THERMUS -- A Thermal Model Package for ROOT

J. Cleymans; M. Hauer; S. Wheaton

REVIEW

THERMUS -- A Thermal Model Package for ROOT

S. Wheaton, J. Cleymans, M. Hauer

High Energy Physics - Phenomenology · Submitted 15 Jul 2004 · 61 references

Pith's verdict: A solid, honestly documented tool paper whose headline feature — per-yield decay chains and efficiencies — is asserted but never actually exercised in the worked example.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0407174 (version 2)

Pith IDGSIXOFGL, Pith's permanent record of this paper and its review

CitationJ. Cleymans, M. Hauer, S. Wheaton. "THERMUS -- A Thermal Model Package for ROOT." arXiv:hep-ph/0407174 (2004). https://pith.science/paper/GSIXOFGL

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

THERMUS is a real, useful piece of software, and this is its manual. Judge it as a tool paper: the physics is imported wholesale from cited sources (Keränen–Becattini for the canonical partition function, Braun-Munzinger et al. for the Z_S reduction, Cleymans et al. for the two-volume scheme), and the authors say so. What is new is the engine: three ensembles in one ROOT-integrated package, per-yield decay chains and per-channel efficiencies, Broyden constraint solving, and a shipped default particle list with 195 decay files. The documentation is genuinely good — class-by-class, with real interactive sessions and their output, and honest about what does not work (the incomplete TDatabasePDG path, Boltzmann-only canonical and strangeness-canonical ensembles, no charm constraining). That honesty counts in the authors' favour and I would not hold those disclosures against them. The stress-test note lands, and it is the sharpest thing to say about the paper. The abstract leads with decay chains and detector efficiencies specific to each yield, and the sole worked fit (§3.9.5) never calls SetPartSet or SetDecayEfficiency: fourteen yields, several sharing the same particle pair, all riding the base set. §3.9.2 says GenerateYields builds one model from the base set and then iterates the yield list 'calculating their specific decay contributions', but never states how fSet1/fSet2 enter or how a yield's own decay lists reach GenerateDecayPartDens. And §3.3.3 warns that UpdateDecaySummary or GenerateBRatios wipes efficiency assignments; since GenerateParticleDens relies on the summary lists, whether an efficiency assigned before a fit survives the fit path is left unstated. That is a correctness question about the feature the abstract leads with, not merely a missing benchmark. Second, and related: nothing is validated against measured yields. The only fit uses explicitly fictitious ratios. One comparison to a published set of ratios would have settled whether the implementation reproduces the cited formalisms. Minor: the Numerical Recipes dependency requires a purchase, and there is no archival identifier or commit hash for version 2.1. None of this is fatal; the fixes are documentation-level. Send it to referees — it deserves them — and cite it if you do thermal fits.

Referee report

Significance

A well-documented, ROOT-integrated implementation of the statistical-thermal model is genuinely useful to the heavy-ion community, and the class structure described here is sensible: the separation of particle properties, parameter sets, thermal particles, thermal models and fits maps cleanly onto how such analyses are actually done, and the decision to inherit from TObject so that everything is reachable from CINT is a real practical advantage over stand-alone codes. The three-ensemble coverage, including the mixed-canonical treatment that is mandatory at SIS energies, and the inclusion of width, quantum statistics and excluded volume in one package are substantive. The paper also does the community a service by documenting the default inputs (particle list, decay files, branching-ratio rescaling) explicitly enough that a user can see what physics is and is not in the box. What is missing is evidence that the implementation reproduces known results: the manuscript is a careful description of a tool whose scientific output is never checked against measurement or against an independent code.

Major objections (4)

[Abstract (abstract:s2) versus §3.8 and §3.3.3] The abstract states that THERMUS 'allows for the assignment of decay chains and detector efficiencies specific to each particle yield'. The decay-chain half is supported by the fSet1/fSet2 members of TTMYield (§3.8), but the efficiency half is not: the TTMYield data members listed in §3.8 (fName, fID1, fID2, fFit, fSet1, fSet2, fExpValue, fExpError, fModelValue, fModelError) contain no efficiency field, and the only efficiency mechanism described anywhere is TTMParticleSet::SetDecayEfficiency (§3.3.3), which acts on a parent-to-daughter decay within a particle set, not on a yield. Worse, §3.3.3 states that 'running UpdateDecaySummary or GenerateBRatios will remove any such changes', and §3.7.1 states that GenerateParticleDens uses the summary decay lists, so an efficiency assigned before a fit may not survive the fit path at all. Either the per-yield efficiency mechanism should be described and demonstrated (with an explicit statement of where in the GenerateYields call chain it is applied and why it is not overwritten), or the abstract claim should be reduced to what the code actually provides.
[§3.9.5] The only worked fit in the paper is explicitly to 'fictitious particle ratios', and no comparison is made anywhere against measured yields, against a published thermal-model fit, or against an independent code such as SHARE [6,7]. For a program paper this is the central missing piece of evidence: the reader is asked to trust that the implementation of Eq. (10), Eq. (26) and the correction factors reproduces the cited formalisms, but nothing in the manuscript tests that. A single fit to published RHIC or SPS yields, showing that the extracted (T, mu_B) agree with the values already in the literature, would settle the question at modest cost; a comparison of primordial densities or correction factors against an independent implementation at one benchmark parameter point would settle it even more directly. As it stands the paper documents an interface thoroughly but does not demonstrate that the physics engine behind it is correct.
[§3.9.2] The mechanism by which per-yield particle sets enter the calculation is left unspecified. Section 3.9.2 says GenerateYields builds one TTMThermalModel from the base particle set and then 'iterates through the list of TTMYield objects, calculating their specific decay contributions', but it never states that a separate thermal model is constructed from fSet1/fSet2 for each yield, nor how a yield's own decay summary lists enter GenerateDecayPartDens. This matters for both correctness and cost: rebuilding a full model per yield is a very different proposition from re-weighting the base-set decay contributions, and the reader cannot tell which is done. The worked example in §3.9.5 compounds the problem, since it lists fourteen yields, several sharing the same particle-antiparticle pair with different descriptors, yet never calls SetPartSet or SetDecayEfficiency; every yield therefore uses the base set, and the feature that distinguishes THERMUS from other thermal-model codes is asserted rather than shown. Please state the algorithm explicitly and add a worked example in which at least two yields carry genuinely different decay chains.
[§3.7.10 and §4] The constraint machinery is load-bearing for the grand-canonical and mixed-canonical results, but its numerical behaviour is undocumented. Section 3.7.10 describes the normalisation of the constraint equations and the special handling of the zero-strangeness case, but says nothing about the convergence tolerance actually used (TOLF), the iteration limit, what the int-returning functions GenerateParticleDens, ConstrainEoverN, ConstrainTotalBaryonDensity and ConstrainSoverT3 return on failure, or what the model does when Broyden does not converge. Since the constrained chemical potentials feed directly into every density, a statement of the achieved residual and a demonstration that the constraints are satisfied to a stated accuracy in the worked example would be appropriate. Relatedly, the dependence on Numerical Recipes means that a user must purchase the routines in order to reproduce any constrained result; a free-software alternative for the nonlinear solve (or a note that the interface is solver-agnostic) would materially improve the reproducibility of the published numbers.

