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Behavior of Charmonium Systems after Deconfinement

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Saumen Datta, Frithjof Karsch, Peter Petreczky, Ines Wetzorke

High Energy Physics - Lattice · Submitted 23 Dec 2003 · 40 references

Pith's verdict: The S-wave survival result is solid and independently cross-checked; the P-wave dissolution claim is the softer half, and the paper mostly knows it.

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arXiv IDhep-lat/0312037 (version 1)
Pith ID57AUTNSK, Pith's permanent record of this paper and its review
CitationFrithjof Karsch, Ines Wetzorke, Peter Petreczky, Saumen Datta. "Behavior of Charmonium Systems after Deconfinement." arXiv:hep-lat/0312037 (2003). https://pith.science/paper/57AUTNSK
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The paper

The paper claims

Lattice spectral functions show the J/ψ and ηc surviving to about 1.5 Tc while the P-wave χ states are already gone near 1.1 Tc, so J/ψ suppression is a gradual melt rather than a sharp deconfinement thermometer.

The reading

The paper asks a concrete question: in a hot gluonic plasma, at what temperature do the charmonium bound states actually come apart? The standard answer came from potential models, which put J/ψ dissolution at roughly 1.1 Tc and made its disappearance a sharp marker of deconfinement. The authors instead compute the thing directly: they measure Euclidean-time correlators of $cbar c$ operators on very fine quenched lattices (spacings 0.02–0.05 fm) at temperatures from 0.6 Tc up to 3 Tc, and reconstruct the spectral function from those correlators with the Maximum Entropy Method. Their answer splits the charmonium family in two. The S-wave states, ηc and J/ψ, show a statistically significant ground-state peak with essentially unchanged position and strength up to 1.5 Tc, a weakened but still present peak at 2.25 Tc, and no meaningful resonance by 3 Tc; the P-wave χc0 and χc1 show large medium-induced changes already at 1.1 Tc, consistent with dissolution. If this is right, the dilepton signature of deconfinement is a two-stage story: a step down as the χ states melt near Tc, then a slow melting of the surviving J/ψ peak over the next factor of two in temperature.

What carries the argument

Two devices carry the argument. The first is the Maximum Entropy Method inversion of $G(τ) = ∫ dω σ(ω) K(ω,τ)$ with $K(ω,τ) = cosh(ω(τ-1/2T))/sinh(ω/2T)$, solved with Bryan's singular-value-decomposition algorithm and a Shannon entropy prior. The second, and the one that makes short temporal extents usable, is the choice of default model: because the high-frequency part of the spectral function is dominated by lattice artifacts and is assumed temperature-independent, the authors transplant the large-ω structure measured at 0.75 Tc or 0.9 Tc into the prior for every high-temperature fit, matching it smoothly to $m_1 ω^2$ at low ω. Alongside this sits a prior-free cross-check: the ratio $G(τ,T)/G_{recon}(τ,T)$, where $G_{recon}$ is built from a lower-temperature spectral function through the same kernel, so that any deviation from one is a genuine change in $σ$ rather than the known temperature dependence of the kernel.

Extended reading notes

Core claim

The central claim is that the 1S charmonia are far more robust in a hot gluon plasma than potential-model arguments suggested, while the 1P states are far more fragile. Above Tc the authors compare each measured temporal correlator with a 'reconstructed' correlator built by feeding the spectral function measured at 0.75 Tc or 0.9 Tc through the finite-temperature kernel; for the pseudoscalar channel the ratio stays at one up to 1.5 Tc and only departs visibly at 2.25 Tc and 3 Tc, while for the scalar and axial channels the measured correlator is already 60–120% larger than the reconstructed one at 1.1–1.5 Tc, the signature of spectral weight having moved down to around twice the quark mass. Reconstructed spectral functions bear this out: a strong peak at the zero-temperature mass persists for ηc and J/ψ through 1.5 Tc, weakens at 2.25 Tc, and is no longer statistically significant at 3 Tc, whereas the χc peaks are absent from the spectral function at 1.12 Tc. A secondary result is that the screening masses rise steadily above Tc even where the pole mass does not move, which the authors trace to a medium-modified dispersion relation with a speed coefficient below one, corroborated by the smaller-than-relativistic shift of the peak with spatial momentum at 1.5 Tc.

