{"id":"5d91af85-577b-4312-b15a-7a631811cdf7","arxiv_id":"2412.14541","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"By fitting an angular-velocity-dependent coupling to LQCD data, the NJL model exhibits chiral vortical catalysis: rotation enhances the chiral condensate and raises the transition temperature and critical endpoint.","lead":"This paper tunes the quark coupling in a Nambu-Jona-Lasinio model to match lattice QCD's prediction that rotating quark matter transitions at higher temperatures. The result is a model phase diagram where rotation strengthens chiral symmetry breaking and pushes the critical endpoint to higher temperature and chemical potential.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central catalysis signal is inherited from the ad hoc exponential G(omega) fitted to a single LQCD curve; the CEP shift is an extrapolation sensitive to the arbitrary functional form.","rationale":"The reader's verdict is CONDITIONAL, and my independent read converges on the same load-bearing point: the G(omega) ansatz of Eq. (11) is the entire engine of the qualitative results. The exponential form is selected for convenience, the fit uses only mu=0 pseudocritical temperatures over omega*r less than about 0.3, and the same function is then extrapolated to omega*r about 0.55 and to all (T,mu) used for the phase diagram. The paper is honest about this: Section IV states that the fit 'enforces' the parabolic T_c(omega) behavior. Therefore the chiral vortical catalysis and the upward CEP shift are statements about a particular fitted model, not independent predictions from QCD. This does not make the computation incorrect; it limits the strength of the claim and supports a conditional acceptance pending a derivation or a second constraint on G(omega). The suggested alternative-ansatz fit is a direct sensitivity test that would show whether the headline is robust or just an artifact of the exponential choice.","tokens_in":13121,"tokens_out":8269,"duration_ms":76316,"concrete_test":"Re-fit G(omega) with at least two alternative forms that also reproduce the Ref. [27] T_c(omega) points within error, e.g., G(omega)=G_0(1+c_1*omega+c_2*omega^2) and G(omega)=G_0/(1-c*omega), using the same cutoff and gap equation. Then recompute the CEP coordinates in Fig. 6 and the susceptibility peak heights in Fig. 4. If the sign or magnitude of the CEP shift changes across forms, the central claim is an artifact of the exponential ansatz; if all forms preserve the shift, the conclusion is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the angular-velocity-dependent coupling G(omega)=G_alpha+G_beta exp(omega/Omega) in Eq. (11) produces chiral vortical catalysis and shifts the CEP to higher (T,mu). The load-bearing step is the identification of this one-observable fit with the gluonic content of rotating QCD. G(omega) is fitted only to the mu=0 pseudocritical curve T_c^LQCD(omega) over a narrow window (omega*r less than about 0.3), and the exponential form is chosen because the plotted G-versus-omega data 'resembles' a shifted exponential. Because the gap equation responds monotonically to an increasing coupling, any increasing G(omega) will raise the condensate and T_c, so the sign of the catalysis is built in rather than predicted. The same G(omega) is then applied at finite chemical potential and extrapolated to omega*r about 0.55 with no lattice check. Section IV concedes that the fit 'enforces' the parabolic T_c(omega) behavior, so the enhanced susceptibility and the upward CEP shift are outputs of the ansatz, not independently derived QCD predictions. The concern is underdetermination, not internal inconsistency: many functional forms can match the same sparse lattice points and would give different CEP locations and susceptibility peaks.