A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC

D. Teaney; E.V. Shuryak; J. Lauret

REVIEW

A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC

D. Teaney, J. Lauret, E.V. Shuryak

Nuclear Theory · Submitted 14 Oct 2001 · 86 references

Pith's verdict: The RHIC flow prediction is the real content here; the 'both features essential' claim is softer than the abstract makes it sound.

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CitationD. Teaney, E.V. Shuryak, J. Lauret. "A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHIC." arXiv:nucl-th/0110037 (2001). https://pith.science/paper/OBLL7QQB

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Editor's note

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The thing worth your time is the prediction, not the fit. LH8 was fixed against SPS spectra and slope systematics before RHIC data existed, and it called both the ~20% rise in radial flow and the ~40% rise in integrated elliptic flow. Those came in. That is a genuine extrapolation and it is why this paper gets cited. What is new relative to their own PRL [21] is the systematic latent-heat scan — LH4 through LH16 plus the resonance gas and LH-infinity — compared against the strange-baryon slope hierarchy (Fig. 12), integrated v2 versus centrality at both energies (Fig. 26), and the v2(pT) shapes (Fig. 27). The Omega argument is clean: small hadronic cross sections mean it comes straight off the switching surface, so its slope reads the flow velocity there. The resonance-gas over-prediction and the LH-infinity under-prediction are visible and point the right way. Soft spots, in order of weight. The EOS family is one-parameter. Only the latent heat moves; Tc = 165 MeV, c_s^2 = 0.02 in the mixed phase, the massless limit above e_Q, and the ideal-gas hadron spectrum below Tc are all held fixed. A one-parameter family interpolating between the two limits the paper argues against will generically have an interior optimum. That does not make LH8 wrong, but 'both features are essential' is stronger than the construction supports. Second, and this is the one I would press: the discrimination runs through the flow velocity at the switching isotherm, fixed at 160 MeV. The paper's own Fig. 3 shows the three EOS flow velocities becoming roughly comparable by Tf = 120 MeV. The counter in Fig. 25 — that the cascade preserves more early anisotropy than continuing hydro would — is a real argument, but it is computed at the same Tswitch. Sect. I B defers Tswitch sensitivity to [38], listed as in preparation. A reader cannot check that, and it is load-bearing for the central claim. Minor, and the authors say so themselves: HBT radii about 50% too large, the SPS v2 comparison is mid-rapidity theory against forward-rapidity data, and s/nB = 150 from UrQMD puts pbar roughly 15% low. One correction to the record: the classifier reports no stated limitations, which is wrong — the paper states several explicitly. Who should read it: anyone working on flow or on extracting the EOS at RHIC energies. It deserves referees.

Referee report

Significance

If the central claim holds, the paper is a substantial contribution: it converts the qualitative statement that the QCD transition leaves a hydrodynamic imprint into a quantitative, multi-observable, multi-energy consistency argument, and it does so with a model that has very few adjustable inputs (the entropy and baryon-number normalizations C_s and C_nB, plus dN/dy). The demonstration that the Omega slope is a clean probe of the flow velocity at the phase boundary, because Omega escapes the cascade essentially unscattered (Sect. III C, Fig. 7), is a genuinely useful methodological point that others can reuse. The paper is also commendably falsifiable in structure: the SPS-to-RHIC increase in v2 and in <M_T> are stated as predictions of LH8 before the RHIC data are shown, and the failure modes of the resonance-gas and LH-infinity limits are exhibited rather than asserted. The frank acknowledgment in Sect. V F that the model's HBT radii are roughly a factor of two above the measured ones is the kind of disclosure that makes the rest of the comparison credible.

