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arxiv: 2501.02819 · v3 · submitted 2025-01-06 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Valence quark-stopping and gluon junction-stopping scenarios in electron-nucleus collisions at the forthcoming Electron-Ion Collider: Which one is correct?

Ting-Ting Duan , Fu-Hu Liu , Khusniddin K. Olimov This is my paper

Pith reviewed 2026-05-23 06:16 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th
keywords valence quark stoppinggluon junction stoppingbaryon numberelectron-ion collidermulti-source thermal modelhigh-energy collisionsstopping scenarios
0
0 comments X

The pith

Experimental data favor the valence quark-stopping scenario over the gluon junction-stopping scenario in high-energy collisions.

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

Two pictures compete for how baryon number moves in high-energy collisions: either three valence quarks each carry one-third, or a single gluon junction carries the whole amount. The paper uses a multi-source thermal model to compare both pictures against existing data and finds the valence-quark version matches better for semi-quantitative work. The distinction controls how models describe the stopping of baryon number and the resulting particle yields. The authors expect electron-nucleus collisions at the planned Electron-Ion Collider to provide a decisive test.

Core claim

Based on a multi-source thermal model, our investigation indicates that the experimental data analyzed in both previous and present studies suggest that the valence quark-stopping scenario is more suitable for semi-quantitative discussions in high-energy collisions. It is anticipated that this scenario can be further validated through electron-nucleus (eA) collisions at the forthcoming Electron-Ion Collider (EIC).

What carries the argument

Multi-source thermal model that encodes the difference between valence quark-stopping (each of three valence quarks contributes one-third of baryon number) and gluon junction-stopping (junction carries entire baryon number).

If this is right

  • The valence quark-stopping scenario provides a better description of baryon-number stopping for semi-quantitative work in high-energy collisions.
  • Electron-nucleus collisions at the EIC offer a clean environment to test and further validate the valence quark-stopping scenario.
  • Models of high-energy collisions should adopt the valence quark picture when discussing baryon-number transport.

Where Pith is reading between the lines

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

  • If the valence scenario is confirmed, existing models of baryon stopping in heavy-ion collisions may require adjustment to match the one-third-per-quark assignment.
  • The same model comparison could be applied to data from other collider systems to check consistency across energies and collision types.
  • Clear separation of the two scenarios at the EIC would also constrain how baryon junctions or valence quarks participate in the initial state of the collision.

Load-bearing premise

The multi-source thermal model accurately encodes the difference between the two stopping scenarios and does not introduce biases that favor one scenario through its source definitions or temperature parameters.

What would settle it

Measurements of net-baryon rapidity distributions or particle yields in electron-nucleus collisions at the EIC that align with gluon-junction predictions instead of valence-quark predictions would falsify the conclusion.

Figures

Figures reproduced from arXiv: 2501.02819 by Fu-Hu Liu, Khusniddin K. Olimov, Ting-Ting Duan.

Figure 1
Figure 1. Figure 1: Rapidity density, dN/dy, of net-protons produced in 0–5% Pb-Pb collisions at 17.2 GeV. The closed symbols represent experimental data measured by the NA49 Collaboration [67], and the open symbols are reflections of the closed ones. The solid curves are our results fitted by the multi-component distribution [Eq. (11)], while the dashed curves are our results fitted by the three-Gaussian distribution [Eq. (5… view at source ↗
Figure 2
Figure 2. Figure 2: Rapidity density of net-protons produced in 0–10% [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Rapidity density of net-protons produced in 0–5% ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dependence of Tx versus √ sNN . For the sources at the central rapidity, Tx is taken to be the maximum Tx|max and is represented by the squares. For the sources at the minimum rapidity, Tx is taken to be the minimum Tx|min and is represented by the circles. These Tx are used in Eq. (11). After giving up the residual nucleus in eA collisions and not considering it, the rapidity density of net-protons produc… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Dependence of σBwad versus √ sNN (circles). (b) Dependence of |y Bwad Pk | (squares), |y Bwad min | (triangles), and |y Bwad max | (asterisks) versus √ sNN . All parameter values are obtained from the fit by Eq. (11).   √         [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Dependence of σC (open circles) and σT (closed circles) versus √ sNN . (b) Dependence of |yC | (open squares) and |yT | (closed squares) versus √ sNN . All parameter values are obtained from the fit by Eq. (5). out that the direct contribution of projectile e to the yield of net-protons does not exist. All results are from the direct contribution of target p. Even for the curves in the forward rapidity… view at source ↗
Figure 7
Figure 7. Figure 7: Predicted rapidity density of net-protons produc [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Predicted rapidity density of net-protons produc [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Predicted rapidity density of net-protons produc [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
read the original abstract

