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arxiv: 2606.13333 · v2 · pith:CNJ2PFATnew · submitted 2026-06-11 · ⚛️ nucl-th

Hadron polarization and equation of state at FAIR/RHIC-BES energies

Dai-Neng Liu , Jan Steinheimer , Kai-Jia Sun , Jin-Hui Chen , Yu-Gang Ma , Marcus Bleicher This is my paper

Pith reviewed 2026-06-27 05:23 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords Lambda polarizationequation of stateheavy-ion collisionsthermal vorticitybaryon stoppingUrQMD modelFAIR energiesRHIC-BES
0
0 comments X

The pith

Lambda polarization in heavy-ion collisions depends on the stiffness of the nuclear equation of state, with softer equations yielding smaller values.

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

The paper calculates the global polarization of Lambda hyperons induced by thermal vorticity in non-central Ag+Ag and Au+Au collisions at beam energies from 2.24 to 7.7 GeV using the UrQMD transport model. It compares two equations of state, one resembling a hadron resonance gas and the other incorporating a chiral mean-field description with a transition consistent with lattice QCD. The results show that polarization is sensitive to the equation of state, with the softer version producing smaller polarization, and that polarization in experimental acceptance does not fall at lower energies. The authors trace the large vorticity to shear in the baryon current arising from its stopping. A sympathetic reader would care because this links an observable polarization signal directly to the medium's collective rotation and its underlying equation of state at energies relevant to FAIR and RHIC-BES.

Core claim

Using the UrQMD transport model with two different equations of state, the thermal vorticity-induced Lambda polarization is found to be sensitive to the equation of state, with a softer EoS producing smaller polarization values. The Lambda polarization within experimental acceptance and centrality cuts does not decrease at even lower beam energies. The large vorticity arises from the shear in the baryon current created by baryon stopping.

What carries the argument

Thermal vorticity-induced polarization of Lambdas calculated in the UrQMD model under two equations of state (hadron resonance gas versus chiral mean-field).

If this is right

  • Polarization measurements can distinguish between stiff and soft equations of state in the baryon-rich regime.
  • The absence of a decrease in polarization at lower energies implies that vorticity remains large even as beam energy drops.
  • Baryon stopping is identified as the dominant source of the shear that generates the observed vorticity.
  • The chiral mean-field equation of state, which includes a lattice-consistent transition, yields systematically different polarization than a pure hadron resonance gas.

Where Pith is reading between the lines

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

  • If the relation holds, future polarization data at FAIR could constrain the location of the chiral transition in dense matter.
  • The stopping-induced shear mechanism may also affect other observables such as directed flow or elliptic flow at the same energies.
  • Extending the calculation to include additional hadrons or different centrality bins could test whether the polarization signal is robust across species.

Load-bearing premise

The UrQMD transport model with the two chosen equations of state correctly produces the thermal vorticity and the resulting polarization from baryon stopping without dominant contributions from other mechanisms.

What would settle it

An experimental measurement at these energies showing Lambda polarization that is either independent of equation-of-state stiffness or that decreases sharply below 2.24 GeV would contradict the central claim.

Figures

Figures reproduced from arXiv: 2606.13333 by Dai-Neng Liu, Jan Steinheimer, Jin-hui Chen, Kai-Jia Sun, Marcus Bleicher, Yu-Gang Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison of UrQMD calculations with the CMF [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows the energy dependence of Λ hyperon po￾larization obtained from the thermal vorticity in Au+Au collisions for two different centrality selections, 20-50% (solid lines, corresponding to STAR data) and 10-40% (dashed lines, corresponding to HADES data). For each case we always combine several sub-bins e.g. 20-30%, 30- 40%, and 40-50% to calculate the thermal vorticity and the spin vector of every Λ hype… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Centrality (upper panel), rapidity (middle panel), [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Predictions for the centrality (upper panel), ra [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

