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REVIEW 2 major objections 5 minor 32 references

Local spin polarization of $\Lambda$ hyperons and its interaction corrections

T0 review · 2 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read CLVisc hydrodynamics reproduces Lambda spin polarization in Au+Au but not in p+Pb.

desk verdict Proceedings-grade summary: reproduces the group's own published curves, honestly flags the p+Pb failure, but adds no new derivation or analysis. read the letter →

arxiv 2509.00377 v1 pith:J7MGVZVX submitted 2025-08-30 nucl-th hep-ph

Cong Yi , Shuo Fang , Dong-Lin Wang , Shi Pu This is my paper
classification nucl-thhep-ph PACS 25.75.-q
keywords Lambdahyperonspinpolarizationlocalshear-inducedCLVischydrodynamicsequilibriumscenariosAu+Aucollisionsp+Pbquantumkinetictheory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports a concrete comparison between hydrodynamic predictions and measured Lambda-hyperon spin polarization. Using the (3+1)-dimensional CLVisc model, the authors compute the second Fourier sine coefficient of the longitudinal spin polarization in Au+Au at 200 GeV and in p+Pb at 8.16 TeV. In Au+Au, the results reproduce the data when the polarization is evaluated in the strange-quark equilibrium or iso-thermal equilibrium scenario, while the Lambda-equilibrium scenario fails. In p+Pb, all three scenarios fail to describe the CMS data because the shear-induced polarization is too weak to flip the sign of the total polarization. The authors also summarize recent quantum-kinetic and spin-hydrodynamic corrections that could eventually resolve the small-system puzzle.

What carries the argument

The machinery is the (3+1)-dimensional CLVisc relativistic hydrodynamic model, used to evolve the quark-gluon plasma and to compute Lambda polarization at freeze-out. The observable is the second Fourier sine coefficient of the longitudinal spin polarization as a function of the event-plane angle Psi_2. The three scenarios—Lambda equilibrium, strange-quark equilibrium, and iso-thermal equilibrium—prescribe different spin-dependent phase-space distributions, coupling thermal vorticity and the shear tensor to the spin vector in different ways. The shear-induced spin polarization term is the mechanism that can reverse the sign of the local polarization. In the companion quantum-kinetic part, th

What would settle it

A decisive check would be to measure the same Fourier coefficient in p+Pb at another collision energy or in even smaller systems, and to run the same CLVisc code with an added pre-equilibrium spin or system-size-dependent spin-transport term; if that extended model reproduces both Au+Au and p+Pb with the same parameters, the reported puzzle is a modeling artifact rather than evidence of new physics.

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Extended reading notes

Core claim

The paper's central claim is that Lambda hyperon spin polarization along the beam direction, quantified by the second Fourier sine coefficient <Pz sin 2(phi_p - Psi_2)>, is governed by hydrodynamic gradients—thermal vorticity plus the shear viscous tensor—and by which species is assumed to be in local equilibrium. In Au+Au collisions at sqrt(s_NN) = 200 GeV, the strange-quark equilibrium and iso-thermal equilibrium scenarios quantitatively reproduce the STAR centrality dependence, while the Lambda-equilibrium scenario does not. In p+Pb collisions at sqrt(s_NN) = 8.16 TeV, none of the three scenarios can describe the CMS data: the shear-induced contribution is insufficient to reverse the sign

Load-bearing premise

The load-bearing premise is that the hydrodynamic parameters tuned to reproduce bulk multiplicity and elliptic flow, with no extra system-size-dependent spin transport or initial spin content, are enough to determine the spin polarization in p+Pb.

