{"id":"e0aef4b2-d1e9-4fc3-b76c-663a4dd25939","arxiv_id":"2507.03708","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper computes rotational susceptibilities up to sixth order in ideal and van der Waals hadron resonance gas models, finds a non-monotonic bump at high baryon chemical potential, and proposes these susceptibilities as a probe of the QCD phase transition.","lead":"This paper uses a model of strongly interacting particles to estimate how much a hot, dense fireball responds to rotation, and finds a bump in the response near a possible phase transition. The authors suggest this rotational response could become a new experimental probe of quark-gluon plasma formation in heavy-ion collisions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The bump cited as a QCD phase-transition signature is likely the van der Waals liquid-gas transition, so the central claim overreaches.","rationale":"The reader's identified weak assumption, that the VDW parameters a and b fitted without rotation remain valid under rotation, is real and is explicitly acknowledged in Section II.A. However, it is not the most load-bearing weakness: even if a and b were allowed to depend on omega, the central interpretive claim could still fail if the bump is a VDW liquid-gas artifact. The more fundamental issue is that the VDWHRG model's only phase transition is the classical liquid-gas transition, and the paper provides no argument that this coincides with the QCD deconfinement/chiral transition. This is a correctness risk in the physical interpretation, not merely a question of parameter dependence. A related secondary concern is that the susceptibilities are evaluated at finite omega rather than in the zero-field limit, so the reported chi_omega are nonlinear response functions; this affects the quantitative values but is less central than the misidentification of the transition. The proposed test of setting a = 0 and comparing with the liquid-gas coexistence curve directly settles whether the bump is a VDW mean-field effect. Since the reader already gave a conditional verdict, and the needed revision is consistent with that verdict, I recommend leaving the verdict unchanged.","tokens_in":16066,"tokens_out":4726,"duration_ms":57343,"concrete_test":"Recompute the rotational susceptibilities at muB = 0.436 GeV and omega = 0.02 fm^-1 with the attractive van der Waals parameter set to a = 0 (EVHRG limit) in Eqs. (12)-(14). If the bump at intermediate T disappears, it is driven by the attractive VDW term. Then overlay the VDWHRG liquid-gas coexistence curve in the (T, muB) plane and check whether muB = 0.436 GeV and the bump's T range (roughly 120-160 MeV) lie on or near that boundary. If both conditions hold, the signal is the VDW liquid-gas transition, not a QCD phase transition, and the paper's central claim must be revised accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The key evidence for the central claim is the non-monotonic bump in all rotational susceptibilities at muB = 0.436 GeV (Section III, Fig. 5), interpreted as a 'possible signature of the QCD phase transition.' However, the only phase transition in the VDWHRG model is the liquid-gas transition generated by the attractive van der Waals term 'a' in Eqs. (12)-(14); the model contains only hadronic degrees of freedom and no deconfinement mechanism. The authors' own previous work on the same rotating VDWHRG model (Ref. [46]) identifies this transition as a liquid-gas phase transition, so reinterpreting the same mechanism as a QCD phase transition requires explicit justification. In particular, the bump location in the (T, muB) plane should be checked against the VDWHRG liquid-gas coexistence boundary rather than assumed to coincide with a QCD transition. Without such a check, the central claim rests on an unsupported identification of a model-internal mean-field transition with the QCD phase transition.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies rotational susceptibilities χω^n = ∂^n(P/T^4)/∂(ω/T)^n in an ideal hadron resonance gas and in a van der Waals HRG model at zero and finite baryon chemical potential. It reports first estimates of these quantities, studies their dependence on particle spin, system size, rotation rate, and μB, and forms higher-order ratios. At μB = 0.436 GeV the authors find a non-monotonic bump in all rotational susceptibilities and interpret it as a possible signature of the QCD phase transition. The paper also maps some ratios to sqrt(sNN) using a standard freeze-out parametrization.","tokens_in":16308,"tokens_out":5990,"duration_ms":73805,"significance":"If the physical interpretation were established, the paper would provide a new model-based observable for angular momentum fluctuations near the QCD phase boundary. The computations are clearly laid out, the figures are internally consistent, and the comparison with the NJL-model result in Fig. 3 is useful. However, the central claim overreaches: the bump at μB = 0.436 GeV is a feature of the van der Waals liquid-gas transition in a purely hadronic model, not a demonstrated QCD phase-transition signal. In addition, the paper explicitly relies on van der Waals parameters a and b that are assumed to be independent of rotation, an assumption that directly affects the derivatives defining the main observables. These issues