Event-by-event vortex rings in fixed-target p+Ar collisions

Chun Shen; David Chinellato; Giorgio Torrieri; Jun Takahashi; Michael Lisa; Willian Serenone

REVIEW 3 major objections 4 minor 14 references

Event-by-event vortex rings in fixed-target p+Ar collisions

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper predicts that a production-plane Lambda polarization observable in central asymmetric p+Ar collisions at 68 GeV can distinguish strong early longitudinal flow from Bjorken flow by a factor of six.

desk verdict Solid extension of the vortex-ring program to p+Ar, but the headline factor-of-six is a sensitivity scan over an unconstrained f, not a standalone prediction. read the letter →

arxiv 2509.00512 v1 pith:ZIPHVN4N submitted 2025-08-30 nucl-th hep-phnucl-ex

David Chinellato , Michael Lisa , Willian Serenone , Chun Shen , Jun Takahashi , Giorgio Torrieri This is my paper

classification nucl-thhep-phnucl-ex

keywords Lambdapolarizationvortexringsp+Arcollisionsfixed-targetthermalvorticityinitiallongitudinalflowevent-by-eventhydrodynamicsLHCbSMOG

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 predicts that a toroidal 'vortex ring' of flow, set up in the first instants of an asymmetric proton-argon collision, leaves a measurable imprint on the spin of Lambda hyperons. In central p+Ar collisions at 68 GeV, the authors find that their production-plane polarization observable is six times larger when the initial longitudinal flow is strong than when it is the classical Bjorken boost-invariant flow, and that it increases with charged-particle multiplicity. They also find that Lambda and anti-Lambda respond oppositely at zero initial longitudinal flow, with positive Lambda signal and negative anti-Lambda signal. Because the collision system is accessible to fixed-target LHCb measurements, these predictions offer a concrete experimental route to determine how quickly colliding nucleons transfer longitudinal momentum to the quark-gluon medium.

What carries the argument

The load-bearing object is the ring observable R_hat_z^Lambda: twice the component of the hyperon spin along the normal to the production plane, averaged over the hyperon's azimuthal angle about the beam. This observable is sensitive to the transverse gradient of longitudinal flow, i.e. to a toroidal 'smoke-ring' velocity pattern. The paper seeds that pattern with the initial longitudinal rapidity profile y_L = f * y_CM, where f is a single number between 0 and 1 and y_CM is set by the nuclear thickness functions T_A and T_B. The spin vectors are then computed from the thermal vorticity tensor over the freeze-out hypersurface, with the chemical potential assigning different emission weights

What would settle it

Measure the production-plane Lambda polarization in 0-5% central p+Ar at 68 GeV as a function of charged multiplicity. The prediction is that the signal grows with multiplicity and is roughly six times larger in the strong-flow (f=1) scenario than in the Bjorken (f=0) scenario, with Lambda positive and anti-Lambda negative at f=0. Seeing no growth, no f-contrast, or the opposite Lambda/anti-Lambda sign pattern would falsify the vortex-ring interpretation.

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Extended reading notes

Core claim

The central claim is that the production-plane spin polarization of Lambda hyperons, R_hat_z^Lambda, is an event-by-event observable that distinguishes the early-time longitudinal velocity profile in central asymmetric p+Ar collisions. Using a collision-geometry-based (3+1)-dimensional initial condition matched to hydrodynamics and hadronic transport, the authors scan the single parameter f that controls how much of the initial net longitudinal momentum is carried by flow. For f=1 (strong initial longitudinal flow) the integrated mid-rapidity ring observable is roughly six times larger than for f=0 (Bjorken flow), increases with charged multiplicity, and remains positive for Lambda while ant

Load-bearing premise

The predictions stand on the assumption that all uncertainty in the early longitudinal flow can be captured by one number f multiplying a fixed transverse profile, and that Lambda spin follows the leading-order thermal-vorticity formula; if the true flow profile has a different shape or another mechanism sets the spin, the predicted sixfold contrast and sign asymmetry will not appear in data.

Editorial extensions

If this is right

If measured, a sixfold multiplier between strong and zero initial longitudinal flow would turn R_hat_z^Lambda into a direct experimental probe of early-time longitudinal momentum deposition.
The rise with charged multiplicity implies the vortex ring strengthens as the fireball lives longer, so multiplicity-binned data would test the time evolution of vorticity, not only its initial seeding.
The opposite signs for Lambda and anti-Lambda at f=0 provide a species-dependent control that can separate flow-geometry effects from baryon transport.
The linear pT rise above 1 GeV, with slope tied to thermal vorticity, gives a way to extract the vorticity magnitude from a differential measurement.
Being measurable at fixed-target energies and in a small asymmetric system, these predictions extend vortex-ring phenomenology beyond large heavy-ion collisions.

