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REVIEW 3 major objections 6 minor 51 references

Global rotation lowers chemical freeze-out temperatures and makes hadron yield ratios, especially Ω−/π+, far more sensitive probes of vorticity than conventional cumulant ratios.

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2026-07-13 17:01 UTC pith:JWJTSRA4

load-bearing objection Solid rotating-HRG extension that maps freeze-out shifts and shows yield ratios beat low-order cumulants for vorticity; the fixed ε/n and s/T³ targets are the main modeling choice, not a hidden flaw. the 3 major comments →

arxiv 2603.27267 v2 pith:JWJTSRA4 submitted 2026-03-28 hep-ph hep-exhep-thnucl-exnucl-th

Vorticity-induced modifications of chemical freeze-out in heavy-ion collisions

Nandita Padhan , Kshitish Kumar Pradhan , Arghya Chatterjee , Raghunath Sahoo This is my paper
classification hep-ph hep-exhep-thnucl-exnucl-th
keywords chemical freeze-outhadron resonance gasvorticityrotationparticle yield ratiosconserved-charge susceptibilitiesheavy-ion collisions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

In ultra-relativistic heavy-ion collisions the produced medium can rotate at enormous rates. This paper asks how that global rotation changes the chemical freeze-out surface on which the final hadron yields are fixed. Working inside the hadron resonance gas model, the authors recompute the standard freeze-out criteria (average energy per particle and scaled entropy density) with rotation included in the single-particle energies. They find a systematic downward shift of the freeze-out curve in the temperature–baryon-chemical-potential plane, together with clear rotational modifications of the electric-charge and strangeness chemical potentials. Most importantly for experiment, particle yield ratios respond strongly to rotation while the usual low-order cumulant ratios of conserved charges stay comparatively flat. The practical claim is therefore that measured hadronic yield ratios, particularly those involving high-spin multi-strange baryons, offer a cleaner experimental handle on the magnitude of vorticity than fluctuation observables.

Core claim

When the conventional freeze-out conditions ε/n ≈ 1.08 GeV or s/T³ ≈ 7 are evaluated inside a rotating hadron resonance gas, the chemical freeze-out curve shifts systematically toward lower temperatures in the T–μ_B plane; simultaneously, particle yield ratios (especially Ω−/π+) display a far stronger dependence on angular velocity than the conventional cumulant ratios χ_{2}/χ_{1}.

What carries the argument

The rotating hadron resonance gas: single-particle energies are replaced by ε = √(k_r^{2} + k_z^{2} + m^{2}) − (l + s)ω with a causal boundary that quantizes radial momenta, so that all thermodynamic densities, chemical potentials, yields and susceptibilities become explicit functions of angular velocity ω.

Load-bearing premise

The numerical targets of the freeze-out criteria themselves (energy per particle ≈ 1.08 GeV and s/T³ ≈ 7) stay exactly the same once rotation is switched on; only the densities that enter them are recomputed.

What would settle it

Extract chemical freeze-out temperatures and selected yield ratios (Ω/π, Δ/π, p/π) from the same peripheral heavy-ion data sets with and without a finite-ω rotating-HRG fit; if the extracted T_ch does not drop and the high-spin ratios do not rise systematically with estimated vorticity, the central claim fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript studies chemical freeze-out in a globally rotating hadron resonance gas. Using the standard rotating-HRG pressure (Eq. 3) with a causality cutoff Rω ≤ 1 and quantized radial momenta, the authors recompute energy density, number density, and entropy density and impose the conventional freeze-out criteria ε/n = 1.08 GeV and s/T³ = 7. They report a systematic downward shift of the freeze-out curve in the T–μ_B plane, map the rotational dependence of μ_Q and μ_S under charge and strangeness constraints, and compare the sensitivity of primary hadron yield ratios (notably Ω⁻/π⁺) to that of low-order conserved-charge cumulant ratios χ₂/χ₁. The main phenomenological claim is that yield ratios are more sensitive to ω and therefore better suited for estimating vorticity in heavy-ion collisions.

