{"id":"e3df9408-4475-4ec9-8ee9-d4774aa85725","arxiv_id":"2602.13618","paper_version":2,"verdict":"REJECT","confidence":"LOW","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper fits hadron transverse-momentum spectra with a rotating Tsallis distribution to extract 'global vorticity', but never writes down the fitted formula or parameter values.","lead":"This paper claims to extract the rotational vorticity of the quark-gluon plasma by fitting hadron momentum spectra with a rotating thermal model. The method is not actually shown: the modified fit formula, its parameters, and uncertainties are absent, so the reported numbers cannot be checked.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Extraction is not falsifiable: the rotation-modified Tsallis formula is never stated, so Ω could be a fitting artifact; no baseline comparison shows the pT data require rotation.","rationale":"The reader's weakest_assumption identifies the same load-bearing gap: the rigid-rotor modification of the Tsallis distribution is asserted but never made explicit, and no sensitivity proof is given. My independent read confirms this is decisive. Without the fit formula and a baseline comparison, the reported Ω values are not verifiable, and the paper's central claim—that inclusive pT spectra provide a complementary, data-driven vorticity probe—cannot be evaluated. I considered whether the discrepancy with observed Λ polarization at LHC (where global polarization is smaller than at RHIC, while the paper claims larger Ω) could be the core issue, but that is secondary because the extraction itself is unfalsifiable. The missing formula is the more fundamental load-bearing problem. Thus the reader's REJECT is appropriate; my concern does not change the verdict.","tokens_in":10160,"tokens_out":4376,"duration_ms":47504,"concrete_test":"Re-analyze the STAR Λ pT spectra of Ref. [54] with the Ω=0 Tsallis baseline and with the authors' Ω-modified distribution (once supplied). Report Δχ²/ndf and best-fit Ω for each centrality/energy. Additionally, generate pseudo-data from the fitted Ω=0 form and refit with the Ω-modified formula to measure the false-positive rate of nonzero Ω extraction. If the Ω=0 fit is statistically indistinguishable or pseudo-data yield nonzero Ω at comparable significance, the extraction is not identifiable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central method is never written down. Section II gives Eq. (2), the standard Tsallis distribution with no Ω, and Eq. (3), the energy shift E = E(lab) − J·Ω, but the paper stops there. It never displays the actual fit formula used for the pT spectra, never reports fit parameters or goodness-of-fit, and never compares against the Ω=0 baseline. This is not a cosmetic omission: for unpolarized, inclusive pT spectra, the substitution in Eq. (3) does not trivially produce a measurable distortion. Tracing over spin states of exp(β Ω·S) yields only a scalar factor independent of pT, while the orbital term Ω·(r×p) integrated over the fireball can largely renormalize the normalization or mimic changes in T and q. Without the explicit distribution, the fitted Ω values in Figs. 2–6 are unreproducible, and the claim that the data require rotation—rather than the same Tsallis form with slightly different T, q, and V—is unsupported. The asserted consistency with polarization-derived vorticity is also not an independent check, because no error budget or quantitative comparison is given. Thus the central claim of a data-driven vorticity extraction rests on an unspecified formula and an unproven sensitivity.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that the global vorticity of the quark-gluon plasma formed in relativistic heavy-ion collisions can be extracted from inclusive transverse-momentum (pT) spectra of hadrons. The idea is to use a thermodynamically consistent Tsallis distribution and modify the single-particle energy by a rigid-rotation shift E = E_lab − J·Ω (Eq. 3), then fit the resulting distribution to published STAR and ALICE pT spectra of hyperons and vector mesons at RHIC and LHC energies. Plotted results show Ω as a function of centrality and beam energy for many particle species, and the abstract claims consistency with polarization-derived vorticity. However, the rotation-modified fit formula is never written down, no fit parameters or goodness-of-fit are reported, and no baseline (Ω=0) comparison is shown.","tokens_in":10525,"tokens_out":4804,"duration_ms":44109,"significance":"If the proposed extraction were demonstrated, it