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arxiv: 2606.09093 · v1 · pith:GIR67URA · submitted 2026-06-08 · nucl-th · nucl-ex

Hyperon polarization in isobaric Zr+Zr collisions at sqrt{s_(NN)}=200 GeV: TRENRo3D + CLVisc with an initial longitudinal flow gradient

Ze-Fang Jiang , Xiang Fan , Jing Jing This is my paper

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classification nucl-th nucl-ex
keywords hyperon polarizationisobaric collisionsinitial vorticityTRENTo3DCLViscglobal polarizationshear polarizationSTAR data
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The pith

A longitudinal flow velocity gradient introduced into TRENTo3D supplies the initial vorticity needed to match observed hyperon polarization in symmetric Zr+Zr collisions.

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

The paper introduces a longitudinal flow velocity gradient controlled by the parameter fv into the TRENTo3D initial condition model for the first time. This gradient acts as the source of vorticity in the symmetric isobaric system where geometric effects alone would not produce it. Coupled to the CLVisc hydrodynamic evolution and an isothermal polarization framework, the model simultaneously reproduces STAR data on global polarization -Py across centrality, transverse momentum, and pseudorapidity, as well as the azimuthal coefficients Py,c0 and Py,c2. The work decomposes the polarization into thermal vorticity and shear contributions, showing their competing effects with increasing pT. Additional scans over fv, kT, nuclear structure, and bulk viscosity provide constraints while leaving the Pz description incomplete.

Core claim

The central claim is that the fv-controlled longitudinal flow velocity gradient in TRENTo3D provides the essential initial vorticity in symmetric isobaric collisions, enabling the TRENTo3D + CLVisc model under the isothermal polarization framework to simultaneously describe the measured global polarization -Py (including its centrality, pT, and eta dependence) and the azimuthal modulation coefficients Py,c0 and Py,c2.

What carries the argument

The longitudinal flow velocity gradient fv added to TRENTo3D, which generates initial vorticity that is then evolved hydrodynamically in CLVisc and converted to hyperon polarization via the isothermal framework.

If this is right

  • The pT dependence of polarization reflects competition in which the thermal vorticity term falls while the shear term rises and dominates the curvature at higher pT.
  • Py,c2 is dominantly shear-driven and therefore serves as a clean experimental probe of shear-induced polarization.
  • Scans over fv, kT, and the five nuclear structure configurations from the STAR isobar analysis constrain the initial-state parameters while yielding nearly identical polarization results.
  • Bulk-viscosity variations produce only small changes in the predicted polarization.

Where Pith is reading between the lines

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

  • The approach could be tested in other symmetric collision systems where geometric vorticity is minimal to see if an analogous fv term is required.
  • The mismatch in Pz at high pT points to a possible need for a momentum-dependent switch between isothermal and thermal polarization prescriptions.
  • The near-independence from nuclear structure suggests polarization observables may offer limited power to discriminate among nuclear density profiles in this energy regime.

Load-bearing premise

The fv gradient supplies the dominant source of initial vorticity in this symmetric system and the isothermal polarization framework remains valid across all measured observables without separate confirmation from a thermal treatment.

What would settle it

A direct experimental measurement of Pz showing a high-pT azimuthal modulation amplitude that neither the isothermal nor standard thermal scenario can reproduce simultaneously with the Py data would challenge the model's unified description.

Figures

Figures reproduced from arXiv: 2606.09093 by Jing Jing, Xiang Fan, Ze-Fang Jiang.

Figure 1
Figure 1. Figure 1: FIG. 1: (Color online) Upper panel: the energy density distribution of the QGP in the reaction plane ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (Color online) Baseline observables in Zr+Zr collisions at [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (Color online) Dependence of the global [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) Dependence of the global [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) Dependence of the global [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: presents the centrality dependence of −Py,c0 and −Py,c2, providing a quantitative theoretical description of these azimuthal-angle-dependent polarization coefficients in isobaric collisions. The two coefficients exhibit different sensitivities to the polarization sources. Since the STAR points combine Zr+Zr and Ru+Ru events, this comparison should be interpreted together with the nuclear-structure scan in … view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) Theoretical prediction for [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) Longitudinal polarization [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: examines the fv dependence of Pz. Panel (a) shows that Pz(ϕ) is remarkably insensitive to fv: all four curves (fv = 0.00 to 0.25) exhibit a nearly identical nega￾tive sinusoidal modulation. Even in the Bjorken limit fv = 0, Pz(ϕ) maintains a finite amplitude (∼ 0.4%–0.5%), indicat￾ing that the tilted fireball geometry alone can generate longi￾tudinal polarization—in sharp contrast to the strong fv de￾pende… view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: (Color online) Dependence of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: (Color online) Comparison between the isothermal (‘iso-total’, solid) and standard thermal (‘th+sh’, dashed) polarization scenarios [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
read the original abstract

