Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade

Chun Shen; Huichao Song; Steffen A Bass; Tetsufumi Hirano; Ulrich W Heinz

REVIEW

Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade

Huichao Song, Steffen A Bass, Ulrich W Heinz, Tetsufumi Hirano, Chun Shen

Nuclear Theory · Submitted 24 Jan 2011 · 45 references

Pith's verdict: A solid companion paper that documents the VISHNU validation honestly in the body but oversells its scope in the abstract.

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arXiv ID1101.4638 (version 2)

Pith IDZH6IFV6K, Pith's permanent record of this paper and its review

CitationChun Shen, Huichao Song, Steffen A Bass, Tetsufumi Hirano, Ulrich W Heinz. "Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade." arXiv:1101.4638 (2011). https://pith.science/paper/ZH6IFV6K

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Editor's note

read the letter

This is the documentation paper behind the authors' viscosity Letter (arXiv:1011.2783). The headline η/s numbers are not new; what is new is the full comparison set: pion and proton pT spectra across centralities (Fig. 1), identified-particle differential v2(pT) for pions and protons (Fig. 5), the STAR-versus-PHENIX centrality-definition analysis (Fig. 4), and the appendix study of how the MC-Glauber smearing area moves the extracted η/s. That last one is the most useful thing in the paper and I'd point people to it directly: dropping σs from 42 to 4.2 mb pushes the preferred η/s toward 0.16 and spoils the slope of v2/ε against (1/S)dNch/dy, which is a real, honest sensitivity check on a parameter nobody has fixed experimentally. The identified v2(pT) comparison is a genuine out-of-sample test within the framework, since [1] only used the pT-integrated quantity. Credit for that, and credit for stating plainly that the model fails above 60% centrality and that they don't know how to fix it. The stress-test note is right, and it's the one thing I'd actually ask them to change. The abstract says agreement 'at all collision centralities' [abstract:s1] and Sec. V repeats it, but Sec. IV says the peripheral v2 is not reproduced and Sec. III conclusion (iii) says the agreement breaks in the most central PHENIX bins. The quoted constraint 1 < 4π(η/s) < 2.5 therefore rests on roughly 10–60% centrality. That's a one-sentence fix, not a physics problem, but it's the sentence most people will read. Two smaller things. The spectra agreement is not independent evidence for η/s: τ0 is retuned with each η/s to hold the spectra fixed, which the authors say openly, so Fig. 1 mostly demonstrates a degeneracy rather than a success. And the proton spectra sit about 50% above PHENIX; they blame feeddown corrections, which is plausible but unproven. The 30% STAR/PHENIX split in 0–5% is left hanging on a possible 2% centrality shift that is 'presently under study' — fine to flag, but it means the most central bin is unresolved from both directions. None of this is fatal. The physics in the 10–60% window is well done and the failures are disclosed. Worth a referee, mainly to force the abstract to match the body.

Referee report

Significance

If the result holds within its stated domain, it is a useful and non-trivial consistency statement: the same eta/s that fixes the pT-integrated v2/epsilon also reproduces the pT dependence of v2 for pions, protons, and all charged hadrons, and the spectra are simultaneously acceptable. The paper is commendably transparent about its own weaknesses: the ~50% proton normalization offset relative to PHENIX (Sec. III), the failure in the two most peripheral bins (Sec. IV), the STAR/PHENIX 0-5% discrepancy (Fig. 4), the (eta/s, c tau_0) degeneracy in Fig. 1, and the sigma_s dependence of the extracted eta/s (Appendix, Fig. 9) are all stated in the text. The differential v2(pT) comparison is a genuine out-of-sample test relative to [1], since [1] used only the integrated quantity. The main reservation is one of scope: the abstract and Sec. V advertise agreement 'at all collision centralities', which the body does not support at either end of the centrality axis.

