pith. sign in

arxiv: 2606.00786 · v1 · pith:APNIMBZGnew · submitted 2026-05-30 · ⚛️ physics.data-an · hep-ex· nucl-ex· nucl-th

Proton High-Order Cumulants in Au+Au Collisions at High Baryon Density from JAM with a Centrality-Independent Framework

Yongcong Xu , Zhaohui Wang , Yu Zhang , Xiaofeng Luo This is my paper

Pith reviewed 2026-06-28 18:12 UTC · model grok-4.3

classification ⚛️ physics.data-an hep-exnucl-exnucl-th
keywords proton cumulantsheavy-ion collisionsQCD critical pointvolume fluctuationsJAM modelAu+Au collisionshigher-order cumulantscentrality correction
0
0 comments X

The pith

The CIGAR method eliminates initial volume fluctuations from higher-order proton cumulants in JAM simulations of Au+Au collisions at 3.2–4.5 GeV.

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

This paper introduces the Centrality-Independent Genuine Cumulant Analysis fRamework (CIGAR) to compute proton number cumulants, factorial cumulants, and ratios in Au+Au collisions simulated by the JAM transport model. The approach is tested at center-of-mass energies of 3.2, 3.5, 3.9, and 4.5 GeV and is compared directly to the conventional Centrality Bin Width Correction method. CIGAR is shown to remove the distorting effects of initial volume fluctuations while also incorporating the role of spectator nucleons. The resulting distributions supply a model-based reference for non-critical behavior at high baryon density, which is needed to interpret experimental searches for the QCD critical point.

Core claim

The CIGAR method effectively eliminates initial volume fluctuations from the calculation of higher-order cumulants of proton number distributions in JAM-simulated Au+Au collisions at √sNN = 3.2, 3.5, 3.9, and 4.5 GeV, yielding results that differ from those obtained with the Centrality Bin Width Correction method and that incorporate spectator effects; these JAM+CIGAR distributions therefore constitute a dynamic non-critical baseline for QCD critical point searches in the high-baryon-density regime.

What carries the argument

Centrality-Independent Genuine Cumulant Analysis fRamework (CIGAR), a centrality-independent procedure that extracts genuine cumulants by removing initial volume fluctuations without binning in centrality.

If this is right

  • CIGAR produces cumulant values that are independent of the chosen centrality estimator and therefore more directly comparable across experiments.
  • The JAM results at these four energies supply a concrete numerical reference for non-critical proton cumulants at high baryon density.
  • Spectator nucleons contribute measurably to the cumulants and must be accounted for when interpreting data.
  • Any experimental excess over the JAM+CIGAR baseline can be attributed more confidently to critical or non-equilibrium dynamics.

Where Pith is reading between the lines

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

  • The method could be applied to other conserved quantities such as net-charge or net-strangeness cumulants within the same model.
  • If other transport models produce different baselines under CIGAR, the spread would quantify model uncertainty in the non-critical reference.
  • The framework may allow re-analysis of existing RHIC data at similar energies without re-deriving centrality bins.

Load-bearing premise

The JAM transport model produces proton number fluctuations that faithfully represent non-critical dynamics at these energies, so that differences between CIGAR and CBWC results can be attributed to volume removal rather than model artifacts.

What would settle it

Direct comparison of experimental proton cumulant ratios at √sNN = 3–5 GeV with the JAM+CIGAR predictions; a statistically significant deviation after experimental acceptance and efficiency corrections would falsify the claim that the baseline is purely non-critical.

Figures

Figures reproduced from arXiv: 2606.00786 by Xiaofeng Luo, Yongcong Xu, Yu Zhang, Zhaohui Wang.

