{"id":"e4e89a15-556c-45a2-976e-b3a5156cfe8f","arxiv_id":"2501.00753","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A model combining nonadiabatic quantum evolution with collisional damping, gluonic dissociation, and regeneration predicts multiplicity-dependent suppression of J/ψ and χc and enhancement of ψ(2S) in p+p collisions at 13 TeV.","lead":"This paper models how charmonia (J/ψ, χc, ψ(2S)) change in high-multiplicity proton-proton collisions at 13 TeV if a transient quark-gluon plasma-like medium forms. It predicts ψ(2S) could become more abundant relative to J/ψ, offering a potential probe of such a medium in small collision systems.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Predicted ψ(2S)/J/ψ enhancement at high multiplicity contradicts the CMS sequential-suppression data cited in the paper, undercutting the 'robust probe' claim; the unspecified α in Eq. (1) is secondary.","rationale":"I agree with the reader that the unspecified α in Eq. (1) is a real defect: the pseudo-temperature profile determines how quickly the Hamiltonian changes, so nonadiabatic transition probabilities and the ψ(2S) enhancement depend directly on α, and no value is given. Without it the figures are not reproducible. However, I see a more load-bearing problem: the model's most distinctive prediction appears to be in direct conflict with the data the paper itself cites. CMS (Ref. [16], PRL 120, 142301 (2018)) observed sequential suppression of charmonia in high-multiplicity pp collisions at 13 TeV, i.e., the ψ(2S)/J/ψ ratio decreases with multiplicity. The model predicts a 130–200% increase of this ratio at high multiplicity (Figs. 5 and 10). If those data are correct, the central claim that these mechanisms can serve as a robust probe for a thermalized QCD medium is not just unverified but contradicted. A direct overlay of the model curves on the CMS measurement would settle the question. The α issue is secondary because fixing α alone cannot resolve the sign conflict with the published data if the data are as reported. For these reasons I would move the verdict from CONDITIONAL to REJECT.","tokens_in":21142,"tokens_out":9270,"duration_ms":89279,"concrete_test":"Overlay the model's ψ(2S)/J/ψ double-ratio curves from Figs. 5 and 10 on the CMS data from Ref. [16] (and ALICE, if available) as a function of charged-particle multiplicity at √s = 13 TeV. If the measured double ratio decreases with multiplicity while the model increases, the central claim is falsified by existing data.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim is that the combined mechanisms can serve as a robust probe for a thermalized QCD medium, with the headline prediction of 130–200% enhancement of ψ(2S) relative to J/ψ at high multiplicity (Sec. IV, Figs. 5 and 10). The paper cites the CMS high-multiplicity pp measurement [16] (PRL 120, 142301 (2018)) but never compares with it. That measurement reports sequential charmonium suppression: the ψ(2S)-to-J/ψ ratio decreases with multiplicity in pp at √s = 13 TeV. The model's defining signature therefore has the opposite sign from the data. Since the paper argues that any yield modification in pp must come from a hot partonic medium (Sec. III), a data trend with the opposite sign invalidates the central 'robust probe' conclusion. A secondary issue is that Eq. (1) contains an unassigned exponent parameter α, making the figures non-reproducible; but fixing α cannot change the sign conflict with existing measurements.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a model for charmonium yield modification in high-multiplicity proton-proton collisions at sqrt(s) = 13 TeV, combining a Gubser-flow medium expansion with a bottom-up pre-equilibrium temperature profile, collisional damping, gluonic dissociation, regeneration, and nonadiabatic time-dependent Schroedinger evolution. It claims that the combined effects of these mechanisms can serve as a robust probe of a thermalized QCD medium in small systems, predicting up to about 50% suppression of J/psi, up to about 80% suppression of chi_c(1P), and a 130% to 200% enhancement of psi(2S) relative to J/psi at high multiplicity.","tokens_in":21413,"tokens_out":6759,"duration_ms":62733,"significance":"The topic is timely, and the attempt to include nonadiabatic evolution together with conventional suppression and regeneration mechanisms in a small-system charmonium calculation is a useful exploratory step. The transport equations and complex-potential formalism are standard, and the paper provides explicit expressions for the survival probabilities and feed-down corrections. However, the paper's headline prediction is