make the central conclusion conditional on two untested identifications.","major_comments":[{"comment":"The non-monotonic bump at μB = 0.436 GeV is presented as 'a possible signature of the QCD phase transition.' Since the VDWHRG model contains only hadronic degrees of freedom and no deconfinement mechanism, the only phase transition in the model is the liquid-gas transition generated by the attractive van der Waals term a; the authors' own Ref. [46] identifies this transition in the same model as a liquid-gas transition. The paper neither maps the bump onto the VDW coexistence boundary nor provides a quantitative argument that this mean-field transition represents the QCD transition. The central conclusion therefore overreaches what the model can support; it should be reframed as a signature of the VDW liquid-gas transition, or a concrete connection to QCD must be established.","section":"Section III, Fig. 5, Eqs. (12)–(14)"},{"comment":"The calculation assumes that the van der Waals parameters a and b are independent of rotation. The manuscript explicitly states that 'in principle, these parameters should vary as a function of rotation' but neglects this dependence. This is load-bearing because the observables are derivatives with respect to ω; an ω-dependence of the interaction would introduce additional terms in χω^n, and the bump in Fig. 5 is controlled by the attractive term a. Please test the robustness of the bump and the ratio ordering under a plausible ω-dependent parameterization or under a comparison with a rotating model that allows a and b to vary, or state explicitly that the result is conditional on this untested assumption.","section":"Section II.A, Eqs. (7)–(16), Eq. (21)"},{"comment":"The statements that χ2ω/χ1ω is related to angular-momentum diffusivity, χ3ω/χ1ω measures skewness, and χ4ω/χ2ω peaks near the phase transition are asserted by analogy with conserved-charge susceptibilities. Angular momentum is not a conserved charge in the same sense as B, Q, or S, and the paper later concedes that 'it is not straightforward to assign a conserved charge associated with the rotational susceptibility' and that measuring angular momentum fluctuations is 'non-trivial.' The experimental relevance of these ratios as a probe therefore remains unsubstantiated; a concrete relation between χω^n and a measurable quantity, for example through spin-vorticity coupling, is needed before the ratios can be called ideal observables.","section":"Section II.B and Section III, ratio discussion"}],"minor_comments":[{"comment":"The caption says the ratios are shown 'as a functions of temperature and rotation,' but each panel is a function of T at fixed ω; please reword the caption to match the plotted quantities.","section":"Section III, Fig. 4 caption"},{"comment":"The text states that causality requires ωR<1 and that saturation occurs near ω=0.2 fm^-1 for R=5 fm, but the figure appears to show χω up to larger ω; please clarify the plotted range and mark the causality boundary.","section":"Section III, Fig. 3 and causality discussion"},{"comment":"The rotating distribution function is written with an overall exponential exp[(p·v)/T] multiplying a Fermi/Bose denominator that shows no ω dependence; please check consistency with the standard rotating-frame distribution, e.g., a denominator of the form exp[(E_i−μ_i−ω·J)/T], and with Ref. [46].","section":"Eq. (1)"},{"comment":"Eq. (3) defines P_i^id using the rotation-dependent f(x,p,ω), but the display does not show the ω dependence explicitly; it would help readers to state how Eqs. (7)–(16) inherit the rotation, given that the VDW parameters themselves do not.","section":"Section II.A, Eq. (3)"},{"comment":"The text states an ordering χ2ω/χ4ω > χ4ω/χ6ω > χ2ω/χ6ω and χ3ω/χ1ω > χ5ω/χ3ω > χ5ω/χ1ω, but the corresponding panels in Fig. 4 appear to plot the inverse ratios; please reconcile the notation and the ordering statement. Minor typographical issues, including 'as a functions' in captions and the empty PACS number line after the abstract, should also be corrected.","section":"Section III, ratio ordering"}],"recommendation":"major_revision","confidential_remarks":"The central claim is not supportable in its current form because the bump attributed to the QCD phase transition is the van der Waals liquid-gas transition, and the paper's explicit admission that a and b are assumed rotation-independent weakens the main observable. The paper can be made acceptable by reframing the claim and adding robustness checks."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before you read it. The calculation is clean, and the higher-order rotational susceptibilities in a van der Waals HRG are genuinely new, as far as I can tell. But the central claim—that the bump at μB = 0.436 GeV is a signature of the QCD phase transition—overreaches. The model contains no deconfinement; the only transition in it is the van der Waals liquid-gas transition, which the authors themselves identified in their earlier paper [46]. They never check whether the bump tracks that liquid-gas boundary, so the 'QCD phase transition' label is an unsupported identification.