{"id":"8df331cd-dd11-4c81-9435-277f8a81eb21","arxiv_id":"2505.11313","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Pseudoscalar quarkonium spectral functions built from a non-perturbative complex thermal potential show eta_c close to melting at 1.6 Tpc while eta_b remains a narrow, well-defined state.","lead":"This paper uses 2+1 flavor lattice QCD to estimate how charmonium and bottomonium pseudoscalar bound states behave in hot quark-gluon plasma. It finds the charmonium ground state (eta_c) broadens dramatically and nears dissolution at 293 MeV, while the bottomonium ground state (eta_b) survives with a smaller thermal width.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The inferred Γ(η_c)≈300–600 MeV is governed by V_im extracted from the Wilson line correlator via the 1/ω^2 spectral ansatz in Eq. (13); since the paper admits an alternative ansatz (ref [35]) describes the same data without screening, the melting claim is not yet robust.","rationale":"The reader's weakest assumption correctly identifies the complex-potential ansatz. I agree. The paper's other steps—solving the Schrödinger equation with a complex potential, matching UV and threshold regions, and comparing with lattice correlators—are internally consistent, and the lattice data are valuable. However, the central physics claim (η_c near dissolution at 1.6 Tpc) hinges on a non-zero V_im; without V_im the spectral function would remain a narrow peak. Because the extraction of V_im is a model-dependent inverse problem and the paper itself presents a competing model (ref [35]) that is compatible with the same kind of data and yields no screening, the burden is on the authors to show that their ansatz is uniquely selected by the data. The proposed refit with the competing model on the same data would settle this. The current CONDITIONAL verdict is appropriate; if the test shows comparable fit quality with V_im ≈ 0, the melting claim should be withdrawn or heavily qualified.","tokens_in":27423,"tokens_out":6241,"duration_ms":58181,"concrete_test":"Refit the Wilson line correlator data of Table II using the alternative spectral ansatz of ref [35] (which produced no color screening) over the same τ ranges and flow times used for Eq. (13); compare χ^2/d.o.f. and the implied V_im(r). If the alternative gives comparable χ^2/d.o.f. while V_im is consistent with zero, the Γ≈300–600 MeV result is an artifact of the chosen spectral ansatz.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central result—η_c(1S) acquires a large thermal width Γ∼300–600 MeV and is close to melting at 293 MeV (Sec. VI)—is controlled by the imaginary part V_im of the thermal potential. V_im is not observed directly; it emerges from fitting the Euclidean Wilson line correlator with the HTL-motivated ansatz in Eq. (13), where the spectral function σ(r,ω) is constrained to behave as 1/ω^2 (Eq. 12). The limit in Eq. (10) shows that this 1/ω^2 behaviour is what converts the periodic τ-dependence of log W into the non-zero V_im in Eq. (14). The paper itself acknowledges the inversion is ill-posed: on p.7 it states that the study of ref [35] finds no color screening, and attributes the discrepancy to the need for physics input. Moreover, Fig. 6 (right) shows that allowing the additional c1, c2 terms in Eq. (13) changes V_im at large distances, and the authors only include the spread as a systematic uncertainty. The validation in Sec. VII fits an overall multiplicative normalization A and restricts the comparison to τ > 0.22–0.28 fm, so it constrains the spectral shape only after V_im has already been fixed by the ansatz. Consequently, if a different but equally good ansatz (e.g., ref [35]) yields V_im ≈ 0, the reported width and dissolution claim do not follow.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a calculation of pseudoscalar quarkonium (η_c and η_b) spectral functions in 2+1 flavor lattice QCD at T = 220, 251, and 293 MeV. The authors extract a complex static potential from Coulomb-gauge Wilson line correlators using the HTL-motivated parametrization in Eq. (13), then solve the Schrödinger equation (4) in the threshold region and match the resulting spectral function to the vacuum perturbative spectral function in the ultraviolet via Eq. (22). The resulting spectral functions are used to compute Euclidean correlators and are compared with directly measured lattice correlators in Figs. 13 and 14. The central phenomenological claims are that η_c(1S) acquires a thermal width Γ ≈ 300–600 MeV and is close to dissolution at 293 MeV, while η_b(1S) remains narrow with Γ ≈ 20–60 MeV.","tokens_in":27801,"tokens_out":6949,"duration_ms":70868,"significance":"If the central claims hold, this is a valuable