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REVIEW 3 major objections 5 minor 44 references

Probing vorticity and fluctuations in a rotating hadron resonance gas at LHC energy

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A rotating hadron resonance gas predicts an enhanced proton-to-pion ratio, and matching it to LHC data bounds the fireball vorticity at freeze-out between about 0.03 and 0.09 GeV.

desk verdict Useful rotating-HRG phenomenology with a genuinely new susceptibility study, but the headline vorticity extraction has a load-bearing internal inconsistency: the peripheral upper limit violates the paper's own causality bound R*omega <= 1. read the letter →

arxiv 2608.10561 v1 pith:MPFQEP67 submitted 2026-08-11 hep-ph nucl-exnucl-th

S. Ipsita Sahoo , Sanjeebani Biswal , D. Dutta , D. K. Mishra This is my paper · ORCID
classification hep-phnucl-exnucl-th PACS 25.75.-q12.38.Mh
keywords rotatinghadronresonancegasvorticityproton-to-pionratioheavy-ioncollisionschemicalfreeze-outconserved-chargefluctuationssusceptibilitiesALICEPb-Pb5.02TeV
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

Rotation of the fireball formed in non-central heavy-ion collisions acts as an extra chemical potential in the hadron resonance gas picture, and this paper argues that its effect survives to chemical freeze-out and shows up in hadron abundances. The model predicts that heavier and higher-spin hadrons—protons, $\Delta(1232)^{++}$, $\Omega$—are progressively enhanced as the angular velocity $\omega$ grows, while pions respond weakly, so the $p/\pi$ ratio rises and $K^+/\pi^+$ falls. The authors compare the calculated $\omega$ dependence of $p/\pi$ with the centrality dependence measured by ALICE in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV and extract upper limits $\omega\sim0.028$ GeV for central and $\sim0.088$ GeV for peripheral collisions. If the identification holds, vorticity is a quantitative thermodynamic parameter at freeze-out and belongs alongside temperature and chemical potentials in thermal-model fits.

What carries the argument

The central object is the rotating ideal hadron resonance gas: a grand-canonical gas of all known hadrons up to 2.5 GeV inside a cylinder of radius $R$, with pressure written as a sum over orbital angular momentum modes $l$ and a squared Bessel function $J_\nu^2(k_r r)$ enforcing cylindrical symmetry. The load-bearing term is the rotation-induced effective chemical potential $\mu_{\rm eff}=(l+s_i)\omega$ in the dispersion relation $E_{l,i}=\sqrt{k_r^2+k_z^2+m_i^2}-(l+s_i)\omega$, which preferentially populates high-spin, high-mass states. The causality constraint $R\omega\leq1$ caps the allowed vorticity and, through the first zeros $\zeta_{l,1}$ of the Bessel functions, introduces an infrared cutoff $\Lambda^{\rm IR}_l=\zeta_{l,1}\omega$ on transverse momenta. This machinery converts a given $\omega$ into definite hadron yields, yield ratios, and susceptibility ratios.

What would settle it

Run a hadronic afterburner with baryon annihilation but no rotation on a hydrodynamic profile of Pb+Pb collisions at 5.02 TeV: if it reproduces the ALICE $p/\pi$ centrality trend, the reported $\omega$ values cannot be cleanly identified from this observable. Alternatively, measure $K^+/\pi^+$ in the same centrality bins; the model predicts a decrease with $\omega$, so a flat or increasing $K^+/\pi^+$ at the $p/\pi$-inferred $\omega$ values would refute the rotation interpretation.

