space formalism to the energy-momentum tensor distributions inside polarized nucleons by focusing on components with transverse indices. It investigates how these distributions appear in a moving nucleon through their multipole expansion. A central result is the demonstration that, when boosted to the infinite-momentum frame, the formalism recovers the familiar light-front distributions, including those involving bad components, while accounting for the reasons behind their specific forms. Such a connection matters because it offers a consistent relativistic description of how energy and momentum are spatially arranged in spinning nucleons, bridging different theoretical frameworks used in high-energy physics.

Core claim

Within the quantum phase-space formalism, the transverse components of the energy-momentum tensor are studied for polarized nucleons. The multipole structure of the distributions is explored in a moving frame. In the infinite-momentum frame, the approach reproduces the standard light-front distributions, including those with a bad component, and explains the origin of their structure.

What carries the argument

Quantum phase-space formalism applied to the transverse energy-momentum tensor distributions in polarized nucleons.

If this is right

  • Transverse EMT distributions in moving nucleons display a multipole structure that can be analyzed systematically.
  • The formalism provides a unified view that includes both good and bad components of light-front distributions.
  • The structure of the distributions originates from the relativistic treatment of the nucleon's internal dynamics.
  • This extends previous studies to complete the description of all EMT components.

Where Pith is reading between the lines

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

  • The reproduction in the infinite-momentum frame suggests that phase-space methods could be used to derive light-front results more generally without direct computation in that frame.
  • Connections to experimental probes of nucleon structure, such as in deep inelastic scattering, may become clearer through this spatial distribution picture.
  • Similar extensions could be applied to other operators or to unpolarized cases to test consistency.

Load-bearing premise

The quantum phase-space formalism accurately describes the relativistic spatial distributions of the energy-momentum tensor inside polarized nucleons.

What would settle it

Explicit computation of the transverse EMT distributions using an alternative method, such as direct light-front wave function overlap, that yields different results for the bad components in the infinite-momentum frame would falsify the reproduction claim.

Figures

Figures reproduced from arXiv: 2604.07616 by C\'edric Lorc\'e, Ho-Yeon Won.

Figure 1
Figure 1. Figure 1: FIG. 1: EF radial distributions in the transverse plane of LT (Π [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: EF distributions of total (i.e., quarks + gluons) LT (Π [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: EF monopolar (upper row) and dipolar (lower row) radial distributions in the transverse plane of 2D [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: EF distributions of total (i.e., quarks + gluons) transverse isotropic stress in the transverse plane for a [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: EF dipolar (upper row), quadrupolar (middle row), and octupolar (lower row) radial distributions in the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: EF distribution of total (i.e., quarks + gluons) transverse anisotropic stress for a nucleon polarized along [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We complete our study of the relativistic spatial distributions of the energy-momentum tensor inside polarized nucleons within the quantum phase-space formalism. In the present work, we focus on the components of the energy-momentum tensor involving at least one transverse index. We also explore the multipole structure of the transverse distributions in a moving nucleon. In the infinite-momentum frame, we show that the formalism reproduces the standard light-front distributions, including those with a ``bad'' component, and explains the origin of their structure.

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 / 3 minor

Summary. The manuscript completes the study of relativistic spatial distributions of the energy-momentum tensor inside polarized nucleons using the quantum phase-space formalism. It focuses on EMT components with at least one transverse index, examines the multipole structure for a moving nucleon, and shows that boosting to the infinite-momentum frame reproduces the standard light-front distributions (including those with a 'bad' component) while explaining the origin of their structure.

Significance. If the derivations hold, the work is significant for providing a unified phase-space framework that connects to and explains established light-front results for the EMT in nucleons. Reproducing known distributions including bad components, together with the multipole analysis, strengthens the formalism's applicability to relativistic nucleon structure and offers insight into transverse energy-momentum distributions.

minor comments (3)
  1. The abstract states that the formalism reproduces light-front distributions including bad components, but the main text should explicitly identify which equations or sections contain the boost to the infinite-momentum frame and the reproduction proof to make the central claim easier to verify.
  2. Notation for transverse indices and polarization vectors should be defined once at the start of the formalism section and used consistently; occasional redefinitions risk confusion when comparing to light-front literature.
  3. Figure captions for multipole distributions should state the frame (lab vs. infinite-momentum) and the specific polarization state to avoid ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, which accurately summarizes our completion of the study on transverse energy-momentum tensor distributions in polarized nucleons using the quantum phase-space formalism. We appreciate the recognition of the work's significance in unifying the phase-space approach with established light-front results, including the reproduction of distributions with bad components and the multipole analysis.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies an established quantum phase-space formalism to derive transverse EMT distributions and multipole structures for polarized nucleons, then verifies that boosting to the infinite-momentum frame recovers known light-front distributions (including bad components). This reproduction functions as an external consistency check against standard results rather than a self-referential fit or redefinition. No load-bearing step reduces by construction to the paper's own inputs, fitted parameters, or unverified self-citations; the derivation chain remains independent and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available so ledger is inferred from typical assumptions in this subfield: standard relativistic quantum mechanics and QCD operator definitions.

axioms (1)
  • domain assumption Quantum phase-space formalism applies to relativistic nucleon states
    Central to the entire calculation as stated in abstract.

pith-pipeline@v0.9.0 · 5374 in / 1053 out tokens · 54843 ms · 2026-05-10T17:01:46.221129+00:00 · methodology

discussion (0)

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Reference graph

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    However, they undergo a Wigner spin rotation, in addition to the distortion arising from the relativistic normalization fac- tor in⟨⟨T ij⟩⟩

    Isotropic stressσ In contrast to vector components, the tensor EMT components involve only transverse indices, and there- fore do not mix under a longitudinal boost. However, they undergo a Wigner spin rotation, in addition to the distortion arising from the relativistic normalization fac- tor in⟨⟨T ij⟩⟩. We then find that the matrix elements of the (tran...

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