Editorial extensions

If this is right

  • Shear-induced spin polarization, rather than thermal vorticity alone, is required to reproduce the measured azimuthal modulation of Lambda polarization in Au+Au.
  • The Lambda-equilibrium scenario is disfavored: only the strange-quark and iso-thermal equilibrium scenarios reproduce the Au+Au data.
  • The p+Pb failure implies the hydrodynamic gradient picture, as implemented with parameters fixed by bulk data, is incomplete for small collision systems.
  • The similarity of the p+Pb and Au+Au signals, despite very different system sizes, indicates a mechanism that depends only weakly on system size and collision energy and remains to be identified.
  • If the reported interaction corrections—side-jump, skew scattering, and self-energy spin torque—are sizable, they could account for the p+Pb discrepancy when included in the same framework.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the p+Pb puzzle is real, a natural next test is to predict the same Fourier coefficient in other small systems such as O+O, Ru+Zr, or p+Au; a universal curve would point to a common early-time spin source.
  • The near system-size independence of the signal hints that spin polarization may be imprinted before hydrodynamics thermalizes, in pre-equilibrium fields; the paper does not model that stage.
  • The pseudo-gauge ambiguity highlighted in Section 4 means different spin-hydrodynamic formulations assign different fractions of angular momentum to the spin tensor; resolving it could change the size of the 'missing' p+Pb contribution.
  • Because the leading collisional side-jump correction cancels the coupling constant, interaction corrections might be largely universal across system sizes; if so, the p+Pb discrepancy may be due to initial conditions rather than transport.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This proceedings-style paper uses the (3+1)-D CLVisc hydrodynamic model to compute the second Fourier sine coefficient of the longitudinal spin polarization of Lambda hyperons, <P_z sin 2(phi_p - Psi_2)>, as a function of centrality/multiplicity in Au+Au at sqrt(s_NN)=200 GeV and p+Pb at sqrt(s_NN)=8.16 TeV. Three spin-equilibration scenarios are compared: Lambda equilibrium, s-quark equilibrium, and iso-thermal equilibrium. The authors report that the s-quark and iso-thermal scenarios reproduce the STAR Au+Au data, while the Lambda-equilibrium scenario does not; in p+Pb, none of the three scenarios describes the CMS data, and the discrepancy is left as an open puzzle. The remaining sections give a compact review of recent quantum-kinetic-theory results on interaction corrections to spin polarization and of selected developments in relativistic spin hydrodynamics.

Significance. If the reported calculations are taken at face value, the paper consolidates evidence that shear-induced polarization combined with the appropriate spin-equilibration scenario accounts for the measured Au+Au observable while exposing a small-system discrepancy in p+Pb. Its strengths are the explicit reporting of the failing scenarios (Lambda equilibrium in Au+Au and all scenarios in p+Pb) and a useful overview of recent literature. The incremental numerical content is limited, however: the quantitative results are carried by Refs. [5,7,10,11], and the derivations reviewed in Sections 3 and 4 are largely the authors' own prior work. The central p+Pb conclusion is conditional on assumptions about gradient expansion and event-plane reconstruction that are not examined in this manuscript.