Minor objections (8)

[Eqs. (39) and (40)] The quantity returned by GetQuadDev is defined as (Model Value - Exp. Value)/Model Value, which is a fractional deviation, not a quadratic one; the name is misleading, particularly since FitData(1) is described as performing a 'quadratic deviation fit'. Please rename or state explicitly that the fit minimises the sum of squares of this fractional deviation.
[§3.7.11] The Wroblewski factor is printed as 'lambda_S = 2 < s sbar >< u ubar > + < d dbar >', which as typeset is dimensionally wrong and omits the division and grouping. The intended definition, consistent with the bullet list that follows, is lambda_S = 2 <s sbar>/(<u ubar> + <d dbar>); please correct the displayed equation.
[Eq. (32)] The proper volume is given as nu_i = 4 (4/3 pi r_i^3) without explanation of the factor 4. If this is the van der Waals convention b = 4v, say so; if it is a free choice, state that and note the sensitivity of the excluded-volume results to it.
[§2.1.1, Eq. (9) versus §3.7.3, Eq. (38)] The Bose-Einstein condensation condition is stated first as exp[beta(m_i - mu_i)] <= 1 and later, with the gamma factors included, as exp[(m_i - mu_i)/T] > gamma_S^{|S_i|} gamma_C^{|C_i|}. The first form is a special case of the second; please cross-reference them so that a reader does not take Eq. (9) as the general condition.
[Program Summary and §4] The Program Summary leaves 'Catalogue identifier' and 'Journal Reference' blank, and §4 instructs the user to 'Download the THERMUS source' without giving a URL, a repository, or a licence. Since the manuscript documents version 2.1, please also state which release the described features (excluded volume, percolation constraint, charm parameters) are present in, and reconcile the header date of 1 January 2014 with the arXiv v2 date of 15 August 2008.
[Program Summary, 'Running time'] The statement that run-times vary 'from seconds to several minutes' is too vague to be useful. A concrete benchmark (particle-set size, ensemble, number of fit parameters, machine) would let a prospective user judge whether the package suits their analysis.
[§2.1.1] The quantitative claim that quantum statistics shift pions by about 10% and kaons by 1-2% rests on Ref. [37], a PhD thesis. Since this is the argument used to justify the Boltzmann approximation elsewhere in the paper, a journal-level reference or a short table of the deviations at a representative freeze-out point would strengthen it.
[§3.3.1 and §3.3.2] The text recommends against the TDatabasePDG constructor because the default pdg_table.txt lacks charm, degeneracy, threshold, strangeness and width, and marks all particles stable. Given that the constructor is nevertheless part of the public interface, a one-line runtime warning when it is used would be more effective than a caveat in the paper.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A ROOT toolkit computes thermal-model particle yields in three statistical ensembles.

The reading

THERMUS is a C++ package that puts statistical-thermal-model calculations of particle production inside ROOT, the analysis framework used across heavy-ion physics. Its aim is to let a user start from a particle list and a set of thermal parameters, compute primordial densities and the feed-down from resonance decays, and then fit the thermal parameters to measured yields or ratios. The package implements three treatments of the conserved charges: grand-canonical baryon number, strangeness and charge; fully canonical conservation of all three; and a mixed case with strangeness conserved canonically while baryon number and charge remain grand-canonical. It also lets each experimental yield carry its own decay chain and detector efficiency, so feed-down corrections can match a particular data set. The paper's worked fit uses explicitly fictitious ratios, so the demonstration is of the workflow and the implementation of cited formalisms rather than a new comparison with measured data.

What carries the argument

The load-bearing mechanism is the ensemble-specific correction factor: in the canonical and strangeness-canonical treatments, the Boltzmann-approximation density, energy density and pressure of a species are the grand-canonical values with the canonically conserved chemical potential set to zero, multiplied by a factor such as $Z_{B-B_i,S-S_i,Q-Q_i}/Z_{B,S,Q}$ or $Z_{S-S_i}/Z_S$. THERMUS computes those factors, stores them in ensemble-specific thermal-model classes, and uses them to populate a hash table of densities keyed by PDG ID. Around that core it wraps particle and decay bookkeeping, a Broyden solver for constraints, and TMinuit for fits, with each yield able to point to its own particle set and decay chain.

Extended reading notes

Core claim

The paper's central claim is that a single ROOT-integrated package can carry out the full chain of a statistical-thermal analysis: define a hadron-resonance gas, choose an ensemble, compute primordial particle, energy, entropy densities and pressure, add resonance-decay contributions to stable particles, impose constraints such as $B/2Q$, strangeness or $E/N$, and fit thermal parameters to experimental yields with the ROOT implementation of MINUIT. The package is organised as a hierarchy of classes for particles, particle sets, parameter sets, thermal particles, thermal models and thermal fits, with ensemble-specific subclasses. Its practical contribution is not a new thermal-model formula but the assembly of the cited formulas into a reusable, interactive tool with per-yield decay chains and efficiency settings.

Load-bearing premise

The implementation reproduces the cited canonical and strangeness-canonical formalisms correctly, and the shipped default particle list, mass cutoff and rescaled branching ratios are adequate; the paper does not benchmark the package against measured yields, using fictitious ratios in its worked fit.