non-perturbative input for quarkonium suppression phenomenology: it provides temperature-dependent masses and widths for pseudoscalar charmonium and bottomonium, and the correlator comparison demonstrates that a screened complex potential is at least consistent with lattice data. The paper is also careful to restrict attention to the pseudoscalar channel, where no transport contribution complicates the analysis, and to confront the reconstructed spectral function with the lattice correlator in a ratio that removes the unknown renormalization constant. The main caveat is that the extracted imaginary part of the potential—and therefore the reported widths—is controlled by the assumed spectral ansatz in Eq. (13), a limitation the paper itself acknowledges. The quantitative claims are thus interesting but not yet uniquely supported.","major_comments":[{"comment":"The non-zero imaginary part of the potential, which is the dominant source of the large η_c width, is not directly measurable from the Euclidean Wilson line correlator; it emerges from the assumed form of the spectral function σ(r,ω) in Eq. (12) and the resulting parametrization Eq. (13). The 1/ω^2 behavior in Eq. (12) is motivated by HTL, but the inversion of Eq. (8) is ill-posed, and the paper explicitly notes on p. 7 that the alternative analysis of ref. [35] finds no color screening. Because V_im ≈ 0 is compatible with the same correlators under a different but equally plausible physics input, the reported width Γ(η_c) = 300–600 MeV and the statement that η_c is near melting at 293 MeV are not uniquely determined by the lattice data. This ansatz uncertainty is not included in the error budget of Fig. 12: the systematic variation in Appendix B changes the number of terms in Eq. (13) and the fit range, but not the form of Eq. (13) itself. The manuscript should either (i) implement an alternative inversion, for example the model of ref. [35], and show that it is statistically disfavored by the Wilson line data, or (ii) reframe the width and dissolution claims as conditional on the ansatz.","section":"Section IV, Eq. (13), and p. 7"},{"comment":"The claimed consistency with the lattice correlators does not by itself select the extracted V_im. In Eq. (26) an overall multiplicative constant A is fitted to the correlator comparison, and the comparison is restricted to τ > τ_min (0.22 fm for η_c and 0.28 fm for η_b). The renormalization constant cancels in the effective-mass ratio Eq. (24), but the remaining comparison is a shape comparison whose normalization is free. Since the spectral shape below and near the peak is already fixed by V_im through the Schrödinger equation, the agreement in Figs. 13 and 14 reflects the internal consistency of the reconstruction chain rather than an independent confirmation of V_im. To make the validation informative, the authors should show the correlator predictions and χ²/ndf for a spectral function with V_im = 0, or with the ref. [35] potential, demonstrating that such alternatives are actually excluded by the lattice correlators.","section":"Section VII, Eq. (26), Figs. 13 and 14"},{"comment":"The reconstruction in the threshold region contains two additional model choices whose impact on the extracted widths is not quantified: the ad hoc factor exp((2M_q − ω)/T) multiplying the imaginary part below threshold, and the choice of matching point ω0 and normalization A0 in Eq. (22). The text states A0 ≈ 1 and that matching is performed where the thermal spectral function has no temperature dependence, but the sensitivity of Γ(1S) and M(1S) to these choices is not reported. Because the spectral function is a prediction of the model rather than of the lattice correlator alone, these uncertainties should be included in the error budget of Fig. 12 or shown to be negligible.","section":"Section VI, Eq. (22), and the ω < 2M_q paragraph"}],"minor_comments":[{"comment":"The charm pole mass is quoted as 1.35 ± 0.01 MeV; the unit should evidently be GeV.","section":"Section V"},{"comment":"In the text following Fig. 2, the sentence 'The real part of the potential ... is shown in Figure 2' should read Figure 3, since Figure 2 shows fit-range stability rather than flow-time dependence.","section":"Section IV"},{"comment":"The sentence 'In Section VIII, it is shown that these spectral functions can predict the lattice correlator' should refer to Section VII, where the comparison is actually presented.","section":"Section VIII"},{"comment":"The title contains a spelling artifact ('Spe ctral') and the Introduction contains typographical errors such as 'qurkonia' and 'foucs'; these should be corrected in the published version.","section":"Title and Introduction"},{"comment":"The