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the two-flavor Nambu–Jona-Lasinio model in a rigidly rotating cylinder in the mean-field approximation, with a homogeneous chiral condensate. To incorporate gluonic effects absent in the NJL model, the authors introduce an angular-velocity-dependent coupling G(omega)=G_alpha+G_beta exp(omega/Omega), Eq. (11), whose three parameters are fixed by requiring the model's pseudocritical temperature T_c(omega) at mu=0 to match the LQCD results of Ref. [27]. With this coupling, the chiral condensate and effective quark mass increase with omega, the chiral susceptibility peak moves to higher temperature and grows, and the CEP shifts to higher temperature and slightly higher chemical potential (Figs. 1-6). The constant-coupling case is presented throughout as a comparison, reproducing the usual suppression of T_c with omega.","tokens_in":13370,"tokens_out":9891,"duration_ms":86084,"significance":"The paper addresses a genuine and timely problem: effective quark models under rotation disagree with LQCD, and a lattice-calibrated coupling is a reasonable phenomenological strategy, in the same spirit as magnetic-field-dependent couplings in the NJL literature. The derivation of the thermodynamic potential and gap equation follows standard steps, and the parameters are stated clearly. The main strength is the clean separation between constant- and running-coupling results, which makes the effect of the new ingredient transparent. However, the paper's central results are not independent predictions: because G(omega) is fitted to LQCD T_c(omega), the agreement with the lattice band in Fig. 5 is a restatement of the input, and the rising condensate follows from the monotonic increase of the fitted coupling. The CEP shift is a model-dependent extrapolation whose robustness is not demonstrated. If reframed as a controlled model study with sensitivity analysis, the paper would be a useful contribution; in its current form the conclusions overstate the strength of the LQCD constraint.","major_comments":[{"comment":"The central phenomenon is enforced by construction. The parameters G_alpha, G_beta, and Omega are chosen so that the NJL T_c(omega) reproduces the LQCD pseudocritical temperatures of Ref. [27]; the authors explicitly state in Sec. IV that the fitting function \"enforces\" the parabolic T_c(omega) behavior. The agreement in Fig. 5 is therefore not a validation of chiral vortical catalysis. Moreover, since the gap equation is monotonic in the coupling, any increasing G(omega) will raise the condensate and T_c; the sign of the effect is built into the ansatz.","section":"Sec. III, Eq. (11), and Fig. 5"},{"comment":"The exponential form of G(omega) is chosen because the plotted G-versus-omega data \"resembles\" a shifted exponential, and the model is then applied up to omega r ~ 0.55 while the fitted LQCD data cover only omega r ≲ 0.3 (the authors state this in the text). The enhancement of the condensate at low temperature and the CEP location for omega=60 MeV thus rely on an uncontrolled extrapolation of an ad hoc functional form. The homogeneous-condensate approximation, which the authors note is valid only for \"moderately small\" angular velocities, is also used in this extrapolated regime without a quantitative check.","section":"Sec. III, right panel of Fig. 2, and Sec. IV"},{"comment":"No uncertainties are propagated from the lattice band (B2 = 1.13153 ± 0.03) into the fit parameters or into the predicted susceptibilities and CEP. The three fit parameters are quoted to five significant digits, but no fit quality measure (e.g., chi-squared or RMS) is reported, and no test with alternative functional forms is given. Because several simple forms can match the sparse lattice points, the quantitative CEP shift and the susceptibility enhancement are not robust predictions.","section":"Eq. (11) and Fig. 5"},{"comment":"The calibration of the angular velocity is not fully specified. The lattice input is expressed in terms of v = omega L_s / 2, while the NJL calculation uses a cylinder radius r = 5 GeV^-1; the relationship between L_s and r, and hence the conversion of omega values, is not stated. The fit parameters in Eq. (11) and all subsequent results depend on this mapping, so the manuscript should specify the conversion and test sensitivity to the choice of r.","section":"Sec. II, Eq. (9), and Sec. III"},{"comment":"The phase diagram is obtained by applying a coupling fitted at mu=0 to finite chemical potential, which is an extrapolation not constrained by any lattice data. The CEP shift should be explicitly labeled as a model prediction under the assumed G(omega), and the numerical (T_CEP, mu_CEP) values for each omega should be reported so that the robustness of the shift can be assessed.","section":"Sec. III, Fig. 6"}],"minor_comments":[{"comment":"The axis labels \"chi G\" and \"chi G(omega)\" are