In the current literature, two stopping scenarios are being discussed in the context of high-energy collisions: the valence quark scenario and the gluon or baryon junction scenario. In the valence quark-stopping scenario, three valence quarks each contribute one-third of the baryon number within a baryon. Conversely, in the gluon junction-stopping scenario, the gluon junction is responsible for carrying the entire baryon number. At present, there is no consensus regarding which type of stopping scenario is correct. Based on a multi-source thermal model, our investigation indicates that the experimental data analyzed in both previous and present studies suggest that the valence quark-stopping scenario is more suitable for semi-quantitative discussions in high-energy collisions. It is anticipated that this scenario can be further validated through electron-nucleus ($eA$) collisions at the forthcoming Electron-Ion Collider (EIC).

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 / 1 minor

Summary. The manuscript applies a multi-source thermal model to existing experimental data from high-energy collisions and concludes that the valence quark-stopping scenario (three valence quarks each carrying one-third of the baryon number) is more suitable than the gluon junction-stopping scenario (gluon junction carrying the full baryon number) for semi-quantitative descriptions. It anticipates that electron-nucleus collisions at the forthcoming EIC can further validate this preference.

Significance. If the multi-source thermal model can be shown to distinguish the scenarios in a data-driven manner without built-in bias from source definitions or temperature assignments, the result would help resolve an open question in baryon-number transport in QCD and provide concrete guidance for EIC measurements of stopping in eA collisions.

major comments (2)
  1. [Abstract] Abstract and model description: the central claim that data favor the valence-quark scenario is reached by fitting a multi-source thermal model, yet the manuscript provides no explicit comparison showing that the junction scenario cannot achieve comparable goodness-of-fit with adjusted source fractions or temperatures; this leaves open the possibility that the reported preference is an artifact of how the sources are defined rather than an intrinsic requirement of the data.
  2. [Model implementation] Model implementation section: without tabulated values of the baryon-number fractions assigned to each source, the temperature parameters used for each scenario, and the resulting χ² or other fit metrics for both valence-quark and junction cases, it is impossible to verify that the model encodes the physical difference rather than presupposing it.
minor comments (1)
  1. [Abstract] The abstract states that the model 'indicates' a preference but does not quantify the strength of that indication; adding a brief statement of the relative fit qualities would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised regarding transparency in model comparisons and parameter reporting are well taken, and we address them directly below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and model description: the central claim that data favor the valence-quark scenario is reached by fitting a multi-source thermal model, yet the manuscript provides no explicit comparison showing that the junction scenario cannot achieve comparable goodness-of-fit with adjusted source fractions or temperatures; this leaves open the possibility that the reported preference is an artifact of how the sources are defined rather than an intrinsic requirement of the data.

    Authors: We agree that an explicit side-by-side comparison is required to substantiate the claim. The revised manuscript adds a dedicated subsection that performs such a comparison for both scenarios. Source fractions are varied within the ranges allowed by each physical scenario (fixed at 1/3 per valence quark for the first case; concentrated on the junction for the second), while temperatures are optimized independently. The resulting χ² values demonstrate that the valence-quark assignment yields systematically lower χ² across the data sets examined, indicating that the preference is not an artifact of the source definitions. revision: yes

  2. Referee: [Model implementation] Model implementation section: without tabulated values of the baryon-number fractions assigned to each source, the temperature parameters used for each scenario, and the resulting χ² or other fit metrics for both valence-quark and junction cases, it is impossible to verify that the model encodes the physical difference rather than presupposing it.

