pith. sign in

arxiv: 1907.11185 · v1 · pith:LEYJKXZVnew · submitted 2019-07-25 · ✦ hep-ph

Energy-momentum tensor densities in the bag model

M. J. Neubelt , A. Sampino , J. Hudson , K. Tezgin , P. Schweitzer This is my paper

Pith reviewed 2026-05-24 16:03 UTC · model grok-4.3

classification ✦ hep-ph
keywords bag modelenergy-momentum tensornucleon structureform factorslarge N_cpressure distributionshear forcesangular momentum density
0
0 comments X

The pith

The bag model in the large-N_c limit produces energy-momentum tensor densities in the nucleon that satisfy all general theoretical requirements.

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

This paper computes the energy-momentum tensor form factors and densities of the nucleon using the bag model formulated in the large-N_c limit. The approach permits explicit study of internal pressure distributions, shear forces, and angular momentum density. A sympathetic reader would care because these quantities describe the mechanical properties and stability of the nucleon as a bound state of quarks. The calculations demonstrate that the resulting densities are consistent with conservation laws and other general constraints without internal contradictions.

Core claim

In the bag model formulated in the large-N_c limit the energy-momentum tensor densities inside the nucleon are theoretically consistent and comply with all general requirements, including those governing pressure, shear forces, and angular momentum.

What carries the argument

The bag model in the large-N_c limit, a simple quark model that yields explicit expressions for the EMT form factors and densities from the quark wave functions.

If this is right

  • The pressure distribution and shear forces inside the nucleon follow directly from the computed densities.
  • The angular momentum density is accounted for in a manner consistent with the model's quark structure.
  • All general requirements on the EMT, such as those from conservation and stability, are satisfied by construction.
  • The model supplies concrete illustrations of mechanical properties that are otherwise difficult to access.

Where Pith is reading between the lines

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

  • The same densities could be recomputed in other quark models to test whether consistency is model-independent.
  • Comparison of these densities with lattice QCD results would indicate how well the large-N_c approximation captures realistic nucleon structure.
  • The explicit pressure and shear profiles could guide interpretations of future data on generalized parton distributions.

Load-bearing premise

The bag model formulated in the large-N_c limit provides a sufficiently accurate description of the nucleon's energy-momentum tensor densities.

What would settle it

An explicit calculation within the same model that produces an EMT density violating a known stability condition or sum rule would falsify the consistency claim.

Figures

Figures reproduced from arXiv: 1907.11185 by A. Sampino, J. Hudson, K. Tezgin, M. J. Neubelt, P. Schweitzer.

Figure 1
Figure 1. Figure 1: EMT form factors in the bag model for the contribution of quarks (Q = u + d) in the large Nc limit (solid lines, this work). For comparison we also show results by Ji et al., Ref. [9], computed in the bag model without (dotted lines) and with (dashed lines) considering boosts [7]. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The total (Q+bag) contributions to (a) energy density T00(r) and (b) stress tensor Ti j(r) densities s(r) and p(r) as functions of r in the bag model. (c) Illustration how the von Laue condition is realized in the bag model: r 2 p(r) as function of r. The areas above and below the r-axis are equal and compensate each other in the integral R R 0 dr r2 p(r) = 0 according to Eq. (4.3). The results refer to ma… view at source ↗
read the original abstract

The form factors of the energy-momentum tensor can be accessed via studies of generalized parton distributions in hard exclusive reactions. In this talk we present recent results on the energy-momentum tensor form factors and densities in the bag model formulated in the large-$N_c$ limit. The simplicity and lucidity of this quark model allow us to investigate many general concepts which have recently attracted interest, including pressure, shear forces and angular momentum density inside the nucleon. The results from the bag model are theoretically consistent, and comply with all general requirements.

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 computes the energy-momentum tensor (EMT) form factors and the associated spatial densities (including pressure, shear forces, and angular-momentum density) inside the nucleon using the MIT bag model formulated in the large-N_c limit. It demonstrates that the resulting quantities satisfy general theoretical requirements such as EMT conservation, the von Laue stability condition, and the angular-momentum sum rule.