Reading between the lines

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

Interpolating f between 0 and 1 would turn the model into a continuous estimator: a single measurement of R_hat_z^Lambda at one multiplicity could infer the degree of early longitudinal flow, something the paper's extreme-case comparison does not attempt.
The Lambda/anti-Lambda difference, which the paper traces to baryon chemical potential, could be measured as a difference observable; subtracting anti-Lambda from Lambda may cancel detector acceptance or non-vortical spin contributions and make the ring signal cleaner.
The same calculation applied to p+Pb or O+O fixed-target systems would map how the vortex-ring imprint scales with system size and stopping power; the paper restricts itself to p+Ar.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a short proceedings that takes the established vortex-ring setup from Refs. [7,9] and points it at p+Ar at 68 GeV. The new numbers are the factor-of-six gap between f=1 and f=0 initial longitudinal flow, the Lambda/anti-Lambda sign asymmetry at f=0, and the multiplicity growth of R_z. All three are internally consistent model outputs. The paper is honest that the observable is expected to be sensitive to f; it doesn't claim f is constrained.

What's good: the framework is not new but it is solid—iEBE-MUSIC, the geometric initial condition, and the Becattini spin formula are all peer-reviewed. The plots match the text. For the LHCb SMOG community, this is a concrete calculation of what to measure. The pT and pseudorapidity dependence in Fig. 2 will help design the experimental cut.

Where it's soft: the headline factor-of-six is a scan over the f dial in Eq. (2), and f is not anchored to any microscopic model or data. If the real initial longitudinal flow profile has a different transverse shape or sits at intermediate f, the numbers could be anywhere between the two curves. The paper gives no error bars or systematic uncertainties on the model outputs, so I'd want at least an estimate of how robust the sign asymmetry and the factor-of-six are to choices like the nucleon smearing width (they fix w=0.5 fm) and to freeze-out details. Also, Eq. (3) is the standard local-equilibrium thermal vorticity formula; in a small p+Ar system, non-equilibrium corrections or feed-down from heavier hyperons could shift the magnitudes, though probably not the ordering between f=1 and f=0. The authors don't discuss feed-down, which is a gap for a quantitative claim.

Bottom line: the central argument—that this observable can discriminate between strong and zero initial longitudinal flow—holds up as a model study. It is not a prediction of the true value in p+Ar because f is free. As a proceedings, it's useful and clear; for a journal I'd send it to a referee with the request that they add error estimates and a discussion of feed-down before publication. I'd probably bring this to reading group as one of the cleaner examples of how spin polarization observables are being pitched, but I wouldn't cite it as evidence for a specific value until f is constrained.

Referee Report

3 major / 4 minor

Summary. This proceedings article reports event-by-event (3+1)-dimensional hydrodynamic simulations of fixed-target p+Ar collisions at sqrt(s_NN)=68 GeV, using the geometric initial condition of Refs [10-13] with the initial longitudinal flow parameterized as y_L = f y_CM(x_perp) (Eq. 2). The authors compute the production-plane polarization observable Rhat_z^Lambda (Eq. 1) from the thermal-vorticity formula (Eq. 3), comparing f=1 (strong initial longitudinal flow) with f=0 (Bjorken flow). They find that Rhat_z^Lambda is about a factor of six larger at f=1 than at f=0, that it grows with charged multiplicity, and that anti-Lambda Rhat_z is negative at f=0 while Lambda's is positive. These patterns are proposed as LHCb-SMOG observables for vortex rings in small asymmetric systems.

Significance. If the calculation were anchored by a physics-determined initial longitudinal flow, the proposed observable would be a novel and potentially powerful probe of early-time longitudinal momentum deposition in small asymmetric systems. The paper builds on peer-reviewed machinery (iEBE-MUSIC, the geometric 3D initial condition, and the standard spin formula), and it makes concrete, falsifiable statements: the multiplicity dependence, the pT slope, and the Lambda/anti-Lambda sign asymmetry. Those are assets. However, in its present form the headline factor-of-six is a sensitivity scan over a free parameter, not a prediction, and the absence of quantitative uncertainties leaves the strength of the claim unclear.

major comments (3)