Editorial extensions

If this is right

A user can go from a particle list and trial thermal parameters to primordial densities, decay feed-down and fitted freeze-out parameters without leaving ROOT.
The same code base can treat high-energy collisions grand-canonically and low-energy collisions with strangeness treated canonically, so ensemble choices become a switch rather than a separate code.
Constraints on $B/2Q$, strangeness, $E/N$, total baryon density or $s/T^3$ can be imposed self-consistently while fitting, which makes the thermal parameters satisfy the collision's conservation conditions.
Quantum statistics, resonance width and excluded-volume corrections can be toggled, allowing systematic studies of how each effect changes the extracted parameters.
Per-yield decay chains and efficiencies let the model match the feed-down corrections of a specific experimental data set rather than a single universal chain.

Reading between the lines

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

If the package reproduces published fits, it could become a common baseline for comparing thermal-model results across experiments, provided the particle-list version and decay files are recorded with each fit.
The per-yield decay-chain machinery could be extended to propagate branching-ratio and efficiency uncertainties into the fitted parameters; the paper does not quantify that error budget.
A direct validation would be to recompute the canonical correction factors independently, for example by numerical integration of the partition-function integrals, and compare them with THERMUS across a grid of $T$, volume and chemical potentials.
Because the data structures already allow charm and beauty quantum numbers, extending the default particle list to charmed hadrons would let the same workflow test $\gamma_C$ at collider energies, although that extension is not demonstrated here.

Original abstract

THERMUS is a package of C++ classes and functions allowing statistical-thermal model analyses of particle production in relativistic heavy-ion collisions to be performed within the ROOT framework of analysis. Calculations are possible within three statistical ensembles; a grand-canonical treatment of the conserved charges B, S and Q, a fully canonical treatment of the conserved charges, and a mixed-canonical ensemble combining a canonical treatment of strangeness with a grand-canonical treatment of baryon number and electric charge. THERMUS allows for the assignment of decay chains and detector efficiencies specific to each particle yield, which enables sensible fitting of model parameters to experimental data.

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, 3,063 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.23.

The abstract, sentence by sentence

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

THERMUS is a package of C++ classes and functions allowing statistical-thermal model analyses of particle production in relativistic heavy-ion collisions to be performed within the ROOT framework of analysis. Calculations are possible within three statistical ensembles; a grand-canonical treatment of the conserved charges B, S and Q, a fully canonical treatment of the conserved charges, and a mixed-canonical ensemble combining a canonical treatment of strangeness with a grand-canonical treatment of baryon number and electric charge. THERMUS allows for the assignment of decay chains and detector efficiencies specific to each particle yield, which enables sensible fitting of model parameters to experimental data.

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	THERMUS is a package of C++ classes and functions allowing statistical-thermal model analyses of particle production in relativistic heavy-ion collisions to be performed within the ROOT framework of analysis.	contribution 0.97	0.53	0.19	asserted 1.00
s1	Calculations are possible within three statistical ensembles; a grand-canonical treatment of the conserved charges B, S and Q, a fully canonical treatment of the conserved charges, and a mixed-canonical ensemble combining a canonical treatment of strangeness with a grand-canonical treatment of baryon number and electric charge.	method 0.85	0.45	0.07	hedged possibility 0.59
s2	THERMUS allows for the assignment of decay chains and detector efficiencies specific to each particle yield, which enables sensible fitting of model parameters to experimental data.	method 0.64	0.51	0.15	asserted 0.98

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.76.

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.** The energy dependence of the decay contribution to th

**Figure 2.** The basic structure of THERMUS (only the most fundame

**Figure 3.** The mass distribution of the resonances included in

Figures reproduced from arXiv:hep-ph/0407174 by the authors.

References

Works cited (61)

[1]

A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys . A772 (2006) 167

View on Pith 2006
[2]

J. Cleymans, H. Oeschler, K. Redlich, S. Wheaton, Phys. R ev. C73 (2006) 034905

View on Pith 2006
[3]

F. Becattini, J. Manninen, M. Gazdzicki, Phys. Rev. C73 ( 2006) 044905

View on Pith 2006
[4]

For a recent review see F. Becattini, plenary talk presen ted at Quark Matter 2008, Jaipur, India, Feb 4 - 10, 2008

View on Pith 2008
[5]

P. Braun-Munzinger, K. Redlich, J. Stachel, nucl-th/03 04013 and in Quark Gluon Plasma 3, eds. R.C. Hwa and X.N. Wang, (World Scientiﬁc Publishing, 2004)

View on Pith 2004
[6]

G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J . Letessier, J. Rafelski, Comput. Phys. Commun. 167 (2005) 229. 49

View on Pith 2005
[7]

G. Torrieri, S. Jeon, J. Letessier, J. Rafelski, Comput. Phys. Commun. 175 (2006) 635

View on Pith 2006
[8]

A. Kisiel, T. Talu´ c, W. Broniowski, W. Florkowski, Comp ut. Phys. Commun. 174 (2006) 669

View on Pith 2006
[9]

R. Brun and F. Rademakers, Nucl. Inst. & Meth. in Phys. Res . A 389 (1997) 81. See also http://root.cern.ch/

View on Pith 1997
[10]

J. Cleymans, I. Kraus, H. Oeschler, K. Redlich and S. Whe aton, Phys. Rev. C 74 (2006) 034903

View on Pith 2006
[11]

I. Kraus, J. Cleymans, H. Oeschler, K. Redlich and S. Whe aton, J. Phys. G 32 (2006) S495

View on Pith 2006
[12]

H. Caines, J. Phys. G 32 (2006) S171

View on Pith 2006
[13]

L.A. Stiles and M. Murray, nucl-ex/0601039

View on Pith Pith review arXiv
[14]

J. Takahashi (for the STAR Collaboration), nucl-ex/07 11.2273

View on Pith
[15]

M. Murray (for the BRAHMS Collaboration), nucl-ex/071 0.4576

View on Pith
[16]

M.I. Gorenstein, M. Hauer, O.N. Moroz, nucl-th/0708.0 137

View on Pith
[17]