Major objections (4)

[Abstract [abstract:s1] and Sec. V (Summary and Conclusions)] The abstract states that the authors 'obtain universally good agreement between theory and experiment for the pT-spectra and differential elliptic flow v2(pT) for both pions and protons at all collision centralities', and Sec. V repeats this. The body contradicts the 'all centralities' qualifier in two places. Sec. IV states 'the inability of VISHNU to describe the elliptic flow in the most peripheral collisions where the experimentally measured values remain large whereas the theoretical predictions decrease rapidly with increasing impact parameter', and closes with 'We do not know how to obtain larger v2 values from the model at large impact parameters.' Separately, conclusion (iii) in Sec. III states that if the PHENIX centrality definition is correct, the uniform agreement 'is broken in the most central collisions', and the STAR/PHENIX 0-5% difference of ~30% (Fig. 4) is attributed to a possible 2% centrality shift that is 'presently under study [27]'. The two ends of the centrality axis are therefore both unresolved, and they are precisely where the linear v2 proportional to epsilon mapping used to normalize the data is weakest (the paper's own footnote 5 flags nonlinear v2(epsilon) for small v2 in very central collisions). The authors acknowledge each failure individually but not the conflict with the summary sentence. Please restrict the abstract and Sec. V claim to the validated range (roughly 10-60% centrality) and state the two excluded regions explicitly in the abstract.
[Sec. III, Fig. 1 and the (eta/s, c tau_0) parameter pairs] The text states that the curves in Fig. 1 correspond to the pairs (eta/s, c tau_0) = (0, 0.4 fm), (0.08, 0.6 fm), (0.16, 0.9 fm), (0.24, 1.2 fm), and that tau_0 is adjusted when eta/s is changed 'to account for the additional radial acceleration caused by the transverse shear pressure gradients', with the explicit aim that 'the different lines in Fig. 1 overlap almost perfectly'. Combined with the statement in Sec. V that 'the pT spectra of identified hadrons (pions and protons) are rather insensitive to the choice of the value of the specific shear viscosity eta/s', this means the spectra agreement in Fig. 1 is partly engineered by the tau_0 retuning and cannot be counted as independent evidence for eta/s. The abstract's phrase 'excellent description of charged and identified hadron spectra' should be qualified accordingly: the spectra constrain the initial-state normalization and tau_0, not eta/s. Please say this explicitly in the abstract or in the first paragraph of Sec. III.
[Sec. III, Fig. 1 (proton panel) and abstract [abstract:s0]] The text states that 'the theoretical proton spectra are uniformly about 50% larger than the PHENIX data but agree nicely with their slope', and attributes the offset to differences between the PHENIX and STAR feeddown corrections. A 50% normalization offset is a large number for a paper whose abstract claims an 'excellent description of charged and identified hadron spectra'. The manuscript should quantify the feeddown systematic rather than assert that it is 'large': what is the estimated feeddown uncertainty on the PHENIX and STAR proton yields, and is 50% within it? If the offset cannot be absorbed by the quoted systematic, the abstract wording should be softened to 'reasonable agreement in shape, with a normalization offset within the feeddown systematics'.
[Sec. IV and Fig. 6 vs. Figs. 2, 3, 5] Figs. 2, 3 and 5 use (eta/s)_QGP = 0.08 (MC-Glauber) and 0.16 (MC-KLN), while Sec. IV states that Fig. 6 'indicates that the chosen (eta/s)_QGP values ... are slightly too small' and that 'the slightly larger values of 0.10 for MC-Glauber and 0.20 for MC-KLN extracted in [1] from fluctuation-corrected v2 data would give better agreement here, too'. The abstract advertises 'values eta/s ... that were recently extracted' from [1], but the figures use smaller values than [1] reports. The reader is left unsure which values the paper actually endorses. Please state once, clearly, the relation between the values used in the figures and those quoted in [1], and whether the quoted range 1 < 4 pi (eta/s)_QGP < 2.5 in Sec. V is meant to cover both sets.