would provide a complementary, data-driven probe of QGP rotation using inclusive pT spectra rather than spin-dependent observables, and the paper covers a broad and relevant dataset. The idea is interesting and the systematic exploration across species, centralities, and beam energies is commendable. However, the central method is missing from the manuscript: the fit formula is not given, the sensitivity of inclusive unpolarized spectra to Ω is not established, and the consistency claim with polarization measurements is not quantified. As it stands, the results are not reproducible and the existence of a measurable rotational imprint on the spectra is unproven.","major_comments":[{"comment":"The paper never writes the rotation-modified Tsallis distribution that is actually fitted. Eq. (2) is the standard Tsallis form with no Ω; Eq. (3) states the energy shift, but the substitutions E → E_lab − J·Ω (including spin and orbital contributions) and the resulting expression for d²N/(dpT dy) are not given. The figures in Section III therefore plot Ω values that cannot be reproduced or checked. This is load-bearing because the paper's central claim is that Ω is extracted from the pT spectra.","section":"Section II, after Eq. (3)"},{"comment":"No fit parameters, uncertainties, or goodness-of-fit measures are reported for the Ω extraction, and no Ω=0 baseline fit is shown. The text itself states (Section I, p.2) that \"all fit parameters are obtained from the spectral analysis,\" so Ω is a fit parameter. Without a comparison of fit quality relative to the Ω=0 Tsallis baseline, the data do not demonstrate that rotation is required; changes in T, q, V, or dN/dy could absorb the effect.","section":"Section III, Figs. 2–6"},{"comment":"The claimed consistency with polarization-derived vorticity is not quantitative. No numerical values, uncertainties, or comparison plot are given, and the comparison is to values \"deduced ... using statistical thermal models,\" which share the same rotating-frame assumption. Thus the agreement is not an independent test of the proposed model.","section":"Abstract and Section III.A.1"},{"comment":"The sensitivity of unpolarized inclusive spectra to Ω is not established. For spin-1/2 and spin-1 particles, tracing over spin states of exp(β Ω·S) yields a scalar factor independent of pT; the orbital contribution Ω·(r×p) integrated over the fireball may be largely degenerate with a renormalization of T, q, or V. The paper should show explicitly, analytically or via a mock-data study, that the inclusive pT shape changes measurably as Ω varies before claiming a constraint.","section":"Section II, Eq. (3)"}],"minor_comments":[{"comment":"Notation is inconsistent: \"the L´evy–Tsallis distribution\" and \"Eq. 2\" versus \"Eq. (3)\"; use consistent style and spell Lévy.","section":"Section II"},{"comment":"Axis labels appear broken in several panels, e.g., \"10 −5 −0 5 10 (GeV) Ω\". Please reformat the vertical-axis labels so the tick values and the symbol Ω are legible.","section":"Figures 2–6"},{"comment":"The mapping between Eq. (1) and Eq. (2) via n → q/(q−1) and nC → T + m(q−1)/(q−1) should be stated more carefully; as written the connection is ambiguous.","section":"Section II, after Eq. (1)"},{"comment":"In Fig. 6 the left-panel label reads \"sNN = 2.76 GeV\" but the text says TeV; correct the unit.","section":"Section III.B.2 and Fig. 6"},{"comment":"Reference [49] is an arXiv preprint; consider citing the published version if available. Also, the list contains a large number of self-citations (e.g., [19], [21], [22], [25]–[27]); please verify that all are necessary.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's central issue is not a matter of taste but of missing evidence: the method is not described concretely enough to be reproduced, and the claimed consistency with polarization is not quantified. The authors should be asked to provide the full rotation-modified Tsallis formula, fit results with uncertainties and χ²/ndf, a baseline comparison, and a quantitative comparison with polarization-derived vorticity. If after these additions the sensitivity of inclusive pT spectra to Ω is shown to be degenerate with standard Tsallis parameters, the approach would need to be reconsidered. I do not see grounds for a novelty or integrity concern beyond the heavy overlap of the reference list with the authors' prior work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper tries to extract global vorticity Ω by fitting a rotating Tsallis distribution to pT spectra of many hadron species across RHIC and LHC energies. That is a reasonable thing to want to do, and the authors have gathered a lot of public data. The qualitative pattern they report—different hadrons giving different Ω values—would be worth knowing if the extraction were solid. But the extraction is not something a reader can verify.