caption says the fit excludes the contributions from 'c0 and c1', but Eq. (13) contains no c0 term; presumably only c1 was meant.","section":"Section IV, Fig. 1 caption"},{"comment":"The reported χ²/ndf values of 0.1–0.9 are quite low; a comment on whether the systematic errors are correlated or conservative would help the reader interpret the quality of the comparison.","section":"Section VII, Eq. (25)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a relevant and difficult problem with a substantial dataset, and the approach is worth publishing after the model-dependence of the central claim is addressed. The main concern is not the internal consistency of the analysis but whether the reported η_c dissolution claim is robust to the assumed Wilson-line spectral ansatz. I recommend major revision rather than rejection because the requested robustness test appears feasible with the data already in hand; without it, the paper overstates the uniqueness of the width and melting conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Things you should know: this is a credible lattice QCD paper that actually delivers something new - pseudoscalar quarkonium spectral functions at 1.2-1.6 Tpc using a non-perturbatively extracted complex potential - and its authors are unusually candid about the ill-posed inversion. The catch: the central widths, especially the claim that eta_c is near melting at 293 MeV, are largely fixed by the assumed 1/omega^2 shape of the Wilson line spectral function in Eq (12), not by something the lattice data uniquely determine. The paper itself notes that the alternative physical input of ref [35] gives no color screening. That is not a hidden flaw; it is stated in the text, but the conclusions are still phrased more strongly than the evidence supports.\n\nWhat genuinely impresses: the real part of the potential is carefully assembled from flow-time matching and zero-flow short distance data, the Schrodinger-plus-UV-matching pipeline is standard and the numerics appear internally consistent, and the final comparison of the resulting correlator to the directly computed lattice correlator is a sensible consistency check. The qualitative ordering - eta_c broadens much more than eta_b - is robust, and the authors have done a reasonable job quantifying mass-tuning and fit-range systematics (Appendix B).\n\nWhere it is soft: the imaginary potential, which controls the entire width budget, is an output of the ansatz. The validation against the pseudoscalar correlator does not break the degeneracy because an overall normalization A is fitted and only tau > 0.22-0.28 fm are used; it confirms that the model spectral function is compatible with the correlator, not that the imaginary part is the right one. The width range 300-600 MeV is a spread over internal variations of that ansatz, not over alternative physically motivated spectral shapes. A quicker, sharper paper could have either pushed the analysis of alternative kernels or softened the melting language to 'model-dependent estimate.' There is also the usual single-lattice-spacing caveat, and a GeV/MeV typo for the charm pole mass.\n\nBottom line: this paper is worth engaging and will be cited in the quarkonia-in-plasma literature, but the headline numbers should be used with that model-dependence disclaimer attached. A serious referee should take it - the methodology is substantial and the authors are honest - with the request that the central claim be reframed and, if possible, the ansatz dependence be probed more explicitly.","headline":"A serious, transparent lattice-QCD study whose headline eta_c melting result is controlled by an assumed spectral ansatz for the Wilson line correlator, so the quantitative widths are model-dependent rather than definitive.","tokens_in":28375,"tokens_out":2769,"would_cite":true,"duration_ms":28780,"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":"In the quark–gluon plasma, pseudoscalar charmonium $\\eta_c(1S)$ is close to melting at 293 MeV with a thermal width of 300–600 MeV, while $\\eta_b(1S)$ stays well-defined at 20–60 MeV.","keywords":["quark-gluon plasma","pseudoscalar quarkonium spectral function","thermal complex potential","lattice QCD","eta_c thermal width","eta_b thermal width","Wilson line correlator","color screening"],"falsifier":"Fit the same Wilson line correlator data with an alternative ansatz that satisfies the long-time limit but does not impose the $1/\\omega^2$ periodic term, and check whether it describes the data equally well with $V_{\\mathrm{im}}=0$; if it does, the quoted $\\eta_c$ width is an artifact of the chosen ansatz. A more direct check would be a model-independent reconstruction of the pseudoscalar