major comments (2)
  1. [Section 2, p+Pb (Fig. 1(b))] The conclusion that the p+Pb data cannot be described and that this constitutes an 'open puzzle' rests on the unstated premise that the CLVisc gradient expansion and the event-plane reconstruction used for Au+Au transfer unchanged to p+Pb. The manuscript provides no estimate of Knudsen/Reynolds numbers, no check of omitted O(g^2) terms, and no sensitivity study of <Pz sin2(phi_p-Psi_2)> to the event-plane definition or resolution correction; all setup is deferred to Ref. [11]. Since spin polarization is itself an O(gradient) correction, in a small system the discrepancy with CMS could be a truncation artifact. Please add such robustness checks, or explicitly restrict the conclusion to the assumptions of Ref. [11] and acknowledge that the puzzle may be a modeling artifact rather than evidence about spin dynamics.
  2. [Section 2, Fig. 1(a)] The central positive claim that the s-quark and iso-thermal equilibrium scenarios 'agree with the experimental data' is not quantitatively supported within this manuscript. No numerical values, theoretical uncertainty bands, or goodness-of-fit measures are given, and the Lambda-equilibrium failure is only described qualitatively. If the paper is intended as a standalone report, it should include a quantitative comparison (e.g., chi^2 or a table of values); if it is a proceedings summary of Refs. [5,6,10], that status should be stated explicitly in the Introduction.
minor comments (5)
  1. [Figure 1] The figure is referenced and captioned, but the plot itself is not visible in the manuscript text provided. Ensure the figure files are included and that axes, legend entries, and error bars are legible.
  2. [Eq. (1), Section 3] The notation in Eq. (1) is not self-contained: the on-shell constraint on p^mu, the sign conventions, and the explicit forms of g_1 and g_2 are not defined in the text. The reader is forced to consult Ref. [17]; at least state the on-shell condition and the physical ranges/orders of g_1 and g_2.
  3. [Introduction] The statement that the data suggest a 'very weak system and collisional energy dependence' compares two different collision systems at two different energies. That two-point comparison is weaker than the wording suggests; consider softening or noting that the similarity may be coincidental.
  4. [Sections 3 and 4] These sections are a review of recent work and are not used in the numerical calculations of Section 2. The title and abstract mention 'interaction corrections,' but the reported numerical results do not include them. Please add a bridging sentence clarifying that Sections 3 and 4 are a separate status report, or connect them to the observable.
  5. [General formatting] There are several typographical artifacts (e.g., 'coe fficient', 'o ff-equilibrium', '∂2') that should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central numerical results are genuine predictions compared against external STAR and CMS data, with parameters tuned to bulk observables, not to spin polarization.

full rationale

The paper's central quantitative claim is a comparison of hydrodynamic predictions for <Pz sin 2(phi_p - Psi_2)> with experimental data from STAR (Au+Au) and CMS (p+Pb). The hydrodynamic parameters are explicitly stated to be 'tuned to reproduce the observed multiplicity and elliptic flow,' not to the spin-polarization observable, so the spin-polarization curves are not fitted inputs renamed as predictions. The Au+Au agreement and p+Pb disagreement are externally falsifiable against data, and the paper reports the p+Pb failure rather than adjusting the model to remove it. The numerical setup is deferred to Refs. [10] and [11], which include the authors' own prior work, but those citations carry independent weight: Ref. [11] is a peer-reviewed hydrodynamic calculation compared to CMS data, and the present paper reproduces that comparison. No equation in the paper is equivalent by construction to its conclusion; Eq. (1) is a reported interaction correction from prior work (Ref. [17]) and is not used to generate Fig. 1. Sections 3 and 4 are literature summaries of the authors' and others' developments, not load-bearing derivations of the main result. The paper's conclusion that p+Pb remains a puzzle is an interpretation of a genuine model-data discrepancy, not a claim that is forced by the model's definition. Therefore no circular step is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper's quantitative claims rest entirely on parameters and scenarios established in the authors' prior published hydrodynamic simulations (Refs [10,11]) and on QKT results from their own papers (Refs [17,18]). No new free parameters or entities are introduced here, but the tuned hydrodynamic parameters are not shown in this manuscript.

free parameters (1)
  • Hydrodynamic parameters (initial conditions, equation of state, shear viscosity, freeze-out temperature) = not specified in this manuscript
    Section 2 states parameters are 'tuned to reproduce the observed multiplicity and elliptic flow', but no numerical values are given; all details are deferred to Refs [10,11]. The central comparison depends on these tuned values.
assumptions (5)
  • domain assumption Hydrodynamic parameters tuned to reproduce multiplicity and elliptic flow are sufficient for computing the spin-polarization observable.
    Section 2: 'The parameters used in our simulations are tuned to reproduce the observed multiplicity and elliptic flow.' The paper assumes no additional system-size-dependent spin transport parameters are needed, which is load-bearing for the p+Pb comparison.
  • domain assumption Spin polarization is dominated by thermal vorticity plus shear-induced contributions; collisional and spin-Hall corrections are small additions.
    Sections 2 and 3 rely on this gradient-expansion hierarchy. The p+Pb result shows the shear contribution is insufficient there, and the paper notes the corrections are not yet numerically included.
  • domain assumption The three spin-equilibration scenarios (Lambda equilibrium, s-quark equilibrium, iso-thermal equilibrium) span the relevant physics of spin equilibration.
    Section 2 and Fig. 1; these scenarios come from Refs [5,6,7] and are not derived in this manuscript.
  • domain assumption Quasi-particle approximation and hard-thermal-loop expansion are valid for the interaction corrections quoted in Eq. (1).
    Section 3: Eq. (1) is quoted from Ref [17] under these approximations; the paper itself notes generalizing beyond the quasi-particle regime remains open.
  • domain assumption A specific pseudo-gauge choice (canonical in the numerical works) is acceptable for computing the polarization observable.
    Section 4 reviews that pseudo-gauge choice is unresolved (Refs [24-27]); the numerical results inherit the choice made in Refs [10,11].