Figure 1
Figure 1. Figure 1: FIG. 1: Proton acceptance in terms of transverse momentum ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Proton dN/dy distributions within the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Proton number distributions and fitting results at [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Centrality dependence of proton cumulant ratios ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Centrality dependence of proton cumulants up to fourth-order using CIGAR method in Au+Au collisions at [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Centrality dependence of proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Collision energy dependence of proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Rapidity dependence of proton cumulant ratios [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

The event-by-event higher-order cumulants of conserved quantities such as net-baryon, net-electric charge, and net-strangeness in heavy-ion collisions have been extensively utilized in experimental searches for the QCD critical point, notably in the RHIC-STAR experiment. In this study, we conduct a systematic analysis of higher-order cumulants of proton number distributions in Au+Au collisions at center-of-mass energies of $\sqrt{s_{\rm NN}} = 3.2$, $3.5$, $3.9$, and $4.5$ GeV using the JAM model. We calculate cumulants, factorial cumulants, and their ratios using a novel method, Centrality-Independent Genuine Cumulant Analysis fRamework (CIGAR), which effectively eliminates initial volume fluctuations. We comprehensively compare the CIGAR method with the traditional Centrality Bin Width Correction (CBWC) method. In addition, the effect of spectators on cumulant is systematically investigated. Our results provide a dynamic non-critical baseline in the high-baryon-density regime which is crucial for QCD critical point searches in heavy-ion collisions.

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 / 2 minor

Summary. The paper computes higher-order cumulants and factorial cumulants of proton number distributions in Au+Au collisions at √s_NN = 3.2–4.5 GeV with the JAM transport model. It introduces the CIGAR framework to remove initial volume fluctuations, performs a systematic comparison against the CBWC method, examines spectator contributions, and positions the resulting JAM+CIGAR results as a dynamic non-critical baseline for QCD critical-point searches.

Significance. If the CIGAR method demonstrably isolates volume effects without model-dependent artifacts and if JAM reproduces generic non-critical proton fluctuations, the work would supply a needed reference baseline at high baryon density. The direct CIGAR–CBWC comparison and spectator study are concrete strengths that could be cited by experimental analyses.

major comments (2)
  1. [Results and discussion sections (comparison of CIGAR vs. CBWC)] The central claim that JAM supplies a usable non-critical baseline rests on the untested assumption that its hadronic dynamics (resonance production, baryon stopping, proton-number fluctuations) reproduce the correct non-critical behavior at these energies. No cross-validation against other transport models (e.g., UrQMD or SMASH) or against known analytic limits is presented; therefore differences between CIGAR and CBWC cannot be unambiguously attributed to volume-fluctuation removal rather than JAM-specific dynamics.
  2. [Method section describing CIGAR implementation] The manuscript does not quantify the residual volume-fluctuation contribution after CIGAR is applied (e.g., via a controlled test with fixed initial volume). Without such a diagnostic, the assertion that CIGAR “effectively eliminates” volume fluctuations remains an unverified modeling choice rather than a demonstrated result.
minor comments (2)
  1. [Abstract] The abstract states that “systematic analysis” and “comprehensive comparison” were performed but supplies no numerical values, error estimates, or key ratios; adding a short quantitative summary would improve readability.
  2. [Throughout] Notation for factorial cumulants versus ordinary cumulants should be defined once in the text and used consistently in all figures and tables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We respond point-by-point below, clarifying the internal nature of the CIGAR–CBWC comparison and agreeing to add a diagnostic test for residual volume fluctuations.

read point-by-point responses

  1. Referee: [Results and discussion sections (comparison of CIGAR vs. CBWC)] The central claim that JAM supplies a usable non-critical baseline rests on the untested assumption that its hadronic dynamics (resonance production, baryon stopping, proton-number fluctuations) reproduce the correct non-critical behavior at these energies. No cross-validation against other transport models (e.g., UrQMD or SMASH) or against known analytic limits is presented; therefore differences between CIGAR and CBWC cannot be unambiguously attributed to volume-fluctuation removal rather than JAM-specific dynamics.