spectral function from the same lattice correlators at finer lattice spacing, looking for a peak whose width is compatible with zero at 293 MeV.","tokens_in":27161,"feed_emoji":"⚛️","tokens_out":11615,"duration_ms":93259,"temperature":0.7,"pith_summary":"This paper tries to determine what happens to charmonium and bottomonium in the quark–gluon plasma by reconstructing their pseudoscalar spectral functions from 2+1 flavor lattice QCD at 1.2, 1.4, and 1.6 times the crossover temperature. Because spectral reconstruction from Euclidean correlators is ill-posed, the authors build the spectral function from physics-motivated pieces: a non-perturbative complex thermal potential near the two-quark threshold and vacuum perturbation theory at high frequencies. The result is that the $\\eta_c(1S)$ ground state acquires a large thermal width of roughly 300–600 MeV and appears close to melting at 293 MeV, while the $\\eta_b(1S)$ ground state remains narrow with width 20–60 MeV. If correct, this means pseudoscalar charmonium is strongly modified in the quark–gluon plasma at temperatures just above the transition, while bottomonium survives largely intact.","feed_headline":"Lattice QCD puts eta_c width at 300–600 MeV, near melting","feed_subtitle":"Bottomonium's eta_b stays narrow at 20–60 MeV, so quarkonium melting splits sharply by flavor in the QGP.","key_machinery":"The load-bearing object is the thermal complex potential $V(r)=V_{\\mathrm{re}}(r)-iV_{\\mathrm{im}}(r)$, extracted from the Coulomb-gauge Wilson line correlator (the Euclidean product of two static quark lines at fixed separation) through the ansatz of Eq. (13): the logarithm of the Euclidean correlator is written as a linear term in $\\tau$ plus a periodic term whose spectral weight behaves as $1/\\omega^2$, with coefficients fixed by the Bose distribution. That structure guarantees the long-time limit defining the potential exists and turns the correlator into a nonzero imaginary part $V_{\\mathrm{im}}$ that grows with distance and temperature. This potential is then inserted into a Schrodinger equation for the point-split pseudoscalar correlator, whose solution gives the spectral function near the two-quark threshold; the threshold spectral function is smoothly matched to the vacuum perturbative spectral function at high frequency, and the resulting full spectral function is compared with lattice correlators through effective masses.","core_discovery":"On its own terms, the paper claims that the pseudoscalar charmonium ground state $\\eta_c(1S)$ is already close to dissolution at $T=293$ MeV ($1.6\\,T_{pc}$), with a thermal width in the range 300–600 MeV, while the bottomonium ground state $\\eta_b(1S)$ keeps a small width of 20–60 MeV, about 10–15 times smaller, and remains a well-defined peak in the spectral function at the same temperatures. The width comes from the imaginary part of a non-perturbatively extracted complex static potential, and the paper further claims that the spectral function assembled from the threshold region (Schrodinger equation with this potential) and the ultraviolet region (vacuum perturbation theory) reproduces the lattice pseudoscalar correlator at large Euclidean times at all three temperatures, with $\\chi^2/\\mathrm{ndf}$ between 0.1 and 0.9.","pith_inferences":["If this picture holds, charmonium suppression in heavy-ion collisions should be visible already at temperatures just above the crossover, and the pseudoscalar $\\eta_c$ channel is a cleaner diagnostic than the vector channel because it is not contaminated by a low-frequency transport peak.","A testable extension is to repeat the same threshold-plus-ultraviolet construction for the vector channel by adding a transport contribution; the comparison between $\\eta_c$ and $J/\\psi$ widths would show whether the near-melting result is channel-specific.","The strong dependence of the imaginary part on the chosen ansatz means the decisive check is a genuinely model-independent spectral reconstruction at finer lattice spacing; until then, the 300–600 MeV width should be read as conditional on Eq. (13).","The method can be carried to nonzero baryon density or to include relativistic corrections to the static potential, where the authors expect the qualitative hierarchy (charm broad, bottom narrow) to persist but with modified numerical widths."],"forward_implications":["The $\\eta_c(1S)$ width grows with temperature and reaches 300–600 MeV at 293 MeV, implying pseudoscalar charmonium is strongly modified or dissolving in the quark–gluon plasma at 1.6 $T_{pc}$.","The $\\eta_b(1S)$ width stays at 20–60 MeV, so bottomonium remains a well-defined state at the same temperatures and should survive as a probe of the