R. Witt, J. Phys. G 34 (2007) S921

View on Pith 2007
[18]

B. Hippolyte, Eur. Phys. J. C49 (2007) 121

View on Pith 2007
[19]

J. Cleymans, R. Sahoo, D.P. Mahapatra, D.K. Srivastava and S. Wheaton, Phys. Lett. B660 (2008) 172

View on Pith 2008
[20]

M. Hauer, V.V. Begun and M.I. Gorenstein, nucl-th/0706 .3290

View on Pith
[21]

M.I. Gorenstein, M. Hauer, D.O. Nikolajenko, Phys. Rev . C 76 (2007) 024901

View on Pith 2007
[22]

V.V. Begun, M. Ga´ zdzicki, M.I. Gorenstein, M. Hauer, V .P. Konchakovski and B. Lungwitz, Phys. Rev. C 76 (2007) 024902

View on Pith 2007
[23]

F. Becattini, Z. Phys. C 69 (1996) 485

View on Pith 1996
[24]

F. Becattini and U. Heinz, Z. Phys. C 76 (1997) 269

View on Pith 1997
[25]

J. Cleymans, D. Elliott, A. Ker¨ anen and E. Suhonen, Phy s. Rev. C 57 (1998) 3319

View on Pith 1998
[26]

K. Redlich, J. Cleymans, H. Oeschler and A. Tounsi, Acta Physica Polonica B33 (2002) 1609

View on Pith 2002
[27]

F. Becattini, J. Cleymans, A. Ker¨ anen, E. Suhonen, K. R edlich, Phys. Rev. C 64 (2001) 024901

View on Pith 2001
[28]

P. Braun-Munzinger, I. Heppe, J. Stachel, Phys. Lett. B465 (1999) 15

View on Pith 1999
[29]

P. Braun-Munzinger et al. , Phys. Lett. B344 (1995) 43, ibid. B365 (1996) 1. 50

View on Pith 1995
[30]

P. Braun-Munzinger, D. Magestro, K. Redlich and J. Stac hel, Phys. Lett. B518 (2001) 41

View on Pith 2001
[31]

J. Sollfrank, J. Phys. G: Nucl. Part. Phys. 23 (1997) 1903

View on Pith 1997
[32]

W. Broniowski and W. Florkowski, Phys. Rev. C 65 (2002) 064905

View on Pith 2002
[33]

W. Florkowski, W. Broniowski and M. Michalec, Acta Phys ica Polonica B33 (2002) 761

View on Pith 2002
[34]

N. Xu and M. Kaneta, Nucl. Phys. A698 (2002) 306c

View on Pith 2002
[35]

M. Kaneta (for the NA44 Collaboration), J. Phys. G: Nucl . Part. Phys. 23 (1997) 1865; M. Kaneta and N. Xu, J. Phys. G: Nucl. Part. Phys. 27 (2001) 589

View on Pith 1997
[36]

J. Cleymans and K. Redlich, Phys. Rev. Lett. 81 (1998) 5284; J. Cleymans and K. Redlich, Phys. Rev. C 60 (1999) 054908

View on Pith 1998
[37]

S. Wheaton, ”The Development and Application of THERMU S- a Statistical- Thermal Model Analysis Package for ROOT”, Ph.D. dissertati on, University of Cape Town, Cape Town, South Africa, 2005

View on Pith 2005
[38]

A. Ker¨ anen and F. Becattini, nucl-th/0112021

View on Pith Pith review arXiv
[39]

P. Braun-Munzinger, J. Cleymans, H. Oeschler and K. Red lich, Nucl. Phys. A697 (2002) 902

View on Pith 2002
[40]

J. Cleymans, H. Oeschler and K. Redlich, Phys. Lett. B485 (2000) 27; K. Redlich, S. Hamieh and A. Tounsi, J. Phys. G: Nucl. Part. Ph ys. 27 (2001) 413

View on Pith 2000
[41]

J. Cleymans, H. Oeschler and K. Redlich, Phys. Rev. C 59 (1999) 1663

View on Pith 1999
[42]

J. Sollfrank, P. Koch and U. Heinz, Z. Phys. C 52 (1991) 593

View on Pith 1991
[43]

M. Kaneta and N. Xu, nucl-th/0405068

View on Pith Pith review arXiv
[44]

J. Cleymans, B. K¨ ampfer, M. Kaneta, S. Wheaton and N. Xu , Phys. Rev. C 71 (2005) 054901

View on Pith 2005
[45]

F. Becattini, M. Ga´ zdzicki and J. Sollfrank, Eur. Phys . J. C 5 (1998) 143

View on Pith 1998
[46]

J. Rafelski, Phys. Lett. B262 (1991) 333; P. Koch, B. M¨ uller, J. Rafelski, Phys. Rep. 142 (1986) 167

View on Pith 1991
[47]

J. Letessier, J. Rafelski, A. Tounsi, Phys. Rev. C 50 (1994) 405; C. Slotta, J. Sollfrank, U. Heinz, AIP Conf. Proc. (Woodbury ) 340 (1995) 462

View on Pith 1994
[48]

F. Becattini, M. Ga´ zdzicki, A. Ker¨ anen, J. Manninen and R. Stock, Phys. Rev. C 69 (2004) 024905

View on Pith 2004
[49]

I.G. Bearden et al. (NA44), Phys. Rev. C 66 (2002) 044907. 51

View on Pith 2002
[50]

J. Cleymans, B. K¨ ampfer and S. Wheaton, Phys. Rev. C 65 (2002) 027901, nucl-th/0110035

View on Pith Pith review arXiv 2002
[51]

J. Cleymans, B. K¨ ampfer and S. Wheaton, Nucl. Phys. A715 (2003) 553c, hep-ph/0208247

View on Pith Pith review arXiv 2003
[52]

J. Cleymans, B. K¨ ampfer, P. Steinberg and S. Wheaton, J . Phys. G: Nucl. Part. Phys. 30 (2004) S595, hep-ph/0311020

View on Pith Pith review arXiv 2004
[53]

J. Lettesier and J. Rafelski, Phys. Rev. C 59 (1999) 947

View on Pith 1999
[54]