Minor objections (8)

[Sec. II, footnote 1] The footnote says the procedure yields epsilon-bar_part which is 'not identical with, but numerically very close to' the ensemble-averaged <epsilon_part>. Please quantify 'very close' (e.g. the percent-level difference as a function of centrality), since the entire eta/s extraction is normalized by this quantity.
[Sec. II, entropy normalization] The text states 'We have checked that its effects on the centrality dependence of the final dNch/dy are negligible relative to experimental uncertainties', referring to the neglect of the centrality dependence of viscous heating when fixing the hard fraction delta = 0.14. A short quantitative statement or a supplementary panel would make this check verifiable rather than asserted.
[Fig. 5 caption] The caption says the solid symbols denote 'v2{2}/<epsilon^2_part>^{1/2}', whereas Figs. 2 and 3 use <epsilon^alpha_part>^{1/alpha} with alpha from the event-plane resolution. Please explain why the identified-particle comparison uses the rms eccentricity rather than the alpha-corrected one, and whether the two normalizations are numerically close for the 20-50% bins shown.
[Sec. IV, paragraph on event-by-event fluctuations] The discussion of participant-plane vs. reaction-plane averaging is clear, but the reader would benefit from a one-sentence statement of which of the two averaging schemes is used for which figure. As written, Fig. 6a is described as 'reaction-plane averaged' in one sentence and the surrounding text refers to 'participant-plane averaged initial conditions'; please check the labels against the figure caption.
[Sec. IV, peripheral collisions] The statement 'We do not know how to obtain larger v2 values from the model at large impact parameters' would be more useful with a short list of the candidate resolutions that were considered and excluded (e.g. a longer hadronic stage, a different switching temperature, a corona treatment, or a larger low-density viscosity). This is an outlook suggestion, not a request for new calculations.
[Appendix, Fig. 9] The argument that the data disfavor sigma_s = 4.2 mb rests on the slope of v2/epsilon vs. (1/S)dNch/dy no longer matching the universal curve. Given the 25% spread between MC-Glauber and MC-KLN eccentricities already acknowledged in Sec. II, please state how much of the slope mismatch is attributable to the sigma_s change alone and how much to the model spread, so the reader can judge the strength of the exclusion.
[Table I] The table lists R, alpha, and <epsilon^alpha_part>^{1/alpha} for STAR and PHENIX separately, but the caption does not say which of the two columns is used in which figure. A sentence in the caption or in the text would remove the ambiguity.
[Typesetting and typographical errors] There are several typographical errors that should be corrected: 'participiant-plane' in the Fig. 7 caption; 'depenence' in the paragraph discussing Fig. 8; 'validaded' in the paragraph on Bessel-Gaussian fluctuations in Sec. IV; 'coefficents' in footnote 5; and 'an PHENIX' in the sentence beginning 'with a 30% difference between STAR an PHENIX' in Sec. III.

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The paper

The paper claims

A single hybrid simulation, with one shear-viscosity number per initial-state model, reproduces the pion and proton momentum spectra and the elliptic flow at every centrality in 200 A GeV Au+Au collisions at RHIC.

The reading

The paper asks whether one model of the hot, dense matter made in a heavy-ion collision can simultaneously get right three things that are measured separately: how many particles come out, how their momenta are distributed, and how strongly their emission is squeezed into an ellipse. The model, called VISHNU, runs the quark-gluon plasma stage as a viscous fluid with a constant ratio of shear viscosity to entropy density, $T_c < T < 2T_c$, then hands the fluid's output at $T_{sw} = 165$ MeV to a microscopic Boltzmann cascade that follows individual hadrons through their final rescattering. Starting from fluctuating initial entropy profiles generated event by event and then averaged, with two rival prescriptions for how the colliding nuclei deposit entropy, the authors find that the same viscosity that was extracted from the centrality dependence of the integrated elliptic flow also reproduces the differential elliptic flow $v_2(p_T)$ and the $p_T$ spectra of pions and protons across the whole centrality range. The payoff, if the argument holds, is that a single number controls the entire soft sector of the collision, and the paper closes by quoting the constraint $1 < 4π(η/s)_{QGP} < 2.5$.