not compared with existing high-multiplicity pp data, and the pre-equilibrium temperature profile contains an unspecified parameter, so the quantitative conclusions are neither validated nor reproducible as presented. The central claim that the proposed mechanisms constitute a robust probe of a thermalized QCD medium is therefore not currently supported.","major_comments":[{"comment":"The abstract and Section V claim that the combined mechanisms can serve as a robust probe of a thermalized QCD medium, with Fig. 5 predicting a 130% to 200% enhancement of psi(2S) relative to J/psi at high multiplicity. The paper cites the CMS high-multiplicity pp measurement [16] as evidence of QGP-like phenomena but never compares its predictions with the measured multiplicity dependence of the psi(2S)-to-J/psi ratio reported in that reference. That measurement shows the ratio decreasing with multiplicity, which is the opposite sign of the model's defining signature. As stated, the central conclusion is therefore contradicted by the existing data, and the paper does not address this conflict.","section":"Section V / Fig. 5"},{"comment":"The pre-equilibrium pseudo-temperature profile in Eq. (1) contains an exponent parameter alpha that is never assigned a numerical value in the text. The nonadiabatic Hamiltonian evolution between tau = 0 and tau_Hydro, and hence the transition probabilities that produce the psi(2S) enhancement, depend directly on this profile. Without a stated value for alpha, the figures are not reproducible and the sensitivity of the predictions to this parameter is unknown. This is a load-bearing modeling choice, not a cosmetic detail.","section":"Sec. II A, Eq. (1)"},{"comment":"The net survival probability is written as the product of the CGR survival probability and the nonadiabatic survival probability, assuming the two sets of mechanisms are statistically independent. Both mechanisms are driven by the same temperature history and the same charmonium wave functions, so the factorization in Eq. (30) needs a dynamical justification. Without such a justification, the 'Net' curves cannot be regarded as a consistent combination of the two mechanisms, and the combined predictions may double-count or miss correlations.","section":"Sec. III E, Eq. (30)"},{"comment":"The thermalization time is set to tau_0 = 0.1 fm for pp collisions in Sec. II B, while the Gubser-flow demonstration quoted from Ref. [27] uses tau_Hydro = 0.3 fm for the initial conditions. The value actually used in the yield calculations is not stated explicitly. The results are likely sensitive to this timescale because it sets the duration of the pre-equilibrium nonadiabatic evolution, so the missing specification is an obstacle to reproducibility.","section":"Sec. II B / Sec. III C"},{"comment":"The initial charmonium numbers N_i and N_{car c} are taken from Ref. [8], a model by the same authors fitted to pp charmonium yield data. The quantitative predictions therefore inherit the calibration of that model, and the paper does not discuss how the results change if these inputs are varied. This does not by itself invalidate the approach, but it limits the strength of the numerical claims and should be discussed explicitly.","section":"Sec. III E, Eq. (26)"}],"minor_comments":[{"comment":"The exponent in Eq. (1) is garbled in the text; the authors should provide the correct LaTeX expression and clearly define the allowed range of alpha.","section":"Eq. (1)"},{"comment":"The captions and legends use the abbreviations CGR, NAb, and Net without defining them; these should be defined in each caption or once in the text.","section":"Figs. 3-12"},{"comment":"The statement that the pT-integrated yield is obtained using a charmonium distribution function 1/E_T^4 is not defined; the explicit formula should be provided.","section":"Sec. IV A"},{"comment":"The estimate tau_ev approximately 0.3 fm for the evolution timescale is quoted without specifying the temperature profile used; this estimate should be derived from the actual Gubser-flow profile used in the calculations.","section":"Sec. III C"},{"comment":"The notation alternates between 'pseudo temperature', 'pseudotemperature', and 'effective temperature'; these terms should be defined consistently and used uniformly.","section":"Sec. II A / Sec. II B"},{"comment":"There are several typographical errors, including 'depeicts' in the discussion of Fig. 5, and the symbol 'gd' in Eq. (12) is not defined in the text.","section":"Sec. IV A"}],"recommendation":"reject","confidential_remarks":"This is a topical phenomenological study, but the central claim is contradicted by the