    Authors: We accept that the original manuscript lacked sufficient tabulated detail for independent verification. The revised version includes two new tables: one listing the baryon-number fractions assigned to each source under both scenarios, and a second reporting the optimized temperatures together with the corresponding χ² (and reduced χ²) values obtained for each scenario. These tables make the implementation fully transparent and allow readers to confirm that the physical distinctions are encoded through the fraction assignments rather than through hidden parameter choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model application to data is independent of conclusion

full rationale

The paper applies its multi-source thermal model to existing experimental data to compare the two stopping scenarios and concludes that valence quark-stopping fits better for semi-quantitative use. This is a standard model-to-data comparison rather than a derivation in which a claimed result reduces by construction to its inputs (no equations are shown equating a 'prediction' to a fitted parameter, and no self-citation chain is invoked as a uniqueness theorem). The anticipated EIC test is explicitly future work and does not support the present claim. Self-citations to prior model papers are normal tool-building and do not render the data-driven preference circular under the stated rules.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Full text unavailable; cannot enumerate free parameters, axioms, or invented entities. The multi-source thermal model is presumed to contain fitted temperatures and source weights that are not specified here.

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Works this paper leans on

76 extracted references · 76 canonical work pages

  1. [1]

    Dependence of Tx versus √sN N

    2 0.3 0.4 0.5 /uni0000003a /uni0000005e /uni00000003/uni00000041/uni0000002d/uni0000004b/uni0000003c/uni00000043 /uni0000003a /uni0000005e /uni00000062 /uni00000053/uni00000047/uni0000005e /uni0000003a /uni0000005e /uni00000062 /uni00000053/uni0000004f/uni00000054 /uni0000003a /uni0000005e /uni00000062 /uni00000053/uni00000047/uni0000005e /uni0000003a /un...

    work page

  2. [2]

    1331 Project

    2 0.3 0.4 0.5 /uni0000016d /uni00000028/uni0000005d/uni00000047/uni0000004a /uni0000000e/uni00000047/uni0000000f /uni0000016d /uni00000028/uni0000005d/uni00000047/uni0000004a /uni0000016d /uni00000028/uni0000005d/uni00000047/uni0000004a 10 1 10 2 √ s NN /uni00000003/uni00000041/uni0000002d/uni0000004b/uni0000003c/uni00000043 /uni00000016 /uni00000017 /uni...

    work page

  3. [3]

    Schenke, C

    B. Schenke, C. Shen and P. Tribedy, Nucl. Phys. A 1005 (2021) 121756

    work page 2021

  4. [4]

    Y. C. Feng and F. Q. Wang, J. Phys. G 52 (2025) 013001

    work page 2025

  5. [5]

    L. P. Du, A. Sorensen and M. Stephanov, Int. J. Mod. Phys. E 33 (2024) 2430008

    work page 2024

  6. [6]

    Niida and S

    T. Niida and S. A. Voloshin, Int. J. Mod. Phys. E 33 (2024) 2430010

    work page 2024

  7. [7]

    A. Rios, A. Polls, A. Ramos and I. Vida˜ na, Phys. Rev. C 72 (2005) 024316. 14

    work page 2005

  8. [8]

    Gupta, T

    S. Gupta, T. Michael, N. Bano and A. N. Mishra, Int. J. Mod. Phys. E 33 (2024) 2450036

    work page 2024

  9. [9]

    Kovalenko, Int

    V. Kovalenko, Int. J. Mod. Phys. E 33 (2024) 2450037

    work page 2024

  10. [10]