G.D. Yen, M.I. Gorenstein, W. Greiner and S.N. Yang, Phy s. Rev. C 56 (1997) 2210

View on Pith 1997
[55]

D.H. Rischke, M.I. Gorenstein, H. St¨ ocker and W. Grein er, Z. Phys. C 51 (1991) 485

View on Pith 1991
[56]

J. Cleymans, M.I. Gorenstein, J. Stalnacke and E. Suhon en, Phys. Scr. 48 (1993) 277

View on Pith 1993
[57]

K. Hagiwara et al. , Phys. Rev. D 66 (2002) 010001

View on Pith 2002
[58]

T. Sj¨ ostrand et al. , Comput. Phys. Commun. 135 (2001) 238

View on Pith 2001
[59]

V. Magas, H. Satz, Eur. Phys. J. C 32 (2003) 115

View on Pith 2003
[60]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flan nery, Numerical Recipes in C: The Art of Scientiﬁc Computing (Cambridge Univ ersity Press, Cambridge, 2002)

View on Pith 2002
[61]

K. Wr` oblewski, Acta Physica Polonica B16 (1985) 379. 52

View on Pith 1985

Forward citations

Cited by 24 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On the equation of state of U(1) lattice gauge theory in three dimensions
hep-lat 2025-01 conditional novelty 6.0 of 10

The equation of state of 3D U(1) lattice gauge theory is consistent with a single massive state below T_c and a free photon gas above T_c, with no Hagedorn tower of states.
Chemical freeze-out systematics of thermal model analysis using hadron yield ratios
hep-ph 2020-09 conditional novelty 6.0 of 10

Exhaustive enumeration of independent hadron yield ratio sets gives freeze-out temperature systematic uncertainties of about 3 MeV at both RHIC 200 GeV and LHC 2.76 TeV.
Global polarization of $\Lambda$ and $\overline{\Lambda}$ hyperons in Pb-Pb collisions at the LHC
nucl-ex 2019-09 accept novelty 6.0 of 10

Global polarization of Lambda and anti-Lambda hyperons in Pb-Pb collisions at 2.76 and 5.02 TeV is consistent with zero, with an average of about 0.01 percent plus or minus 0.06 percent statistical uncertainty.
Entropy production in pp and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
hep-ph 2019-08 conditional novelty 6.0 of 10

From LHC data on particle spectra and femtoscopic radii, the entropy per unit rapidity is determined for pp and Pb-Pb collisions, and simulations trace about 95% of that entropy to the first fm/c.
Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV
nucl-ex 2019-08 accept novelty 6.0 of 10

Strange hadron yields in 13 TeV pp collisions rise faster than charged-particle multiplicity, increasingly so with strangeness content, and appear to scale with midrapidity multiplicity across energies.

Show 19 more citing papers

Measurements of Strange Particle Production in $p+p$ Collisions at $\sqrt{s}$= 200 GeV
nucl-ex 2006-07 conditional novelty 6.0 of 10

STAR reports strange hadron spectra and yields in 200 GeV p+p collisions, observing a breakdown of transverse-mass scaling and a baryon-meson shape difference, and inferring gluon-jet dominance.
More uses for Thermal Models
hep-ph 2026-02 unverdicted novelty 5.0 of 10

Combinations of particle yields enable parameter-free tests of thermal models and extraction of μ_B/T, μ_S/T, μ_Q/T from RHIC BES data, matching published parameters and allowing predictions for other particles and nuclei.
Deconfining Phase Boundary of Rapidly Rotating Hot and Dense Matter and Analysis of Moment of Inertia
hep-ph 2021-01 conditional novelty 5.0 of 10

In a rotating hadron resonance gas model, the deconfinement temperature falls as angular velocity rises, mirroring the effect of baryon chemical potential.
Multiplicity dependence of light nuclei production at LHC energies in the canonical statistical model
hep-ph 2018-08 conditional novelty 5.0 of 10

Canonical suppression of multi-baryon light nuclei, computed with exact conservation of baryon number, charge and strangeness, reproduces the observed monotonic rise and saturation of light-nucleus-to-proton ratios wi...
Testing coalescence and statistical-thermal production scenarios for (anti-)(hyper-)nuclei and exotic QCD objects at energies available at the CERN Large Hadron Collider
hep-ph 2018-07 conditional novelty 5.0 of 10

Coalescence and thermal-statistical models predict similar yields for deuterons and helium-3 but differ by up to two orders of magnitude for the hypertriton, offering an experimental discriminant.
Finite resonance widths influence the thermal-model description of hadron yields
nucl-th 2018-07 accept novelty 5.0 of 10

Giving broad hadronic resonances energy-dependent Breit-Wigner widths suppresses Delta feeddown into protons and improves the thermal-model fit to ALICE Pb-Pb hadron yields, partially resolving the proton anomaly.
Production of $^{4}$He and $^{4}\overline{\textrm{He}}$ in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV at the LHC
nucl-ex 2017-10 conditional novelty 5.0 of 10

ALICE measures the rapidity densities of 4He and 4He-bar in central Pb-Pb collisions at 2.76 TeV and finds them consistent with a 156 MeV statistical thermal model.
Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential
hep-ph 2017-08 conditional novelty 5.0 of 10

A hadron resonance gas with a single baryon excluded-volume parameter of about 1 fm^3 reproduces the first four Fourier coefficients of the lattice net-baryon density at imaginary chemical potential up to T approximat...
Measurement of transverse energy at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV
nucl-ex 2016-03 accept novelty 5.0 of 10

ALICE reports dET/deta = 1737 +/- 6 (stat) +/- 97 (sys) GeV in 0-5% central Pb-Pb collisions at 2.76 TeV, implying an energy density roughly 2.3 times that of central Au-Au collisions at RHIC.
THERMINATOR 2: THERMal heavy IoN generATOR 2
nucl-th 2011-02 conditional novelty 5.0 of 10

THERMINATOR 2 packages statistical hadronization on arbitrary freeze-out hypersurfaces into a shipped C++/ROOT Monte Carlo generator with a femtoscopy module and analysis scripts.
Thermal hadron production in relativistic nuclear collisions: the hadron mass spectrum, the horn, and the QCD phase transition
nucl-th 2008-12 conditional novelty 5.0 of 10