high-multiplicity pp data cited in the paper itself, and the model as presented is not fully reproducible because of the unspecified parameter alpha. The unjustified factorization in Eq. (30) is an additional concern. I do not see a simple revision that would preserve the 'robust probe' claim without major reworking, including a direct quantitative comparison with the CMS multiplicity-dependent psi(2S)/J/psi measurement. A substantially revised version that addresses these points could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper is a serious phenomenological calculation with a headline prediction that I think is already dead on arrival against data the authors themselves cite. They predict a 130–200% enhancement of ψ(2S) relative to J/ψ in high-multiplicity pp at 13 TeV, driven by nonadiabatic evolution. CMS (PRL 120, 142301 (2018)), which they cite as [16], reports that the ψ(2S)-to-J/ψ ratio actually decreases with multiplicity in pp at that same energy. The paper never compares with that measurement. If the CMS result is right, the central claim that these mechanisms are a “robust probe” of a thermalized medium in pp has the wrong sign.\n\nWhat is new here: the specific combination of pre-equilibrium bottom-up thermalization, Gubser flow, nonadiabatic evolution via the Crank-Nicolson solver, plus the usual collisional damping/gluonic dissociation/regeneration machinery applied to J/ψ, χc, and ψ(2S) in pp. The idea that rapid cooling can cause transitions into ψ(2S) is an interesting mechanism, and the calculation is internally coherent. The authors also include feed-down corrections and give pT- and multiplicity-dependent predictions, which is the right level of detail for a model paper.\n\nThe soft spots are real. Eq. (1) contains an unassigned exponent α, so the pre-equilibrium temperature profile is not fully specified and the figures are not reproducible as written. The initial charmonium numbers come from the authors' own earlier fit, so the predictions inherit that calibration. More importantly, the paper's assertion that any yield modification in pp must come from a hot partonic medium glosses over other small-system effects. But the biggest issue is empirical: a model whose defining signature is the opposite of the existing measurement cannot be called a robust probe.\n\nThe paper deserves serious peer review, not a desk rejection. The conflict with CMS data is important, and the α dependence should be explored. I would send it to a referee with instructions to check the sign mismatch and the sensitivity to α. If the authors confront the data, either the model changes or we learn something about what the nonadiabatic mechanism cannot do. I would not cite it as established, but I would mention it in a review as a cautionary example.\n\nYours,","headline":"A coherent model calculation that predicts ψ(2S) enhancement in high-multiplicity pp, but the prediction conflicts with the CMS data the authors cite and never compare to, so the 'robust probe' claim is not credible as written.","tokens_in":21931,"tokens_out":6089,"would_cite":true,"duration_ms":54765,"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":"This paper predicts that combined nonadiabatic evolution and in-medium dissociation/regeneration of charmonia produce a distinctive, multiplicity-dependent yield pattern—up to 50% J/ψ suppression, up to 80% χc(1P) suppression, and…","keywords":["charmonium suppression","quark-gluon plasma","small collision systems","nonadiabatic evolution","proton-proton collisions","J/psi","psi(2S)","Gubser flow"],"falsifier":"Measure the $\\psi(2S)/J/\\psi$ double ratio as a function of charged-particle multiplicity and $p_{\\rm T}$ in 13 TeV proton-proton collisions. The model predicts the ratio rises to 1.3–2.0 at low $p_{\\rm T}$ in the highest-multiplicity class; data showing no rise above unity, or a decline, would falsify the central claim. A second check is to recompute the model with the pre-equilibrium parameter $\\alpha$ varied over its plausible range; if the enhancement disappears for some allowed value, the predicted signature is not a stable probe.","tokens_in":20945,"feed_emoji":"⚛️","tokens_out":11194,"duration_ms":97800,"temperature":0.7,"pith_summary":"The paper argues that the very short, hot fireball formed in high-multiplicity proton-proton collisions at $\\sqrt{s}=13$ TeV may be hot enough to form a quark-gluon plasma, and that charmonium states (bound charm-anticharm mesons such as $J/\\psi$) can detect it. Because the fireball cools so quickly, the usual adiabatic assumption fails, so the paper solves a time-dependent Schrodinger equation for the evolving