Watch

Extended reading notes

Core claim

At fixed chemical freeze-out conditions ($T=158$ MeV, $\mu_B=0$), the rotating hadron resonance gas shifts each single-particle energy by $\mu_{\rm eff}=(l+s_i)\omega$, where $l$ is the orbital angular momentum quantum number and $s_i$ the spin. That shift lowers the effective energy of high-angular-momentum and high-spin states, producing a mass–spin ordering in the yield ratios: $p/\pi^+$, $\Delta^{++}/\pi^+$, $\Omega/\pi^+$, and $\rho^+/\pi^+$ increase with $\omega$, whereas $K^+/\pi^+$ decreases. Taking the centrality trend of the ALICE $p/\pi$ ratio as a proxy for growing vorticity from central to peripheral collisions, and assuming the $0$–$5\%$ bin has negligible rotation, the paper obtains an upper bound on freeze-out vorticity of about $0.028$ GeV ($\sim10^{22}$ s$^{-1}$) for central and $0.088$ GeV ($\sim10^{23}$ s$^{-1}$) for peripheral Pb+Pb collisions. It further reports that rotation enhances quadratic and mixed conserved-charge susceptibilities, leaves $\chi_3/\chi_2$ nearly unchanged, and generates an $\omega$-dependent split between $-3\chi^{BS}_{11}/\chi^S_2$ and $3\chi^{QS}_{11}/\chi^S_2$.

Load-bearing premise

The extraction rests on the assumption that the $0$–$5\%$ most central collisions have negligible vorticity and that the remaining centrality variation of the measured $p/\pi$ ratio is caused by rotation rather than by baryon annihilation or other centrality-dependent effects.

Editorial extensions

If this is right

  • Thermal-model fits that omit rotation will systematically misread the proton yield: part of the $p/\pi$ enhancement now attributed to freeze-out parameters would be reassigned to vorticity, shifting the extracted $T$ and $\mu_B$.
  • The same matching procedure applied to $\Omega/\pi$, $\Delta^{++}/\pi$, and $\rho^+/\pi$ should show a mass–spin ordering with centrality, a signature that distinguishes rotation from baryon annihilation.
  • The predicted suppression of $K^+/\pi^+$ with $\omega$ provides a consistency check on the vorticity values extracted from $p/\pi$.
  • Conserved-charge fluctuation observables such as $\chi^B_2$ and $\chi^{BS}_{11}$ increase sharply with rotation while $\chi_3/\chi_2$ stays flat, giving independent data-comparable probes of freeze-out vorticity.
  • The reported upper bounds, $\sim0.028$ GeV central and $\sim0.088$ GeV peripheral, set the scale at which rotation must be considered in freeze-out physics at LHC energies.

Reading between the lines

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

  • A decisive cross-check would be to repeat the extraction at several collision energies: since deposited angular momentum grows with $\sqrt{s_{NN}}$ and impact parameter, the inferred $\omega$ should grow accordingly if the interpretation is right, and should vanish for $p$+$p$ collisions where no vorticity is expected.
  • The model's near-flat prediction for $K^+/\pi^+$ across centrality already constrains how large $\omega$ can be at freeze-out; a combined fit to both $p/\pi$ and $K^+/\pi$ would tighten the upper bounds.
  • If the same vorticity drives both hadron abundances and global polarization, the centrality dependence of $\Lambda$ and $\bar\Lambda$ polarization from the STAR measurement could be compared point-by-point with the $\omega$ values extracted here.
  • The extracted central value $\omega\sim0.028$ GeV sits close to the causality bound $R\omega\leq1$ for $R\approx6$ fm, so central collisions may already probe the model's physical ceiling; smaller systems or larger radii would clarify whether the bound or the data set the limit.
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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

3 major / 5 minor

Summary. The paper extends the ideal hadron resonance gas model to a rigidly rotating system by modifying the single-particle energy with a rotational term -(l+s)ω (Eq. 2) and imposing a causality bound Rω≤1 (Section II). At fixed T=158 MeV and μ_B=0, the authors compute particle densities, hadron-to-pion ratios, and conserved-charge susceptibilities as functions of ω, finding strong enhancement for high-spin and high-mass hadrons and a moderate suppression of K+/π+. They then use the ALICE centrality dependence of (p+pbar)/(π+ + π-) in Pb+Pb at 5.02 TeV, normalized to the 0-5% bin, to map each centrality to a value of ω; this yields approximately 0.028 GeV for central and 0.088 GeV for peripheral collisions. The final part presents the ω dependence of χ2, χ3, χ4, mixed susceptibilities, and ratios such as χ3/χ2 and χ4/χ2, and argues these are rotation-sensitive observables.