Adding high-mass resonances and the sigma meson to the thermal model reproduces the K+/pi+ horn at SPS energies, which the authors interpret as evidence linking the horn to the QCD phase transition.
SHAREv2: fluctuations and a comprehensive treatment of decay feed-down
nucl-th 2006-03 conditional novelty 5.0 of 10

SHAREv2 is a released Fortran package that computes and fits particle yields, ratios, and event-by-event fluctuations in the statistical hadronization model, with flexible decay feed-down handling.
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.
Antimatter production in proton-proton and heavy-ion collisions at ultrarelativistic energies
hep-ph 2011-05 conditional novelty 4.0 of 10

Fitting one baryochemical-potential curve to proton-proton data lets a thermal model reproduce measured antiproton/proton ratios and generate antihypernuclei predictions for the LHC.
Hadron production in central nucleus-nucleus collisions at chemical freeze-out
nucl-th 2005-11 conditional novelty 4.0 of 10

Fitting a thermal model to hadron yield ratios from 2.7 to 200 GeV produces a chemical freeze-out curve in the temperature versus baryon chemical potential plane that meets the lattice QCD phase boundary near 40 AGeV ...
Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions
hep-ph 2005-11 conditional novelty 4.0 of 10

A systematic comparison of four chemical freeze-out criteria in heavy-ion collisions finds that fixed energy per particle (about 1.08 GeV) is the most robust unified condition, especially at low beam energies.
Light nucleus and hypernucleus production at RHIC and LHC energies: a comparative study of phenomenological models
nucl-th 2026-11 conditional novelty 3.0 of 10

A community task-force review concludes that statistical hadronization, coalescence, and transport models each reproduce parts of the light-nucleus data, but existing measurements cannot yet distinguish them.
Hadron yields and the phase diagram of strongly interacting matter
nucl-ex 2014-08 accept novelty 1.0 of 10

Thermal models still describe hadron yields from 2.5 GeV to 5 TeV, but the LHC proton-to-pion ratio and the p-Pb multistrange yields remain unexplained, with four competing mechanisms spanning freeze-out temperatures ...
The equation of state for neutron stars
nucl-th 2026-07 unverdicted

A textbook-style review of the neutron-star equation of state covering the models, experimental and observational constraints, and open questions, with no new result claimed or derived.

How later papers used it

62 later papers cite it

Evidence: substantial. 57 of the citing papers share no author with it, and 28 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 88 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

9 later papers by other authors are listed below: 9 used its method or tool. 3 more papers by the same authors are listed: 3 used its method or tool.

Uses its method or tool 12 of 25 papers with this label · 3 by the same authors

Obtained its proton and antiproton results using the THERMUS code.

More uses for Thermal Models (2026) · 0.99 · paraphrased: the licence does not allow quoting
Did all its fits using the THERMUS thermal code with particle ratios calculated from mid-rapidity yields.

Energy and System Size Dependence of Strangeness Production from SPS to RHIC (2007) · 1.00 · paraphrased: the licence does not allow quoting
Used the THERMUS package to include the contribution from resonance decays, with the chemical freeze-out temperature and baryon chemical potential determined in another work.

Probing QCD critical fluctuations from the yield ratio of strange hadrons in relativistic heavy-ion collisions (2019) · 0.97 · paraphrased: the licence does not allow quoting
Used the thermal statistical model THERMUS to estimate the relative yield of primary particles.

Global spin polarization of multistrange hyperons and feed-down effect in heavy-ion collisions (2021) · 0.99 · paraphrased: the licence does not allow quoting
Used the Baryon Canonical ensemble approach as implemented in the THERMUS package to perform the fitting to the data.

Canonical treatment of strangeness and light nuclei production (2025) · 1.00 · paraphrased: the licence does not allow quoting
Utilized the open code THERMUS ver.2.1 to calculate the entropy density and baryon number density at various temperatures.

Phase diagram of hot and dense QCD constrained by the Statistical Model (2010) · 1.00 · paraphrased: the licence does not allow quoting
Utilised the implementation in the THERMUS code for its study.

Multiplicity dependence of light flavour hadron production at LHC energies in the strangeness canonical suppression picture (2016) · 1.00 · paraphrased: the licence does not allow quoting
We have performed our analysis for grand canonical, canonical and strangeness canonical ensembles using a thermal model called THERMUS [ref] .

Multiplicity dependence freeze-out scenarios in pp collisions at $\sqrt{s}$ = 7 TeV (2021) · Multiplicity dependence freeze-out scenarios in p+p collision at LHC · 0.86
Determined the yield of particle A at a point on the trajectory with the statistical thermal model THERMUS.

Search for the QCD Critical Point by Transverse Velocity Dependence of Anti-deuteron to Deuteron Ratio (2018) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

Did all its calculations using the latest version of THERMUS.

A Comparison of p-p, p-Pb, Pb-Pb Collisions in the Thermal Model: Multiplicity Dependence of Thermal Parameters (2018) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Calculated the excluded volume correction factor and the entropy density using the THERMUS package.

Viscosity in the excluded volume hadron gas model (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Used an extended version of the THERMUS framework for its calculations.

Multiplicity fluctuations in relativistic nuclear collisions (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

50 arXiv papers cite this in 72 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 the same result 1 paper

THERMUS is a package of C++ classes and functions allowing statistical-thermal model analyses of particle production in relativistic heavy-ion collisions to be performed within the ROOT framework of analysis.

THERMUS · 1.00

Papers citing it · 32 sentences without a confident label

Uses its method or tool 21 papers

All fits were done using the THERMUS thermal code [ref] , using particle ratios calculated from mid-rapidity yields (dN/dy).

Energy and System Size Dependence of Strangeness Production from SPS to RHIC · Energy Dependence · 1.00
However, corrections due to the weak-decay feed-down for protons still need to be performed. for STAR's $p$ and $p̅$ at were obtained using the THERMUS code [ref] .

More uses for Thermal Models · Data and analysis details · 0.99
The ratio $𝒪_K-$Ξ$--$ in this model is then given by [equation] To include the contribution from resonance decays, we use the THERMUS package [ref] with the chemical freeze-out temperature and baryon chemical potential determined in Ref. [ref] .