plasma.","Because the pseudoscalar channel has no low-frequency transport peak, the full spectral function built from threshold plus ultraviolet contributions already matches the lattice correlator ($\\chi^2/\\mathrm{ndf}$ 0.1–0.9), confirming that no extra low-frequency structure is needed.","Excited quarkonium states melt already at the lowest plasma temperature studied, 220 MeV, leaving only the ground-state peak.","The thermal mass behavior differs: the $\\eta_c$ mass stays near its zero-temperature value while the $\\eta_b$ mass drops with temperature, reflecting that the imaginary part dominates for charm and the real part for bottom."],"supporting_citations":[{"why":"Derives the complex thermal potential and the HTL Wilson line correlator structure that motivates the linear-plus-periodic ansatz.","marker":"[23]"},{"why":"Provides the matching framework: perturbative vacuum spectral function in the ultraviolet, exponential suppression below threshold, and the absence of a transport peak in the pseudoscalar channel.","marker":"[27]"},{"why":"Introduces extraction of the thermal potential from Coulomb-gauge Wilson line correlators used here.","marker":"[32]"},{"why":"Supplies the HTL-motivated parametrization of the Wilson line correlator that becomes the fit ansatz in Eq. (13).","marker":"[33]"},{"why":"Provides Wilson line correlator data and the no-color-screening contrast case that the present screened result must be distinguished from.","marker":"[35]"},{"why":"Gives the algorithm for solving the Schrodinger equation to obtain the threshold spectral function from the complex potential.","marker":"[26]"},{"why":"Shows how to extract quarkonium spectral functions from a non-perturbative potential and supplies the skewed Breit-Wigner fit form used for the widths.","marker":"[30]"},{"why":"Shows that the Wilson line correlator suppresses the ultraviolet contribution while yielding the same thermal potential, justifying the choice of observable.","marker":"[51]"}],"fun_headline_variants":["Eta_c width 300–600 MeV: charmonium nears dissolution in QGP","Bottomonium eta_b stays narrow while charmonium eta_c melts","Near-dissolution of eta_c at 1.6 Tpc from lattice QCD","Quarkonium melting split: eta_c 300–600 MeV vs eta_b 20–60 MeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole extraction of the imaginary part and hence the thermal width rests on the assumed spectral shape of the Wilson line correlator in Eq. (13), namely the linear-plus-periodic form with $1/\\omega^2$ spectral weight; if the true spectral function has a different shape that still fits the lattice data, the imaginary part, and with it the claim that $\\eta_c$ is near melting, does not follow.","fun_headline_variants_meta":{"raw":{"variants":["Eta_c width 300–600 MeV: charmonium nears dissolution in QGP","Bottomonium eta_b stays narrow while charmonium eta_c melts","Near-dissolution of eta_c at 1.6 Tpc from lattice QCD","Quarkonium melting split: eta_c 300–600 MeV vs eta_b 20–60 MeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000982,"raw_usage":{"total_tokens":4238,"prompt_tokens":1087,"completion_tokens":3151,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":3057}},"tokens_in":703,"tokens_out":3151,"duration_ms":22453,"temperature":1.0,"reasoning_tokens":3057,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:53:55.258863+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit the same Wilson line correlator data with an alternative ansatz that satisfies the long-time limit but does not impose the $1/\\omega^2$ periodic term, and check whether it describes the data equally well with $V_{\\mathrm{im}}=0$; if it does, the quoted $\\eta_c$ width is an artifact of the chosen ansatz. A more direct check would be a model-independent reconstruction of the pseudoscalar spectral function from the same lattice correlators at finer lattice spacing, looking for a peak whose width is compatible with zero at 293 MeV.","supporting_citations":[{"cited_title":"We find that color screening is weaker in the non-perturbative potential than in the perturbative one","cited_arxiv_id":null,"evidence_quote":"Derives the complex thermal potential and the HTL Wilson line correlator structure that motivates the linear-plus-periodic ansatz."},{"cited_title":"pole-mass","cited_arxiv_id":null,"evidence_quote":"Introduces extraction of the thermal potential from Coulomb-gauge Wilson line correlators used here."},{"cited_title":"Nonperturbative potential for study of quarkonia in QGP","cited_arxiv_id":"1909.10548","evidence_quote":"Provides Wilson line correlator data and the no-color-screening contrast case that the present screened result must be distinguished from."}],"review_version":1}