REVIEW
$J/\psi$ and $\eta_c$ in the Deconfined Plasma from Lattice QCD
High Energy Physics - Lattice · Submitted 28 Aug 2003 · 22 references
Pith's verdict: The Nτ=46 lattice makes the survival claim credible; the 1.87 Tc null is the softer half of the bracket and the prior-shape scan is asserted rather than shown.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
Lattice spectral functions show the charmonium bound states $J/ψ$ and $η_c$ surviving as sharp peaks in the deconfined plasma up to about $1.6$ times the critical temperature, then vanishing by $1.9$ times it.
The reading
What carries the argument
The engine is the maximum entropy method applied to finite-temperature lattice correlators. The spectral function enters through $D(τ) = ∫_0^∞ K(τ,ω)A(ω)dω$ with the continuum kernel $K(τ,ω) = (e^{-τω}+e^{-(1/T-τ)ω})/(1-e^{-ω/T})$, an integral equation with infinitely many solutions at finite $N_{data}$. MEM picks the most probable one by maximising $P[A|D] ∝ e^{αS-L}$, where $L$ is the likelihood and $S$ is the Shannon–Jaynes entropy relative to a default model $m(ω)$ fixed from the perturbative high-frequency behaviour of $A(ω)$. The parameter $α$ is integrated out by Bayes' theorem, and the error on $A(ω)$ comes from the second variation of $P[A|D]$. The other half of the machinery is the anisotropic lattice itself: $ξ = a_σ/a_τ = 4.0$ at $β=7.0$ gives $a_τ ≈ 0.00975$ fm, which is what allows $N_τ$ as large as 46 at $1.62T_c$ and therefore enough temporal points for the inversion to be controlled.
Extended reading notes
Core claim
The central claim is that $J/ψ$ and $η_c$ persist as distinct resonances in the quark-gluon plasma up to $T ≃ 1.6T_c$ and dissociate between $1.6T_c$ and $1.9T_c$. The evidence is a sequence of MEM-reconstructed spectral functions at $T/T_c = 0.78, 1.38, 1.62, 1.87, 2.33$ on lattices with temporal extent $N_τ = 96, 54, 46, 40, 32$ respectively, keeping the number of temporal data points $N_{data}$ as large as 89 down to 25. The authors stress two reliability tests. First, the MEM error bars show that the peak at $1.62T_c$ is statistically significant and that its absence at the same frequency at $1.87T_c$ is also statistically significant. Second, truncating the data set from $N_{data}=39$ to $34$ at $1.62T_c$, and from $33$ to $26$ at $1.87T_c$, leaves the spectral functions essentially unchanged, which rules out the qualitative change being an artefact of too few time slices. They also note what they cannot yet claim: the observed peak width is dominated by statistical broadening of a few hundred MeV, so no definite statement about thermal mass shift or physical broadening is made, and the second and third peaks at lower temperature may be fermion-doubler artefacts whose $1/a_σ$ scaling remains untested.
Load-bearing premise
The load-bearing premise is that the maximum-entropy reconstruction is faithful at low frequency, so that the presence or absence of a peak reflects the medium rather than the Bayesian prior: the default model is fixed in functional form to the perturbative high-frequency behaviour, and the $N_{data}$ test varies how many time slices enter but never the shape of that prior.
Editorial extensions
If this is right
- Charmonium suppression in heavy-ion collisions becomes a thermometer of how far above $T_c$ the medium actually sits, rather than a binary signal of deconfinement.
- The melting temperature of a quarkonium state depends on its binding energy, so the same lattice machinery predicts an ordered sequence of dissociation temperatures across the upsilon and charmonium families.
- A plasma that still binds heavy quarks at $1.6T_c$ must be described by strongly coupled rather than weakly coupled quasi-particle pictures in that temperature window.
- The paper sets a minimum standard for finite-temperature MEM work: a temporal lattice too short to pass the $N_{data}$ stability test cannot support claims about peaks appearing or disappearing.
Reading between the lines
- The obvious next check is the one the authors flag as future work: repeat the analysis with dynamical quarks, since a quenched plasma lacks light-quark screening and would if anything overstate how long charmonium survives.
- Because the default model is fixed in shape and only its normalisation is scanned, a natural extension is to vary the functional form of $m(ω)$ and see whether the $1.62T_c$ peak and its $1.87T_c$ absence move together or separately; that would convert the current prior choice into a controlled systematic error.
- The peak-position versus $1/a_σ$ scaling test the authors propose for the higher peaks would also give a clean way to separate genuine in-medium structure from lattice doublers in the low-frequency region.
- If the surviving states are real, they should leave a measurable imprint in the spatial profile of the correlator, so extracting the in-medium Bethe-Salpeter amplitude on the same configurations is a direct consistency check.
Original abstract
Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3\times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/\psi$ and $\eta_c$ survive as distinct resonances in the plasma even up to $T \simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. The importance of having sufficient number of temporal data points in MEM analyses is also emphasized.
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.