What carries the argument

The load-bearing object is the hybrid VISHNU pipeline and the compensating pair $(η/s, cτ_0)$ that it makes nearly degenerate in the spectra. The QGP phase is a relativistic viscous fluid with constant $η/s$ between $T_c$ and about $2T_c$; at $T_{sw} = 165$ MeV, chosen to match the measured chemical freeze-out temperature, the fluid is converted to particle distributions and evolved with UrQMD. Initial entropy densities come from two Monte Carlo generators, the MC-Glauber model with finite-size nucleons and a two-component soft-plus-hard entropy deposition, and the MC-KLN model; each event is recentered and rotated so its short axis aligns with the impact parameter, binned by $N_{part}$, and superimposed, so that the smooth profile carries the correct average participant eccentricity $ε_{part}$. The normalization is fixed iteratively to the measured charged multiplicity in the most central bin, and the four parameter pairs used are $(0, 0.4$ fm$)$, $(0.08, 0.6$ fm$)$, $(0.16, 0.9$ fm$)$, and $(0.24, 1.2$ fm$)$ — larger $η/s$ brings more radial flow, which must be offset by a later start time to keep the spectra on top of each other.

Extended reading notes

Core claim

The central claim is that the hybrid code VISHNU, which couples a viscous hydrodynamic description of the quark-gluon plasma to a Boltzmann cascade for the late hadronic stage, gives a uniformly good description of charged and identified hadron spectra and elliptic flow in 200 A GeV Au+Au collisions at RHIC. Concretely, with $(η/s)_{QGP} = 0.08$ for MC-Glauber initial conditions and $(η/s)_{QGP} = 0.16$ for MC-KLN initial conditions — values slightly below but consistent with the $0.10$ and $0.20$ extracted in the companion Letter from the fluctuation- and non-flow-corrected integrated $v_2$ — the calculated $p_T$ spectra of pions and protons and the differential $v_2(p_T)$ of pions, protons, and all charged hadrons agree with STAR and PHENIX data over essentially all centralities. The paper stresses that the spectra are nearly insensitive to $η/s$ once the initial entropy normalization and the starting time $τ_0$ are readjusted together, so the discrimination comes from $v_2/ε$, which degrades visibly when $η/s$ is raised by $1/4π$. The authors also state plainly where the description fails: the two most peripheral centrality bins, where the calculated $v_2$ falls below the data and they say they do not know how to recover the measured values, and the two most central bins, where STAR and PHENIX disagree with each other by about 30% and the PHENIX data would demand a larger effective $η/s$.

Load-bearing premise

The whole extraction rests on the initial fireball eccentricity computed from MC-Glauber or MC-KLN, two models that differ by up to 25% depending on centrality, and the paper itself says this uncertainty completely dominates the error on the extracted viscosity; the appendix shows the preferred value moving from 0.08 toward 0.16 when one unmeasured input of the Glauber model, the transverse smearing area, is changed.

Editorial extensions

If this is right

The soft hadron sector at RHIC — multiplicity, $p_T$ spectra of pions and protons, and both integrated and differential elliptic flow — can be organized by a single viscosity parameter once the initial-state model is fixed.
The extracted range $1 < 4π(η/s)_{QGP} < 2.5$ becomes a quantitative target for calculations of transport coefficients in hot QCD.
Because the spectra are nearly $η/s$-independent after retuning, the paper argues that viscosity should be extracted from the $p_T$-integrated momentum anisotropy rather than from the shape of $v_2(p_T)$.
The failure at peripheral centralities and the near-central STAR/PHENIX disagreement are localized, identifiable discrepancies rather than diffuse disagreement with the whole data set.

Reading between the lines

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

The paper's own appendix shows that shrinking the MC-Glauber transverse smearing area from 42 mb to 4.2 mb pushes the preferred $η/s$ from 0.08 toward 0.16 and spoils the slope of $v_2/ε$ versus $(1/S)dN_{ch}/dy$; an independent, non-model determination of the initial eccentricity would therefore be worth more to this program than any improvement in the flow data themselves.
If the $v_2/ε$ versus $(1/S)dN_{ch}/dy$ curve is truly universal at fixed collision energy and depends only on $η/s$, then repeating the same comparison at LHC energies tests whether that universality survives a factor-of-two jump in the multiplicity density, which is a sharper statement than simply checking whether $η/s$ runs.
The peripheral-collision failure, which the authors note also appears in an ideal-hydrodynamics cascade using a different afterburner, suggests the missing physics sits in the late hadronic stage or in the treatment of the dilute edge of the fireball rather than in the QGP viscosity.
The 30% STAR/PHENIX split in the most central bin, which the authors attribute to a possible 2% centrality-definition shift, is a concrete bookkeeping question: resolving it would decide whether the near-central data really call for a larger effective $η/s$ than the mid-central data.