[Section 2, Eq. (2) and Figs. 1-2] All quantitative results are generated at the two endpoints f=1 and f=0, with f an unconstrained interpolation parameter of the initial longitudinal flow. The factor-of-six contrast and the anti-Lambda sign asymmetry are therefore a response of the model to its own f dial, and the paper itself states in Section 2 that the observable 'is expected to be sensitive to the value of parameter f.' To elevate this to a prediction for p+Ar, the authors must either fix f from a microscopic nucleon-stopping model, scan a physically motivated range of f and show Rhat_z vs f (not just endpoints), or test the assumed transverse shape y_L=f y_CM(x_perp). Without one of these, the LHCb-relevant predictions are not yet anchored.
[Figs. 1-2 (statistical/systematic robustness)] No statistical or systematic uncertainties are shown on the factor-of-six and sign claims. The curves are single choices (w=0.5 fm, 0.5<pT<3 GeV, 0-5% centrality), with no variation in nucleon width, centrality selection, hydrodynamic parameters, or freeze-out prescription. For a polarization observable of order 0.01-0.08, these choices can easily change the magnitude and even the sign. The paper should report event-sample statistical errors and at least one robustness scan (e.g., w=0.3/0.7 fm), and should state the multiplicity bin to which the 'factor of six' refers.
[Section 2, Eq. (3) and the anti-Lambda sign] The spin observable is computed from the leading-order thermal-vorticity formula, which assumes that Lambda spin in a small p+Ar system is set at local thermodynamic equilibrium and that competing mechanisms (magnetic field, feed-down, non-equilibrium corrections) are negligible. Since this assumption is common to both f values it does not drive the factor-six contrast, but it is load-bearing for the absolute predictions and for the Lambda vs anti-Lambda sign difference at f=0. The authors should add a brief validity discussion for p+Ar, and ideally compare with an alternative treatment (e.g., different decoupling temperature or a hadronic afterburner with spin) to show the sign is robust.

minor comments (4)

[Figures 1-2] The pseudo-rapidity ranges appear as 'eta in [□0.5, 0.5]' due to a typesetting issue; use proper minus signs. Figure 2 caption also contains 'vortext' (typo).
[Section 3] The phrase 'demonstrating that the vortex ring flow structure develops with the produced fireball lifetime' is too strong; the multiplicity growth is consistent with that interpretation but does not demonstrate it by itself.
[Abstract/Introduction] The term 'central asymmetric p+Ar collisions' is ambiguous; centrality in p+A is not a standard geometric centrality. Please define the selection (e.g., 0-5% in Nch) in the text, not only in the figure.
[Acknowledgments/Contact] The email address 'chunshen@wayene.edu' appears to be a typo for 'wayne.edu'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the f=0 vs f=1 comparison is an explicit initial-condition sensitivity study, not a fitted prediction; self-citations are supportive, not load-bearing.

full rationale

The paper's derivation chain is: Eq. (2) imposes a family of initial longitudinal flow profiles y_L = f y_CM(x_perp), with f a free interpolation parameter; Eqs. (1) and (3) define the spin observable and compute it from thermal vorticity; Figs. 1–2 report hydrodynamic outcomes at the endpoints f=1 and f=0. This is a controlled model comparison, not a circular reduction: the factor-of-six contrast and the Lambda/anti-Lambda sign asymmetry are emergent results of the iEBE-MUSIC evolution folded with Eq. (3), and they are not analytic restatements of Eq. (2). The paper explicitly flags that the observable is expected to be sensitive to f, which is an honest statement of model dependence rather than a disguised fit. No parameter is fitted to a data subset and then renamed a prediction; no uniqueness theorem is imported; and the cited prior works (Refs. [7], [9], [12], [13]) provide the model setup but do not themselves contain the p+Ar results claimed here. The main weakness is physical plausibility of Eq. (2) (the transverse shape and the single-parameter f are unconstrained), but that is a correctness/model-validity risk, not circularity. Hence score 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

Everything nontrivial that the predictions rest on is imported from prior work: the Eq. (2) initial-condition parameterization (Refs [10-13]), the hydrodynamic framework (Ref [9]), and the spin formula (Eq. (3), Ref [14]). The observable distinguishes f=1 from f=0, but the quantitative reliability of the absolute R_hat_z values inherits the unvalidated assumptions of these imports rather than any new data or derivation.

free parameters (2)

f (initial longitudinal flow fraction) = 0 and 1 (scanned endpoints)
Fraction of initial net longitudinal momentum assigned to flow velocity in Eq. (2); the f=1 vs f=0 contrast is the paper's central axis and the basis of the factor-of-six claim.
w (Gaussian nucleon smearing width) = 0.5 fm
Chosen model width stated in the figure captions; it affects the initial-condition gradients that seed the vortex ring.