Major objections (5)

[Sect. I B and Sect. IV A] The EOS discrimination is routed through the flow velocity on the switching isotherm, which is held fixed at T_switch = 160 MeV throughout, and the sensitivity to this choice is explicitly deferred to a companion paper [38] listed as 'in preparation.' This matters because the paper's own Fig. 3 shows that along the T_f = 120 MeV isotherm the flow velocities of LH8, RG, and LH∞ become 'roughly comparable,' i.e. the discriminator that drives the conclusion is weakest precisely where the switching surface would move if T_switch were lowered. The cleanest discriminator, the Omega slope in Fig. 12, is a direct measurement of that velocity (Sect. IV A). The manuscript should therefore either add at least one alternate-T_switch run (e.g. 140 MeV, or 120 MeV) showing that the ordering T_slope(LH8) < T_slope(RG) and T_slope(LH8) > T_slope(LH∞) in Fig. 12, and the v2 ordering in Fig. 26, survives, or it should soften the abstract's 'essential' to a statement explicitly conditioned on T_switch ≈ T_c. As written, a reader cannot check the deferred sensitivity, and the load-bearing claim rests on an unvaried parameter.
[Sect. II C and Fig. 2] The 'both hard and soft features are essential' conclusion is a statement about a one-parameter family in which only the latent heat is varied while T_c = 165 MeV, the mixed-phase c_s^2 = 0.02, the massless-gas limit above e_Q, and the ideal-gas hadron spectrum below T_c are all held fixed. In particular the resonance-gas limit is not a realistic extrapolation of a hadron resonance gas to high temperature: it keeps c_s^2 ≈ 1/5 constant above e_H rather than rising toward 1/3, so its over-prediction of the Lambda/Xi/Omega slopes (Fig. 12b) and of integrated v2 (Fig. 26) may reflect that specific choice rather than the absence of a phase transition. The paper should state this scope explicitly, and ideally show one variant (for instance a resonance gas whose c_s^2 rises at high e, or a different mixed-phase c_s^2) to demonstrate that the failure of the 'hard-only' and 'soft-only' limits is robust to the fixed ingredients and not an artifact of the family's construction.
[Sect. V B, Fig. 26] The manuscript states that for LH8-LH16 the model integrated pion v2 at the SPS is 'about 20% above the data' and attributes the residual to the rapidity integration of the data versus mid-rapidity model points. That attribution is plausible but is not tested; the same 20% level of agreement is then used to argue that LH4 and the resonance gas are excluded. Since the exclusion of LH4/RG rests on their being substantially above LH8, a 20% systematic on the normalization weakens the discrimination. The authors should quantify the rapidity-integration correction (even approximately, using the measured dN/dy and v2(y) at the SPS) or present the comparison in a rapidity window where the model is valid.
[Sect. V F] The paper acknowledges that the model HBT radii at RHIC are approximately 50% larger than measured while the final velocities are correct, and identifies this as an unresolved problem. This is more than a loose end for the central claim: if the expansion time is too long, the same hydrodynamic trajectory that produces the correct radial and elliptic flow is being tuned against data that constrain the space-time extent, and the agreement in the spectra may be partly fortuitous. The manuscript should discuss, at least qualitatively, whether the HBT discrepancy can be accommodated within the LH8 scenario (for example through a shorter QGP lifetime, a different initial profile, or pre-equilibrium flow) or whether it points to a structural problem with the hydrodynamic stage. As it stands the reader is left with a model that gets the momentum anisotropy right and the spatial extent wrong, and no assessment of whether the two are independent.
[Sect. II B and Sect. IV E, Fig. 19] The initial s/n_B = 150 is taken from an UrQMD estimate rather than from the measured pbar/p ratio, and the paper states that this makes the model pbar yield approximately 15% too low and the proton yield approximately 15% too high. Since headline item (ii) in the abstract is the anomalous pbar/pi^- ratio near p_T ≈ 2 GeV, and Fig. 19 is the demonstration of that item, a 15% normalization error on pbar is directly relevant to the claim. The authors should show Fig. 19 (and the corresponding spectra in Fig. 18) with the normalization corrected to the measured pbar/p = 0.65, or at minimum state how much the crossing point of the pi^- and pbar spectra moves under that correction.

Minor objections (9)