Significance. If the central extraction were sound, the paper would provide a quantitative estimate of freeze-out vorticity from measured hadron yields, a useful input to the rotating-QCD program, and the fluctuation section offers falsifiable predictions for future measurements. The authors are transparent about the main assumptions: negligible vorticity in the 0-5% bin, rotation as one possible contributor to the p/π centrality trend, and survival of ω to chemical freeze-out. The model curves are internally consistent for ω within the stated causality bound, and the qualitative mass/spin ordering of the rotational enhancement is clear. However, the headline peripheral value lies outside the model's own validity domain, and the extraction is a mapping through a precomputed model curve rather than an independent test; these issues need to be fixed before the quantitative conclusion can be accepted.

major comments (3)
  1. [Sec. III B / Sec. II] The reported peripheral vorticity ω≈0.088 GeV violates the causality constraint Rω≤1 stated in Section II. The text assigns peripheral Pb+Pb collisions a maximum radius R=12.5 GeV^-1, giving Rω≈1.1>1. The peripheral point therefore lies in the region where the rotational term in Eq. (2) can exceed the free-particle energy component and where the IR-cutoff replacement in Eq. (4) is not a controlled approximation. The extracted peripheral value should be capped at 1/R=0.080 GeV, or the geometry used in the calculation should be changed so that every reported point satisfies the bound; either way, the abstract, the summary, and Fig. 5(b) must be revised.
  2. [Sec. III B] The extraction procedure computes p/π(ω) from the model in Fig. 4 and then inverts the measured ALICE p/π centrality ratios through that same curve. Consequently, the statement that rotation may explain the observed centrality dependence is a restatement of the inversion assumption rather than a model test. The extraction also assumes that the 0-5% bin has negligible vorticity and that the centrality variation of p/π is caused by rotation rather than by baryon annihilation or other final-state effects. The authors acknowledge the annihilation ambiguity, but the 'upper limit' wording in the abstract and Section IV should be qualified throughout, and the degeneracy should be quantified or at least discussed more concretely, for example by estimating the expected annihilation contribution.
  3. [Sec. II, Eq. (4) / Fig. 4] The model curves used for the extraction are computed at a fixed radial distance r=3 GeV^-1, while the centrality geometry is described by R=30 GeV^-1 for central and R=12.5 GeV^-1 for peripheral collisions. The paper does not clarify whether r or R is the radius that enters the causality bound and the IR cutoff in Eq. (4), nor why a single fixed r is appropriate for all centralities. If r=3 GeV^-1 is the actual size of the system in the calculation, the stated peripheral geometry is not being used; if R is the relevant radius, the extraction must be redone with the per-centrality boundary condition. This ambiguity directly affects the extracted ω values and should be resolved.
minor comments (5)
  1. [Abstract and Sec. IV] The values 0.028 and 0.088 GeV are described as 'upper limits', but under the assumptions listed in Sec. III B they are better characterized as conditional estimates; this wording should be adjusted for accuracy.
  2. [Eqs. (1), (3), and (4)] The definition of the IR cutoff Λ_IR_l = ζ_{l,1}ω and the modified integration in Eq. (4) should specify the lower limit of the k_r integral explicitly and explain how the l=0 mode is treated, since the current notation is not sufficient for reproducing the numerical results.
  3. [Fig. 5 and Sec. III B] The experimental quantity is (p+pbar)/(π+ + π-) from Ref. [37], but the text frequently writes p/π; please use consistent notation and state explicitly whether the calculated p/π(ω) curve used for the extraction includes feed-down contributions in the same way as the experimental ratio.
  4. [Fig. 5 caption] The uncertainty propagation is described only as 'uncertainties associated with the p/π ratio are propagated'; please specify whether the shaded band includes uncorrelated uncertainties only and how the correlation between the numerator and denominator in the ratio was handled.
  5. [References and text] There are several typographical issues: 'V orticity' in Ref. [5], 'Barun-Mumnzinger' in Ref. [31] should be 'Braun-Munzinger', 'Rev. Part. Phys. C38' in Ref. [35] should be corrected, and 'asses' in Sec. III C should be 'assess'.