The abstract, sentence by sentence
Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3\times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/\psi$ and $\eta_c$ survive as distinct resonances in the plasma even up to $T \simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. The importance of having sufficient number of temporal data points in MEM analyses is also emphasized.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3\times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/\psi$ and $\eta_c$ survive as distinct resonances in the plasma even up to $T \simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). | result 0.99 | 0.97 | 0.94 | asserted 1.00 |
| s1 | This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. | interpretation 1.00 | 0.34 | 0.16 | hedged possibility 1.00 |
| s2 | The importance of having sufficient number of temporal data points in MEM analyses is also emphasized. | limitation 0.44 | 0.37 | 0.03 | asserted 0.97 |
What was examined, and what was not
- arXiv listing abstract v2
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- references and citing sentences
- relations to other papers
- P abstract
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Figures
Showing 2 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0308034 by the authors.
References
How later papers used it
68 later papers cite it
2 later papers by other authors are listed below: 2 cited it as support. 1 more paper by the same authors is listed: 1 used its data or values.
Uses its data or values 1 of 3 papers with this label · 1 by the same authors
By the same authors
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Used the same physical lattice spacing and anisotropy as the first reference in this paper, a_sigma = 4 a_tau = 0.039 fm.
Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop (2009) (same authors) · 0.91 · paraphrased: the licence does not allow quoting
Cites it as support 2 papers
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Said its conclusion was supported by calculations of Minkowski-space spectral functions in lattice-regularized QCD in this paper.
Prediction of a Photon Peak in Heavy Ion Collisions (2008) · 1.00 · paraphrased: the licence does not allow quoting
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Said its first property was supported by calculations of Minkowski-space spectral functions in lattice-regularized QCD in this paper.
Cherenkov mesons as in-medium quark energy loss (2010) · 0.98 · paraphrased: the licence does not allow quoting
How the literature uses it
61 arXiv papers cite this in 82 sentences
Papers whose main result relates to this one's
States the same result 2 papers
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Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3\times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/\psi$ and $\eta_c$ survive as distinct resonances in the plasma even up to $T \simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement).
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J/psi and eta_c are found to survive well into the deconfined phase before melting away at T<~2T_c.
States a conflicting result 2 papers
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As a result, it is found that while J/psi and eta_c manifest themselves as significant peaks in the spectral function below the deconfinement temperature T_c, they quickly dissolve into the continuum and almost completely disappear at temperatures between 1.0 T_c and 1.1 T_c.
Charmonium spectra at finite temperature from QCD sum rules with the maximum entropy method · 0.94
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We find that charmonium correlators in the vector channel can be well reproduced by perturbative spectral functions above $T_c$ where no resonance peaks for $J/\psi$ are needed at and above 1.1 $T_c$, while for bottomonium correlators a resonance peak for $\Upsilon$ is still needed up to 1.5 $T_c$.
Charm and beauty in the deconfined plasma from quenched lattice QCD · 0.90
Papers citing it · 50 sentences without a confident label
Contests it 1 paper
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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 data or values 3 papers
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The temporal lattice spacing in physical unit is $a_τ=0.00975$ fm [ref] .
In-medium dispersion relations of charmonia studied by maximum entropy method · Simulation set up · 0.88
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The physical lattice spacing and anisotropy are the same with the first reference in [ref] , $a_σ=4a_τ=0.039fm$.
Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop · Quenched QCD results at low and high $T$ · 0.91
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Using the MEM method for spectral function reconstruction, Ref. [ref] found that the $J/ψ$ and $η_c$ can survive well-above the transition temperature, at least up to temperatures of $1.6 T_c$, as seen in Fig. [ref].
Hadron properties at finite temperature · Lattice-QCD for quarkonia · 0.82
Compares with it 4 papers
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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
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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
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Lattice results in the quenched approximation, in contrast, suggest a scaling of the transition temperature of meson destabilization with the transition temperature for the gauge fields $T_fund∝T_gauge$ [ref] .
In-medium effects in the holographic quark-gluon plasma · Confinement/deconfinement · 0.93
Cites it as support 2 papers
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This conclusion is supported by calculations of both the static quark-antiquark potential [ref] and of Minkowski-space spectral functions in lattice-regularized QCD [ref] .
Prediction of a Photon Peak in Heavy Ion Collisions · Introduction · 1.00
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The first property is suggested by the fact that sufficiently heavy mesons are smaller than the screening length in the plasma [ref] , and is supported by calculations of both the static quark-antiquark potential [ref] and of Minkowski-space spectral functions in lattice-regularized QCD [ref] .[In some models light mesons also remain bound above $T_c$ by Coulomb-like forces [ref] .] The second property, which goes back to ref.
Cherenkov mesons as in-medium quark energy loss · Phenomenological implications for HIC experiments · 0.98
Cites it as background 20 papers
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In particular, attempts to reconstruct quarkonium spectral functions using the Maximum Entropy Method (MEM) were presented in Refs. [ref] .
On temperature dependence of quarkonium correlators · Introduction · 0.83
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The study of the properties of charmonia at finite temperature is one of the longstanding subjects on the lattice [ref] .
In-medium dispersion relations of charmonia studied by maximum entropy method · introduction · 0.96
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Extensive efforts have been devoted to studying charmonium [ref] and bottomonium [ref] in lattice QCD.
Charmonium properties at high temperatures from lattice QCD · Introduction · 0.96
Discussion
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