[Sect. II A] 'Gudunov' should be 'Godunov' (Sect. II A), and the same paragraph's 'RHLLE Riemann solver' should be spelled out at first use.
[Fig. 12(a)] The legend reads 'Hydro+Only'; this should be 'Hydro Only' to match the convention defined in Sect. I B and used elsewhere.
[Fig. 19] The label 'Themal Hadronization' should read 'Thermal Hadronization.'
[Fig. 13] The legend labels 'Cern PbPb' and 'RHIC AuAu' should specify the collision energy or centrality, since the SPS and RHIC curves are compared directly.
[References] References [62] and [63] are identical (H. Sorge, Phys. Rev. Lett. 82, 2048 (1999)); one should be removed or corrected. Reference [38] is listed as 'in preparation' and is cited for a load-bearing sensitivity study; if it remains unpublished at the time of publication, the relevant check should be included here instead.
[Fig. 1] The two ordinates (epsilon and R_rms/R_A) are plotted on the same axes with a single scale from 0 to 1; the caption should state explicitly which curve corresponds to which quantity, since the figure is used quantitatively in Sect. III D and Sect. V B.
[Eq. (5)] The expression for dN_p/dx dy is difficult to parse as typeset, with the products of the two thickness functions and the bracketed exponentials run together; a cleaner display or a reference to the small-sigma limit in the following sentence would help.
[Sect. III C, Eq. (19)] The fit of Eq. (19) uses a single drift velocity v_T ≈ 0.42c for all species, but the text later notes that nucleons receive roughly 20% of their transverse kinetic energy from the pion wind. The caption of Fig. 7 should state over which species the quoted v_T is obtained, since the fit is presented as validating the simple freezeout picture.
[Sect. IV A] The statement that bag-model equations of state 'typically have a latent heat from 1-1.5 GeV/fm^3' and that this is 'usually compensated by adjusting the freezeout temperature' would be strengthened by citing the specific calculations and their T_f values, since this is the paper's main point of contrast with prior hydrodynamic work.

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The paper

The paper claims

The paper argues that the collective flow of particles produced in heavy-ion collisions can be reproduced only by a fluid whose equation of state has both a stiff quark-gluon phase and a soft mixed phase, and that the best such equation of态

The reading

The paper asks whether the collective motion seen in heavy-ion collisions — the outward push called radial flow and the almond-shaped squeeze called elliptic flow — can be reproduced by a fluid model whose equation of state passes through the QCD phase transition. The authors couple a two-dimensional boost-invariant hydrodynamic solver to the RQMD hadronic cascade, so that hadrons are emitted thermally at the phase boundary and then rescatter until they stop interacting. They then sweep a one-parameter family of equations of state, labelled by latent heat, and compare every member against flow data from the SPS and RHIC. The conclusion they argue for is that only an equation of state with both a stiff quark-gluon phase and a soft mixed phase — LH8, with a latent heat of $0.8~GeV/fm^3$ — matches the whole body of data, and that removing either feature breaks the agreement.

What carries the argument

Three pieces carry the argument. First, a thermodynamically consistent family of equations of state built by specifying the speed of sound along the adiabatic path $n_B/s = text{const}$: an ideal-gas hadron resonance spectrum below $T_c = 165$ MeV, a mixed phase with $c_s^2 approx 0.02$ whose width is the latent heat, and a massless limit with $c_s^2 = 1/3$ above it; varying only the latent heat generates LH4, LH8, LH16 and LH$infty$, with a resonance-gas equation of state as the no-transition limit. Second, the Cooper-Frye prescription applied on the $T = 160$ MeV isotherm, with a $\theta$ function rejecting particles entering the surface, which converts fluid variables into a hadron ensemble at a sharply defined switching surface. Third, the RQMD hadronic cascade as an afterburner, which produces differential freeze-out: mesons decouple around $tau approx 14$ fm/c, nucleons and hyperons around $18$ fm/c, while $phi$ and $Omega^-$ escape almost directly from the phase boundary. That last piece matters quantitatively, because roughly twenty percent of a nucleon's transverse kinetic energy is delivered by pion scattering — the authors' 'pion wind' — after the pions themselves have essentially decoupled.

Extended reading notes

Core claim

The central claim is that a hydrodynamic-plus-cascade model with a phase transition of modest latent heat simultaneously reproduces radial and elliptic flow across particle species, collision energies, and impact parameters, and that this success is diagnostic of the equation of state. The authors make the claim comparative rather than merely descriptive: a resonance-gas equation of state, which has only the stiff feature, over-predicts the slope parameters of $Lambda$, $Xi$ and $Omega$ at the SPS and over-predicts integrated elliptic flow at both SPS and RHIC, while an equation of state with an infinite latent heat, which has only the soft feature, under-predicts those slopes and gives a qualitatively wrong transverse-momentum dependence of elliptic flow. LH8 sits between them and matches the data, including the roughly forty percent rise in elliptic flow from SPS to RHIC and the strong versus weak impact-parameter dependence of the $bar{p}$ and $phi$ slope parameters respectively. The paper also accounts for the anomalous $bar{p}/pi^{-}$ ratio near $p_T approx 2.0$ GeV and for the difference between the STAR and PHENIX slope measurements as consequences of a radially flowing thermal source followed by hadronic rescattering.