ambiguous; please state the normalization of the susceptibility or indicate that it is plotted in arbitrary units.","section":"Fig. 4"},{"comment":"There are several language slips, e.g., \"end o Sec.II\" (end of Sec. II), \"qualitative the same\" (qualitatively the same), and \"In order complete the analysis\" (In order to complete the analysis).","section":"Throughout"},{"comment":"The caption describes the effective quark masses as a function of the angular velocity, while the horizontal axis is the temperature; please correct the caption.","section":"Fig. 3 caption"},{"comment":"Equation (8) uses m0 while the text and Eq. (2) use m and \\hat m; please define m0 explicitly and state that m_u=m_d=m.","section":"Eq. (8)"},{"comment":"Please report the number of LQCD points used in the fit to Eq. (11) and the numerical goodness of fit, rather than only \"very good agreement\".","section":"Sec. III"},{"comment":"The term \"running coupling\" is nonstandard because G(omega) does not run with a momentum scale; consider \"omega-dependent coupling\" to avoid confusion with the usual QCD running coupling.","section":"Sec. II"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically transparent and the authors are honest about the constructed nature of the T_c(omega) agreement (Sec. IV). The main problem is framing: the paper presents the fitted input as a finding. I recommend requiring a resubmission in which the abstract and conclusions clearly distinguish input from prediction, the scale mapping is specified, and robustness tests with alternative G(omega) forms and error propagation are added. This is a fixable scientific-claims issue rather than a fundamental error in the NJL calculation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take after reading the paper. It is a straightforward, honestly presented NJL study. The new piece is the exponential running coupling G(omega) fitted to the LQCD pseudocritical temperatures, plus the finite-mu phase diagram that follows from it. That extends Jiang's earlier linear-coupling idea and gives a concrete parameterization others can use. The formalism is standard and all parameters are given, so the calculation is reproducible.\n\nThe soft spot is the one you flagged: the central qualitative result is loaded in by construction. Since the gap equation responds monotonically to an increasing coupling, fitting G(omega) to a rising T_c(omega) guarantees that the condensate is enhanced and the transition temperature rises. The paper actually concedes this in Section IV, where it says the fit 'enforces the parabolic behavior' seen on the lattice. So calling the result 'chiral vortical catalysis' is fair as a model output, but it is not an independent prediction. The exponential form is admittedly ad hoc; no error bars from the lattice are propagated; and the same G(omega) is used at finite chemical potential and extrapolated to omega*r~0.55, beyond the fitted window. Those are real limitations, and they mean the CEP shift is best read as a sensitivity study of the ansatz, not a robust QCD prediction.\n\nI don't think the paper is trying to paper over any of this. The fitting is explicit, the literature on magnetic-field-dependent couplings is cited, and the comparison with other model results is useful. For someone working on rotating QCD matter, this is a convenient reference for what an LQCD-constrained NJL looks like. I would send it to a referee if a journal in this area gets it; the referee should ask for a sensitivity check on the functional form and a discussion of the extrapolation. For our reading group I'd say maybe—the circularity discussion is instructive, but the physics is not going to change anyone's research agenda.","headline":"A transparent NJL study that fits a running coupling to lattice Tc(omega) and thereby builds in the chiral vortical catalysis it then reports.","tokens_in":13960,"tokens_out":2807,"would_cite":true,"duration_ms":24150,"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":"The paper claims that rotation can strengthen chiral symmetry breaking in quark matter when gluonic effects are put back into a quark model as an angular-velocity-dependent coupling fitted to lattice QCD data.","keywords":["chiral vortical catalysis","Nambu-Jona-Lasinio model","rotating quark-gluon plasma","running coupling","lattice QCD","chiral