Probing QCD critical fluctuations from the yield ratio of strange hadrons in relativistic heavy-ion collisions · Introduction · 0.97

Uses its data or values 4 papers

The masses and branching ratios used are as given in [ref] .

Novel scheme for parametrizing the chemical freeze-out surface in Heavy Ion Collision Experiments · Introduction · 0.99
HIJING [ref] simulations indicate that $F$ = 0.67 and if the scales with the yield, THERMUS [ref] indicates that $F$ = 0.532.

Measurement of transverse energy at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV · Correction factors and · 0.87
The masses and branching ratios used are as given in [ref] .

Systematics of chemical freeze-out parameters in heavy-ion collision experiments · Data Analysis · 0.96

Compares with it 3 papers

In this paper, we implement this technique on published hadron yields and compare the extracted chemical potential ratios with the results of thermal-model fit obtained by STAR [ref] using THERMUS [ref] .

More uses for Thermal Models · Introduction · 0.98
Finally, the values and behaviour of $$ as a function of centrality are in very good agreement with previous findings, especially with the ones [ref] calculated with the THERMUS [ref] package.

Chemical freeze-out in ultra-relativistic heavy ion collisions at sqrt(s)_NN = 130 and 200 GeV · Comparison with previous analyses · 0.96
Figure [ref] shows the /(no contribution considered here), / and / ratios compared to calculations from grand-canonical thermal models [ref] , which were found to satisfactorily describe central Pb-Pb data at = 2.76 TeV.

Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV · Results and discussion · 0.80

Cites it as background 5 papers

Strange hadron production in heavy-ion collisions is currently usually described in the framework of statistical-hadronisation (or thermal) models [ref] .

Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV · Introduction · 0.90
Examples of commonly used hadron lists can be found in [ref] where, in some instances, additional states from the quark model have been included [ref] .

Updated Hadron List for Transport Simulations of Heavy-Ion Collisions · Introduction · 0.85
In canonical ensemble (CE) all the charges are exactly conserved (CE) [ref] whereas in strangeness canonical ensemble (SCE) [ref] only strangeness is exactly conserved.

Multiplicity dependence freeze-out scenarios in pp collisions at $\sqrt{s}$ = 7 TeV · Canonical and strangeness canonical ensemble · 0.96

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.

[1] [1]

A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys . A772 (2006) 167

View on Pith 2006

[2] [2]

J. Cleymans, H. Oeschler, K. Redlich, S. Wheaton, Phys. R ev. C73 (2006) 034905

View on Pith 2006

[3] [3]

F. Becattini, J. Manninen, M. Gazdzicki, Phys. Rev. C73 ( 2006) 044905

View on Pith 2006

[4] [4]

For a recent review see F. Becattini, plenary talk presen ted at Quark Matter 2008, Jaipur, India, Feb 4 - 10, 2008

View on Pith 2008

[5] [5]

P. Braun-Munzinger, K. Redlich, J. Stachel, nucl-th/03 04013 and in Quark Gluon Plasma 3, eds. R.C. Hwa and X.N. Wang, (World Scientiﬁc Publishing, 2004)

View on Pith 2004

[6] [6]

G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J . Letessier, J. Rafelski, Comput. Phys. Commun. 167 (2005) 229. 49

View on Pith 2005

[7] [7]

G. Torrieri, S. Jeon, J. Letessier, J. Rafelski, Comput. Phys. Commun. 175 (2006) 635

View on Pith 2006

[8] [8]

A. Kisiel, T. Talu´ c, W. Broniowski, W. Florkowski, Comp ut. Phys. Commun. 174 (2006) 669

View on Pith 2006

[9] [9]

R. Brun and F. Rademakers, Nucl. Inst. & Meth. in Phys. Res . A 389 (1997) 81. See also http://root.cern.ch/

View on Pith 1997

[10] [10]

J. Cleymans, I. Kraus, H. Oeschler, K. Redlich and S. Whe aton, Phys. Rev. C 74 (2006) 034903

View on Pith 2006

[11] [11]

I. Kraus, J. Cleymans, H. Oeschler, K. Redlich and S. Whe aton, J. Phys. G 32 (2006) S495

View on Pith 2006

[12] [12]

H. Caines, J. Phys. G 32 (2006) S171

View on Pith 2006

[13] [13]

L.A. Stiles and M. Murray, nucl-ex/0601039

View on Pith Pith review arXiv

[14] [14]

J. Takahashi (for the STAR Collaboration), nucl-ex/07 11.2273

View on Pith

[15] [15]

M. Murray (for the BRAHMS Collaboration), nucl-ex/071 0.4576

View on Pith

[16] [16]

M.I. Gorenstein, M. Hauer, O.N. Moroz, nucl-th/0708.0 137

View on Pith

[17] [17]

R. Witt, J. Phys. G 34 (2007) S921

View on Pith 2007

[18] [18]

B. Hippolyte, Eur. Phys. J. C49 (2007) 121

View on Pith 2007

[19] [19]

J. Cleymans, R. Sahoo, D.P. Mahapatra, D.K. Srivastava and S. Wheaton, Phys. Lett. B660 (2008) 172

View on Pith 2008

[20] [20]

M. Hauer, V.V. Begun and M.I. Gorenstein, nucl-th/0706 .3290

View on Pith

[21] [21]

M.I. Gorenstein, M. Hauer, D.O. Nikolajenko, Phys. Rev . C 76 (2007) 024901

View on Pith 2007

[22] [22]

V.V. Begun, M. Ga´ zdzicki, M.I. Gorenstein, M. Hauer, V .P. Konchakovski and B. Lungwitz, Phys. Rev. C 76 (2007) 024902

View on Pith 2007

[23] [23]

F. Becattini, Z. Phys. C 69 (1996) 485

View on Pith 1996

[24] [24]

F. Becattini and U. Heinz, Z. Phys. C 76 (1997) 269

View on Pith 1997

[25] [25]

J. Cleymans, D. Elliott, A. Ker¨ anen and E. Suhonen, Phy s. Rev. C 57 (1998) 3319

View on Pith 1998

[26] [26]

K. Redlich, J. Cleymans, H. Oeschler and A. Tounsi, Acta Physica Polonica B33 (2002) 1609

View on Pith 2002

[27] [27]