Circularity Check

1 steps flagged · score 4.0 of 10

The p/pi-to-vorticity extraction is a calibration, and the claim that rotation 'may explain' the p/pi centrality dependence is a restatement of that calibration; the fluctuation and K/pi results retain independent content.

  1. fitted input called prediction [Section III B, Figure 5]
    "For each centrality class, the p/π ratios, normalized to the corresponding values of the 0−5% centrality interval, is mapped with the one given by nonzero vorticity values shown in Fig 4. This correspondence enables the extraction of the vorticity strength at a given centrality."

    The p/pi ratio is first computed as a function of omega (Fig. 4). The measured centrality-dependent p/pi ratios are then inverted through this same function to read off omega. Therefore the later statement, in Section III B, that rotation 'may significantly influence the hadron yields and potentially explain the observed centrality dependence of the p/π yield ratio' is not a test of the model: the data were used to set omega, so the agreement is enforced by construction. The only independent inputs are the assumed zero-vorticity 0-5% baseline and the model's functional shape; the extracted omega values inherit the data and provide no additional confirmation of the rotation mechanism for p/pi itself. The separate K/pi and susceptibility calculations are not forced by this step.

full rationale

The paper's central quantitative result is an extraction, not a prediction: omega is obtained by equating the model's p/pi ratio to the ALICE centrality data. The abstract and summary honestly call this an 'estimate' or 'upper limit', and the text explicitly assumes 0-5% centrality has negligible vorticity and lists baryon annihilation as a competing mechanism. Thus the circularity is limited to the rhetorical step of saying the fitted curve 'explains' the data. No self-citation is load-bearing: the rotating-HRG formulas are also attributed to non-overlapping references, and the susceptibility and K/pi sections are self-contained model calculations. A separate internal-consistency concern exists: if the peripheral radius R=12.5 GeV^-1 were used, the extracted omega=0.088 GeV would exceed the stated causality bound R*omega<=1 (giving 1.1>1); however, the paper fixes r=3 GeV^-1 for the calculations, making R*omega=0.264<1. That ambiguity is a correctness risk, not a circularity. Overall, the paper is mostly a calibration study with one overreaching explanatory claim, so a moderate score is appropriate.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The model rests on standard HRG assumptions plus a rotating-frame energy shift and a causality-motivated cutoff. The per-centrality omega values are fitted to ALICE p/pi data, and the freeze-out temperature, radial position, and zero-vorticity central bin are model choices. No new particles, forces, or conserved quantities are introduced.