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Cite this review

Pith. "Pith review of Local spin polarization of $\Lambda$ hyperons and its interaction corrections." pith.science (2026). https://pith.science/paper/J7MGVZVX

@misc{pith2026250900377,
  author       = {Pith},
  title        = {Pith review of: Local spin polarization of $\Lambda$ hyperons and its interaction corrections},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J7MGVZVX}},
  note         = {Machine review of arXiv:2509.00377}
}
abstract

We have computed the second Fourier sine coefficient of the longitudinal spin polarization, $\langle P_{z} \sin 2(\phi_{p} - \Psi_{2}) \rangle$, as a function of multiplicity or centrality in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and in $p$+Pb collisions at $\sqrt{s_{NN}} = 8.16$ TeV using the CLVisc hydrodynamic framework. The numerical results successfully describe the data in Au+Au collisions. However, understanding the data in $p$+Pb collisions remains a puzzle. Additionally, we have reported some recent developments in quantum kinetic theory and spin hydrodynamics.

Figures

Figures reproduced from arXiv: 2509.00377 by the authors.

Figure 1
Figure 1. The ⟨Pz sin(2ϕp−2Ψ2)⟩ for Λ hyperons as function of centrality or multiplicity: (a) in Au+Au collisions at √ sNN = 200 GeV and (b) in p+Pb collisions at √ sNN = 8.16 TeV. The blue dashed, orange dash-dotted, and green solid lines represent the results in the Λ equilibrium, s-quark equilibrium, and iso-thermal equilibrium scenarios, respectively. Red markers denote experimental data from Ref. [4] for Au+Au collisions… view at source ↗

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Works this paper leans on

32 extracted references · 1 canonical work pages

  1. [10]

    X.Y . Wu, C. Yi, G.Y . Qin, S. Pu, Local and global polarization of Λ hyperons across RHIC-BES energies: The roles of spin hall e ffect, initial condition, and baryon di ffu- sion, Phys. Rev. C 105, 064909 (2022), 2204.02218. 10.1103/PhysRevC.105.064909

    arXiv 2022

  2. [11]

    C. Yi, X.Y . Wu, J. Zhu, S. Pu, G.Y . Qin, Spin polarization ofΛ hyperons along the beam direction in p+Pb collisions at sNN=8.16 TeV using hydrodynamic approaches, Phys. Rev. C 111, 044901 (2025), 2408.04296. 10.1103/PhysRevC.111.044901

    arXiv 2025

  3. [17]

    S. Fang, S. Pu, Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion (2024), 2408.09877

    arXiv 2024

  4. [1]

    Liang, X.N

    Z.T. Liang, X.N. Wang, Globally polarized quark-gluon plasma in non-central A +A collisions, Phys. Rev. Lett. 94, 102301 (2005), [Erratum: Phys.Rev.Lett. 96, 039901 (2006)], nucl-th/0410079. 10.1103/PhysRevLett.94.102301

    arXiv 2005

  5. [2]

    Adamczyk et al

    L. Adamczyk et al. (STAR), Global Λ hyperon polarization in nuclear collisions: ev- idence for the most vortical fluid, Nature 548, 62 (2017), 1701.06657. 10.1038/na- ture23004

    arXiv 2017

  6. [3]