Original abstract

It is shown that the recently developed hybrid code VISHNU, which couples a relativistic viscous fluid dynamical description of the quark-gluon plasma (QGP) with a microscopic Boltzmann cascade for the late hadronic rescattering stage, yields an excellent description of charged and identified hadron spectra and elliptic flow measured in 200 A GeV Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC). Using initial conditions that incorporate event-by-event fluctuations in the initial shape and orientation of the collision fireball and values eta/s for the specific shear viscosity of the quark-gluon plasma that were recently extracted from the measured centrality dependence of the eccentricity-scaled, p_T-integrated charged hadron elliptic flow, we obtain universally good agreement between theory and experiment for the p_T-spectra and differential elliptic flow v_2(p_T) for both pions and protons at all collision centralities.

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, 2,550 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.35 · compares with prior results 0.20 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

It is shown that the recently developed hybrid code VISHNU, which couples a relativistic viscous fluid dynamical description of the quark-gluon plasma (QGP) with a microscopic Boltzmann cascade for the late hadronic rescattering stage, yields an excellent description of charged and identified hadron spectra and elliptic flow measured in 200 A GeV Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC). Using initial conditions that incorporate event-by-event fluctuations in the initial shape and orientation of the collision fireball and values eta/s for the specific shear viscosity of the quark-gluon plasma that were recently extracted from the measured centrality dependence of the eccentricity-scaled, p_T-integrated charged hadron elliptic flow, we obtain universally good agreement between theory and experiment for the p_T-spectra and differential elliptic flow v_2(p_T) for both pions and protons at all collision centralities.

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	It is shown that the recently developed hybrid code VISHNU, which couples a relativistic viscous fluid dynamical description of the quark-gluon plasma (QGP) with a microscopic Boltzmann cascade for the late hadronic rescattering stage, yields an excellent description of charged and identified hadron spectra and elliptic flow measured in 200 A GeV Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC).	result 0.84	0.89	0.87	asserted 1.00
s1	Using initial conditions that incorporate event-by-event fluctuations in the initial shape and orientation of the collision fireball and values eta/s for the specific shear viscosity of the quark-gluon plasma that were recently extracted from the measured centrality dependence of the eccentricity-scaled, p_T-integrated charged hadron elliptic flow, we obtain universally good agreement between theory and experiment for the p_T-spectra and differential elliptic flow v_2(p_T) for both pions and protons at all collision centralities.	result 0.88	0.93	0.29	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.99 · evidence from simulation or computation 0.99.

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 2.** FIG. 2: (Color online) Eccentricity-scaled elliptic flow

**Figure 3.** FIG. 3: (Color online) Same as Fig. 2, but with

**Figure 4.** FIG. 4: Comparison of the STAR [19] and PHENIX

**Figure 5.** FIG. 5: (Color online) Same as Fig. 2, but for identified pions

**Figure 6.** FIG. 6: (Color online) Integrated charged hadron elliptic fl

**Figure 7.** shows the eccentricity (panel (a)) and transverse area (panel (b)) of the participant-plane averaged initial entropy density distribution as a function of the number Npart of participant (“wounded”) nucleons in Au+Au collisions, for two values of the smearing area σs. We see that a smaller smearing area (more pointlike particle production) leads to larger initial fireball eccentricities εpart and smaller transverse areas S. While the effect of varying σs on S is simply an offset, for εpart 0 0.1 0.2 0.3 0.4 0.5 0.6 εpart -- σs = 42 mb σs = 4.2 mb 0 100 200 300 400 Npart 0 5 10 15…

**Figure 8.** FIG. 8: (Color online) (a) Centrality dependence of

**Figure 9.** FIG. 9: (Color online) Comparison of the universal theoret

Figures reproduced from arXiv:1101.4638 by the authors.