free parameters (2)
  • Vorticity omega per centrality = 0.028 to 0.088 GeV
    Extracted by matching the HRG p/pi(omega) curve to the measured ALICE p/pi centrality ratios, assuming the 0-5% bin has zero vorticity. This is the headline result, but it is fitted to the data rather than independently predicted.
  • Radial distance r in the Bessel integrand = 3.0 GeV^-1
    Chosen by hand in Sec. II to allow access to a wider range of omega. Results in Fig. 1 depend strongly on r (3, 12.5, 30 GeV^-1), so this choice directly affects the extracted omega values.
assumptions (7)
  • domain assumption Ideal gas of non-interacting hadrons and resonances from the PDG list up to 2.5 GeV.
    Used throughout Sec. II as the baseline HRG assumption.
  • domain assumption Rotation modifies the single-particle energy as E = sqrt(k_r^2+k_z^2+m_i^2) - (l+s_i)omega.
    Eq. (2); the form is taken from refs [10,18,22] and is an input modeling choice, not derived in this paper.
  • domain assumption Causality bound R*omega <= 1 and the Bessel infrared cutoff Lambda_IR = zeta_{l,1} omega.
    Introduced after Eq. (3) via a normalization boundary condition; it changes the phase-space integration and affects the numerical yields.
  • domain assumption Chemical freeze-out at T=158 MeV with mu_B=mu_Q=mu_S=0 for Pb-Pb at 5.02 TeV.
    Taken from standard LHC freeze-out fits [36]; the paper notes T may itself change under rotation but keeps it fixed.
  • ad hoc to paper The 0-5% central collision bin has negligible vorticity.
    Sec. III B: 'This idea is based on the assumption that 0-5% centrality corresponds to a system with negligible vorticity.' This baseline is load-bearing for every extracted omega value.
  • ad hoc to paper The measured p/pi centrality dependence is attributed to rotation rather than to baryon annihilation or other centrality effects.
    Sec. III B: 'we assume the presence of vorticity as one possible contributing factors.' The authors acknowledge baryon annihilation as an alternative explanation, so this is an explicit identification assumption.
  • ad hoc to paper Vorticity survives undiminished until chemical freeze-out.
    Sec. III B limitation paragraph: the analysis neglects 'any possible evolution or dissipation of the system's initial vorticity during its dynamical expansion.'

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Cite this review

Pith. "Pith review of Probing vorticity and fluctuations in a rotating hadron resonance gas at LHC energy." pith.science (2026). https://pith.science/paper/MPFQEP67

@misc{pith2026260810561,
  author       = {Pith},
  title        = {Pith review of: Probing vorticity and fluctuations in a rotating hadron resonance gas at LHC energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MPFQEP67}},
  note         = {Machine review of arXiv:2608.10561}
}
abstract

A large vorticity produced in non-central ultra-relativistic heavy-ion collisions induces an effective chemical potential in both partonic and hadronic matter, thereby influencing the quark-hadron transition and its associated properties. In this work, we investigate the influence of rotation on hadron yields within the framework of Hadron Resonance Gas (HRG) model. Our results show that vorticity significantly modifies hadron yields and their ratios. Most notably, rotation enhances the $p/\pi^+$ ratio while suppressing the $K^+/\pi^+$ ratio, suggesting that these observables may serve as sensitive probes of the rotational properties of the medium created in heavy-ion collisions. To quantify the effect of rotation, the calculated dependence of the $p/\pi^+$ ratio on vorticity is compared with the centrality dependence of the $p/\pi$ ratio measured by the ALICE collaboration in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ = 5.02 TeV. From this comparison, we estimate the maximum vorticity produced at freeze-out for different collision centralities. In case of peripheral collisions, the freeze-out vorticity ($\omega$) is found to reach an upper bound value of approximately 0.088 GeV, whereas for central collisions it is about 0.028 GeV. Furthermore, we investigate the effect of rotation on fluctuations of conserved quantities and their correlations. This study provides a quantitative framework for assessing the role of rotation in the thermodynamics of hadronic matter and its phenomenological consequences for heavy-ion collisions.

Figures

Figures reproduced from arXiv: 2608.10561 by the authors.

Figure 2
Figure 2. FIG. 2. Dependence of various hadron yields (normalized by their [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Particle densities normalized to their corresponding densities [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Dependence of various hadron-to-pion yield ratios (normal [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (6 more)
Figure 6
Figure 6. Figure 6: FIG. 6. Multiplicity dependence of hadron yields [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Top: Multiplicity dependence of the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The dependence of quadratic susceptibilities of conserved [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (top):The dependence of normalized higher order suscepti [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The dependence of [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The dependence of [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]

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