assumptions (3)

domain assumption Eq. (3), the leading-order thermal-vorticity spin formula of Becattini et al. (Ref [14]), gives the correct mean spin vector for Lambdas at freeze-out in this system.
The entire observable is computed from this formula; higher-order corrections, feed-down, and magnetic terms are not addressed in this proceedings.
domain assumption A (3+1)D hydrodynamic description (iEBE-MUSIC) is valid for p+Ar collisions at 68 GeV, a small and short-lived system.
All predictions inherit the uncertainties of applying relativistic hydrodynamics and a particular equation of state to a small asymmetric system.
domain assumption The initial-condition model of Refs [10-13] with the y_L = f*y_CM parameterization (Eq. 2) correctly maps nucleon geometry and stopping onto hydrodynamic fields, including the baryon chemical potential profile.
The Lambda/anti-Lambda asymmetry depends on the mu_B distribution; no validation against p+Ar data is shown.

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Cite this review

Pith. "Pith review of Event-by-event vortex rings in fixed-target p+Ar collisions." pith.science (2026). https://pith.science/paper/ZIPHVN4N

@misc{pith2026250900512,
  author       = {Pith},
  title        = {Pith review of: Event-by-event vortex rings in fixed-target p+Ar collisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZIPHVN4N}},
  note         = {Machine review of arXiv:2509.00512}
}

abstract

We present event-by-event simulations for central asymmetric p+Ar collisions at $\sqrt{s_\mathrm{NN}} = 68$ GeV to investigate the formation and evolution of vortex-ring structures from the early-stage longitudinal flow velocity profile. Our predictions for their imprints on Lambda hyperon's polarization observables are complementary to those presented in Ref. [Phys.Rev.C 110 (2024) 5, 054908] and can be explored in the future fixed-target collisions at the Large Hadron Collider beauty (LHCb) experiment.

Figures

Figures reproduced from arXiv: 2509.00512 by the authors.

**Figure 1.** The vortex ring observable R zˆ Λ as function of charged hadron multiplicity for Λ and anti-Λ hyperons in p+Ar collisions at √ sNN = 68 GeV with two different initial-state longitudinal flow profiles. The pseudo-rapidity is in the center-of-mass frame. cases. While the anti-Λ’s R zˆ Λ is negative with the zero initial longitudinal flow setup. To understand this difference, we need to study the differential dependenc… view at source ↗

**Figure 2.** The vortext ring observables R zˆ Λ as functions of the center-of-mass pseudo-rapidity (left panel) and pT (right panel) for Λ and anti-Λ hyperons in p+Ar collisions at √ sNN = 68 GeV. of pseudo-rapidity in the center-of-mass frame and their transverse momentum. The R zˆ Λ (η) shows a rich structure of pseudo-rapidity dependence, demonstrating that the proposed ring observable could provide valuable insights into th… view at source ↗

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Reference graph

Works this paper leans on

14 extracted references · 6 canonical work pages

[1]

Becattini, M.A

F. Becattini, M.A. Lisa, Polarization and V orticity in the Quark–Gluon Plasma, Ann. Rev. Nucl. Part. Sci. 70, 395 (2020), 2003.03640. 10.1146 /annurev-nucl-021920- 095245

arXiv 2020
[2]

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arXiv 2017
[3]

B. Betz, M. Gyulassy, G. Torrieri, Polarization probes of vorticity in heavy ion colli- sions, Phys. Rev. C 76, 044901 (2007), 0708.0035. 10.1103/PhysRevC.76.044901

arXiv 2007
[4]

{\Lambda} polarization from thermalized jet energy

W.M. Serenone, J.G.P. Barbon, D.D. Chinellato, M.A. Lisa, C. Shen, J. Takahashi, G. Torrieri, Λ polarization from thermalized jet energy, Phys. Lett. B 820, 136500 (2021), 2102.11919. 10.1016/j.physletb.2021.136500

work page Pith review arXiv 2021
[5]

$\Lambda$ polarization from vortex ring as medium response for jet thermalization

V .H. Ribeiro, D. Dobrigkeit Chinellato, M.A. Lisa, W. Matioli Serenone, C. Shen, J. Takahashi, G. Torrieri, Λ polarization from vortex rings as the medium response for jet thermalization, Phys. Rev. C 109, 014905 (2024), 2305.02428. 10.1103/Phys- RevC.109.014905

work page Pith review arXiv 2024
[6]

V oloshin, V orticity and particle polarization in heavy ion collisions (experi- mental perspective), EPJ Web Conf