The $\Lambda$ global polarization indicates that hot and dense matter created in non-central heavy-ion collisions carries large orbital angular momentum. However, the relation between hadronic polarization and the medium's collective rotation remains to be validated. Using the UrQMD transport model, we calculate the thermal vorticity-induced polarization of $\Lambda$s in Ag+Ag and Au+Au collisions from $\sqrt{s_{\rm NN}}=2.24$-$7.7$ GeV and a range of centralities. Two different equations of state used in the UrQMD simulation are compared: one resembles a hadron resonance gas, while the other is based on the chiral mean field (CMF) model, providing a more realistic description of dense nuclear matter including a chiral transition that is consistent with lattice QCD expectations. The polarization is sensitive to the equation of state and a softer EoS leads to smaller values. In addition, we show that the $\Lambda$ polarization in the experimental acceptance and centrality selection does not decrease for even lower beam energies. Our results indicate that the process leading to the large vorticity is a result of the large shear in the baryon current created by its stopping.

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 employs the UrQMD transport model to compute thermal vorticity-induced global polarization of Λ hyperons in Ag+Ag and Au+Au collisions at √sNN = 2.24–7.7 GeV across centralities. Two equations of state are compared: a hadron resonance gas and a chiral mean field (CMF) model incorporating a chiral transition. The polarization is reported to be sensitive to the EoS (softer EoS yields smaller values), does not decrease at lower energies within experimental acceptance, and is attributed to shear in the baryon current arising from stopping.

Significance. If the thermal vorticity to polarization mapping is robust, the EoS sensitivity and non-decreasing low-energy behavior could provide a new observable for dense nuclear matter at FAIR/RHIC-BES energies. The mechanistic link to baryon stopping offers a testable interpretation of vorticity generation.

major comments (2)
  1. [Abstract] Abstract: the text explicitly states that 'the relation between hadronic polarization and the medium's collective rotation remains to be validated,' yet proceeds to report quantitative EoS dependence and a specific shear mechanism without supplying validation against data, alternative polarization mechanisms, or model cross-checks; this assumption is load-bearing for all headline claims.
  2. [Results] Results section (comparison of EoS implementations): the reported sensitivity of polarization to the CMF versus HRG EoS lacks accompanying error bars, explicit centrality cuts, or quantitative model validation metrics, making it impossible to assess whether the difference exceeds statistical or systematic uncertainties.
minor comments (1)
  1. Notation for thermal vorticity and polarization definitions should be cross-referenced to prior UrQMD literature for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity of our manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the text explicitly states that 'the relation between hadronic polarization and the medium's collective rotation remains to be validated,' yet proceeds to report quantitative EoS dependence and a specific shear mechanism without supplying validation against data, alternative polarization mechanisms, or model cross-checks; this assumption is load-bearing for all headline claims.

    Authors: The abstract already states that the polarization-rotation relation remains to be validated, and our work operates strictly within the standard thermal-vorticity framework employed throughout the literature. The quantitative EoS dependence and shear interpretation are presented as model predictions under that assumption, not as experimentally validated results. To address the concern we will revise the abstract and introduction to explicitly note that the mapping is an assumption (with references to its use at higher energies) and that alternative mechanisms are outside the present scope. revision: partial

  2. Referee: [Results] Results section (comparison of EoS implementations): the reported sensitivity of polarization to the CMF versus HRG EoS lacks accompanying error bars, explicit centrality cuts, or quantitative model validation metrics, making it impossible to assess whether the difference exceeds statistical or systematic uncertainties.

    Authors: We agree that the presentation can be improved. In the revised manuscript we will add statistical error bars to all polarization results, state the exact centrality intervals used for each data set, and include a short discussion quantifying the size of the EoS-induced difference relative to the statistical uncertainties. Because both EoS implementations are run inside the identical UrQMD code, the comparison is internal; we will clarify this point to avoid implying external validation. revision: yes

Circularity Check

0 steps flagged

No circularity; polarization computed directly from UrQMD thermal vorticity with independent EoS inputs

full rationale

The paper runs UrQMD transport simulations for two distinct EoS (hadron resonance gas vs. chiral mean field) and extracts thermal vorticity-induced Λ polarization as a numerical output. No parameter is fitted to polarization observables and then relabeled as a prediction. No self-citation chain justifies a uniqueness theorem or smuggles an ansatz. The relation between vorticity and polarization is treated as an input assumption (explicitly noted as remaining to be validated), not derived from the paper's own equations. Results are therefore independent of the target observables and score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no information on free parameters, axioms, or invented entities.

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