Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?

C. Ratti; K. K. Szabo; S. Borsanyi; S. D. Katz; S. Krieg; Z. Fodor

REVIEW

Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?

S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, K. K. Szabo

High Energy Physics - Lattice · Submitted 18 Mar 2014 · 33 references

Pith's verdict: A genuine first cross-channel freeze-out check, but the baryon–charge agreement lives inside an assumed 140–150 MeV window that the authors themselves flag as the dominant error.

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arXiv ID1403.4576 (version 2)

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CitationC. Ratti, K. K. Szabo, S. Borsanyi, S. D. Katz, S. Krieg, Z. Fodor. "Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?." arXiv:1403.4576 (2014). https://pith.science/paper/FPLFLFWE

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Editor's note

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Bottom line: this is a short, candid follow-up to the Wuppertal-Budapest PRL (Ref. [11]) that does one genuinely new thing — it runs the freeze-out extraction through both the net-proton and net-charge channels and finds the chemical potentials agree at the four highest STAR energies. That cross-check is worth having, and the paper is honest about its own limits. But the agreement is established inside an assumed 140–150 MeV temperature window, and the authors say so in the Table I caption rather than burying it. Read it with that in mind and it holds up; read the abstract alone and you'd think the consistency was a free test of thermal equilibrium, which it isn't quite. [abstract:s3] is a bit stronger than the evidence supports, while [abstract:s2] is accurate — the temperature result really is an upper bound, not a measurement. The lattice side is solid: 2+1 flavors, physical quark masses, continuum extrapolated, and the comparison is against published STAR data, not the authors' own numbers. The shift in mu_B relative to their earlier uncorrected-data extraction is stated plainly, which I appreciate. The soft spots, in order of weight. First, the one the stress-test note raises and which lands: the Fig. 4 ratio-of-ratios is presented as a thermometer giving Tf = 144 +/- 6 MeV, but the text itself calls it 'a consistency criterion' that assumes a common temperature and chemical potential for charge and protons. It cannot independently validate the hypothesis it assumes. The only data-driven handle on Tf is R_B31, which gives an upper bound only; the 140 MeV lower edge is a lattice-systematics choice, so the B–Q agreement is simply untested below that. Second, the baryon channel equates net-proton with net-baryon moments, leaning on Ref. [23], which is an unpublished preprint with an overlapping author (Ratti). That's a real dependency, not a fatal one, but it should be flagged. Third, the statistical-hadronization agreement in Fig. 3 is asserted visually with no quantitative measure — minor, but easy to fix. The 27 GeV baryon point being dropped for non-monotonicity is fine and properly explained. Who should read it: anyone working on freeze-out from fluctuations, and anyone who wants a clean worked example of how to compare lattice cumulants to beam-energy-scan moments. It deserves a serious referee — the physics is sound and the caveats are stated, so the review should focus on whether the consistency claim is worded to match what was actually shown.

Referee report

Significance

If it holds, the result is a genuinely new and useful check: it is the first time the lattice-QCD freeze-out extraction has been carried out for two distinct conserved charges with continuum-extrapolated, physical-mass input, and the agreement (or failure) of the two channels is a falsifiable statement about the thermal-equilibrium assumption. The paper is commendably concrete about what it can and cannot determine — the upper bound rather than a value for Tf from R_B31, the explicit temperature window used for µB, and the statement that the earlier uncorrected-data extraction shifted the chemical potentials. The µB values in Table I are directly comparable to statistical-hadronization fits and the agreement shown in Fig. 3 is a nontrivial outcome. The proposed ratio-of-ratios thermometer, if validated, would be a practically useful observable because it avoids skewness and kurtosis. These strengths are real and should be weighed alongside the concerns below.