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arXiv 2018
[7]

Vortex rings from high energy central p+A collisions

M.A. Lisa, J.G.P. Barbon, D.D. Chinellato, W.M. Serenone, C. Shen, J. Takahashi, G. Torrieri, V ortex rings from high energy central p +A collisions, Phys. Rev. C 104, 011901 (2021), 2101.10872. 10.1103/PhysRevC.104.L011901

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[8]

Vortex rings in fragmentation regions in heavy-ion collisions at $\sqrt{s_{NN}}=$ 39 GeV

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work page Pith review arXiv 2018

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[9]

Dobrigkeit Chinellato, M.A

D. Dobrigkeit Chinellato, M.A. Lisa, W. Matioli Serenone, C. Shen, J. Takahashi, G. Torrieri, V ortex rings in event-by-event relativistic heavy-ion collisions, Phys. Rev. C 110, 054908 (2024), 2407.02212. 10.1103/PhysRevC.110.054908

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2020 arXiv
[12]

S. Ryu, V . Jupic, C. Shen, Probing early-time longitudinal dynamics with the Λ hy- peron’s spin polarization in relativistic heavy-ion collisions, Phys. Rev. C 104, 054908 (2021), 2106.08125. 10.1103/PhysRevC.104.054908

2021 arXiv
[13]

Alzhrani, S

S. Alzhrani, S. Ryu, C. Shen, Λ spin polarization in event-by-event relativistic heavy-ion collisions, Phys. Rev. C 106, 014905 (2022), 2203.15718. 10.1103/Phys- RevC.106.014905

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[14]

Becattini, I

F. Becattini, I. Karpenko, M. Lisa, I. Upsal, S. V oloshin, Global hyperon polarization at local thermodynamic equilibrium with vorticity, magnetic field and feed-down, Phys. Rev. C 95, 054902 (2017), 1610.02506. 10.1103/PhysRevC.95.054902

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Becattini, M.A

F. Becattini, M.A. Lisa, Polarization and V orticity in the Quark–Gluon Plasma, Ann. Rev. Nucl. Part. Sci. 70, 395 (2020), 2003.03640. 10.1146 /annurev-nucl-021920- 095245

arXiv 2020

[2] [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

[3] [3]

B. Betz, M. Gyulassy, G. Torrieri, Polarization probes of vorticity in heavy ion colli- sions, Phys. Rev. C 76, 044901 (2007), 0708.0035. 10.1103/PhysRevC.76.044901

arXiv 2007

[4] [4]

{\Lambda} polarization from thermalized jet energy

W.M. Serenone, J.G.P. Barbon, D.D. Chinellato, M.A. Lisa, C. Shen, J. Takahashi, G. Torrieri, Λ polarization from thermalized jet energy, Phys. Lett. B 820, 136500 (2021), 2102.11919. 10.1016/j.physletb.2021.136500

work page Pith review arXiv 2021

[5] [5]

$\Lambda$ polarization from vortex ring as medium response for jet thermalization

V .H. Ribeiro, D. Dobrigkeit Chinellato, M.A. Lisa, W. Matioli Serenone, C. Shen, J. Takahashi, G. Torrieri, Λ polarization from vortex rings as the medium response for jet thermalization, Phys. Rev. C 109, 014905 (2024), 2305.02428. 10.1103/Phys- RevC.109.014905

work page Pith review arXiv 2024

[6] [6]

V oloshin, V orticity and particle polarization in heavy ion collisions (experi- mental perspective), EPJ Web Conf

S.A. V oloshin, V orticity and particle polarization in heavy ion collisions (experi- mental perspective), EPJ Web Conf. 171, 07002 (2018), 1710.08934. 10.1051 /epj- conf/201817107002

arXiv 2018

[7] [7]

Vortex rings from high energy central p+A collisions

M.A. Lisa, J.G.P. Barbon, D.D. Chinellato, W.M. Serenone, C. Shen, J. Takahashi, G. Torrieri, V ortex rings from high energy central p +A collisions, Phys. Rev. C 104, 011901 (2021), 2101.10872. 10.1103/PhysRevC.104.L011901

work page Pith review arXiv 2021

[8] [8]

Vortex rings in fragmentation regions in heavy-ion collisions at $\sqrt{s_{NN}}=$ 39 GeV

Y .B. Ivanov, A.A. Soldatov, V ortex rings in fragmentation regions in heavy-ion colli- sions at√sNN = 39 GeV, Phys. Rev. C97, 044915 (2018), 1803.01525. 10.1103/Phys- RevC.97.044915

work page Pith review arXiv 2018