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(Non)Thermal Aspects of Charmonium Production and a New Look at J/$\psi$ Suppression

Nuclear Theory · Submitted 26 Jul 2000 · 39 references

Pith's verdict: The negative claim (charm is not thermally produced at SPS) is solid; the positive one (statistical hadronization of hard-produced charm) is the real contribution, but its Fig. 3 normalization is quadratically sensitive to a charm yield the authors themselves admit is uncertain by a factor of 2-3.

T0 · AI review

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arXiv IDnucl-th/0007059 (version 2)
Pith IDTTGRZXW7, Pith's permanent record of this paper and its review
CitationDarmstadt, Germany), Germany) J. Stachel (Physikalisches Institut der Universit\"at Heidelberg, Heidelberg, P. Braun-Munzinger (Gesellschaft f\"ur Schwerionenforschung. "(Non)Thermal Aspects of Charmonium Production and a New Look at J/$\psi$ Suppression." arXiv:nucl-th/0007059 (2000). https://pith.science/paper/TTGRZXW7
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Referee report
The paper

The paper claims

The J/ψ yield in Pb+Pb collisions is not thermal, but the ψ′ to J/ψ ratio looks thermal — and that combination points to statistical hadronization of hard-produced charm quarks.

The reading

The paper asks a sharp question: is hidden charm (the J/ψ and its relatives) produced thermally in ultra-relativistic nuclear collisions, as had recently been proposed? The authors extend the statistical hadronization model that successfully describes all other hadron yields at SPS energies — chemical freeze-out at $T = 168$ MeV, $μ_B = 266$ MeV, volume 3085 fm$^3$ for 400 participants — to include open and hidden charm, and find that it underpredicts the measured J/ψ yield per collision by more than a factor of two in the most central Pb+Pb events. So the answer to the opening question is no: the absolute charmonium yield is not thermal. But the ψ′/(J/ψ) ratio is a different story. In pp and p-nucleus collisions that ratio sits near 12%, which would require about 280 MeV to reproduce thermally; in central nucleus-nucleus collisions it falls and saturates at roughly the thermal prediction of 3.7%. The authors take that split — non-thermal normalization, thermal-looking ratio — as the clue that charm quarks are all made in hard collisions and only their hadronization is statistical.

What carries the argument

The load-bearing device is a charm-enhancement factor $g_c$, defined by requiring that the statistically hadronized yields add back up to the number of directly produced charm pairs: $N^{direct}_{c̄c} = ½ g_c V (∑_i n^{therm}_{D_i} + n^{therm}_{Λ_i}) + g_c^2 V (∑_i n^{therm}_{ψ_i}) + …$, with the $g_c^2$ and higher terms negligible. Because a $D$ meson carries one charm quark and a J/ψ carries two, the prescription gives $N_D = g_c V n^{therm}_D$ and $N_{J/ψ} = g_c^2 V n^{therm}_{J/ψ}$ — a linear versus quadratic dependence on a single number. At $N_{part} = 400$ the PYTHIA-based direct charm yield of 0.173 pairs per collision implies $g_c = 1.38$, and the resulting J/ψ curve tracks the NA50 data across centrality without any new fitted parameter. The same machinery makes the collider predictions: $g_c = 6.8$ at RHIC gives $dN_{J/ψ}/dy ≈ 10^{-2}$, essentially the unsuppressed hard-scattering value.

Extended reading notes

Core claim

The paper establishes that a chemically equilibrated thermal model including charm cannot reproduce the measured J/ψ yield in central Pb+Pb collisions at the SPS: the thermal prediction falls short by more than a factor of two at $N_{part} = 400$ and by about a factor of three at $N_{part} = 200$, and closing the gap would need $T ≈ 180$ MeV, outside the $168 ± 4$ MeV range fixed by the rest of the hadron spectrum. The authors also argue that charm cannot chemically equilibrate in any case, since hadronic open-charm cross sections are at the sub-$μ$b level and a parton-cascade estimate gives fewer than 0.01 thermal $c̄c$ pairs in central Pb+Pb, a factor of 40 short. What survives is the ratio: ψ′/(J/ψ) drops with participant number and saturates near the thermal value of 3.7% in the most central S+U and Pb+Pb data, while remaining near 12% in pp and p-nucleus collisions. The proposed reading is that all $c̄c$ pairs come from direct hard scattering at the expected pp rate, and that these quarks then hadronize statistically at the phase boundary, so that the J/ψ yield scales as the square of a charm-enhancement factor while open-charm meson yields scale linearly with it.

Load-bearing premise

The normalization of the whole prediction rests on the assumed number of charm quark pairs made directly in a central Pb+Pb collision, 0.173, which comes from extrapolating proton-proton charm with a factor-of-two uncertainty and could plausibly be three times larger.

Editorial extensions

If this is right

  • If the picture holds, there should be no J/ψ suppression at RHIC energies relative to hard-scattering expectations, even though no J/ψ survives inside a deconfined phase — the mesons are regenerated at hadronization from charm quarks.
  • At LHC energies the same accounting predicts a significant enhancement of charmonium above the directly produced hard-scattering yield, since $g_c$ grows with the charm cross section.
  • The scenario requires a deconfined phase: either directly produced J/ψ mesons are never formed before the plasma stage, or they are broken up in it, so the observed charmonia must come from quarks that survived the plasma.
  • Thermal (not chemical) equilibration of charm quark momenta near $T_c$ is needed, and the measured J/ψ transverse spectra with inverse slopes around 230 MeV are consistent with that.
  • Secondary charmonium production during the mixed phase, computed elsewhere under the assumption that all charm ends in D mesons, should be added on top of these yields rather than compete with them.