Major objections (3)

[Abstract (s3); Table I and its caption; paragraph beginning 'The comparison of our lattice results to the latest'] The consistency claim is stated unconditionally in the abstract but is conditional in the body. The Table I caption says the µB values 'have been obtained under the assumption that 140 MeV ≤ Tf ≤ 150 MeV' and that this uncertainty 'dominates the overall errors', and the text itself says the data 'hints at a consistency of the freeze-out chemical potential if we assume an agreement in the temperature'. Two consequences deserve explicit treatment. First, the abstract sentence 'Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found' should carry the same qualification as the body. Second, because the dominant uncertainty is a common systematic that shifts both channels in the same direction as Tf is varied, the per-channel errors quoted in Table I (e.g. 25.6 ± 2.4 versus 22.6 ± 2.4 MeV) overstate the independence of the two determinations; the agreement is being tested at a precision set by the non-common part of the error, which is not quoted. I would ask the authors to (a) reword the abstract, (b) show µB extracted from R_B12 and from R_Q12 as functions of the assumed Tf over at least 130–160 MeV, so that a reader can see whether the two channels track each other across the window or only meet near 145 MeV, and (c) state the residual channel-to-channel difference relative to the non-common uncertainty. This is a robustness demonstration using curves the authors already have, not new physics.
[Fig. 4 and the concluding paragraph] The band Tf = 144 ± 6 MeV is obtained from R_Q12/R_B12 under the assumption of a common temperature and chemical potential for charge and protons, and the text says so: 'The thermometer in Fig. 4 is, in fact, a consistency criterion'. It therefore cannot be used as independent support for the equilibrium/common-freeze-out hypothesis, yet the conclusion presents it alongside the R_B31 bound as if the two were separate handles on Tf ('Notice that this temperature range lies just below the upper limit that we determined independently in Fig. 1'). The word 'independently' is doing work it cannot bear, since the Fig. 4 number presupposes what Fig. 1 does not test. Please state the conditionality at the point where 144 ± 6 MeV is first quoted and in the conclusion, and say explicitly which observable, if any, could break the degeneracy between Tf and the common-µB assumption.
[p. 2, paragraph on net-proton versus net-baryon moments] The identification of measured net-proton cumulant ratios with lattice net-baryon fluctuations is load-bearing for the entire baryon column of Table I, and the numerical justification rests on Ref. [23], which is listed as an arXiv preprint (1402.1238) with an overlapping author. Refs. [21,22] supply the method (resonance feed-down, isospin randomization) but not the size of the residual difference. Since a percent-level shift in Mp/σp² propagates directly into the extracted µB, please quantify the residual (even a rough percentage for the relevant cumulant ratios) and indicate its effect on Table I, or cite a published quantification. If the residual is small compared with the Tf-window error this can be settled in a sentence; if it is not, it belongs in the error budget.

Minor objections (11)

[p. 2] Typo: 'pyhsical conditions' should read 'physical conditions'.
[Fig. 1] The vertical axis label is garbled ('RB31=SB mB3 / MB'); please replace it with a clean definition of R_B31.
[Fig. 3] The horizontal axis label reads '3s [GeV]' and should be '√s [GeV]'.
[Fig. 1 caption and surrounding text] The experimental band is formed by averaging the four highest energies, justified by the small curvature of the phase diagram near µB = 0. At √s = 27 GeV the chemical potential is of order 135 MeV, which is not small; please give a quantitative estimate of the residual µB-dependence of R_B31 beyond leading order, or restrict the average to the three highest energies and show that the bound is unchanged.
[Table I] The dash in the '27 GeV, from B' entry is explained only in the body text; add a one-clause note to the caption so the table is self-contained.
[Table I caption] The statement that the temperature-window uncertainty dominates the quoted errors should be made quantitative, e.g. by quoting the partial error from the Tf window separately from the lattice-statistics and experimental contributions.
[p. 2, isospin paragraph] Z/A = 0.4 is quoted for both Pb-Pb and Au-Au; the STAR data are Au-Au only (Z/A ≈ 0.395). Please state the value actually used and the sensitivity of the extracted µB to it.
[p. 3, R_B31 discussion] The two-sigma statement 'the highest possible Tf is 151 MeV' should be accompanied by a sentence on how it was obtained (which lattice and experimental uncertainties were combined, and in what way).
[Reference [29]] The efficiency-corrected c2/c1 net-proton data are cited only via a public web page; please give a dated or versioned reference so the comparison is reproducible.
[Reference [20]] 'S. DKatz' is missing a space and should read 'S. D. Katz'.
[Methods] The paper refers to Ref. [11] for simulation details. A brief statement here of the number of configurations and the continuum extrapolation procedure (the Nt values shown in Fig. 1) would make the manuscript self-contained for readers assessing the systematic error on the low-temperature end of the valid range.