\n\nThe core problem is that the paper never writes down the actual fit formula. Section II gives the standard Tsallis distribution and then Eq. (3), the rotating-frame energy shift E = E_lab − J·Ω, and stops. There is no expression showing how the spin trace is done, how the orbital term r×p is handled, or what replaces E in Eq. (2). Without that, the Ω values in Figs. 2–6 are unfalsifiable. No fit parameters, uncertainties, or goodness-of-fit are reported either. The authors admit Ω is a fit parameter, so the data trends could simply be the Tsallis shape absorbing Ω into T and q. The paper never shows a baseline fit with Ω=0, so there is no evidence the spectra require rotation at all.\n\nThe stress-test note makes a sharper physics point: for unpolarized, inclusive spectra, the spin part of J·Ω may reduce to a pT-independent scalar, and the orbital part can largely renormalize the volume or mimic changes in T and q. The paper does not address this. That is not a cosmetic omission; it goes to whether pT spectra are sensitive to Ω in the way the authors assume.\n\nThe comparison with hyperon polarization is not an independent check, because both approaches use the same thermal-model rotation assumptions. The paper says the values are 'consistent within uncertainties' but gives no error budget, so this is a verbal agreement, not a quantitative test.\n\nOn the positive side, the paper is honest that Ω is a fit parameter, the data coverage is broad, and the discussion of particle-species dependence is careful. But the novelty is thin: the rotating Tsallis framework appears in earlier references from the same group, so the new content is the systematic scan, not the formalism.\n\nI would not take the numbers seriously until the authors write down the full distribution, show that it is actually sensitive to Ω, and provide fits with and without rotation. As submitted, I would reject. But it deserves a serious referee, not a desk rejection—the idea is testable and the data are already public. With a rewrite that supplies the missing formula and a baseline comparison, this could become a useful cross-check for the polarization-based vorticity estimates.","headline":"An intriguing but unreproducible vorticity extraction: the fit formula is never written, so the central numbers hang unsupported.","tokens_in":10885,"tokens_out":3952,"would_cite":false,"duration_ms":35468,"reading_group":"maybe","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.75.-q"],"model":"deepseek-v4-flash","headline":"A rotating-frame energy shift embedded in the Tsallis distribution makes inclusive hadron transverse-momentum spectra a direct probe of the quark–gluon plasma's global vorticity.","keywords":["global vorticity","quark-gluon plasma","transverse momentum spectra","spin-vorticity coupling","Tsallis non-extensive distribution","hyperon polarization","vector meson spin alignment","relativistic heavy-ion collisions"],"falsifier":"Take one centrality and beam-energy bin, fit Ω from the pT spectrum of Λ, and compare it with Ω deduced from the measured Λ polarization in the same bin under the same non-relativistic thermal model; a disagreement beyond quoted uncertainties would falsify the spectral-shift interpretation. Alternatively, a viscous-hydrodynamic simulation yielding a space-averaged vorticity an order of magnitude below the fitted Ω would rule out the rigid-rotor assumption.","tokens_in":10114,"feed_emoji":"🌀","tokens_out":5113,"duration_ms":47085,"temperature":0.7,"pith_summary":"The paper argues that the global vorticity of the quark–gluon plasma can be measured without spin-polarization experiments, by fitting inclusive transverse-momentum spectra of hyperons and vector mesons with a thermodynamically consistent distribution modified for rigid rotation. If right, the fits show a rotation rate on the order of 10^22 per second, matching earlier values inferred from Lambda polarization, and reveal a clear dependence on hadron species, collision centrality, and beam energy. This would make ordinary unpolarized spectra a complementary, data-driven probe of the rotational state of QCD matter at freeze-out.","feed_headline":"Hadron spectra reveal the quark–gluon plasma's spin