We present a theoretical study of global and azimuthal-angle-dependent $\Lambda$ hyperon polarization in isobaric $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{NN}}=200$~GeV using the TRENTo3D initial condition model coupled to the (3+1)-D viscous hydrodynamic model CLVisc. A longitudinal flow velocity gradient, controlled by $f_v$, is introduced into TRENTo3D for the first time, providing an essential source of initial vorticity in this symmetric isobaric system. Within the isothermal polarization framework, the model provides a simultaneous description of STAR measurements of the global polarization $-P^{y}$ (centrality, $p_T$, and $\eta$ dependences) and the azimuthal modulation coefficients $P_{y,\mathrm{c0}}$ and $P_{y,\mathrm{c2}}$. The $p_T$ dependence reflects the competition between thermal vorticity and shear contributions: the thermal term decreases with $p_T$, while the shear term rises and increasingly shapes the curvature of the total polarization. In this decomposition, $P_{y,\mathrm{c2}}$ is dominantly shear-driven and serves as a clean probe of shear-induced polarization. Scans of $f_v$, $k_T$, and nuclear structure provide complementary constraints on the initial state, while the bulk-viscosity dependence is also examined; the five nuclear structure configurations from the STAR isobar blind analysis yield nearly indistinguishable polarization. For $P_z$, the isothermal scenario captures the azimuthal modulation but overpredicts the high-$p_T$ modulation amplitude, and comparison with the standard thermal treatment shows that neither scenario achieves a unified description of all observables.

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

3 major / 1 minor

Summary. The manuscript studies global and azimuthal Lambda hyperon polarization in isobaric Zr+Zr collisions at 200 GeV using TRENTo3D initial conditions augmented by a longitudinal flow velocity gradient fv, coupled to CLVisc (3+1)D viscous hydrodynamics. Within an isothermal polarization framework, it claims a simultaneous description of STAR data on global polarization -Py (centrality, pT, and eta dependences) and the azimuthal coefficients Py,c0 and Py,c2, with pT dependence arising from competition between thermal-vorticity and shear terms (Py,c2 being shear-dominated). Parameter scans over fv, kT, and five nuclear-structure configurations are presented; bulk-viscosity dependence is examined. For Pz the isothermal treatment captures azimuthal modulation but overpredicts high-pT amplitude, and neither isothermal nor standard thermal vorticity unifies all observables.

Significance. If the central claim holds after addressing the noted issues, the work provides a concrete mechanism (fv-driven initial vorticity) for polarization in symmetric isobar systems and isolates shear-induced polarization via Py,c2. The multi-observable comparison and nuclear-structure scans add value. The explicit acknowledgment that the framework fails to unify Pz observables is a strength. However, the tuning of fv to the polarization data itself limits the independence of the prediction.

major comments (3)
  1. [Abstract] Abstract and results on Py observables: The central claim of simultaneous description of -Py, Py,c0, and Py,c2 is made within the isothermal framework, yet the manuscript provides no side-by-side comparison of isothermal versus standard thermal-vorticity calculations for these specific Py observables (in contrast to the comparison reported for Pz). Because the pT decomposition explicitly involves competing thermal-vorticity and shear terms, any systematic offset between the two prescriptions would directly affect the reported curvature and the attribution of Py,c2 to shear.
  2. [Parameter scans] Parameter scans and initial-condition section: The longitudinal gradient fv is scanned to reproduce the polarization data that constitute the central claim. This introduces circularity: the initial vorticity source is adjusted to fit the very observables whose description is asserted, so the result is not an independent prediction from the hydrodynamic fields but partly a parameter adjustment.
  3. [Pz results] Pz discussion: The reported overprediction of high-pT azimuthal modulation for Pz, together with the statement that neither isothermal nor thermal treatment achieves a unified description of all observables, indicates that the framework's applicability is limited. This limitation bears on the interpretation of the successful Py description and should be quantified with respect to the same hydrodynamic fields used for Py.
minor comments (1)
  1. [Methods] The notation for the azimuthal coefficients (Py,c0, Py,c2) and the precise definition of the isothermal mapping should be stated explicitly in the methods section to allow direct reproduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help clarify the scope and limitations of our study. We address each major comment below and will revise the manuscript to incorporate clarifications and additional comparisons where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results on Py observables: The central claim of simultaneous description of -Py, Py,c0, and Py,c2 is made within the isothermal framework, yet the manuscript provides no side-by-side comparison of isothermal versus standard thermal-vorticity calculations for these specific Py observables (in contrast to the comparison reported for Pz). Because the pT decomposition explicitly involves competing thermal-vorticity and shear terms, any systematic offset between the two prescriptions would directly affect the reported curvature and the attribution of Py,c2 to shear.