charmonium wavefunction while also including collisional damping, gluonic dissociation, and regeneration. Its central prediction is a distinctive, multiplicity- and $p_{\\rm T}$-dependent pattern: up to 50% suppression of $J/\\psi$, up to 80% suppression of $\\chi_c(1P)$, and a 130% to 200% enhancement of $\\psi(2S)$ relative to $J/\\psi$ at high multiplicity. If observed, this pattern would be evidence that a thermalized QCD medium forms in small collision systems. The calculation combines a pre-equilibrium temperature profile from bottom-up thermalization, a Gubser-type transverse expansion for the thermalized medium, and a transport equation for the charmonium yields.","feed_headline":"Charmonia in p+p collisions can reveal a quark-gluon plasma","feed_subtitle":"Model predicts up to 50% J/ψ suppression and 130–200% ψ(2S) enhancement in high-multiplicity 13 TeV p+p events.","key_machinery":"The central object is the time-dependent Hamiltonian of a charmonium state, which starts as the zero-temperature Cornell potential and becomes the finite-temperature complex potential once the medium thermalizes. Its real part drives nonadiabatic transitions: solving the time-dependent Schrodinger equation by the Crank-Nicolson finite-difference scheme gives survival probabilities as overlaps of the evolved wavefunction with the initial $J/\\psi$, $\\chi_c(1P)$, and $\\psi(2S)$ states. The imaginary part gives collisional damping, while gluonic dissociation adds a thermal decay width and regeneration is fixed by detailed balance from the dissociation cross section. Temperature evolution is supplied by a pre-equilibrium pseudo-temperature scaling followed by a Gubser-type flow with third-order viscous corrections, and the moving charmonium feels a Doppler-shifted effective temperature. The net yield is governed by the transport equation $dN/d\\tau = \\Gamma_F N_c N_{\\bar c}/V(\\tau) - \\Gamma_D N$, whose solution is multiplied by the nonadiabatic survival probabilities and feed-down corrections to produce the reported patterns.","core_discovery":"The paper claims that in proton-proton collisions at $\\sqrt{s}=13$ TeV, the combined action of nonadiabatic evolution and in-medium dissociation/regeneration produces a calculable, testable modification of charmonium yields. In the highest-multiplicity events, the $J/\\psi$ survival probability falls to roughly 50% after feed-down from higher resonances, $\\chi_c(1P)$ is suppressed by up to 80%, and $\\psi(2S)$ is enhanced by 130% to 200% relative to $J/\\psi$ at low $p_{\\rm T}$. The authors contend that this pattern is a probe for the existence of a thermalized QCD medium in a small system, because the only medium effects present in $p+p$ are hot-partonic ones and the adiabatic approximation fails when the QGP lifetime is shorter than the charmonium transition timescale.","pith_inferences":["Because the pre-equilibrium parameter $\\alpha$ is left free, a natural extension is to scan it over its plausible range to map how much of the $\\psi(2S)$ enhancement is genuine and how much is an artifact of the chosen thermalization history.","The same nonadiabatic treatment should apply to peripheral and ultraperipheral heavy-ion collisions, where rapid cooling could produce a $\\psi(2S)$ enhancement that would complicate the standard sequential-suppression interpretation.","The paper multiplies nonadiabatic survival probabilities with transport-equation survival probabilities, treating the two as independent; a coupled calculation in which the evolving wavefunction and the decay widths feed back on each other could either strengthen or weaken the predicted pattern."],"forward_implications":["At high multiplicity (0–1%) and low $p_{\\rm T}$, the $J/\\psi$ suppression reaches about 40–50% once feed-down is included, so high-multiplicity $p+p$ data should show a clear multiplicity-dependent suppression.","The $\\psi(2S)/J/\\psi$ double ratio should rise with multiplicity to 1.3–2.0 at low $p_{\\rm T}$, opposite to the $\\psi(2S)$ suppression seen in heavy-ion collisions; this is the paper's sharpest signature.","The $\\chi_c(1P)/J/\\psi$ ratio should fall by 30–70% with increasing multiplicity, a prediction that could be tested once $\\chi_c(1P)$ reconstruction in $p+p$ becomes practical.","At $p_{\\rm T}\\gtrsim 30$ GeV the nonadiabatic contribution dies out and the remaining suppression is mostly collisional damping, so the $p_{\\rm T}$ dependence separates the two mechanism classes.","If confirmed, $p+p$ collisions can no longer be treated as a purely baseline system for quarkonia; the baseline itself would carry a QGP-like medium effect."],"supporting_citations":[{"why":"Supplies