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The paper

The paper claims

Comparing two independent fluctuation measurements from the STAR beam energy scan against continuum-extrapolated lattice QCD, the paper argues that net-proton and net-charge data give the same freeze-out temperature and baryon chemical潜在 —

The reading

The paper asks whether the conditions at which a heavy-ion fireball stops interacting chemically can be read off first-principles lattice QCD, and whether two different conserved charges give the same answer. The authors take continuum-extrapolated lattice results for fluctuations of baryon number and electric charge and match them, ratio by ratio, to STAR measurements of net-proton and net-charge multiplicity moments at the four highest beam energies ($27$, $39$, $62.4$ and $200$ GeV). The skewness ratio $R^{B}_{31}$ bounds the freeze-out temperature from above at roughly $148$ MeV, and the inverse width ratios $R^{B}_{12}$ and $R^{Q}_{12}$ then yield baryon chemical potentials of about $26$, $69$, $104$ and $135$ MeV as the collision energy falls. The point the authors are trying to establish is that these two chemical potentials, obtained from different quantum numbers, land on top of each other — which would mean the system really is close to thermal equilibrium at freeze-out and that lattice QCD can describe it. If that holds, the extracted potentials also match the curve long used by statistical hadronization models, closing a gap between two ways of characterising the same freeze-out curve.

What carries the argument

The machinery is the set of volume-independent ratios of conserved-charge susceptibilities, $chi_n / chi_m$, evaluated on the lattice at physical quark masses in the continuum limit and at chemical potentials constrained by two physical conditions: strangeness density vanishes, $langle n_S rangle = 0$, and electric charge tracks baryon number, $langle n_Q rangle = 0.4 langle n_B rangle$, matching the isospin asymmetry of gold or lead nuclei. The constraints are imposed by Taylor-expanding $mu_Q(T,mu_B)$ and $mu_S(T,mu_B)$ in $mu_B$ up to cubic order, which makes the ratios functions of $T$ and $mu_B$ alone. The load-bearing structural fact is that $R^{B}_{31}$ is, to leading order, independent of $mu_B$ while $R^{B}_{12}$ and $R^{Q}_{12}$ are linear in it — so the first serves as a thermometer and the latter two as separate chemical-potential readings from different charges. The ratio of ratios $R^{Q}_{12}/R^{B}_{12}$ removes the shared $mu_B$ dependence and leaves a monotonic function of temperature, which is why it can pin a band instead of only an upper limit.

Extended reading notes

Core claim

The central claim is a consistency result: freeze-out parameters extracted from baryon-number (net-proton) fluctuations and from electric-charge (net-charge) fluctuations agree. Concretely, the ratio $R^{B}_{31} = (Ssigma^3/M)_p$ measured by STAR sits below the lattice curve over the whole plotted temperature range, so only an upper bound follows, $T_f lesssim 148$ MeV (rising to $151$ MeV allowing a two-$\sigma$ excursion). Fixing the temperature inside $140$–$150$ MeV, the authors then read off $mu_B$ from $R^{B}_{12} = (M/sigma^2)_p$ and independently from $R^{Q}_{12} = (M/sigma^2)_Q$, obtaining $25.6 pm 2.4$ versus $22.6 pm 2.4$ MeV at $200$ GeV, $69 pm 5.7$ versus $65.9 pm 7.2$ MeV at $62.4$ GeV, $104 pm 10$ versus $100 pm 9$ MeV at $39$ GeV, and $134.5 pm 12.5$ MeV from charge alone at $27$ GeV, where the non-monotonic behaviour of $R^{B}_{12}$ above $mu_B approx 130$ MeV prevents a baryon-channel reading. Taking the assumption further, the authors form the ratio of ratios $R^{Q}_{12}/R^{B}_{12}$, in which the separate volume factors cancel, and find that it reproduces the data for $sqrt{s} geq 39$ GeV when $T_f = 144 pm 6$ MeV — a band rather than a bound, and one lying just below the skewness upper limit.