    Authors: We agree that an explicit comparison for the Py observables would strengthen the presentation of the thermal-vorticity versus shear decomposition. Although the isothermal framework is used for the primary results because it better captures the data, we will add a side-by-side comparison (e.g., an additional figure panel or subsection) showing the pT dependence under both prescriptions for -Py, Py,c0, and Py,c2 using the same hydrodynamic fields. This will quantify any systematic offsets and reinforce the attribution of Py,c2 to shear. revision: yes

  2. Referee: [Parameter scans] Parameter scans and initial-condition section: The longitudinal gradient fv is scanned to reproduce the polarization data that constitute the central claim. This introduces circularity: the initial vorticity source is adjusted to fit the very observables whose description is asserted, so the result is not an independent prediction from the hydrodynamic fields but partly a parameter adjustment.

    Authors: We acknowledge that fv is calibrated to the global polarization data. However, once fixed, the same hydrodynamic evolution is used to predict the azimuthal coefficients Py,c0 and Py,c2 (which are not used in the fv scan) as well as their pT and centrality dependences. The multi-observable consistency, together with the nuclear-structure and kT scans, provides nontrivial tests. We will revise the text to explicitly note the calibration step and emphasize the independent predictions for the azimuthal modulations and Pz behavior. revision: partial

  3. Referee: [Pz results] Pz discussion: The reported overprediction of high-pT azimuthal modulation for Pz, together with the statement that neither isothermal nor thermal treatment achieves a unified description of all observables, indicates that the framework's applicability is limited. This limitation bears on the interpretation of the successful Py description and should be quantified with respect to the same hydrodynamic fields used for Py.

    Authors: The manuscript already states that the isothermal treatment overpredicts the high-pT Pz modulation amplitude and that neither prescription unifies all observables. To address the quantification request, we will add explicit numbers (e.g., the overprediction factor at high pT) and confirm that the hydrodynamic fields are identical to those used for the Py results. This will better contextualize the framework's applicability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; parameter calibration for description is standard modeling practice

full rationale

The provided text introduces fv as a new tunable parameter in TRENTo3D to generate initial vorticity and states that scans of fv (along with kT and nuclear structure) provide constraints while the model achieves a simultaneous description of the polarization observables within the isothermal framework. This is ordinary hydrodynamic model calibration against data rather than any derivation step that reduces by construction to its own inputs. No quoted equations or claims exhibit self-definition, a fitted quantity renamed as an independent prediction, or load-bearing self-citation. The central result is a post-calibration description, which does not meet the criteria for circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the new free parameter fv, the isothermal polarization assumption, and standard hydrodynamic evolution; no new particles or forces are postulated.

free parameters (2)
  • fv
    Controls the strength of the longitudinal flow velocity gradient added to TRENTo3D to generate initial vorticity; scanned to match polarization data.
  • kT
    Temperature-related cutoff or scale parameter appearing in the polarization calculation; scanned alongside fv.
axioms (2)
  • domain assumption The isothermal polarization framework correctly converts hydrodynamic fields into hyperon polarization.
    Invoked to compute both global and azimuthal components from thermal vorticity and shear.
  • domain assumption CLVisc viscous hydrodynamics faithfully evolves the TRENTo3D initial conditions including the added fv gradient.
    Required for the vorticity and shear fields that enter the polarization formulas.

pith-pipeline@v0.9.1-grok · 5866 in / 1532 out tokens · 30246 ms · 2026-06-27T14:59:36.153733+00:00 · methodology

discussion (0)

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Reference graph

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