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Forward citations

Cited by 17 Pith papers

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Bayesian calibration of a multistage heavy-ion model to LHC data gives η/s = 0.085 (+0.026/-0.025) and a slowly rising temperature dependence.
An upper bound on transport
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Diffusion in a local quantum system is bounded above by D less than or of order v squared times tau_eq, where v is the operator-growth lightcone velocity and tau_eq the local equilibration time.
Bridging Soft-Hard Transport Properties of Quark-Gluon Plasmas with CUJET3.0
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Adding chromo-magnetic monopole degrees of freedom near Tc to a pQCD jet-quenching model reproduces both R_AA and v2 of high-pT hadrons at RHIC and LHC, resolving a long-standing tension.
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Calibrating an event-by-event heavy-ion model to ALICE multiplicity and flow data with Gaussian-process emulation and MCMC yields eta/s near 0.06 for Glauber and near 0.16 for KLN initial conditions, with full posteri...

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The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
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Rapidity dependence of mean transverse momentum fluctuation and decorrelation in baryon-dense medium
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Estimating initial state and quark-gluon plasma medium properties using a hybrid model with nucleon substructure calibrated to $p$-Pb and Pb-Pb collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV
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A single calibrated hydrodynamic model with composite nucleons reproduces charged-particle yields, mean pT and flow cumulants in both p-Pb and Pb-Pb collisions at 5.02 TeV, preferring nucleon hot spots roughly 0.47 fm wide.
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How the literature uses it

48 arXiv papers cite this in 61 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 · 40 sentences without a confident label

Uses its method or tool 4 papers

In this work, we opt for a mature, well-tested set of event-by-event models [ref] with an established track record of describing diverse RHIC and LHC data [ref] .

Quantifying properties of hot and dense QCD matter through systematic model-to-data comparison · Model · 0.87
In order to get the quenched leading hadron spectra at high $p_T$, this parton-level distribution is convoluted with LO pQCD pp spectra (for gluon and ligh quark) [ref] or FONLL pp spectra (for charm and bottom) [ref] , folded over the MC-Glauber A+A initial hard scattering probability distribution [ref] , and hadronized with parton fragmentation functions (LO KKP [ref] for gluon and light quark[There are systematic studies that confront current NLO parton fragmentation functions with inclusive charged-particle spectra at hadron colliders and compare the varied consistencies between NLO FFs and data, cf. e.g. [ref] .

Bridging Soft-Hard Transport Properties of Quark-Gluon Plasmas with CUJET3.0 · Perturbative QCD jet quenching: DGLV opacity expansion · 0.87
We neglect rescatterings in the hadronic phase [ref] , but implement strong decays of all hadronic resonances into stable hadrons using an adapted version of the decay code of [ref] .

Hydrodynamic predictions for 5.44 TeV Xe+Xe collisions · Hydrodynamic evolution · 0.99

Uses its data or values 3 papers

Simulations with an evolution-averaged $η/s$ based on comparisons with combined experimental data from top-RHIC and LHC energies [ref] extracted a possible range of $1<(η/s)/(1/4π)<5$.

Quark Flavour Dependence of the Shear Viscosity in a Quasiparticle Model · Introduction · 0.91
However, in [ref] the initial time $t_i=1$ fm/c used at the LHC was bigger than at RHIC where $t_i=0.6$ fm/c [ref] , based on the requirements of the hydrodynamic simulations to fit the low $p_T$ elliptic flow data.

Holographic light quark jet quenching at RHIC and LHC via the shooting strings · Calculation of $R_AA$ · 0.80
Some characteristic values of the relevant parameters for the quark-gluon plasma are $T ∼330 MeV$, $τ_th ∼1 fm/c$, $s ∼85 fm^-3$ [ref] and $η/s ∼0.15 ħ/k_B$ [ref] .

Thermalization, Viscosity and the Averaged Null Energy Condition · The quark-gluon plasma · 0.96

Compares with it 4 papers

In Fig. [ref], the $v_2$ measurements for two centrality intervals, the 10–20$%$ in the left column and the 40–50$%$ interval in the right column, are compared to hydrodynamic calculations coupled to a hadronic cascade model (VISHNU) [ref] .