Load-bearing premise

The chemical potentials are not measured independently: they are read off after the freeze-out temperature has been fixed to the window $140$–$150$ MeV, so the agreement between the baryon and charge channels is established inside a shared assumed temperature and against a single lattice ensemble.

Editorial extensions

If this is right

The freeze-out temperature sits at or slightly below the crossover region that lattice calculations place between roughly $147$ and $157$ MeV, which is what one expects if chemical freeze-out happens just after the system has passed out of the quark-gluon phase.
Baryon chemical potentials of about $26$, $69$, $104$ and $135$ MeV for $200$, $62.4$, $39$ and $27$ GeV collisions fall on the curve obtained by fitting hadron yields in the statistical hadronization model, so two independent routes to the freeze-out curve now agree.
Because two different conserved charges give the same chemical potential, the equilibrium, grand-canonical description of the measured moments survives a check it had not previously faced.
The ratio of ratios $R^{Q}_{12}/R^{B}_{12}$ is proposed as the preferred thermometer for future work, since it needs only means and variances rather than skewness or kurtosis, which are harder to measure and harder to compute on the lattice.
The method gives a concrete procedure for assigning freeze-out parameters to any future beam-energy-scan dataset for which both net-proton and net-charge moments are published with efficiency corrections.

Reading between the lines

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

The consistency test is run inside a temperature window assumed in advance ($140$–$150$ MeV), and the table of chemical potentials states that this window dominates the quoted errors; a genuinely independent test would extract $T_f$ and $mu_B$ jointly from each charge channel and compare the resulting pairs, which the present data do not yet allow.
The baryon channel is measured as net protons, not net baryons; the identification rests on resonance feed-down and isospin-randomisation arguments made elsewhere, so any breakdown of that mapping at the lower beam energies would look like a failure of the equilibrium picture rather than of the mapping.
The $27$ GeV point, where only the charge channel yields a potential, is the natural place to look for a decisive test: a future efficiency-corrected net-proton measurement there that agrees with $134.5 pm 12.5$ MeV would extend the consistency check to the edge of the monotonic regime.
Because the ratio-of-ratios thermometer needs only first and second moments, it could be applied to published data from other experiments and other collision systems without new lattice input beyond what already exists.

Original abstract

Recent results for moments of multiplicity distributions of net-protons and net-electric charge from the STAR collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryo-chemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.

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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, 4,344 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.43 · human participants 0.02 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.90 · mentions code or data availability 0.02.

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

Recent results for moments of multiplicity distributions of net-protons and net-electric charge from the STAR collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryo-chemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recent results for moments of multiplicity distributions of net-protons and net-electric charge from the STAR collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest collaboration, with the purpose of extracting the freeze-out temperature and chemical potential.	contribution 0.78	0.69	0.06	asserted 0.84
s1	All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated.	method 1.00	0.40	0.02	asserted 0.99
s2	We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryo-chemical potential values corresponding to the four highest collision energies of the experimental beam energy scan.	result 0.99	0.92	0.17	hedged possibility 0.64
s3	Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found.	result 0.99	0.92	0.65	asserted 1.00
s4	The freeze-out chemical potentials are now in agreement with the statistical hadronization model.	interpretation 0.72	0.60	0.21	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.81 · evidence from analysis of existing data 0.90.