Load-bearing premise

The whole high-temperature reconstruction rests on the premise that the large-frequency part of the spectral function is a temperature-independent lattice artifact, so the same high-energy shape can be reused as the prior at every temperature; if that shape drifts with temperature, the low-frequency peak that carries the survival claim is pulled by the prior.

Editorial extensions

If this is right

  • The sequential-melting picture changes quantitatively: χc0 and χc1 dissolution near Tc removes the roughly 40% indirect contribution to the observed J/ψ yield first, and the directly produced J/ψ then survives with little further loss until about 1.5 Tc.
  • Dilepton spectra from a thermalized plasma should show a J/ψ peak that weakens gradually between roughly 1.5 Tc and 3 Tc rather than switching off at a single temperature, with about a 25% further reduction in integrated strength at 2.25 Tc for a near-charm quark mass.
  • Because screening masses rise while pole masses stay put, a lattice calculation that quotes only screening masses above Tc will overstate the in-medium mass shift; the two quantities must be separated through a modified dispersion relation.
  • The melting temperature depends on quark mass: for lighter quarks the pseudoscalar correlator departs from the reconstructed one already at 1.24 Tc, while the heaviest quark studied shows no modification through 1.5 Tc.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the S-wave survival is real, the sharpness of J/ψ suppression as a thermometer is set by the χ states, not the J/ψ, which suggests that the experimentally cleaner signal near Tc is the step in the dilepton yield from P-wave feed-down rather than the endpoint of the J/ψ peak itself.
  • The claim that the high-frequency spectral structure is temperature-independent is testable independently of charmonium: a finer lattice at fixed temperature with more temporal points should reproduce the same large-ω bump structure, and any drift in it would propagate straight into the low-ω peak positions reported here.
  • The modified dispersion relation inferred from the screening-versus-pole mismatch is a prediction for lattice spectroscopy at nonzero momentum in any heavy-quark channel, not just charmonium, and could be checked against the momentum dependence of the restored correlator ratio.
  • An unquenched version of this study would be the decisive comparison: dynamical light quarks add pion-induced broadening below Tc and could push the χ dissolution temperature below the transition, which would sharpen rather than weaken the two-stage melting picture.
Original abstract

We present a study of charmonia in hot gluonic plasma, for temperatures upto three times the deconfinement transition temperature Tc. q \bar{q} systems with quark masses close to the charm mass and different spin-parity quantum numbers were studied on very fine isotropic lattices. The analysis of temporal correlators, and spectral functions constructed from them, shows that the J/psi and eta_c survive up to quite high temperatures, with little observable change up to 1.5 Tc, and then gradually weakening and disappearing by 3 Tc. For the scalar and axial vector channels, serious modifications are induced by the hot medium already close to Tc, possibly dissociating the mesons by 1.1 Tc.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,110 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present a study of charmonia in hot gluonic plasma, for temperatures upto three times the deconfinement transition temperature Tc. q \bar{q} systems with quark masses close to the charm mass and different spin-parity quantum numbers were studied on very fine isotropic lattices. The analysis of temporal correlators, and spectral functions constructed from them, shows that the J/psi and eta_c survive up to quite high temperatures, with little observable change up to 1.5 Tc, and then gradually weakening and disappearing by 3 Tc. For the scalar and axial vector channels, serious modifications are induced by the hot medium already close to Tc, possibly dissociating the mesons by 1.1 Tc.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a study of charmonia in hot gluonic plasma, for temperatures upto three times the deconfinement transition temperature Tc. q \bar{q} systems with quark masses close to the charm mass and different spin-parity quantum numbers were studied on very fine isotropic lattices. contribution 0.75 0.95 0.04 asserted 0.79
s1 The analysis of temporal correlators, and spectral functions constructed from them, shows that the J/psi and eta_c survive up to quite high temperatures, with little observable change up to 1.5 Tc, and then gradually weakening and disappearing by 3 Tc. result 1.00 0.95 0.52 asserted 1.00
s2 For the scalar and axial vector channels, serious modifications are induced by the hot medium already close to Tc, possibly dissociating the mesons by 1.1 Tc. result 0.98 0.89 0.16 hedged possibility 0.89

