{"id":"bc805661-62a9-4063-8eaa-4b5729a981ee","arxiv_id":"2608.10561","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A rotating hadron resonance gas calculation maps ALICE's centrality-dependent p/pi ratio into freeze-out vorticity estimates and predicts rotation-induced changes in conserved-charge fluctuations.","lead":"Particle ratios measured by ALICE in lead-lead collisions are used inside a model of hot hadronic matter with rotation to estimate how fast the fireball spins at freeze-out: about 0.088 GeV in peripheral collisions and 0.028 GeV in central collisions. A generalist should care because it offers a quantitative way to test whether vorticity survives to the end of the collision and alters the particles produced.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Peripheral extraction violates the model's own causality bound: quoted omega ~ 0.088 GeV for R = 12.5 GeV^-1 exceeds 1/R = 0.080 GeV, so the headline upper limit lies outside the stated validity domain.","rationale":"The reader's weakest_assumption concerns the degeneracy of rotation with baryon annihilation, which the authors acknowledge and which makes the extracted omega an upper limit rather than a clean measurement. A sharper, internal problem is that the peripheral extraction violates the model's own causality constraint R*omega <= 1: with R = 12.5 GeV^-1 the maximum allowed omega is 0.080 GeV, but the paper quotes 0.088 GeV. This is not a matter of external consensus; the quoted number lies outside the validity domain of the formalism used to produce it. The central value 0.028 GeV is below the central cap 1/30 GeV^-1 and is not affected. Correcting the peripheral cap would leave the qualitative framework intact but changes the headline number, so the conditional verdict stands pending a straightforward consistency check.","tokens_in":11339,"tokens_out":12580,"duration_ms":139168,"concrete_test":"Add a horizontal line at omega = 1/R = 0.080 GeV to Fig. 5(b) and identify the peripheral point by its dN_ch/d_eta value. If that point lies above the line, recompute the extraction with the constraint omega <= 1/R enforced, either by rejecting or explicitly capping omega values above 0.080 GeV, and report the revised peripheral upper limit; a value of 0.088 GeV cannot be quoted under the model's stated causality bound.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. II the authors impose the causality constraint R*omega <= 1 for a finite cylinder of radius R, stating that 'the causality requirement reduces to R*omega <= 1'. In Sec. III B the peripheral geometry is assigned R = 12.5 GeV^-1 (2.5 fm), yet the extracted upper limit for peripheral Pb+Pb collisions is omega ~ 0.088 GeV, giving R*omega ~ 1.1 > 1. Thus the peripheral point in Fig. 5(b) lies in the acausal region where the rotational term can exceed the free-particle energy component, and the IR-cutoff regularization in Eq. (4) is no longer a controlled approximation. The reported peripheral value is therefore not a valid prediction of the model as formulated; at minimum it should be capped at 1/R = 0.080 GeV. This is an internal consistency failure in the headline extraction, independent of the acknowledged baryon-annihilation degeneracy.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":11496,"tokens_out":7158,"duration_ms":74813,"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":[{"comment":"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.","section":"Sec. III B / Sec. II"},{"comment":"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.","section":"Sec. III B"},{"comment":"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.","section":"Sec. II, Eq. (4) / Fig. 4"}],"minor_comments":[{"comment":"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.","section":"Abstract and Sec. IV"},{"comment":"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.","section":"Eqs. (1), (3), and (4)"},{"comment":"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.","section":"Fig. 5 and Sec. III B"},{"comment":"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.","section":"Fig. 5 caption"},{"comment":"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'.","section":"References and text"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the qualitative phenomenology is interesting. The main technical problem is localized to the extraction section and can be fixed by enforcing the causality bound and clarifying the role of r versus R; the fluctuation results are less affected. I would support publication after major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a rotating-HRG study that does two things: it computes how rotation modifies hadron yields, ratios, and conserved-charge susceptibilities, and it tries to extract a per-centrality freeze-out vorticity from ALICE p/pi data. The second part is the headline and it has a genuine problem the authors appear to have missed.\n\nWhat's new and good: the susceptibility calculations are new and internally consistent; the observation that rotation enhances p/pi while suppressing K/pi, with stronger effects for high-spin/high-mass states, is cleanly demonstrated in Figs. 2 and 4. The authors are upfront about the main degeneracy between rotation and baryon annihilation, and they correctly label the extracted omega as an upper limit.