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

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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 3.** FIG. 3. Freeze-out chemical potential

Showing 2 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1403.4576 by the authors.

References

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hep-lat 2018-05 conditional novelty 5.0 of 10

Imaginary-chemical-potential lattice QCD at physical quark masses yields sixth-order conserved-charge fluctuations and cumulant ratios whose Taylor extrapolation qualitatively reproduces the STAR net-proton trend.
Higher order quark number fluctuations via imaginary chemical potentials in $N_f=2+1$ QCD
hep-lat 2016-11 conditional novelty 5.0 of 10

A global fit to lattice data at imaginary chemical potentials yields quark-number susceptibilities up to eighth order in Nf=2+1 QCD, quantifies when this beats direct simulation, and finds no convergence of radius-of-...
Fluctuations and correlations in high temperature QCD
hep-lat 2015-07 conditional novelty 5.0 of 10

Continuum-extrapolated lattice QCD shows the hadron resonance gas describes charge fluctuations below the crossover and three-loop hard thermal loop perturbation theory describes them above about 250 MeV.
Reaching percolation and conformal limits in neutron stars
nucl-th 2022-07 conditional novelty 4.0 of 10

Across an ensemble of neutron-star equations of state, the speed of sound peaks near the nucleon percolation density and falls to roughly the conformal value at the center of the most massive stars.
Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams
hep-ph 2018-12 accept novelty 4.0 of 10

A community planning report that sets the heavy-ion physics priorities for LHC Runs 3 and 4 and estimates the luminosity and detector performance needed to reach them.
Decoding the phase structure of QCD via particle production at high energy
nucl-th 2017-10 conditional novelty 4.0 of 10

Thermal fits to hadron yields in nuclear collisions yield a freeze-out temperature that tracks the lattice-QCD pseudo-critical line, which the authors read as an experimental determination of the QCD phase boundary.
Freeze-out conditions from net-proton and net-charge fluctuations at RHIC
hep-ph 2014-03 conditional novelty 4.0 of 10

Fitting hadron-resonance-gas susceptibility ratios to STAR net-charge and net-proton fluctuation data gives chemical freeze-out temperatures of 135 to 151 MeV and baryon chemical potentials of 24 to 327 MeV across six...
QCD at finite temperature and density within the fRG approach: An overview
hep-ph 2022-05 conditional novelty 2.0 of 10

Functional renormalization group and Dyson-Schwinger calculations place the QCD critical end point near baryon chemical potential 600 MeV and identify an inhomogeneous instability above about 420 MeV.
Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions
nucl-th 2020-01 accept novelty 2.0 of 10

The report argues that fluctuation observables can only be interpreted with a fully dynamical framework, and compares stochastic fluid dynamics, hydro-kinetics, and the experimental corrections each requires.
Lattice QCD and heavy ion collisions: a review of recent progress
hep-lat 2018-04 accept novelty 2.0 of 10

Lattice QCD, now run at physical quark masses in the continuum limit, reproduces heavy-ion freeze-out temperatures and the QCD equation of state, and this review documents where theory and data agree and where they st...
Properties of hot and dense matter from relativistic heavy ion collisions
nucl-th 2015-10 accept novelty 2.0 of 10

Collisions of heavy nuclei at RHIC and the LHC produce a locally thermalized, nearly perfect fluid whose equation of state, transport coefficients, and freeze-out conditions can be read off bulk observables.
Thermodynamics of strong-interaction matter from Lattice QCD
hep-lat 2015-04 accept novelty 2.0 of 10

First-principles lattice QCD fixes the crossover temperature of hot strong-interaction matter at 154 ± 9 MeV and its equation of state, with controlled but limited extensions to nonzero baryon density.

How later papers used it

78 later papers cite it

Evidence: substantial. 57 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 102 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

2 later papers by other authors are listed below: 2 compared their own results with it.