condensate","critical end point","phase diagram"],"falsifier":"Look for the chiral condensate or the chiral susceptibility directly in lattice QCD at angular velocities beyond the fitted range ($\\omega r$ between about 0.3 and 0.55): if the condensate stops rising or the pseudocritical temperature flattens or falls, the exponential running coupling is falsified. A second check would compare the model's prediction for the quark-mass dependence of $T_c(\\omega)$ with a lattice calculation, since the fit currently uses only the $T_c(\\omega)$ curve at one quark mass.","tokens_in":12880,"feed_emoji":"🌀","tokens_out":5748,"duration_ms":46185,"temperature":0.7,"pith_summary":"The paper sets out to resolve a disagreement: lattice QCD says real rotation raises the chiral transition temperature of QCD matter, while effective quark models without gluons say rotation lowers it. The authors put a rotation-dependent coupling into the two-flavor Nambu-Jona-Lasinio model, fitting that coupling to the lattice pseudocritical temperatures. With this fitted coupling, rotation enhances the chiral condensate and the effective quark mass, strengthens chiral symmetry breaking (the effect called chiral vortical catalysis), makes the chiral susceptibility peak taller and hotter, and moves the critical end point to higher temperatures and chemical potentials. This matters because heavy-ion collisions create strongly rotating quark-gluon plasma, and effective models are the main tool for exploring the baryon-rich region where lattice methods are difficult.","feed_headline":"Rotation can strengthen chiral symmetry breaking in quark matter","feed_subtitle":"Fitting the quark model's coupling to lattice data reverses rotation's effect and lifts the critical endpoint.","key_machinery":"The load-bearing object is the angular-velocity-dependent coupling $G(\\omega)=G_\\alpha+G_\\beta\\exp(\\omega/\\Omega)$, with parameters $G_\\alpha=4.97667~\\mathrm{GeV}^{-2}$, $G_\\beta=0.05840~\\mathrm{GeV}^{-2}$, and $\\Omega=0.02457~\\mathrm{GeV}$, fitted so the model's pseudocritical temperature reproduces the lattice relation $T_c(v)/T_c(0)=1+B_2 v^2/c^2$ with $B_2\\approx 1.13153$ over the lattice range of $\\omega$. This coupling enters the mean-field thermodynamic potential of the two-flavor NJL model in a rigid rotating cylinder, where the quark energy dispersion $\\epsilon_n=\\sqrt{M^2+p_z^2+p_t^2-(n+1/2)\\omega}$ and the Bessel-function weights $J_n(p_t r)^2+J_{n+1}(p_t r)^2$ carry the rotation effects. Changing $G$ from a constant to $G(\\omega)$ is what flips every qualitative result of the paper.","core_discovery":"On the paper's own terms, the central discovery is that the rotational behavior of the NJL model reverses when gluonic effects are encoded in a running coupling $G(\\omega)=G_\\alpha+G_\\beta e^{\\omega/\\Omega}$ fitted to lattice QCD's pseudocritical temperatures. With fixed $G$, increasing angular velocity lowers the chiral condensate and the crossover temperature, reproducing the generic quark-model result that disagrees with lattice data. With $G(\\omega)$, increasing angular velocity raises the pseudocritical temperature along the lattice band, enhances the chiral condensate and effective quark mass at low temperature (chiral vortical catalysis), produces a stronger and hotter peak in the chiral susceptibility, and shifts both the crossover lines and the critical end point toward higher $T$ and $\\mu$. The authors present this as evidence that gluonic degrees of freedom, normally absent from NJL-type models, are the decisive missing ingredient for rotating QCD matter.","pith_inferences":["Because $G(\\omega)$ is fitted only to $T_c(\\omega)$, the predicted enhancement of the condensate is not an independent confirmation of chiral vortical catalysis; a lattice measurement of the condensate itself versus $\\omega$ would test the mechanism directly.","The exponential form is extrapolated from the lattice range $\\omega r \\lesssim 0.3$ up to $\\omega r \\approx 0.55$; if lattice data at larger $\\omega$ show $T_c$ flattening or decreasing, the catalysis prediction would fail.","The same fitting philosophy used for magnetic-field inverse catalysis is here applied to vorticity, suggesting a general strategy: absorb unmodeled gluonic effects into a medium-dependent coupling constrained by lattice data, then