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. shows the spectral functions at 0.9 Tc, recon￾structed from the correlators for this set in the different channels. In order to remove the uninteresting ω 2 rise in the spectral function, here and in everywhere else we plot the ‘reduced spectral function’ ρ(ω) = σ(ω)/ω2 . (22) At T = 0.9Tc the physical distance available for the analysis of the temporal correlators is about 0.82 fm, and we have 40 data points. This allows us to have a good resolution of the ground state spectral function. We also found that omitting the data point at smallest τ enhances the peak structure for this…
Figure 2. FIG. 2: Spectral functions at 0.75
Figure 3. FIG. 3: Spectral functions for different channels at 0
Figure 4. FIG. 4: Spectral functions for the vector channel below
Figure 5. FIG. 5: Ratio of the measured correlators at 0.9
Figure 6. FIG. 6: Ratio of the measured temporal correlators with the
Figure 8. FIG. 8: The spectral function for the a) pseudoscalar and b)
Figure 9. FIG. 9: Ratio of the measured temporal correlators with the
Figure 10. FIG. 10: The spectral function for a) pseudoscalar and b)
Figure 11. FIG. 11: The mass dependence of
Figure 12. FIG. 12: The pseudoscalar (top) and vector (bottom) spec
Figure 13. FIG. 13: The spectral functions for a) pseudoscalar and b)
Figure 15. FIG. 15: Spectral functions for set II for pseudoscalar and
Figure 16. FIG. 16: Spectral functions for scalar (top) and axial vecto
Figure 17. FIG. 17: Spectral functions from set II for scalar and axial
Figure 18. FIG. 18: The vector spectral function at 1
Figure 19. FIG. 19: Screening masses for the a) vector and b) pseu
Figure 20. FIG. 20: Spectral functions for the a) pseudoscalar and b)

Showing 18 of the paper's 20 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0312037 by the authors.

References
How later papers used it

60 later papers cite it

Evidence: some. 45 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 109 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 7 papers with this label · 1 by the same authors

By the same authors

  • Followed the procedure proposed in this paper to eliminate the trivial temperature dependence of the integration kernel and calculate reconstructed correlators.

    On temperature dependence of quarkonium correlators (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

54 arXiv papers cite this in 101 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 2 papers

Papers citing it · 54 sentences without a confident label

Contests it 1 paper
  • This seems to contradict the conclusions made in Refs. [ref] , where the analysis of the spectral function using the MEM indicated that the first peak survives.

    Can quarkonia survive deconfinement ? · Numerical results with the potential $V(r,T)$ · contest 0.86

Uses its method or tool 7 papers
  • Let us start from the Euclidean correlator [ref] [equation] and take the integral ($β= 1/T$) [equation] Together with the definition of the reconstructed correlator [ref] [equation] i.e. taking the spectral density at zero temperature, one finds equivalently to ([ref]) but in terms of the Euclidean correlators [ref] , [equation]

    R-charge thermodynamical spectral sum rule in N=4 Yang-Mills theory · Euclidean correlator · 0.83

  • Therefore to eliminate the trivial temperature dependence of the integration kernel we follow the procedure proposed in Ref. [ref] and calculate the so-called reconstructed correlators [equation] where $T^*$ is some reference temperature well below $T_c$.

    On temperature dependence of quarkonium correlators · Lattice calculations of quarkonium correlators · 1.00

  • This can be investigated using so-called reconstructed correlators [ref] .

    Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD · Reconstructed correlators · 0.97

Uses its data or values 3 papers
Compares with it 7 papers
  • The results are consistent with previous lattice studies of charmonium spectral functions [ref] , in which the spectral functions for the Ps and V channels in the deconfinement phase (but at not so high temperature) show a peak structure around the $η_c$ and $J/ψ$ masses like the result at zero temperature.

    Study of constant mode in charmonium correlators at finite temperature · Finite temperature results · 0.87

  • We compare the calculated correlators to recent numerical results calculated from isotropic [ref] and anisotropic [ref] lattice formulations.

    Can quarkonia survive deconfinement ? · Quarkonium correlators at zero temperature · 1.00

  • This coincides with the thermal properties of heavy quarkonia observed by model calculation and lattice numerical studies [ref] , but different from the observation of a previous lattice study on glueballs where the observed pole-mass reduction start even at $T≃0.8 T_c$ [ref] .

    A Quenched Study of SU(3) Glueballs at Finite Temperature · Results of the single-cosh fit · 0.93

Cites it as background 18 papers

Discussion

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