Compares with it 2 of 5 papers with this label

Illustrated its calculated relation between the baryon chemical potential and the collision center-of-mass energy, comparing it with lattice QCD simulations such as this paper and with model calculations.

Chemical Freeze-out Parameters via a Non-perturbative QCD Approach (2021) · 1.00 · paraphrased: the licence does not allow quoting
Reported that its own extracted baryon chemical potential and the values reported in this paper agree within stated uncertainties, with some tension at 27 GeV.

Measurement of higher cumulants of net-charge multiplicity distributions in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV (2015) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

69 arXiv papers cite this in 88 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 · 62 sentences without a confident label

Uses its method or tool 1 paper

In order to extract the chemical freeze-out temperature from the lattice we use ratios of susceptibilities as discussed in [ref] .

Strangeness at finite temperature from Lattice QCD · Introduction · 0.98

Uses its data or values 4 papers

We employ the freeze-out line in [ref] , consistent with that in [ref] .

Correlating the skewness and kurtosis of baryon number distributions · Skewness and kurtosis of the baryon number distribution · 0.99
In this case the double ratio $R_12^Q/R_12^B$ constrains the freeze out temperature to within $T_f=144±6$ [ref] .

Properties of hot and dense matter from relativistic heavy ion collisions · Freeze-out conditions · 0.93
From the latest lattice [ref] and HRG analyses [ref] using the STAR net-charge and net-proton results for central Au+Au collisions at 7.7 to 200 GeV, the extracted freeze-out temperatures range from 135 to 151 MeV and values range from 326 to 23 MeV.

Beam energy dependence of moments of the net-charge multiplicity distributions in Au+Au collisions at RHIC · Introduction · 0.81

Compares with it 4 papers

The freeze-out conditions obtained in the analysis [ref] are shown in Fig. [ref] (left panel) together with other results found from SHM fits [ref] and in the recent lattice QCD study [ref] .

Determination of freeze-out conditions from fluctuation observables measured at RHIC · Freeze-out conditions from net-electric charge and net-proton fluctuations · 0.99
It is evident that our results agree with the lattice QCD results [ref] qualitatively very well.

Chemical Freeze-out Parameters via a Non-perturbative QCD Approach · Freeze-out Parameters · 1.00
The latter also agrees with the freeze-out temperature [ref] .

Correlating the skewness and kurtosis of baryon number distributions · Skewness and kurtosis of the baryon number distribution · 0.80

Cites it as support 2 papers

Now, first-principles calculations of thermodynamic fluctuations in QCD give results in agreement with a hadron gas [ref] in the relevant temperature range.

Cumulants of conserved charges in hydrodynamic simulations · Introduction · 0.97
Indeed, there have been indications that equilibrium lattice QCD susceptibilities cannot account for the moments of net-proton multiplicity distributions at low energy [ref] , which may be a hint that the low-energy heavy ion collision at higher chemical potential is not really a thermodynamic equilibrium process.

Octet meson spectra and chiral phase diagram in the improved soft-wall AdS/QCD model · Conclusion and remarks · 0.96

Cites it as background 13 papers

In recent year, the QCD equation of state (EoS), fluctuations and correlations of conserved charges, etc. have been computed and studied systematically in lattice QCD at finite chemical potential, see e.g. [ref] .

Baryon number fluctuations in the 2+1 flavor low energy effective model · Introduction · 0.98
In the past several years the fluctuations and correlations of conserved charges have been studied on the lattice using stout and highly improved staggered quark (HISQ) actions, and physical quark masses [ref] .

Hadron Resonance Gas with Repulsive Interactions and Fluctuations of Conserved Charges · Introduction · 0.93
In theoretical aspects, the freeze-out conditions have been studied in Dyson-Schwinger equations (DSE) approach [ref] , functional renormalization group (FRG) approach [ref] , lattice QCD simulations [ref] , statistical hadronization models [ref] and other models [ref] .

Chemical freeze-out parameters via functional renormalization group approach · introduction · 0.95

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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