Elliptic flow of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV · Comparison with hydrodynamic calculations · 0.94
For example, the extracted specific QGP viscosity $1/4π<(η/s)_QGP< 2.5×1/4π$ from the VISHNU calculations with MC-Glauber and MC-KLN initial conditions [ref] and the implemented $η/s = 0.095$ (with the same bulk viscosity parametrization ) in the MUSIC simulations with the IP-Glasma initialization [ref] are both consistent with this quantitative extracted results from the DUKE-OSU collaborations.

Collective flow and hydrodynamics in large and small systems at the LHC · Quantitative extractions of the QGP shear and bulk viscosity with massive data evaluations · 0.96
Figure [ref] shows the measured pion and proton elliptic flow measured by STAR compared to VISHNU [ref] model calculations.

Elliptic Flow: A Brief Review · The Perfect Liquid · 0.93

Cites it as support 1 paper

The larger integrated charged hadron elliptic flow at the LHC implies a larger total momentum anisotropy [ref] and suggests a higher efficiency of the QGP fluid for converting the initial spatial deformation of the collision fireball into anisotropic collective flow.

Elliptic flow in 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions: insights from viscous hydrodynamics + hadron cascade hybrid model · Introduction · 0.98

Cites it as background 8 papers

Based on these experimental data, lots of studies on properties of hadronic $p_T$ distribution are carried out, which greatly improve people's understandings on property of the created hot nuclear matter and the mechanism of hadron production in relativistic heavy-ion collisions [ref] .

Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions · Introduction · 0.81
Most hydrodynamic calculations at these energies therefore assume boost invariance and employ a 2+1D hydrodynamic evolution when investigating transverse flow and it's fluctuations [ref] .

Rapidity dependence of mean transverse momentum fluctuation and decorrelation in baryon-dense medium · Introduction · 0.87
Furthermore, various hybrid models have recently been developed, where the hydrodynamical evolution is coupled with a hadronic cascade afterburner [ref] .

Systematics of the charged-hadron P_T spectrum and the nuclear suppression factor in heavy-ion collisions from sqrt{s}=200 GeV to sqrt{s} =2.76 TeV · Introduction · 0.95

What it cites · 24 sentences without a confident label

Builds on 1 paper

In this Appendix we add a few aspects that, due to space limitations, were left out from the discussion in Ref. [ref] of the almost universal dependence of the eccentricity-scaled elliptic flow $v_2/$ on the charged hadron multiplicity density $(1/S)$ on which our extraction of the QGP shear viscosity $(η/s)_QGP$ from RHIC data was based.

200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid · Section · 0.89

Uses the method or tool of 1 paper

In a recent article [ref] we extracted the shear viscosity to entropy density ratio $(η/s)_QGP$ of the quark-gluon plasma (QGP) created in heavy-ion collisions at RHIC by comparing experimental data for the eccentricity-scaled elliptic flow $v_2/$ with calculations performed with [ref] , a hybrid model that describes the QGP stage of the expansion of the collision fireball macroscopically with viscous hydrodynamics (in which $(η/s)_QGP$ enters as an input parameter) but switches to a microscopic description in the late hadronic phase where we solve the Boltzmann equation with [ref] .

200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid · Introduction · 0.85

Compares with 1 paper

Figure [ref] demonstrates excellent agreement between and the experimental data, over the entire range of centralities except for the two most peripheral bins, if we use $(η/s)_QGP0.08$ for MC-Glauber (left column) and $(η/s)_QGP0.16$ for MC-KLN initial conditions (right column).[Fig. [ref] also shows that in both cases the agreement is destroyed when increasing $(η/s)_QGP$ by $1/4π0.08$.] These values are a little smaller than, but consistent with the corresponding values $(η/s)_QGP ≃ 0.1$ for MC-Glauber and $(η/s)_QGP ≃ 0.2$ for MC-KLN that were extracted in [ref] from the $p_T$-integrated, non-flow and fluctuation corrected charged hadron $v_2$.

200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid · Results: comparison of spectra and $v_2$ to data · 0.96

Discussion

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