F. Becattini, J. Cleymans, A. Ker¨ anen, E. Suhonen, K. R edlich, Phys. Rev. C 64 (2001) 024901

View on Pith 2001

[28] [28]

P. Braun-Munzinger, I. Heppe, J. Stachel, Phys. Lett. B465 (1999) 15

View on Pith 1999

[29] [29]

P. Braun-Munzinger et al. , Phys. Lett. B344 (1995) 43, ibid. B365 (1996) 1. 50

View on Pith 1995

[30] [30]

P. Braun-Munzinger, D. Magestro, K. Redlich and J. Stac hel, Phys. Lett. B518 (2001) 41

View on Pith 2001

[31] [31]

J. Sollfrank, J. Phys. G: Nucl. Part. Phys. 23 (1997) 1903

View on Pith 1997

[32] [32]

W. Broniowski and W. Florkowski, Phys. Rev. C 65 (2002) 064905

View on Pith 2002

[33] [33]

W. Florkowski, W. Broniowski and M. Michalec, Acta Phys ica Polonica B33 (2002) 761

View on Pith 2002

[34] [34]

N. Xu and M. Kaneta, Nucl. Phys. A698 (2002) 306c

View on Pith 2002

[35] [35]

M. Kaneta (for the NA44 Collaboration), J. Phys. G: Nucl . Part. Phys. 23 (1997) 1865; M. Kaneta and N. Xu, J. Phys. G: Nucl. Part. Phys. 27 (2001) 589

View on Pith 1997

[36] [36]

J. Cleymans and K. Redlich, Phys. Rev. Lett. 81 (1998) 5284; J. Cleymans and K. Redlich, Phys. Rev. C 60 (1999) 054908

View on Pith 1998

[37] [37]

S. Wheaton, ”The Development and Application of THERMU S- a Statistical- Thermal Model Analysis Package for ROOT”, Ph.D. dissertati on, University of Cape Town, Cape Town, South Africa, 2005

View on Pith 2005

[38] [38]

A. Ker¨ anen and F. Becattini, nucl-th/0112021

View on Pith Pith review arXiv

[39] [39]

P. Braun-Munzinger, J. Cleymans, H. Oeschler and K. Red lich, Nucl. Phys. A697 (2002) 902

View on Pith 2002

[40] [40]

J. Cleymans, H. Oeschler and K. Redlich, Phys. Lett. B485 (2000) 27; K. Redlich, S. Hamieh and A. Tounsi, J. Phys. G: Nucl. Part. Ph ys. 27 (2001) 413

View on Pith 2000

[41] [41]

J. Cleymans, H. Oeschler and K. Redlich, Phys. Rev. C 59 (1999) 1663

View on Pith 1999

[42] [42]

J. Sollfrank, P. Koch and U. Heinz, Z. Phys. C 52 (1991) 593

View on Pith 1991

[43] [43]

M. Kaneta and N. Xu, nucl-th/0405068

View on Pith Pith review arXiv

[44] [44]

J. Cleymans, B. K¨ ampfer, M. Kaneta, S. Wheaton and N. Xu , Phys. Rev. C 71 (2005) 054901

View on Pith 2005

[45] [45]

F. Becattini, M. Ga´ zdzicki and J. Sollfrank, Eur. Phys . J. C 5 (1998) 143

View on Pith 1998

[46] [46]

J. Rafelski, Phys. Lett. B262 (1991) 333; P. Koch, B. M¨ uller, J. Rafelski, Phys. Rep. 142 (1986) 167

View on Pith 1991

[47] [47]

J. Letessier, J. Rafelski, A. Tounsi, Phys. Rev. C 50 (1994) 405; C. Slotta, J. Sollfrank, U. Heinz, AIP Conf. Proc. (Woodbury ) 340 (1995) 462

View on Pith 1994

[48] [48]

F. Becattini, M. Ga´ zdzicki, A. Ker¨ anen, J. Manninen and R. Stock, Phys. Rev. C 69 (2004) 024905

View on Pith 2004

[49] [49]

I.G. Bearden et al. (NA44), Phys. Rev. C 66 (2002) 044907. 51

View on Pith 2002

[50] [50]

J. Cleymans, B. K¨ ampfer and S. Wheaton, Phys. Rev. C 65 (2002) 027901, nucl-th/0110035

View on Pith Pith review arXiv 2002

[51] [51]

J. Cleymans, B. K¨ ampfer and S. Wheaton, Nucl. Phys. A715 (2003) 553c, hep-ph/0208247

View on Pith Pith review arXiv 2003

[52] [52]

J. Cleymans, B. K¨ ampfer, P. Steinberg and S. Wheaton, J . Phys. G: Nucl. Part. Phys. 30 (2004) S595, hep-ph/0311020

View on Pith Pith review arXiv 2004

[53] [53]

J. Lettesier and J. Rafelski, Phys. Rev. C 59 (1999) 947

View on Pith 1999

[54] [54]

G.D. Yen, M.I. Gorenstein, W. Greiner and S.N. Yang, Phy s. Rev. C 56 (1997) 2210

View on Pith 1997

[55] [55]

D.H. Rischke, M.I. Gorenstein, H. St¨ ocker and W. Grein er, Z. Phys. C 51 (1991) 485

View on Pith 1991

[56] [56]

J. Cleymans, M.I. Gorenstein, J. Stalnacke and E. Suhon en, Phys. Scr. 48 (1993) 277

View on Pith 1993

[57] [57]

K. Hagiwara et al. , Phys. Rev. D 66 (2002) 010001

View on Pith 2002

[58] [58]

T. Sj¨ ostrand et al. , Comput. Phys. Commun. 135 (2001) 238

View on Pith 2001

[59] [59]

V. Magas, H. Satz, Eur. Phys. J. C 32 (2003) 115

View on Pith 2003

[60] [60]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flan nery, Numerical Recipes in C: The Art of Scientiﬁc Computing (Cambridge Univ ersity Press, Cambridge, 2002)

View on Pith 2002

[61] [61]

K. Wr` oblewski, Acta Physica Polonica B16 (1985) 379. 52

View on Pith 1985