the unified quarkonia-suppression framework, the regeneration cross section from detailed balance, and the initial charmonium and charm-pair yields used as inputs for p+p at 13 TeV.","marker":"[8]"},{"why":"Provides the earlier Gubser-flow study of small systems that motivates the nonadiabatic evolution and the rapid-cooling timescales used here.","marker":"[27]"},{"why":"Gives the bottom-up thermalization kinetic-theory description from which the pre-equilibrium pseudo-temperature profile is taken.","marker":"[28]"},{"why":"Defines the Gubser flow solution adopted for the transverse-expanding thermalized medium.","marker":"[34]"},{"why":"Supplies the third-order viscous-correction equations for energy density and shear stress used in the temperature evolution.","marker":"[36]"},{"why":"Provides the complex singlet potential with the imaginary part that gives collisional damping and the transport-equation formulation.","marker":"[4]"},{"why":"The Crank-Nicolson method used to solve the time-dependent Schrodinger equation for nonadiabatic survival probabilities.","marker":"[45]"},{"why":"The Glauber model with an anisotropic proton profile that fixes multiplicity bins and impact-parameter weights for the pT-dependent averages.","marker":"[48]"}],"fun_headline_variants":["Charmonia reveal hot QCD medium in p+p collisions","QGP-like signatures from charmonia in small systems","J/ψ suppression and ψ(2S) boost in high-multiplicity p+p","Probing a thermalized medium with charmonia in p+p","p+p charmonia hint at quark-gluon plasma"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions depend on the rate at which the pre-equilibrium fireball heats up, which is controlled by a parameter $\\alpha$ in the temperature profile that the paper never assigns a numerical value; a different thermalization history could change or remove the nonadiabatic transitions, including the $\\psi(2S)$ enhancement.","fun_headline_variants_meta":{"raw":{"variants":["Charmonia reveal hot QCD medium in p+p collisions","QGP-like signatures from charmonia in small systems","J/ψ suppression and ψ(2S) boost in high-multiplicity p+p","Probing a thermalized medium with charmonia in p+p","p+p charmonia hint at quark-gluon plasma"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000636,"raw_usage":{"total_tokens":2965,"prompt_tokens":1011,"completion_tokens":1954,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":627,"completion_tokens_details":{"reasoning_tokens":1876}},"tokens_in":627,"tokens_out":1954,"duration_ms":15104,"temperature":1.0,"reasoning_tokens":1876,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:43:25.227288+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the $\\psi(2S)/J/\\psi$ double ratio as a function of charged-particle multiplicity and $p_{\\rm T}$ in 13 TeV proton-proton collisions. The model predicts the ratio rises to 1.3–2.0 at low $p_{\\rm T}$ in the highest-multiplicity class; data showing no rise above unity, or a decline, would falsify the central claim. A second check is to recompute the model with the pre-equilibrium parameter $\\alpha$ varied over its plausible range; if the enhancement disappears for some allowed value, the predicted signature is not a stable probe.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the unified quarkonia-suppression framework, the regeneration cross section from detailed balance, and the initial charmonium and charm-pair yields used as inputs for p+p at 13 TeV."},{"cited_title":"Dutta, P","cited_arxiv_id":null,"evidence_quote":"Provides the earlier Gubser-flow study of small systems that motivates the nonadiabatic evolution and the rapid-cooling timescales used here."},{"cited_title":"Bagchi, N","cited_arxiv_id":null,"evidence_quote":"Gives the bottom-up thermalization kinetic-theory description from which the pre-equilibrium pseudo-temperature profile is taken."},{"cited_title":"Kurkela and A","cited_arxiv_id":null,"evidence_quote":"Supplies the third-order viscous-correction equations for energy density and shear stress used in the temperature evolution."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the complex singlet potential with the imaginary part that gives collisional damping and the transport-equation formulation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Crank-Nicolson method used to solve the time-dependent Schrodinger equation for nonadiabatic survival probabilities."},{"cited_title":"Laine, O","cited_arxiv_id":null,"evidence_quote":"The Glauber model with an anisotropic proton profile that fixes multiplicity bins and impact-parameter weights for the pT-dependent averages."}],"review_version":1}