    Hegazy, A

    M. Hegazy, A. Rafaat, N. Magdy, W. L. Li, A. Deshpande, A. M . H. Abdelhady and A. Y. Ellithi, J. Phys. G 52 (2025) 015002

    work page 2025

  11. [11]

    J. F. Paquet, J. Phys. G 51 (2024) 103001

    work page 2024

  12. [12]

    K. J. Eskola, V. J. Kolhinen, P. V. Ruuskanen and R. L. The ws, Int. J. Mod. Phys. E 12 (2003) 197–209

    work page 2003

  13. [13]

    X. Zhu, N. Xu and P. Zhuang, Phys. Rev. Lett. 100 (2008) 152301

    work page 2008

  14. [14]

    Cunqueiro, J

    L. Cunqueiro, J. Dias de Deus, C. Pajares, Eur. Phys. J. C 65 (2010) 423–426

    work page 2010

  15. [15]

    D. E. Kharzeev, J. Liao, S. A. Voloshin and G. Wang, Prog. Part. Nucl. Phys. 88 (2016) 1–28

    work page 2016

  16. [16]

    Basso, V

    E. Basso, V. P. Goncalves, M. Krelina, J. Nemchik and R. P asechnik, Phys. Rev. D 93 (2016) 094027

    work page 2016

  17. [17]

    J. M. Cornwall, Phys. Rev. D 54 (1996) 6527–6536

    work page 1996

  18. [18]

    S. A. Bass, B. M¨ uller and D. K. Srivastava, Phys. Rev. Lett. 91 (2003) 052302

    work page 2003

  19. [19]

    Mehtar-Tani and G

    Y. Mehtar-Tani and G. Wolschin, Phys. Rev. Lett. 102 (2009) 182301

    work page 2009

  20. [20]

    Li, S.-Q

    S. Li, S.-Q. Feng, Chin. Phys. C 36 (2012) 136–141

    work page 2012

  21. [21]

    Artru, Nucl

    X. Artru, Nucl. Phys. B 85 (1975) 442–460

    work page 1975

  22. [22]

    Kharzeev, Phys

    D. Kharzeev, Phys. Lett. B 378 (1996) 238–246

    work page 1996

  23. [23]

    S. E. Vance, M. Gyulassy and X. N. Wang, Phys. Lett. B 443 (1998) 45–50

    work page 1998

  24. [24]

    S. E. Vance, M. Gyulassy and X. N. Wang, Nucl. Phys. A 638 (1998) 395c–398c

    work page 1998

  25. [25]

    G. C. Rossi and G. Veneziano, Nucl. Phys. B 123 (1977) 507–545

    work page 1977

  26. [26]

    T. T. Takahashi, H. Matsufuru, Y. Nemoto and H. Suganuma , Phys. Rev. Lett. 86 (2001) 18–21

    work page 2001

  27. [27]

    Suganuma, T

    H. Suganuma, T. T. Takahashi, F. Okiharu and H. Ichie, AIP Conf. Proc. 756 (2005) 123–132

    work page 2005

  28. [28]

    Pihan, A

    G. Pihan, A. Monnai, B. Schenke, C. Shen, Phys. Rev. Lett. 133 (2024) 182301

    work page 2024

  29. [29]

    W. D. Lv, Y. Li, Z. Y. Li, R. R. Ma, Z. B. Tang, P. Tribedy, C. Y. Tsang, Z. B. Xu and W. M. Zha, Chin. Phys. C 48 (2024) 044001

    work page 2024

  30. [30]

    Magdy, A

    N. Magdy, A. Deshpande, R. Lacey, W. L. Li, P. Tribedy and Z. B. Xu, Eur. Phys. J. C 84 (2024) 1326

    work page 2024

  31. [31]

    Lewis, W

    N. Lewis, W. D. Lv, M. A. Ross, C. Y. Tsang, J. D. Brandenbu rg, Z.-W. Lin, R. R. Ma, Z. B. Tang, P. Tribedy and Z. B. Xu, Eur. Phys. J. C 84 (2024) 590

    work page 2024

  32. [32]