    Becattini, I

    F. Becattini, I. Karpenko, Collective Longitudinal Polarization in Relativistic Heavy- Ion Collisions at Very High Energy, Phys. Rev. Lett.120, 012302 (2018), 1707.07984. 10.1103/PhysRevLett.120.012302

    arXiv 2018

  7. [4]

    Adam et al

    J. Adam et al. (STAR), Polarization of Λ ( ¯Λ) hyperons along the beam direction in Au +Au collisions at √sNN = 200 GeV, Phys. Rev. Lett. 123, 132301 (2019), 1905.11917. 10.1103/PhysRevLett.123.132301

    arXiv 2019

  8. [5]

    Fu, S.Y .F

    B. Fu, S.Y .F. Liu, L. Pang, H. Song, Y . Yin, Shear-Induced Spin Polarization in Heavy- Ion Collisions, Phys. Rev. Lett. 127, 142301 (2021), 2103.10403. 10.1103 /Phys- RevLett.127.142301

    arXiv 2021

Show all 32 references
  1. [6]

    Becattini, M

    F. Becattini, M. Buzzegoli, G. Inghirami, I. Karpenko, A. Palermo, Local Polarization and Isothermal Local Equilibrium in Relativistic Heavy Ion Collisions, Phys. Rev. Lett. 127, 272302 (2021), 2103.14621. 10.1103/PhysRevLett.127.272302

    2021 arXiv

  2. [7]

    C. Yi, S. Pu, D.L. Yang, Reexamination of local spin polarization beyond global equilib- rium in relativistic heavy ion collisions, Phys. Rev. C104, 064901 (2021), 2106.00238. 10.1103/PhysRevC.104.064901

    2021 arXiv

  3. [8]

    Becattini, M

    F. Becattini, M. Buzzegoli, T. Niida, S. Pu, A.H. Tang, Q. Wang, Spin polarization in relativistic heavy-ion collisions, Int. J. Mod. Phys. E33, 2430006 (2024), 2402.04540. 10.1142/9789811294679_0005

    2024 arXiv

  4. [9]

    Hayrapetyan et al

    A. Hayrapetyan et al. (CMS), Observation of Λ hyperon local polarization in pPb colli- sions at√sNN = 8.16 TeV (2025), 2502.07898

    2025

  5. [12]

    Hidaka, S

    Y . Hidaka, S. Pu, Q. Wang, D.L. Yang, Foundations and Applications of Quantum Ki- netic Theory (2022), 2201.07644

    2022 arXiv

  6. [13]

    Weickgenannt, D

    N. Weickgenannt, D. Wagner, E. Speranza, D.H. Rischke, Relativistic second-order dissipative spin hydrodynamics from the method of moments, Phys. Rev. D106, 096014 (2022), 2203.04766. 10.1103/PhysRevD.106.096014

    2022 arXiv

  7. [14]

    Weickgenannt, D

    N. Weickgenannt, D. Wagner, E. Speranza, D.H. Rischke, Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term, Phys. Rev. D 106, L091901 (2022), 2208.01955. 10.1103/PhysRevD.106.L091901

    2022 arXiv

  8. [15]

    Wagner, Resummed spin hydrodynamics from quantum kinetic theory, Phys

    D. Wagner, Resummed spin hydrodynamics from quantum kinetic theory, Phys. Rev. D 111, 016008 (2025), 2409.07143. 10.1103/PhysRevD.111.016008

    2025

  9. [16]

    Singh, D

    Sapna, S.K. Singh, D. Wagner, Spin Polarization of Λ hyperons from Dissipative Spin Hydrodynamics (2025), 2503.22552

    2025

  10. [18]

    S. Fang, S. Pu, D.L. Yang, Spin polarization and spin alignment from quantum kinetic theory with self-energy corrections, Phys. Rev. D 109, 034034 (2024), 2311.15197. 10.1103/PhysRevD.109.034034