    Authors: We note that both CIGAR and CBWC results are derived from the identical set of JAM events. Consequently, observed differences between the methods can be attributed only to their respective treatments of volume fluctuations, not to differences in the underlying hadronic dynamics. We will revise the text to state this explicitly and to place the JAM choice in the context of prior validations for baryon stopping at these energies. revision: partial

  2. Referee: [Method section describing CIGAR implementation] The manuscript does not quantify the residual volume-fluctuation contribution after CIGAR is applied (e.g., via a controlled test with fixed initial volume). Without such a diagnostic, the assertion that CIGAR “effectively eliminates” volume fluctuations remains an unverified modeling choice rather than a demonstrated result.

    Authors: We agree that a controlled diagnostic would strengthen the claim. In the revised manuscript we will add a test using events generated with fixed initial volume to quantify any residual fluctuations remaining after CIGAR and report the outcome. revision: yes

Circularity Check

0 steps flagged

No circularity: JAM simulation and CIGAR method supply independent baseline

full rationale

The paper's central claim rests on running the external JAM transport model to generate proton-number cumulants at the stated energies, then applying the CIGAR centrality-independent framework to remove volume fluctuations and comparing the output to the standard CBWC procedure. No equation, parameter fit, or result is shown to be defined in terms of the target cumulant ratios themselves; the model dynamics (resonance production, baryon stopping) are treated as an independent input whose outputs serve as the non-critical reference. Self-citations are not invoked as load-bearing uniqueness theorems, and no ansatz or renaming reduces the reported baseline to a tautology. The derivation chain therefore remains self-contained against external benchmarks.

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 from the provided text.

pith-pipeline@v0.9.1-grok · 5753 in / 1136 out tokens · 25831 ms · 2026-06-28T18:12:42.487878+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

41 extracted references · 12 canonical work pages

  1. [1]

    Bzdak, S

    A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, Phys. Rept.853, 1 (2020), 1906.00936

    arXiv 2020

  2. [2]

    Braun-Munzinger, A

    P. Braun-Munzinger, A. Rustamov, and N. Xu (2026), 2601.18666

    arXiv 2026

  3. [3]

    X. Luo, Q. Wang, N. Xu, and P. Zhuang, eds.,Properties of QCD Matter at High Baryon Density(Springer, 2022), ISBN 978-981-19-4440-6, 978-981-19-4443-7, 978-981-19-4441-3

    2022

  4. [4]

    D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt, S. Singh, and K. Zambello, Phys. Rev. D112, L091504 (2025), 2405.10196

    arXiv 2025

  5. [5]

    Hippert, J

    M. Hippert, J. Grefa, T. A. Manning, J. Noronha, J. Noronha-Hostler, I. P. Vazquez, C. Ratti, R. Rougemont, and M. Trujillo, Phys. Rev. D110, 094006 (2024), URL https://link.aps.org/doi/10.1103/PhysRevD.110.094006

    work page doi:10.1103/physrevd.110.094006 2024

  6. [6]

    W.-j. Fu, J. M. Pawlowski, and F. Rennecke, Phys. Rev. D101, 054032 (2020), URL https://link.aps.org/doi/10.1103/ PhysRevD.101.054032

    2020

  7. [7]

    P. J. Gunkel and C. S. Fischer, Phys. Rev. D104, 054022 (2021), URL https://link.aps.org/doi/10.1103/PhysRevD.104. 054022

    work page doi:10.1103/physrevd.104 2021

  8. [8]

    Gao and J

    F. Gao and J. M. Pawlowski, Phys. Lett. B820, 136584 (2021), 2010.13705, URL https://www.sciencedirect.com/science/ article/pii/S0370269321005244

    arXiv 2021

  9. [9]

    Sorensen and P

    A. Sorensen and P. Sorensen, arXiv preprint (2024), 2405.10278

    arXiv 2024

  10. [10]

    R.-G. Cai, S. He, L. Li, and H.-A. Zeng, Sci. China Phys. Mech. Astron.69, 240414 (2026), 2406.12772

    arXiv 2026

  11. [11]