explore regions lattice cannot reach, such as high baryon density.","If the critical-end-point shift is real, rotation could serve as an experimental dial: collisions with higher vorticity might probe a different critical region than static matter."],"forward_implications":["At zero chemical potential the chiral crossover temperature increases with angular velocity, in quantitative agreement with the lattice band used for the fit.","The critical end point moves to higher temperature and slightly higher chemical potential, so rotating matter is predicted to keep a crossover over a larger region of the phase diagram.","Chiral condensate and effective quark mass are enhanced by rotation at low temperature, meaning chiral symmetry is more strongly broken in fast-spinning matter.","Chiral susceptibility peaks grow with $\\omega$, indicating stronger fluctuations near the transition under rotation.","The constant-coupling case gives the opposite behavior, so quark-model studies of rotating matter that ignore gluon effects should be treated with caution."],"supporting_citations":[{"why":"Supplies the lattice pseudocritical temperatures and the $B_2$ coefficient that the running coupling is fitted to.","marker":"[27]"},{"why":"Introduced chiral vortical catalysis and the idea of an angular-velocity-dependent coupling.","marker":"[75]"},{"why":"Provides the rotating-NJL formalism with total angular momentum eigenvalues used here.","marker":"[35]"},{"why":"Gives the thermodynamic potential for rotating fermions and the causality constraint $\\omega r<1$ used in the setup.","marker":"[36]"},{"why":"Provides the constant-coupling NJL phase diagram and parameter set that the paper compares against.","marker":"[37]"},{"why":"Shows a PPNJL parametrization with increasing pseudocritical temperature, used as a qualitative comparison for the running-coupling case.","marker":"[31]"},{"why":"Cited as the prediction that rotation enhances the chiral condensate, with which the running-coupling results agree.","marker":"[28]"}],"fun_headline_variants":["Rotation flips quark behavior when gluons are included","Gluon effects turn rotation into chiral vortical catalysis","Lattice-fitted coupling reverses rotation's effect on quarks","Rotating quark matter: gluons restore chiral symmetry breaking","Chiral vortical catalysis emerges with lattice-matched coupling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole prediction rests on one fitted curve: the assumption that a single momentum-independent coupling of the form $G(\\omega)=G_\\alpha+G_\\beta e^{\\omega/\\Omega}$, fitted to lattice pseudocritical temperatures at small $\\omega$, correctly captures all gluonic rotational effects and remains valid when extrapolated to larger angular velocities.","fun_headline_variants_meta":{"raw":{"variants":["Rotation flips quark behavior when gluons are included","Gluon effects turn rotation into chiral vortical catalysis","Lattice-fitted coupling reverses rotation's effect on quarks","Rotating quark matter: gluons restore chiral symmetry breaking","Chiral vortical catalysis emerges with lattice-matched coupling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000195,"raw_usage":{"total_tokens":1370,"prompt_tokens":973,"completion_tokens":397,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":589,"completion_tokens_details":{"reasoning_tokens":317}},"tokens_in":589,"tokens_out":397,"duration_ms":3245,"temperature":1.0,"reasoning_tokens":317,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:08:28.534572+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Look for the chiral condensate or the chiral susceptibility directly in lattice QCD at angular velocities beyond the fitted range ($\\omega r$ between about 0.3 and 0.55): if the condensate stops rising or the pseudocritical temperature flattens or falls, the exponential running coupling is falsified. A second check would compare the model's prediction for the quark-mass dependence of $T_c(\\omega)$ with a lattice calculation, since the fit currently uses only the $T_c(\\omega)$ curve at one quark mass.","supporting_citations":[{"cited_title":"Moment of inertia and supervortical temperature of gluon plasma","cited_arxiv_id":"2311.03947","evidence_quote":"Provides the rotating-NJL formalism with total angular momentum eigenvalues used here."}],"review_version":1}