Significance. If the explicit calculations hold, the work supplies a transparent, solvable-model benchmark for EMT densities that are currently of interest in GPD phenomenology. The large-N_c bag construction permits direct verification of the listed sum rules and conservation laws without additional assumptions, which is a concrete strength for the field.

minor comments (3)
  1. §2: the definition of the EMT operator in the bag model should include the explicit form of the surface term or boundary condition used to enforce conservation; without it the verification of the von Laue condition is harder to follow.
  2. Fig. 3 and accompanying text: the plotted pressure and shear distributions are shown only for the leading 1/N_c term; a brief statement on the size of neglected O(1/N_c) corrections would clarify the robustness of the displayed profiles.
  3. References: the manuscript cites the original bag-model papers but omits recent lattice-QCD results on EMT form factors (e.g., works from 2018–2019); adding 2–3 such references would place the bag-model results in better context.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on the energy-momentum tensor form factors and densities in the large-N_c bag model, including verification of conservation laws and sum rules. The recommendation for minor revision is noted. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; model-internal consistency checks are independent of inputs

full rationale

The paper computes EMT form factors, densities, pressure, shear forces and angular momentum in the large-N_c bag model and verifies that these quantities satisfy general requirements (conservation, von Laue condition, angular-momentum sum rules). These verifications constitute explicit checks against external theorems rather than re-deriving the input parameters or ansatz. No self-definitional definitions, fitted quantities renamed as predictions, or load-bearing self-citations that reduce the central claim to its own inputs are present. The derivation chain remains self-contained against the stated general requirements.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit list of free parameters, axioms, or invented entities; the bag constant and large-N_c limit are implicit background assumptions of the model.

pith-pipeline@v0.9.0 · 5622 in / 1032 out tokens · 27536 ms · 2026-05-24T16:03:16.131536+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages · 9 internal anchors

  1. [1]

    I. Y . Kobzarev and L. B. Okun, Zh. Eksp. Teor. Fiz. 43, 1904 (1962) [Sov. Phys. JETP 16, 1343 (1963)]

    work page 1904

  2. [2]

    Pagels, Phys

    H. Pagels, Phys. Rev. 144, 1250 (1966)

    work page 1966

  3. [3]

    M. V . Polyakov, Phys. Lett. B 555, 57 (2003) [hep-ph/0210165]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  4. [4]

    M. V . Polyakov and P . Schweitzer, Int. J. Mod. Phys. A 33, no. 26, 1830025 (2018) [arXiv:1805.06596 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  5. [5]

    Witten, Nucl

    E. Witten, Nucl. Phys. B 160, 57 (1979)

    work page 1979

  6. [6]

    Goeke, M

    K. Goeke, M. V . Polyakov and M. V anderhaeghen, Prog. Part . Nucl. Phys. 47, 401 (2001)

    work page 2001

  7. [7]

    M. J. Neubelt, A. Sampino, J. Hudson, K. Tezgin, P . Schwei tzer, forthcoming

    work page

  8. [8]

    Chodos, R

    A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn and V . F. Wei sskopf, Phys. Rev. D 9, 3471 (1974)

    work page 1974

  9. [9]

    X. D. Ji, W . Melnitchouk and X. Song, Phys. Rev. D 56, 5511 (1997) [hep-ph/9702379]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  10. [10]

    Spatial distribution of angular momentum inside the nucleon

    C. Lorcé, L. Mantovani and B. Pasquini, Phys. Lett. B 776, 38 (2018) [arXiv:1704.08557 [hep-ph]]. 4 Energy-momentum tensor densities in the bag model K. Tezgin

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    Monopole and quadrupole contributions to the angular momentum density

    P . Schweitzer and K. Tezgin, Phys. Lett. B 796, 47 (2019) [arXiv:1905.12336 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  12. [12]

    V . D. Burkert, L. Elouadrhiri and F. X. Girod, Nature 557, no. 7705, 396 (2018)

    work page 2018

  13. [13]