Reading between the lines

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

  • The sharpest test is a direct open-charm measurement in Pb+Pb: the whole normalization rests on 0.173 $c̄c$ pairs per central collision, and the authors themselves flag a possible factor-of-three enhancement of open charm over the pp extrapolation, which would move $g_c$ and hence the J/ψ curve by the same factor.
  • The linear-versus-quadratic splitting between D and J/ψ yields gives a clean experimental discriminant: a measured open-charm yield combined with a measured J/ψ yield over-determines $g_c$, so the two channels can be checked against each other rather than each against theory separately.
  • The proposal makes the ψ′/(J/ψ) ratio a thermometer-like diagnostic of the hadronization stage rather than of the initial temperature, which suggests looking for the same saturation pattern in the χ states, where the authors note thermal feeding into J/ψ would be under 3%.
  • Because the argument leans on the Npart dependence rather than on absolute yields, the shape of $dN_{J/ψ}/dN_{part}$ at RHIC and the LHC — flat or rising rather than falling — is the cheapest falsification available.
Original abstract

To investigate a recent proposal that J/$\psi$ production in ultra-relativistic nuclear collisions is of thermal origin we have reanalyzed the data from the NA38/50 collaboration within a thermal model including charm. Comparison of the calculated with measured yields demonstrates the non-thermal origin of hidden charm production at SPS energy. However, the ratio $\psi^{'}$/(J/$\psi)$ exhibits, in central nucleus-nucleus collisions, thermal features which lead us to a new interpretation of open charm and charmonium production at SPS energy. Implications for RHIC and LHC energy measurements will be discussed.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,634 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.17 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.84 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

To investigate a recent proposal that J/$\psi$ production in ultra-relativistic nuclear collisions is of thermal origin we have reanalyzed the data from the NA38/50 collaboration within a thermal model including charm. Comparison of the calculated with measured yields demonstrates the non-thermal origin of hidden charm production at SPS energy. However, the ratio $\psi^{'}$/(J/$\psi)$ exhibits, in central nucleus-nucleus collisions, thermal features which lead us to a new interpretation of open charm and charmonium production at SPS energy. Implications for RHIC and LHC energy measurements will be discussed.

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 To investigate a recent proposal that J/$\psi$ production in ultra-relativistic nuclear collisions is of thermal origin we have reanalyzed the data from the NA38/50 collaboration within a thermal model including charm. contribution 0.75 0.91 0.05 unclear 0.44
s1 Comparison of the calculated with measured yields demonstrates the non-thermal origin of hidden charm production at SPS energy. result 0.96 0.89 0.58 asserted 1.00
s2 However, the ratio $\psi^{'}$/(J/$\psi)$ exhibits, in central nucleus-nucleus collisions, thermal features which lead us to a new interpretation of open charm and charmonium production at SPS energy. interpretation 0.66 0.88 0.39 asserted 0.91
s3 Implications for RHIC and LHC energy measurements will be discussed. future work 0.96 0.17 0.03 unclear 0.89

What kind of paper the classifier reports this is: theoretical result 0.53 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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. Comparison of measured J/ψ yield per Pb+Pb collision as a function of centrality with the predictions of the thermal model (dashed line). The data are from [21,22] as analyzed in [23]. For details see text
Figure 2. Comparison of the dependence of the measured
Figure 3. Comparison of the dependence of the measured (J/

Figures reproduced from arXiv:nucl-th/0007059 by the authors.

References
How later papers used it

128 later papers cite it

Evidence: some. 114 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 171 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

Cites it as support 1 of 3 papers with this label
  • The SHM provides a good description of the production yield within uncertainties, supporting the statistical (re)combination of charm and anticharm quark pairs at the phase boundary [ref] .

    The ALICE experiment: a journey through QCD (2022) · Hadron gas composition and QCD thermodynamics · 0.98

How the literature uses it

116 arXiv papers cite this in 156 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 citing it · 105 sentences without a confident label

Contests it 5 papers
Uses its method or tool 2 papers
  • A regeneration model used [ref] , which is based on a first-order rate equation to compute the local particle density function,

    Bottomonium suppression at RHIC and LHC · Model implementation and results · 0.99

  • To implement this condition we introduce a fugacity factor [ref] g_c(T) = N_$cc̅$/2 ·3 ·V(T) ( M_c T/2 π )^3/2 e^-M_c/T , where $M_c=1.7$ GeV is the charm-quark mass.

    Prediction of a Photon Peak in Heavy Ion Collisions · Introduction · 0.85

Uses its data or values 1 paper
  • The nuclear modification factor $R_AA∼0.3$ in central Au+Au collisions at RHIC [ref] goes up to about 0.5 in central Pb+Pb collisions at $√(s_NN)=2.76$ TeV at LHC [ref] due to the increasing contribution of charmonium regeneration [ref] .

    Physics perspectives of heavy-ion collisions at very high energy · $J/ψ$ production · 0.93

Compares with it 2 papers
Cites it as support 3 papers
Cites it as background 37 papers

Discussion

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