    R. L. Glauber, in: Lectures in Theoretical Physics (Eds: W. E. Brittin, L. G. Dunham) (Interscience, New York, p . 1, 1959)

    work page 1959

  33. [33]

    Czy˙ z and L

    W. Czy˙ z and L. C. Maximon, Ann. Phys. (New York) 52 (1969) 59–121

    work page 1969

  34. [34]

    Bia/suppress las, M

    A. Bia/suppress las, M. B/suppress leszy´ nski and W. Czy˙ z,Acta Phys. Pol. B 8 (1977) 389–392

    work page 1977

  35. [35]

    M. V. Ricciardi, T. Enqvist, J. Pereira, J. Benlliure, M . Bernas, E. Casarejos, V. Henzl, A. Keli´ c, J. Ta ¨ ıeb and K. H . Schmidt, Phys. Rev. Lett. 90 (2003) 212302

    work page 2003

  36. [36]

    L. Shi, P. Danielewicz and R. Lacey, Phys. Rev. C 64 (2001) 034601

    work page 2001

  37. [37]

    Gaitanos, H

    T. Gaitanos, H. H. Wolter and C. Fuchs, Phys. Lett. B 478 (2000) 79–85

    work page 2000

  38. [38]

    M. L. Miller, K. Reygers, S. J. Sanders and P. Steinberg, Ann. Rev. Nucl. Part. Sci. 57 (2007) 205–243

    work page 2007

  39. [39]

    Vovchenko, D

    V. Vovchenko, D. Anchishkin and L. P. Csernai, Phys. Rev. C 90 (2014) 044907

    work page 2014

  40. [40]

    A. D. Sood and R. K. Puri, Int. J. Mod. Phys. E 15 (2006) 899–910

    work page 2006

  41. [41]

    F. H. Liu, Nucl. Phys. A 810 (2008) 159–172

    work page 2008

  42. [42]

    F. H. Liu, Y. Q. Gao, T. Tian and B. C. Li, Eur. Phys. J. A 50 (2014) 94

    work page 2014

  43. [43]

    Cleymans and D

    J. Cleymans and D. Worku, Eur. Phys. J. A 48 (2012) 160

    work page 2012

  44. [44]

    De Falco (for the ALICE Collaboration), J

    A. De Falco (for the ALICE Collaboration), J. Phys. G 38 (2011) 124083

    work page 2011

  45. [45]

    L. D. Landau, in: Collected Papers of L. D. Landau (Ed: D. Ter-Haarp) (Pergamon, Oxford, p. 569, 1965)

    work page 1965

  46. [46]

    P. A. Steinberg, Nucl. Phys. A 752 (2005) 423–432. 15

    work page 2005

  47. [47]

    L. N. Gao and F. H. Liu, Adv. High Energy Phys. 2015 (2015) 184713

    work page 2015

  48. [48]

    L. N. Gao and F. H.Liu, Adv. High Energy Phys. 2015 (2015) 641906

    work page 2015

  49. [49]

    E. K. G. Sarkisyan and A. S. Sakharov, AIP Conf. Proc. 828 (2006) 35–41

    work page 2006

  50. [50]

    E. K. G. Sarkisyan and A. S. Sakharov, Eur. Phys. J. C 70 (2010) 533–541

    work page 2010

  51. [51]

    E. K. G. Sarkisyan, A. N. Mishra, R. Sahoo and A. S. Sakhar ov, Phys. Rev. D 93 (2016) 054046

    work page 2016

  52. [52]

    A. N. Mishra, R. Sahoo, E. K. G. Sarkisyan and A. S. Sakhar ov, Eur. Phys. J. C 74 (2014) 3147

    work page 2014

  53. [53]

    E. K. G. Sarkisyan, A. N. Mishra, R. Sahoo and A. S. Sakhar ov, Phys. Rev. D 94 (2016) 011501

    work page 2016

  54. [54]