\n\nThe soft spots are real. First, the extraction is circular in the sense the reader identified: the same computed p/pi(omega) curve is used to map data to omega, and then cited as evidence that rotation explains the centrality trend. Second, the 0-5% bin is assumed vorticity-free without external support. Third, and more serious, the peripheral omega value violates the model's own causality bound. The paper imposes R*omega <= 1 for a finite cylinder; peripheral geometry is R = 12.5 GeV^-1 (2.5 fm), so the allowed omega is capped at 0.080 GeV. Yet the headline upper limit for peripheral collisions is 0.088 GeV, giving R*omega ~ 1.1. The peripheral point in Fig. 5(b) sits in the acausal region where the IR-cutoff regularization in Eq. (4) is no longer controlled. At minimum, that value should be capped at 1/R. This is an internal consistency failure, independent of the baryon-annihilation degeneracy.\n\nThe fluctuation part (Sec. III D) is much safer, and the ratios chi3/chi2 being nearly rotation-independent while chi4/chi2 varies is a potentially useful signature.\n\nWho gets value: heavy-ion phenomenologists working on rotational effects and thermal-model analyses of hadron yields. It deserves a serious referee, because the model calculations are reproducible in principle, the caveats are mostly stated, and the causality violation is fixable. My recommendation: send to peer review, but the referee report should require the authors to reconcile the peripheral omega with R*omega <= 1, and to reframe the p/pi comparison as an upper-limit exercise rather than an explanation of the centrality dependence.","headline":"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.","tokens_in":12083,"tokens_out":1535,"would_cite":false,"duration_ms":15200,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.75.-q","12.38.Mh"],"model":"deepseek-v4-flash","headline":"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.","keywords":["rotating hadron resonance gas","vorticity","proton-to-pion ratio","heavy-ion collisions","chemical freeze-out","conserved-charge fluctuations","susceptibilities","ALICE Pb-Pb 5.02 TeV"],"falsifier":"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.","tokens_in":11060,"feed_emoji":"🌀","tokens_out":11090,"duration_ms":100833,"temperature":0.7,"pith_summary":"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.","feed_headline":"Proton-to-pion ratios bound freeze-out fireball vorticity","feed_subtitle":"Rotating hadron gas model reads LHC data as vorticity near 0.03 GeV central and 0.09 GeV peripheral.","key_machinery":"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.","core_discovery":"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 $3\\chi^{QS}_{11}/\\chi^S_2$.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the ALICE centrality dependence of $(p+\\bar p)/(\\pi^++\\pi^-)$ in Pb+Pb at 5.02 TeV that the extraction maps onto.","marker":"[37]"},{"why":"Gives the rotating-medium single-particle dispersion and pressure formula used in the model.","marker":"[10]"},{"why":"Provides the earlier rotating hadron resonance gas treatment that this calculation extends.","marker":"[18]"},{"why":"Derives the grand-canonical pressure for rotating QCD matter adopted for the mode sum in Eq. (1).","marker":"[22]"},{"why":"Supplies the cylindrical Bessel-mode expansion and the $R\\omega\\le1$ causality bound that fixes the infrared cutoff.","marker":"[33]"},{"why":"Frames the expected vorticity magnitude, about 0.01–0.1 GeV, against which the extracted values are assessed.","marker":"[8]"},{"why":"Provides the STAR global hyperon polarization evidence that finite vorticity exists in the medium.","marker":"[9]"},{"why":"Fixes the chemical freeze-out parameters ($T\\approx158$ MeV, $\\mu_B=0$) at which the yields are evaluated.","marker":"[36]"}],"fun_headline_variants":["Proton-to-pion ratio reveals freeze-out vorticity","Rotating fireball: p/pi up, K/pi down","Freeze-out vorticity bounded by ALICE p/pi trend","Vorticity extracted from LHC proton-pion ratios"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Proton-to-pion ratio reveals freeze-out vorticity","Rotating fireball: p/pi up, K/pi down","Freeze-out vorticity bounded by ALICE p/pi trend","Vorticity extracted from LHC proton-pion ratios"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00106,"raw_usage":{"total_tokens":4546,"prompt_tokens":1147,"completion_tokens":3399,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":763,"completion_tokens_details":{"reasoning_tokens":3327}},"tokens_in":763,"tokens_out":3399,"duration_ms":23201,"temperature":1.0,"reasoning_tokens":3327,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T21:46:20.947769+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Acharyaet al.(ALICE), Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the ALICE centrality dependence of $(p+\\bar p)/(\\pi^++\\pi^-)$ in Pb+Pb at 5.02 TeV that the extraction maps onto."},{"cited_title":"Fujimoto, K","cited_arxiv_id":null,"evidence_quote":"Gives the rotating-medium single-particle dispersion and pressure formula used in the model."},{"cited_title":"Mukherjee, D","cited_arxiv_id":null,"evidence_quote":"Provides the earlier rotating hadron resonance gas treatment that this calculation extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the grand-canonical pressure for rotating QCD matter adopted for the mode sum in Eq. (1)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the cylindrical Bessel-mode expansion and the $R\\omega\\le1$ causality bound that fixes the infrared cutoff."},{"cited_title":"Jiang and J","cited_arxiv_id":null,"evidence_quote":"Frames the expected vorticity magnitude, about 0.01–0.1 GeV, against which the extracted values are assessed."},{"cited_title":"Adamczyket al.(STAR), Nature548, 62 (2017)","cited_arxiv_id":null,"evidence_quote":"Provides the STAR global hyperon polarization evidence that finite vorticity exists in the medium."}],"review_version":1}