    2024 arXiv

  11. [19]

    Florkowski, R

    W. Florkowski, R. Ryblewski, A. Kumar, Relativistic hydrodynamics for spin- polarized fluids, Prog. Part. Nucl. Phys. 108, 103709 (2019), 1811.04409. 10.1016/j.ppnp.2019.07.001

    2019 arXiv

  12. [20]

    Hattori, M

    K. Hattori, M. Hongo, X.G. Huang, M. Matsuo, H. Taya, Fate of spin polarization in a relativistic fluid: An entropy-current analysis, Phys. Lett. B 795, 100 (2019), 1901.06615. 10.1016/j.physletb.2019.05.040

    2019 arXiv

  13. [21]

    Fukushima, S

    K. Fukushima, S. Pu, Spin hydrodynamics and symmetric energy-momentum ten- sors – A current induced by the spin vorticity –, Phys. Lett. B 817, 136346 (2021), 2010.01608. 10.1016/j.physletb.2021.136346

    2021 arXiv

  14. [22]

    P. Shi, H. Xu-Guang, Relativistic spin hydrodynamics, Acta Phys. Sin. 72, 071202 (2023). 10.7498/aps.72.20230036

    2023 doi

  15. [23]

    S. Fang, K. Fukushima, S. Pu, D.L. Wang, Relativistic spin hydrodynamics with an- tisymmetric spin tensors and an extension of the Bargmann-Michel-Telegdi equation (2025), 2506.20698

    2025 arXiv

  16. [24]

    Speranza, N

    E. Speranza, N. Weickgenannt, Spin tensor and pseudo-gauges: from nuclear col- lisions to gravitational physics, Eur. Phys. J. A 57, 155 (2021), 2007.00138. 10.1140/epja/s10050-021-00455-2

    2021 arXiv

  17. [25]

    Buzzegoli, Pseudogauge dependence of the spin polarization and of the axial vortical effect, Phys

    M. Buzzegoli, Pseudogauge dependence of the spin polarization and of the axial vortical effect, Phys. Rev. C105, 044907 (2022), 2109.12084. 10.1103/PhysRevC.105.044907

    2022 arXiv

  18. [26]

    Buzzegoli, A

    M. Buzzegoli, A. Palermo, Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD, Phys. Rev. Lett. 133, 262301 (2024), 2407.14345. 10.1103 /Phys- RevLett.133.262301

    2024 arXiv

  19. [27]

    Becattini, C

    F. Becattini, C. Hoyos, Pseudo-gauge invariant non-equilibrium density operator (2025), 2507.09249

    2025 arXiv

  20. [28]

    Becattini, A

    F. Becattini, A. Daher, X.L. Sheng, Entropy current and entropy production in relativistic spin hydrodynamics, Phys. Lett. B 850, 138533 (2024), 2309.05789. 10.1016/j.physletb.2024.138533

    2024 arXiv

  21. [29]

    Becattini, R

    F. Becattini, R. Singh, On the local thermodynamic relations in relativistic spin hydro- dynamics (2025), 2506.20681

    2025 arXiv

  22. [30]

    Florkowski, M

    W. Florkowski, M. Hontarenko, Generalized Thermodynamic Relations for Perfect Spin Hydrodynamics, Phys. Rev. Lett. 134, 082302 (2025), 2405.03263. 10.1103 /Phys- RevLett.134.082302

    2025 arXiv

  23. [31]

    Xie, D.L

    X.Q. Xie, D.L. Wang, C. Yang, S. Pu, Causality and stability analysis for the min- imal causal spin hydrodynamics, Phys. Rev. D 108, 094031 (2023), 2306.13880. 10.1103/PhysRevD.108.094031

    2023 arXiv

  24. [32]

    Daher, A

    A. Daher, A. Das, R. Ryblewski, Stability studies of first-order spin-hydrodynamic frameworks, Phys. Rev. D 107, 054043 (2023), 2209.10460. 10.1103 /Phys- RevD.107.054043

    2023 arXiv

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