    L. Zhu, X. Chen, K. Zhou, H. Zhang, and M. Huang, Phys. Rev. D112, 026019 (2025), 2501.17763

    arXiv 2025

  12. [12]

    Luo and N

    X. Luo and N. Xu, Nucl. Sci. Tech.28, 112 (2017), 1701.02105, URL https://link.springer.com/article/10.1007/ s41365-017-0257-0

    Pith/arXiv arXiv 2017

  13. [13]

    M. A. Stephanov, Phys. Rev. Lett.102, 032301 (2009), 0809.3450

    Pith/arXiv arXiv 2009

  14. [14]

    Asakawa and M

    M. Asakawa and M. Kitazawa, Progress in Particle and Nuclear Physics90, 299 (2016), ISSN 0146-6410, URL https: //www.sciencedirect.com/science/article/pii/S0146641016300023

    2016

  15. [15]

    Kitazawa and X

    M. Kitazawa and X. Luo, Phys. Rev. C96, 024910 (2017), URL https://link.aps.org/doi/10.1103/PhysRevC.96.024910

    work page doi:10.1103/physrevc.96.024910 2017

  16. [16]

    Z. Li, Y. Chen, D. Li, and M. Huang, Chin. Phys. C42, 013103 (2018), 1706.02238

    Pith/arXiv arXiv 2018

  17. [17]

    Z. Li, K. Xu, X. Wang, and M. Huang, Eur. Phys. J. C79, 245 (2019), 1801.09215

    Pith/arXiv arXiv 2019

  18. [18]

    W.-j. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, and S. Yin, Phys. Rev. D111, L031502 (2025), 2308.15508

    arXiv 2025

  19. [19]

    Y. Lu, C. S. Fischer, F. Gao, Y.-x. Liu, and J. M. Pawlowski (2026), 2603.09336

    arXiv 2026

  20. [20]

    M. M. Aggarwal, Z. Ahammed, A. V. Alakhverdyants, I. Alekseev, J. Alford, B. D. Anderson, D. Arkhipkin, G. S. Averichev, J. Balewski, L. S. Barnby, et al. (STAR Collaboration), Phys. Rev. Lett.105, 022302 (2010), URL https: //link.aps.org/doi/10.1103/PhysRevLett.105.022302

    work page doi:10.1103/physrevlett.105.022302 2010

  21. [21]

    Adamczyk, J

    L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, et al. (STAR Collaboration), Phys. Rev. Lett.112, 032302 (2014), URL https://link.aps.org/doi/10.1103/ PhysRevLett.112.032302

    2014

  22. [22]

    Adamczyk, J

    L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, et al. (STAR Collaboration), Phys. Rev. Lett.113, 092301 (2014), URL https://link.aps.org/doi/10.1103/ PhysRevLett.113.092301. 10

    2014

  23. [23]

    J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, D. M. Anderson, R. Aoyama, et al. (STAR Collaboration), Phys. Rev. C100, 014902 (2019), URL https://link.aps.org/doi/10. 1103/PhysRevC.100.014902

    2019

  24. [24]

    J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, D. M. Anderson, A. Aparin, et al. (STAR Collaboration), Phys. Rev. Lett.126, 092301 (2021), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.126.092301

    work page doi:10.1103/physrevlett.126.092301 2021

  25. [25]

    M. S. Abdallah, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, I. Aggarwal, M. M. Aggarwal, Z. Ahammed, I. Alekseev, et al. (STAR Collaboration), Phys. Rev. C104, 024902 (2021), URL https://link.aps.org/doi/ 10.1103/PhysRevC.104.024902

    work page doi:10.1103/physrevc.104.024902 2021

  26. [26]

    M. S. Abdallah, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, I. Aggarwal, M. M. Aggarwal, Z. Ahammed, I. Alekseev, et al. (STAR Collaboration), Phys. Rev. Lett.127, 262301 (2021), URL https://link.aps.org/ doi/10.1103/PhysRevLett.127.262301

    work page doi:10.1103/physrevlett.127.262301 2021

  27. [27]