Significance. If the modeling premises hold, the work supplies a concrete, experimentally oriented extension of rotating HRG thermodynamics to chemical freeze-out, including the first systematic HRG study of μ_Q(ω) and μ_S(ω) and a direct ranking of yield ratios versus cumulant ratios as vorticity probes. The formalism follows established rotating-HRG formulas, the conservation constraints are solved consistently, and the LO coefficients q₁, s₁ are cross-checked against the direct n_Q/n_B and n_S = 0 conditions. These elements make the paper a useful reference for interpreting freeze-out extractions and hyperon-related observables in peripheral collisions, provided the fixed numerical freeze-out targets and the neglect of resonance feed-down are adequately controlled.

major comments (3)
  1. [Sec. III, Fig. 1] Sec. III and Fig. 1: The central T-shift result is obtained by imposing the same numerical targets ε/n = 1.08 GeV and s/T³ = 7 that were calibrated at ω = 0. Rotation already modifies the single-particle spectrum ε_ℓ = E − (ℓ + s)ω and the entire thermodynamic surface (Eqs. 4–6), so there is no a-priori reason that those empirical thresholds remain the correct chemical-freeze-out markers at finite ω. The manuscript should either (i) justify why the targets are universal under rotation (e.g., by reference to an underlying dynamical freeze-out condition), or (ii) quantify how the reported ΔT and the yield-vs-cumulant ranking change if the targets themselves drift with ω. Without that discussion the magnitude of the shift and the phenomenological recommendation remain model-dependent.
  2. [Sec. III, Figs. 6–8] Sec. III (discussion of Figs. 6–8) and Conclusion: The claim that hadronic yield ratios are a more suitable vorticity probe than χ₂/χ₁ rests on primary densities only. The authors note that resonance-decay feed-down is neglected for computational cost, yet feed-down is known to reshape both absolute yields and ratios (especially for protons, Λ, and multi-strange baryons). Because the ranking of observables is a main conclusion of the paper, at least a representative estimate of feed-down for the key ratios (Ω⁻/π⁺, p/π⁺, Λ/π⁺) at a few (T, μ_B, ω) points is needed, or a clear demonstration that the relative sensitivity ordering is stable under feed-down.
  3. [Sec. II] Sec. II: The system radius is fixed at R = 30 GeV⁻¹ (≈ 6 fm) for all ω, with the causality bound Rω ≤ 1. The discretization k_r = ξ_{ℓ,i}/R and the lower integration limit ξ_{ℓ,i}ω make thermodynamic densities explicitly R-dependent. A short sensitivity scan in R (or an argument that freeze-out loci and normalized ratios are stable under reasonable R variations at fixed Rω) is required to establish that the reported shifts and observable rankings are not artifacts of this particular infrared cutoff.
minor comments (6)
  1. [Sec. IV] Conclusion, first bullet: typographical error “roation” → “rotation”.
  2. [Fig. 1] Fig. 1 caption and text: clarify that the Cleymans et al. comparison is for the non-rotating case only, and state explicitly which particle list / mass cutoff was used in that reference versus the PDG list up to 2.6 GeV adopted here.
  3. [Sec. II, Eq. (3)] Eq. (3) and surrounding text: define the range of the spin sum and the meaning of S_i more carefully for bosons versus fermions; a brief note on how anti-particles are treated under rotation would help reproducibility.
  4. [Fig. 3] Fig. 3: the color scale for μ_Q and μ_S is hard to read in grayscale; consider contour labels or separate line plots at fixed μ_B slices.
  5. [Introduction] Introduction / Sec. III: when citing the magnetic-field freeze-out study (Ref. [33]), note more explicitly the analogy and the differences (spin–rotation vs. charge–magnetic coupling) so that the parallel is not overstated.
  6. [Sec. III] Throughout: ω is given in GeV; a parenthetical conversion to s⁻¹ (or to the STAR polarization scale) at first use would help experimental readers assess realism of the 5–15 MeV scan.

Circularity Check

0 steps flagged

No significant circularity: freeze-out targets are external constants applied to independently recomputed rotating densities; minor self-cites of prior rotating-HRG formalism are not load-bearing.

full rationale

The derivation chain is a direct numerical evaluation inside the rotating HRG. Single-particle energies are modified by the standard rotational coupling ε_ℓ = E - (ℓ + s)ω (Eq. 3), thermodynamic densities follow by differentiation (Eqs. 4–6), and the two empirical freeze-out conditions ε/n = 1.08 GeV and s/T^{3} = 7 are taken unchanged from the external Cleymans et al. literature. Solving the same algebraic constraints n_Q/n_B = 0.4 and n_S = 0 at finite ω then yields a lower T_ch; the subsequent yield-ratio and susceptibility-ratio comparisons are likewise pure outputs of those densities. Nothing is fitted to data inside the paper and then re-labeled a prediction, no uniqueness theorem is imported from the authors’ prior work, and the LO coefficients q1, s1 are cross-checked against the direct constraints rather than assumed. Self-citations to earlier rotating-HRG papers by overlapping authors supply only the model setup already written out in Sec. II; they do not force the reported T-shift or the ranking of observables. The modeling choice to keep the numerical targets fixed under rotation is an assumption (potentially debatable on physical grounds) but is not a circular reduction of the claimed results to their inputs. Hence the circularity score is minimal.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The central claims rest on the standard ideal HRG plus a rigid-rotation modification of single-particle energies, two externally fixed freeze-out numbers, a fixed system radius, and conservation constraints. No new particles or forces are invented; the free parameters are the usual phenomenological inputs of the program plus the illustrative ω scan.