\n\nWhat the paper does well: the formalism is laid out carefully. The distribution function from [46] is used consistently, the pressure, densities, and modified chemical potentials are defined, and the numerical work appears internally consistent. The spin decomposition of χω^2 is a nice touch, and the comparison with the three-flavor NJL results for the first two orders is useful. The higher-order ratios and their ordering are new results, so the paper adds something to the rotating-HRG literature.\n\nSoft spots, in order. First, the phase-transition interpretation. This is the load-bearing issue. If you take the bump as a VDW liquid-gas signal, the paper still has some interest, but the title's 'probe of QCD phase transition' is not earned. Second, the VDW parameters a and b are assumed rotation-independent. The authors flag this explicitly, but it means the model is not self-consistent for a rotating medium; the size of the effect is unknown. Third, the susceptibilities are computed at finite ω rather than in the zero-ω limit. That makes them response functions at a given rotation, which is acceptable, but it differs from the usual susceptibility definition and should be stated more carefully. The experimental connection is also mostly hand-waving—there's no concrete proposal for how to extract χω from spin-polarization data, beyond a proportionality.\n\nNet: the math seems right, the interpretation is overstated. A serious referee should ask them to compare the bump location with the VDWHRG liquid-gas coexistence curve and to reframe the conclusions if that is what the bump is. The paper deserves peer review; it's a competent model calculation, and the overclaim can be fixed in revision.","headline":"Clean higher-order rotational susceptibility calculation in a rotating VDW HRG, but the 'QCD phase transition' bump is the model's liquid-gas transition—the claim overreaches.","tokens_in":16824,"tokens_out":3635,"would_cite":false,"duration_ms":41559,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A rotating hadron gas shows a non-monotonic response near the QCD phase transition.","keywords":["rotational susceptibility","hadron resonance gas","van der Waals interaction","QCD phase transition","angular momentum fluctuations","baryon chemical potential","heavy-ion collisions","vorticity"],"falsifier":"Recompute the rotational susceptibilities with $a$ and $b$ as functions of angular velocity, for example fitted to rotating lattice QCD or derived from a microscopic model, and check whether the bump at $\\mu_B = 0.436$ GeV survives; if it disappears, the claimed phase-transition signature is an artifact of neglecting the $\\omega$-dependence of the interaction parameters.","tokens_in":1628,"feed_emoji":"🌀","tokens_out":4137,"duration_ms":88092,"temperature":0.7,"pith_summary":"The paper tries to establish that rotational susceptibilities, which quantify how a hot, dense hadron gas responds to a small angular velocity, can expose the QCD phase transition. Calculating these susceptibilities up to sixth order in both an ideal and a van der Waals hadron resonance gas, the authors find that at baryon chemical potential $\\mu_B = 0.436$ GeV every order develops a bump at intermediate temperatures. They interpret this non-monotonic behavior as a possible signature of the phase transition, a feature that is absent when hadrons are treated as non-interacting. If this holds, the result supplies a new, interaction-sensitive observable for angular momentum fluctuations in heavy-ion collisions.","feed_headline":"Rotating hadron gas shows a phase-transition bump","feed_subtitle":"At high baryon chemical potential, rotational susceptibilities turn non-monotonic.","key_machinery":"The central object is the rotational susceptibility $\\chi^n_\\omega$, defined through the pressure expansion in $\\omega/T$. The calculation starts from a phase-space distribution for a rigidly rotating relativistic gas that contains the spin factor $\\sinh\\left(\\left(s+\\frac12\\right)\\omega/T\\right)/\\sinh(\\omega/2T)$, then feeds it into the van der Waals equation of state, whose attractive parameter $a$ and repulsive excluded-volume parameter $b$ modify the chemical potentials. The bump arises from the interplay of these interactions with finite baryon chemical potential and is the main carrier of the paper's phase-transition argument.","core_discovery":"The central claim is that the rotational susceptibility $\\chi^n_\\omega = \\partial^n[P(T,\\mu,\\omega)/T^4]/\\partial(\\omega/T)^n$, defined as the pressure response to angular velocity, is a phase-transition probe. In the van der Waals hadron resonance gas, at $\\mu_B = 0.436$ GeV all computed orders ($n=1$ through $6$) show a bump structure at intermediate temperatures, which the authors present as a possible signature of the QCD phase transition. The paper also establishes that all susceptibilities grow with temperature and rotation, that hadronic interactions suppress their magnitude, that spin-0 hadrons dominate the second-order response at high temperature, and that the susceptibility ratios obey a fixed ordering between even and odd orders.","pith_inferences":["A natural extension is to compute the same susceptibilities with rotation-dependent $a$ and $b$; if the bump persists, the signal is robust, and if not, the current result is an artifact of that approximation.","The same formalism could be adapted to the partonic phase, for instance with a rotating Nambu-Jona-Lasinio model, to see whether the bump sharpens or