REVIEW
(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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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
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
- 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.
The abstract, sentence by sentence
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
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| 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 was examined, and what was not
- arXiv listing abstract v2
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Figures
Figures reproduced from arXiv:nucl-th/0007059 by the authors.
References
How later papers used it
128 later papers cite it
1 later paper by other authors is listed below: 1 cited it as support.
Cites it as support 1 of 3 papers with this label
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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
Papers citing it · 105 sentences without a confident label
Contests it 5 papers
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However, such an enhancement of heavy quarkonia is not supported at RHIC energy by the statistical model [ref] and has never been observed at RHIC or LHC [ref] .
B_c meson enhancement and the momentum dependence in Pb+Pb collisions at LHC energy · Introduction · contest 0.78
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Both the PHENIX data on $J/ψ$ production in Au+Au and in Cu+Cu collisions, are not consistent with models which predict $J/ψ$ enhancement [ref] .
$J/\psi$ suppression in the threshold model at RHIC and LHC energy · introduction · contest 0.85
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Apparently, both the PHENIX data on $J/ψ$ production in Au+Au and in Cu+Cu collisions, are not consistent with models which predict $J/ψ$ enhancement [ref] . $J/ψ$'s are suppressed both in Au+Au and Cu+Cu collisions, suppression is more in central collisions than in peripheral collisions.
Hydrodynamical model for $J/\psi$ suppression and elliptic flow · Introduction · contest 0.84
Uses its method or tool 2 papers
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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
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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
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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
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The results are compared with statistical [ref] , microscopic parton transport [ref] , and comover [ref] model calculations.
Centrality and transverse momentum dependence of inclusive J/$\psi$ production at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV · Introduction · 0.98
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Furthermore, we show, in Fig. [ref], the transverse momentum spectra of J/$ψ$ mesons decaying into dielectrons at mid-rapidity compared with a statistical hadronisation model approach [ref] for the production which is combined with a hydrodynamic model calculation to describe its spectrum in the shown band [ref] .
Loosely-bound objects produced in nuclear collisions at the LHC · Discussion · 0.94
Cites it as support 3 papers
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is further evidence that the main concept of SHMc, proposed in [ref] is realized.
Emergence of New Systematics for Open Charm Production in High Energy Collisions · Summary and Conclusions · 0.98
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The success of the SHM in the charm sector which provides a natural explanation of the increase with collision energy of $R_AA$ for J/$ψ$ is deeply connected to and provides unique evidence for the deconfinement of charm quarks [ref] in the hot medium.
Hadron yields in central nucleus-nucleus collisions, the statistical hadronization model and the QCD phase diagram · Statistical hadronization of charm quarks · 0.99
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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 · Hadron gas composition and QCD thermodynamics · 0.98
Cites it as background 37 papers
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The suppression [ref] and (re-)combination mechanism [ref] reflect the underlying dynamics of charm and anti-charm quarks in the quark-gluon plasma (QGP) and at the phase boundary.
Testing charm quark thermalisation within the Statistical Hadronisation Model · Introduction · 0.95
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In 2000, two phenomenological publications [ref] introduced the picture of quarkonium regenerated at a late stage of the collision history, either during the deconfined state or at the phase boundary between QGP and hadrons.
Heavy quarks and jets as probes of the QGP · Heavy-Flavor and Quarkonia · 0.99
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How to extend the SHM to the charm sector, i.e., to SHMc, was outlined more than 20 years ago [ref] and further developed in [ref] .
The multiple-charm hierarchy in the statistical hadronization model · Introduction · 0.90
Discussion
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