free parameters (6)
  • E/N freeze-out target = 1.08 GeV
    Fixed at 1.08 GeV from Cleymans et al.; not re-derived under rotation; load-bearing for the left panel of Fig. 1 and the ΔT curves.
  • s/T³ freeze-out target = 7
    Fixed at 7 from the literature; used for the right panel of Fig. 1 and the lower panel of Fig. 2.
  • system radius R = 30 GeV^{-1}
    Fixed by hand at 30 GeV⁻¹ (≈6 fm) to enforce causality Rω ≤ 1 and to quantize radial momenta; enters every thermodynamic integral.
  • angular velocity scan ω = 0–0.015 GeV
    Illustrative values 0, 0.005, 0.010, 0.015 GeV chosen by hand; not extracted from a hydrodynamic or transport simulation of a specific collision system.
  • n_Q/n_B ratio = 0.4
    Fixed at 0.4 (Z/A of heavy nuclei) to determine μ_Q; standard but still a free input of the freeze-out setup.
  • hadron mass cutoff = 2.6 GeV
    All PDG hadrons and resonances up to 2.6 GeV included; cutoff choice affects densities of high-spin states that drive the Ω enhancement.
axioms (5)
  • domain assumption Ideal HRG pressure is the sum of free hadron and resonance contributions (Eq. 1 / Eq. 3).
    Standard low-T QCD approximation; validity near freeze-out is assumed throughout Sec. II–III.
  • domain assumption In a rigidly rotating frame the single-particle energy is ε = √(k_r²+k_z²+m²) − (l+s)ω with Bessel-zero quantization of k_r at the causal boundary.
    Taken from the rotating-HRG literature (Fujimoto et al., Mukherjee et al.); enters Eq. 3 and all subsequent densities.
  • ad hoc to paper Chemical freeze-out is realized when ε/n = 1.08 GeV or s/T³ = 7, and these numerical targets remain valid at finite ω.
    The numbers are external; the assumption that they do not themselves depend on ω is the paper’s modeling choice (Sec. III).
  • domain assumption Strangeness neutrality n_S = 0 and n_Q/n_B = 0.4 fix μ_S and μ_Q at every (T, μ_B, ω).
    Standard experimental constraints (Eqs. 8–9); used for all freeze-out and chemical-potential results.
  • ad hoc to paper Resonance-decay feed-down can be neglected for the yield and susceptibility ratios presented.
    Explicitly stated near the end of Sec. III as a computational approximation; authors note it may enhance the observed effects.

pith-pipeline@v1.1.0-grok45 · 20116 in / 3763 out tokens · 33919 ms · 2026-07-13T17:01:53.992612+00:00 · methodology

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read the original abstract

We investigate the influence of global rotation on the chemical freeze-out parameters in ultra-relativistic heavy-ion collisions. Within the framework of the hadron resonance gas (HRG) model, the freeze-out parameters are determined using commonly employed freeze-out criteria, namely the fixed energy per particle and the scaled entropy density, extended here to include rotational effects. We find that the presence of rotation leads to a systematic shift of the chemical freeze-out curve toward lower temperatures in the $T\text{--}\mu_B$ phase diagram. The behavior of the electric charge and strangeness chemical potentials in the presence of rotation is also analyzed, providing the first systematic study of their rotational dependence within the HRG framework. Furthermore, we examine the impact of rotation on experimentally relevant observables, including hadron yield ratios and susceptibility ratios of conserved charges. Our results show that while particle yield ratios exhibit noticeable sensitivity to rotation, the conventional cumulant ratios remain comparatively less affected. This indicates that hadronic yield ratios may provide a more suitable observable for estimating the magnitude of rotational effects generated in heavy-ion collisions.

Figures

Figures reproduced from arXiv: 2603.27267 by Arghya Chatterjee, Kshitish Kumar Pradhan, Nandita Padhan, Raghunath Sahoo.

Figure 1
Figure 1. Figure 1: FIG. 1: (Colour Online) The freeze-out curve in the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (Colour Online) The shift in freeze-out temperature [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (Colour Online) The electric charge and Strangeness chemical potential as a function of T and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Colour Online) The leading-order expansion coefficients of the negative of electric charge (left) and strangeness [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Colour Online) The chemical potentials [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Colour Online) Particle densities (left) and hadron-to-pion densities ratios (right) normalized to their values at zero [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) Ratios of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: (Colour Online) Comparison of the sensitivity of the [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

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