shifts across the crossover.","The dominance of spin-0 pions in the high-temperature rotational response suggests that measurements of vector-meson versus hyperon polarization might discriminate between the model's spin dependence.","Since centrality controls the initial orbital angular momentum, a centrality-dependent measurement of rotational susceptibility ratios could be a sharper experimental test than energy dependence alone."],"forward_implications":["Angular-momentum fluctuation measurements in beam energy scan experiments could look for a non-monotonic response at the highest baryon densities.","The even-odd ordering of susceptibility ratios gives a model-specific pattern that can be tested independently of overall normalization.","The paper argues rotational susceptibilities are less affected by diffusion and smearing than baryon-number susceptibilities, making them a complementary probe.","The strong sensitivity to the van der Waals parameters suggests the observable could constrain hadronic interaction strengths if measured.","The increase of the ratios at low $\\sqrt{s_{NN}}$ points to the low-energy region as the most promising place to search for the effect."],"supporting_citations":[{"why":"Provides the van der Waals hadron resonance gas model with attractive and repulsive interactions that this paper extends to rotation.","marker":"[20]"},{"why":"Supplies the rotating hadron resonance gas phase-space distribution and the rotating van der Waals equation of state from which the susceptibilities are derived.","marker":"[46]"},{"why":"Gives three-flavor NJL model estimates of first- and second-order rotational susceptibility used for qualitative comparison.","marker":"[39]"},{"why":"Provides the STAR polarization measurements used to set the range of angular velocities considered in the study.","marker":"[21]"},{"why":"Supplies the temperature-baryon chemical potential-center-of-mass energy parametrization used to convert susceptibility ratios to a function of $\\sqrt{s_{NN}}$.","marker":"[58]"},{"why":"Justifies the system size R = 0.02 fm used in the NJL comparison.","marker":"[56]"},{"why":"Connects spin polarization to the rotational susceptibility, supporting the claim that the observable is experimentally accessible.","marker":"[65]"}],"fun_headline_variants":["Rotational susceptibility flags QCD phase transition","Spin and rotation reveal hadron gas phase transition","Hot hadron gas's rotation response spikes at phase transition","Rotating matter probes QCD transition in heavy-ion collisions"],"cache_read_input_tokens":19072,"weakest_assumption_plain":"The van der Waals attraction and repulsion parameters, fitted to non-rotating matter, are taken to be unchanged when the system rotates; if interaction strengths actually depend on rotation, the predicted bump could be an artifact of that approximation.","fun_headline_variants_meta":{"raw":{"variants":["Rotational susceptibility flags QCD phase transition","Spin and rotation reveal hadron gas phase transition","Hot hadron gas's rotation response spikes at phase transition","Rotating matter probes QCD transition in heavy-ion collisions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000149,"raw_usage":{"total_tokens":1160,"prompt_tokens":877,"completion_tokens":283,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":493,"completion_tokens_details":{"reasoning_tokens":221}},"tokens_in":493,"tokens_out":283,"duration_ms":3462,"temperature":1.0,"reasoning_tokens":221,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:04:31.488501+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the rotational susceptibilities with $a$ and $b$ as functions of angular velocity, for example fitted to rotating lattice QCD or derived from a microscopic model, and check whether the bump at $\\mu_B = 0.436$ GeV survives; if it disappears, the claimed phase-transition signature is an artifact of neglecting the $\\omega$-dependence of the interaction parameters.","supporting_citations":[{"cited_title":"Samanta and B","cited_arxiv_id":null,"evidence_quote":"Provides the van der Waals hadron resonance gas model with attractive and repulsive interactions that this paper extends to rotation."},{"cited_title":"Karsch, K","cited_arxiv_id":null,"evidence_quote":"Supplies the rotating hadron resonance gas phase-space distribution and the rotating van der Waals equation of state from which the susceptibilities are derived."},{"cited_title":"Florkowski, B","cited_arxiv_id":null,"evidence_quote":"Gives three-flavor NJL model estimates of first- and second-order rotational susceptibility used for qualitative comparison."},{"cited_title":"Vovchenko, M","cited_arxiv_id":null,"evidence_quote":"Provides the STAR polarization measurements used to set the range of angular velocities considered in the study."},{"cited_title":"Braun-Munzinger, D","cited_arxiv_id":null,"evidence_quote":"Supplies the temperature-baryon chemical potential-center-of-mass energy parametrization used to convert susceptibility ratios to a function of $\\sqrt{s_{NN}}$."},{"cited_title":"Proton number cumulants in a modified van der Waals hadron resonance gas","cited_arxiv_id":"2308.09337","evidence_quote":"Connects spin polarization to the rotational susceptibility, supporting the claim that the observable is experimentally accessible."}],"review_version":1}