rate","feed_subtitle":"Fitting inclusive transverse-momentum spectra returns a global vorticity matching hyperon-polarization estimates.","key_machinery":"The central object is the global angular velocity Ω of a rigidly rotating fireball. It enters through the rotating-frame energy shift E = E_lab − J·Ω, which couples a hadron's total angular momentum J to the rotation. The paper inserts this shift into the Tsallis non-extensive distribution (a two-parameter fit function that reproduces the exponential-to-power-law shape of hadron spectra) and treats Ω as a free parameter; the entire analysis hinges on this single energy shift being visible in inclusive spectra.","core_discovery":"The paper's central claim is that the global rotation of the deconfined fireball leaves a detectable imprint in the shape of unpolarized transverse-momentum spectra. Substituting E_lab − J·Ω for the single-particle energy in a thermodynamically consistent non-extensive (Tsallis) distribution, and fitting published spectra of eight hadron species across RHIC and LHC energies, yields a global vorticity Ω whose magnitude agrees with the ~10^22 s^-1 inferred from Λ and anti-Λ polarization. The fitted Ω varies with hadron species, centrality, and beam energy, and it behaves identically for particles and antiparticles, as expected for vorticity rather than magnetic-field coupling.","pith_inferences":["If the spectral-shift interpretation is correct, Ω extracted from pT spectra should track the measured global polarization of Λ in the same centrality and energy bins; a bin-by-bin cross-check would be a direct test the paper does not report.","The species dependence could be turned into a freeze-out chronometer: comparing Ω across hadrons with different decoupling times would map how the vortical field evolves during the hadronic stage.","The method assumes a single global Ω, so the fitted numbers are best read as an effective rotation; comparing them against the full vorticity profile from viscous hydrodynamics would show how much of the local vortical structure survives averaging."],"forward_implications":["Inclusive pT spectra, already measured for many species and centralities, become an independent cross-check of vorticity values obtained from hyperon polarization.","A particle-species-dependent Ω implies that estimates of global vorticity must account for freeze-out time and hadron structure, not just the common collective flow field.","The rise of Ω from RHIC to LHC energies provides a quantitative handle on how initial orbital angular momentum is converted into global rotation of the medium.","The extracted Ω values can serve as an input parameter for hydrodynamic and transport simulations of rotating QCD matter.","Extending the analysis to charmed vector mesons links global vorticity to the spin-alignment puzzle in the heavy-quark sector."],"fun_headline_variants":["Hadron spectra expose the plasma's global vorticity","Vorticity from hadron spectra agrees with hyperon polarization","Spectra probe QGP rotation via vorticity imprint","Global rotation of QGP read from hadron spectra"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the entire fireball rotates as a rigid body with one angular velocity, so the same J·Ω shift distorts every hadron's spectrum; if the medium's rotation is not rigid, the fitted Ω is not a physical global vorticity.","fun_headline_variants_meta":{"raw":{"variants":["Hadron spectra expose the plasma's global vorticity","Vorticity from hadron spectra agrees with hyperon polarization","Spectra probe QGP rotation via vorticity imprint","Global rotation of QGP read from hadron spectra"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00027,"raw_usage":{"total_tokens":1507,"prompt_tokens":834,"completion_tokens":673,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":608}},"tokens_in":578,"tokens_out":673,"duration_ms":6506,"temperature":1.0,"reasoning_tokens":608,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T23:27:10.257431+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take one centrality and beam-energy bin, fit Ω from the pT spectrum of Λ, and compare it with Ω deduced from the measured Λ polarization in the same bin under the same non-relativistic thermal model; a disagreement beyond quoted uncertainties would falsify the spectral-shift interpretation. Alternatively, a viscous-hydrodynamic simulation yielding a space-averaged vorticity an order of magnitude below the fitted Ω would rule out the rigid-rotor assumption.","supporting_citations":[],"review_version":1}