Load-bearing premise

The conclusion that both a hard and a soft feature are required rests on a hand-built family of equations of state in which only the latent heat varies while the transition temperature, the mixed-phase speed of sound, the massless high-density limit, and the hadron spectrum below the transition are all held fixed.

Editorial extensions

If this is right

If the argument holds, the measured flow systematics constrain the latent heat of the QCD transition to roughly $0.8~GeV/fm^3$, well below the $1$–$1.5~GeV/fm^3$ typical of bag-model equations of state used in earlier hydrodynamic fits.
The rise in elliptic flow from SPS to RHIC, and its linear rise with $p_T$ for negative hadrons, become direct evidence that a stiff quark-gluon phase exists and dominates the early evolution at RHIC.
The mass ordering and curvature of the transverse-mass spectra, and the split between STAR low-$M_T$ and PHENIX high-$M_T$ slope measurements, are consequences of differential freeze-out rather than of distinct physics, so the two measurements are reconcilable within one model.
Particles with small hadronic cross sections, such as the $phi$ and $Omega^-$, become clean probes of the flow velocity at the end of the mixed phase, since they carry the hydrodynamic signal without a hadronic afterburner.
The strong impact-parameter dependence of the $bar{p}$ slope and the weak dependence of the $phi$ slope are attributable to pion-nucleon scattering in the late stage, which gives an experimentally accessible handle on how much of the observed flow is hadronic rather than partonic.

Reading between the lines

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

The comparative logic could be sharpened into a genuine prediction: if the latent heat is the controlling variable, then the $phi$ and $Omega^-$ elliptic flow at RHIC should track the LH8 curve in $p_T$ without needing a hadronic afterburner, which is a cleaner test than the inclusive charged-hadron $v_2$.
Because the model's HBT radii come out roughly twice the measured values while the velocities are right, the same framework implies that the late-time spatial extent, not the collective velocity field, is where the description is incomplete — a mismatch that a viscosity or a shorter mixed phase would address rather than a different latent heat.
The claim that the resonance-gas equation of state over-predicts elliptic flow suggests a cross-check at lower beam energies, where the mixed phase would occupy a larger fraction of the lifetime and the soft feature should matter more; an energy scan could separate the latent-heat explanation from a simple initial-geometry explanation.
Since the switching temperature, the mixed-phase sound speed, and the hadronic degrees of freedom are all held fixed across the family, the paper's conclusion is really about the presence of a soft region of finite width rather than about the specific latent heat value, and a broader scan would be needed to turn LH8 into a measurement.

Original abstract

A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its dependence on $p_{T}$ and mass, (ii) the anomalous $\bar{p}/\pi^{-}$ ratio for $p_{T} \approx 2.0$ GeV, (iii) the difference in the slope parameters measured by the STAR and PHENIX collaborations, and (iv) the respectively strong and weak impact parameter dependence of the $\bar{p}$ and $\phi$ slope parameters. For an EOS without the hard and soft features of the QCD phase transition, the broad consistency with the data is lost.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,497 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.60 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its dependence on $p_{T}$ and mass, (ii) the anomalous $\bar{p}/\pi^{-}$ ratio for $p_{T} \approx 2.0$ GeV, (iii) the difference in the slope parameters measured by the STAR and PHENIX collaborations, and (iv) the respectively strong and weak impact parameter dependence of the $\bar{p}$ and $\phi$ slope parameters. For an EOS without the hard and soft features of the QCD phase transition, the broad consistency with the data is lost.