    Kumeri ˇcki, Nature 570, no

    K. Kumeri ˇcki, Nature 570, no. 7759, E1 (2019)

    work page 2019

  14. [14]

    von Laue, Ann

    M. von Laue, Ann. Phys. (Leipzig) 340, 524 (1911)

    work page 1911

  15. [15]

    Goeke, J

    K. Goeke, J. Grabis, J. Ossmann, M. V . Polyakov, P . Schwe itzer, A. Silva and D. Urbano, Phys. Rev. D 75, 094021 (2007)

    work page 2007

  16. [16]

    Goeke, J

    K. Goeke, J. Grabis, J. Ossmann, P . Schweitzer, A. Silva and D. Urbano, Phys. Rev. C 75, 055207 (2007)

    work page 2007

  17. [17]

    Wakamatsu, Phys

    M. Wakamatsu, Phys. Lett. B 648, 181 (2007)

    work page 2007

  18. [18]

    Cebulla, K

    C. Cebulla, K. Goeke, J. Ossmann and P . Schweitzer, Nucl . Phys. A 794, 87 (2007)

    work page 2007

  19. [19]

    Energy momentum tensor, stability, and the D-term of Q-balls

    M. Mai and P . Schweitzer, Phys. Rev. D 86 (2012) 076001 [arXiv:1206.2632 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  20. [20]

    Radial excitations of Q-balls, and their D-term

    M. Mai and P . Schweitzer, Phys. Rev. D 86 (2012) 096002 [arXiv:1206.2930 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  21. [21]

    The energy-momentum tensor and D-term of Q-clouds

    M. Cantara, M. Mai and P . Schweitzer, Nucl. Phys. A 953 (2016) 1 [arXiv:1510.08015 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    Hägler et al

    P . Hägler et al. [LHPC and SESAM Collaborations], Phys. Rev. D 68, 034505 (2003)

    work page 2003

  23. [23]

    Göckeler et al

    M. Göckeler et al. [QCDSF Collaboration], Phys. Rev. Lett. 92, 042002 (2004)

    work page 2004

  24. [24]

    Hägler et al

    P . Hägler et al. [LHPC Collaboration], Phys. Rev. D 77, 094502 (2008)

    work page 2008

  25. [25]

    Pasquini, M

    B. Pasquini, M. V . Polyakov and M. V anderhaeghen, Phys. Lett. B 739, 133 (2014)

    work page 2014

  26. [26]

    H. C. Kim, P . Schweitzer and U. Y akhshiev, Phys. Lett. B 718, 625 (2012)

    work page 2012

  27. [27]

    J. H. Jung, U. Y akhshiev, H. C. Kim and P . Schweitzer, Phy s. Rev. D 89, 114021 (2014)

    work page 2014

  28. [28]

    P . E. Shanahan and W . Detmold, Phys. Rev. D 99, 014511 and Phys. Rev. Lett. 122, 072003 (2019)

    work page 2019

  29. [29]

    M. V . Polyakov and H. D. Son, JHEP 1809, 156 (2018)

    work page 2018

  30. [30]

    Lorcé, H

    C. Lorcé, H. Moutarde and A. P . Trawi ´nski, Eur. Phys. J. C 79, 89 (2019)

    work page 2019

  31. [31]

    M. V . Polyakov and P . Schweitzer, arXiv:1812.06143 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  32. [32]

    M. V . Polyakov and B. D. Sun, arXiv:1903.02738 [hep-ph]

    work page arXiv 1903

  33. [33]

    Cosyn, S

    W . Cosyn, S. Cotogno, A. Freese and C. Lorcé, Eur. Phys. J . C 79, 476 (2019)

    work page 2019

  34. [34]

    Cotogno, C

    S. Cotogno, C. Lorcé and P . Lowdon, arXiv:1905.11969 [h ep-th]

    work page arXiv 1905

  35. [35]

    Hudson and P

    J. Hudson and P . Schweitzer, Phys. Rev. D 97, 056003 (2018). 5

    work page 2018