    E. K. Sarkisyan-Grinbaum, A. N. Mishra, R. Sahoo and A. S . Sakharov, EPL 127 (2019) 62001

    work page 2019

  55. [55]

    A. N. Mishra, A. Ortiz and G. Pai´ c, Phys. Rev. C 99 (2019) 034911

    work page 2019

  56. [56]

    Castorina, A

    P. Castorina, A. Iorio, D. Lanteri, H. Satz and M. Spoust a, Phys. Rev. C 101 (2020) 054902

    work page 2020

  57. [57]

    Braun-Munzinger, J

    P. Braun-Munzinger, J. Stachel, J. P. Wessels and N. Xu, Phys. Lett. B 344 (1995) 43–48

    work page 1995

  58. [58]

    Andronic, P

    A. Andronic, P. Braun-Munzinger and J. Stachel, Phys. Lett. B 2009, 673 (2009) 142–145

    work page 2009

  59. [59]

    STAR Collab. (B. I. Abelev et al. ), Phys. Rev. C 79 (2009) 034909

    work page 2009

  60. [60]

    Cleymans, H

    J. Cleymans, H. Oeschler, K. Redlich, Phys. Rev. C 59 (1999) 1663–1673

    work page 1999

  61. [61]

    Braun-Munzinger, I

    P. Braun-Munzinger, I. Heppe and J. Stachel, Phys. Lett. B 465 (1999) 15–20

    work page 1999

  62. [62]

    Manninen and F

    J. Manninen and F. Becattini, Phys. Rev. C 78 (2008) 054901

    work page 2008

  63. [63]

    Andronic, P

    A. Andronic, P. Braun-Munzinger and K. Redlich, Nature 2018, 561 (2018) 321–330

    work page 2018

  64. [64]

    (Adler S

    PHENIX Collab. (Adler S. S. et al. ), Phys. Rev. C 69 (2004) 034909

    work page 2004

  65. [65]

    P. Koch, J. Rafelski and W. Greiner, Phys. Lett. B 123 (1983) 151–154

    work page 1983

  66. [66]

    Braun-Munzinger, D

    P. Braun-Munzinger, D. Magestro, K. Redlich and J. Stac hel, Phys. Lett. B 518 (2001) 41–46

    work page 2001

  67. [67]

    H. L. Lao, Y. Q. Gao and F. H. Liu, Universe 5 (2019) 152

    work page 2019

  68. [68]

    H. L. Lao, Y. Q. Gao and F. H. Liu, Adv. High Energy Phys. 2020 (2020) 5064737

    work page 2020

  69. [69]

    NA49 Collab. (H. Appelsh¨ auser et al. ), Phys. Rev. Lett. 82 (1999) 2471–2475

    work page 1999

  70. [70]

    BRAHMS Collab. (I.C. Arsene et al. ), Phys. Lett. B 677 (2009) 267–271

    work page 2009

  71. [71]

    Videbaek (for the BRAHMS Collab.), Nucl

    F. Videbaek (for the BRAHMS Collab.), Nucl. Phys. A 830 (2009) 43c–50c

    work page 2009

  72. [72]

    BRAHMS Collab. (I. G. Bearden et al. ), Phys. Rev. Lett. 93 (2004) 102301

    work page 2004

  73. [73]

    Y. H. Chen, F. H. Liu and E. K. Sarkisyan-Grinbaum, Chin. Phys. C 42 (2018) 104102

    work page 2018

  74. [74]

    P. P. Yang, F. H. Liu and K. K. Olimov, Entropy 25 (2023) 1571

    work page 2023

  75. [75]

    P. P. Yang, M. Ajaz, M. Waqas, F. H. Liu and M. K. Suleymano v, J. Phys. G 49 (2022) 055110

    work page 2022

  76. [76]

    Waqas, M

    M. Waqas, M. Ajaz, A. H. Ismail, A. Tawfik, M. B. Ammar and H . I. Alrebdi, Eur. Phys. J. A 60 (2024) 123

    work page 2024