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	A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC.	contribution 0.89	0.89	0.10	asserted 0.97
s1	The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters.	result 1.00	0.87	0.49	asserted 1.00
s2	Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering.	interpretation 0.83	0.76	0.40	asserted 1.00
s3	Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its dependence on $p_{T}$ and mass, (ii) the anomalous $\bar{p}/\pi^{-}$ ratio for $p_{T} \approx 2.0$ GeV, (iii) the difference in the slope parameters measured by the STAR and PHENIX collaborations, and (iv) the respectively strong and weak impact parameter dependence of the $\bar{p}$ and $\phi$ slope parameters.	result 0.71	0.61	0.11	asserted 0.74
s4	For an EOS without the hard and soft features of the QCD phase transition, the broad consistency with the data is lost.	result 0.78	0.79	0.21	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.78 · evidence from simulation or computation 0.86.

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.** FIG. 1: The derived quantities

**Figure 3.** FIG. 3: The left and right sides show the hydrodynamic

**Figure 5.** , between the SPS and RHIC, p 2 T weighted elliptic flow should increase by almost a factor of two as the QGP replaces the mixed phase and dominates the early evolution. Second with

**Figure 6.** FIG. 6: The fraction of pions emitted into RQMD per unit

**Figure 7.** FIG. 7: The mean (a) emission time, (b) number of collisions,

**Figure 8.** FIG. 8: The mean emission time

**Figure 9.** FIG. 9: The density of pions at freezeout (see text) versus

**Figure 10.** FIG. 10: The mean pion (a) emission time, (b) emission

**Figure 11.** FIG. 11: A comparison to NA49 [66] (a) negative hadron

**Figure 12.** FIG. 12: A compilation of slope parameters from the SPS

**Figure 14.** FIG. 14: For PbPb collisions at b=6 fm, (a) shows

**Figure 15.** FIG. 15: Each particle spectrum in central AuAu collisions,

**Figure 16.** FIG. 16: For nucleons in central AuAu collisions, (a) an

**Figure 18.** FIG. 18: A comparison to PHENIX [72] and STAR [71] ¯p

**Figure 21.** FIG. 21: Model and preliminary STAR

**Figure 23.** FIG. 23: The absolutely normalized model spectra for LH8

**Figure 24.** FIG. 24: Panels (a)-(c) show three related quantities as

**Figure 27.** (a), (b) and (c) show v2(pT ) min−bias for negative hadrons, kaons, and nucleons at RHIC. Look first at the negative hadrons (a): Although LH8 and LH16 both show a strong linear rise, the slope is smaller for LH16. For LH∞, v2(pT ) is curved and bends over. For small pT , LH∞ is above LH8, but by pT ≈ 2.0 GeV, LH∞ is substantially below LH8. The data show a strong linear rise and agree remarkably well with the slope of LH8. v2(pT ) slightly favors LH8 over LH16. The kaon v2(pT ) curve has the same shape and magnitude as the h − spectrum. At the SPS the kaon elliptic flow is…

Showing 23 of the paper's 30 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:nucl-th/0110037 by the authors.

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Forward citations

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How later papers used it

130 later papers cite it

Evidence: substantial. 116 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 185 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 used its method or tool. 4 more papers by the same authors are listed: 4 used its method or tool.

Uses its method or tool 6 of 9 papers with this label · 4 by the same authors

Treated the evolution of the collision region with a hydrodynamical model based on this paper.

Low mass dilepton radiation at RHIC (2007) · 1.00 · paraphrased: the licence does not allow quoting
Based its hydrodynamic model, aside from the equation of state, upon this paper.

Hydrodynamic Description of Dilepton Production (2009) · 0.93 · paraphrased: the licence does not allow quoting

By the same authors

Used a hydrodynamical simulation developed in this paper, known to describe accurately the radial and elliptic collective flows observed in heavy-ion collisions.

Recombinant Charmonium in strongly coupled Quark-Gluon Plasma (2009) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Used hydrodynamical calculations such as this paper for a quantitative description of the mixed phase.

Charmonium in strongly coupled quark-gluon plasma (2008) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Based its hydrodynamic model, aside from the equation of state, upon this paper.

Simulating elliptic flow with viscous hydrodynamics (2007) (same authors) · 0.83 · paraphrased: the licence does not allow quoting
Followed hydro calculations such as this paper to scale entropy density with local participant density for the Glauber initial condition.