    B. E. Aboona, J. Adam, L. Adamczyk, J. R. Adams, I. Aggarwal, M. M. Aggarwal, Z. Ahammed, D. M. Anderson, E. C. Aschenauer, J. Atchison, et al. (STAR Collaboration), Phys. Rev. Lett.130, 082301 (2023), URL https://link.aps.org/ doi/10.1103/PhysRevLett.130.082301

    work page doi:10.1103/physrevlett.130.082301 2023

  28. [28]

    Chen et al., Nucl

    J. Chen et al., Nucl. Sci. Tech.35, 214 (2024), 2407.02935, URL https://link.springer.com/article/10.1007/ s41365-024-01591-2

    arXiv 2024

  29. [29]

    B. E. Aboona et al. (STAR), Phys. Rev. Lett.135, 142301 (2025), 2504.00817

    arXiv 2025

  30. [30]

    M. S. Abdallah, B. E. Aboona, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, I. Aggarwal, M. M. Aggarwal, Z. Ahammed, D. M. Anderson, et al. (The STAR Collaboration), Phys. Rev. C107, 024908 (2023), URL https://link.aps. org/doi/10.1103/PhysRevC.107.024908

    work page doi:10.1103/physrevc.107.024908 2023

  31. [31]

    X. Luo, J. Xu, B. Mohanty, and N. Xu, Journal of Physics G: Nuclear and Particle Physics40, 105104 (2013), URL https://doi.org/10.1088/0954-3899/40/10/105104

    work page doi:10.1088/0954-3899/40/10/105104 2013

  32. [32]

    Wang and X

    Z. Wang and X. Luo, Physics Letters B871, 139984 (2025), ISSN 0370-2693, URL https://www.sciencedirect.com/science/ article/pii/S0370269325007427

    2025

  33. [33]

    Nara, EPJ Web Conf.208, 11004 (2019)

    Y. Nara, EPJ Web Conf.208, 11004 (2019)

    2019

  34. [34]

    Y. Nara, N. Otuka, A. Ohnishi, K. Niita, and S. Chiba, Phys. Rev. C61, 024901 (1999), URL https://link.aps.org/doi/ 10.1103/PhysRevC.61.024901

    work page doi:10.1103/physrevc.61.024901 1999

  35. [35]

    S. He, X. Luo, Y. Nara, S. Esumi, and N. Xu, Physics Letters B762, 296 (2016), 1607.06376

    Pith/arXiv arXiv 2016

  36. [36]

    Zhang, S

    Y. Zhang, S. He, H. Liu, Z. Yang, and X. Luo, Phys. Rev. C101, 034909 (2020), URL https://link.aps.org/doi/10.1103/ PhysRevC.101.034909

    2020

  37. [37]

    Chatterjee, Y

    A. Chatterjee, Y. Zhang, H. Liu, R. Wang, S. He, and X. Luo, Chinese Physics C45, 064003 (2021), 2009.03755

    arXiv 2021

  38. [38]

    Savchuk, Phys

    O. Savchuk, Phys. Rev. C111, 024913 (2025), URL https://link.aps.org/doi/10.1103/PhysRevC.111.024913

    work page doi:10.1103/physrevc.111.024913 2025

  39. [39]

    S. He, X. Luo, Y. Nara, S. Esumi, and N. Xu, Physics Letters B762, 296 (2016), ISSN 0370-2693, URL https://www. sciencedirect.com/science/article/pii/S0370269316305585

    2016

  40. [40]

    Sweger and S

    Z. Sweger and S. Collaboration, inProceedings of the 31st International Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter 2025)(2025), oral presentation

    2025

  41. [41]

    CBM Collaboration,Cbm progress report 2023, Online (2023), accessed on 16 June 2025, URL https://doi.org/10.15120/ GSI-2024-00765

    2023