Angular Dependence of Jet Quenching Indicates Its Strong Enhancement Near the QCD Phase Transition (2008) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

132 arXiv papers cite this in 187 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 · 140 sentences without a confident label

Contests it 1 paper

Nevertheless, such a comparison was often ignored since almost all dynamic models, which pretend to be complete and therefore describe the evolution of the matter as well as its gradual decay, e.g., the hybrid (hydrodynamic plus UrQMD) models [ref] failed to reproduce pion out-, side-, long- interferometry radii simultaneously with the hadronic spectra at RHIC.

Kaon and pion femtoscopy at the highest energies available at the BNL Relativistic Heavy Ion Collider (RHIC) in a hydrokinetic model · Introduction · contest 0.85

Uses its method or tool 9 papers

The evolution of the collision region is treated with a hydrodynamical model based on reference [ref] .

Low mass dilepton radiation at RHIC · Evolution · 1.00
We use a hydrodynamical simulation developed in [ref] which is known to describe accurately the radial and elliptic collective flows observed in heavy-ion collisions.

Recombinant Charmonium in strongly coupled Quark-Gluon Plasma · The results · 1.00
The same bag model equation of state and Glauber model initial conditions of [ref] are used since it was able to predict many hadronic observables.

Photons as a viscometer of heavy ion collisions · Spectra in Ultra-relativistic Heavy-Ion Collisions · 0.85

Uses its data or values 2 papers

At freeze-out ($τ_ ≃ 15-17$ fm/$c$ [ref] ) the expansion rate at RHIC is thus about 25% larger than at the SPS $((∂·u)_ ≈ 0.21$ fm$^-1$ for Au+Au at $√(s)130 A$ GeV vs. $(∂·u)_ ≈ 0.16$ fm$^-1$ for Pb+Pb at $√(s)17 A$ GeV$)$.

Early collective expansion: Relativistic hydrodynamics and the transport properties of QCD matter · Phenomenology of the transverse expansion · 0.93
The energy excitation curves of $v_2$ from [ref] and [ref] are shown in Fig. [ref], left and right.

Physics of Strongly coupled Quark-Gluon Plasma · Collective flows and hydrodynamics · 0.85

Compares with it 2 papers

Although the gap between the two branches of the EoS is much smaller here than for the previously used models which assume non-interacting quarks and gluons above $T_c$ [ref] , a certain degree of ambiguity remains in the interpolation process.

A Family of Equations of State Based on Lattice QCD: Impact on Flow in Ultrarelativistic Heavy-Ion Collisions · Introduction · 0.87
Actually this time-scale can be well compared with the known hydrodynamic simulation requirement $t_th < 2 [fm/c]$ discussed for example in [ref] .

Rapid Thermalization by Baryon Injection in Gauge/Gravity Duality · Introduction · 0.99

Cites it as support 5 papers

The main argument for such early equilibration comes from the observation that the space-time evolution of matter is very well explained by the relativistic hydrodynamics of perfect fluid [ref] or by viscous hydrodynamics with a small viscosity to entropy ratio [ref] .

Collective phenomena in the early stages of relativistic heavy-ion collisions · Evidence for early thermalization · 0.97
In the experimental data this phase transition signature is, unfortunately, washed out by strong viscous effects in the late hadronic stage of the fireball expansion which become increasingly important at low collision energies [ref] (where the fireball spends most of its time in the hadronic phase).

Hydrodynamic radial and elliptic flow in heavy-ion collisions from AGS to LHC energies · Elliptic Flow · 0.96
Much of this discrepancy can be explained by incorporating the viscous contribution from the hadronic phase [ref] .

Parton Collectivity from RHIC to the LHC · The perfect liquid? · 0.97

Cites it as background 24 papers

Hybrid codes that coupled an ideal fluid dynamical description of an expanding QGP to such hadronic rescattering codes and compared the results with purely fluid dynamical calculations began to appear about ten years ago [ref] .

Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach · Introduction · 0.89
Ideal hydrodynamics has been successful in predicting and explaining the measured elliptic flow in Au+Au collisions at RHIC [ref] .

Event-by-event hydrodynamics and elliptic flow from fluctuating initial state · Introduction · 0.84
The phenomenological model of continuous emission was proposed in Ref. [ref] ; another approach is the so-called hybrid models [ref] , where kinetic evolution is matched with hydro one at the hypersurface of hadronization.

Kinetics vs hydrodynamics: generalization of Landau/Cooper-Frye prescription for freeze-out · Introduction · 0.94

Discussion

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