Azimuthal anisotropy in Au+Au collisions at sqrtsNN = 200 GeV

STAR Collaboration

REVIEW

Azimuthal anisotropy in Au+Au collisions at sqrtsNN = 200 GeV

STAR Collaboration

Nuclear Experiment · Submitted 29 Sep 2004 · 70 references

Pith's verdict: A consolidation paper whose real value is the method bookkeeping, not the scaling headline; the v2/n collapse is weaker than 'within statistical errors' implies.

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arXiv IDnucl-ex/0409033 (version 3)

Pith ID7BGBJWWD, Pith's permanent record of this paper and its review

CitationSTAR Collaboration. "Azimuthal anisotropy in Au+Au collisions at sqrtsNN = 200 GeV." arXiv:nucl-ex/0409033 (2004). https://pith.science/paper/7BGBJWWD

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Editor's note

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This is a STAR summary paper, and it is honest about being one: v1{3}, v4, v6, and most of the charged-hadron v2 systematics are already published. The genuinely new material is narrower than the title suggests — the six-method comparison on identical events and cuts (Fig. 29), the nonflow parameter g2 versus centrality at 200 GeV set against 130 GeV and SPS 17 GeV (Fig. 31), the eccentricity-fluctuation comparison (Fig. 32), and identified-particle v4 for pions, anti-protons, K0S and Lambda (Fig. 25, Table III). That is a real contribution and it is done carefully. Running six methods on the same events with the same cuts, then quoting the residual two-particle versus multi-particle spread as a 10-20% systematic instead of burying it, is exactly the right instinct. The Blast Wave is labeled a toy model and a parameterization throughout, and the paper does not dress fits as predictions. The half-field discrepancy is disclosed as unexplained rather than smoothed over. Credit where due: this is the reference I would hand someone who wants to know how much of a v2 number is method and how much is physics. Now the soft spot, and it is the one the stress test points at. Sec. VI A says the scaled v2 of kaons, anti-protons and Lambda 'lie on a universal curve within statistical errors.' That phrasing overstates. Fig. 33 carries a 10% systematic band, and Sec. V B is explicit that the two-particle versus multi-particle gap cannot be split into nonflow versus fluctuations. A species-dependent bias of that order would be invisible in the ratio panel. The species also come from different PID chains with different pt reach and residual backgrounds, and the baryon anchor is the anti-proton — the species with the acknowledged negative-v2 anomaly in central collisions. The paper is candid about all of this in pieces; it just does not add it up in the sentence that carries the claim. The baryon-over-meson crossing, which is what actually distinguishes coalescence from mass-ordering, is hedged ('seem to indicate') and rests on RICH points with large errors. None of this makes the scaling wrong. It makes the evidence weaker than the headline. The v4/v22 = 1.2 against a coalescence expectation of 0.75 is a genuine tension the authors state plainly, and I give them credit for not hiding it. Who should read it: anyone in the RHIC flow program, and anyone who needs a citable treatment of method systematics. Send it to referees — the method-comparison section will be cited for years even if the scaling sentence gets walked back.

Referee report

Significance

The paper is a reference compilation for RHIC flow measurements and is significant in several respects. It runs multiple independent analysis methods on the same events and the same cuts, which is the right way to expose method-dependent systematics, and it quotes the residual two-particle versus multi-particle spread as a 10 to 20 percent systematic rather than suppressing it. The quark-number scaling observation (Fig. 33, Fig. 34) is a falsifiable, parameter-free-in-form prediction of coalescence, and the paper states where it fails (pions) as clearly as where it holds. The v4/v2^2 ratio near 1.2 is a genuinely non-trivial number that any coalescence or hydrodynamic account must reproduce, and the paper reports it even though it sits uneasily with the simplest coalescence estimate. Data tables are made public, and the Blast Wave parameters are tabulated for reuse. These are real strengths and they are why the paper is worth publishing in essentially its present form.

Major objections (4)

[Sec. VI A, Fig. 33] The central scaling claim is tested by fitting a polynomial to the scaled v2 of the species that are then said to collapse onto it, so the ratio panel of Fig. 33 is a residual plot by construction and its flatness is not by itself evidence of a universal curve. No goodness-of-fit measure is quoted for that fit, and no pt/n range over which the fit is performed is stated. Please report χ2/ndf for the ratio panel, separately for each species, and strengthen the test by fitting to a subset (for example kaons only, or kaons plus Lambdas) and then showing that the remaining species fall on the extrapolated curve. As written, the reader cannot distinguish a genuine collapse from a fit flexible enough to absorb modest species-dependent offsets of the size of the quoted 10 percent band.
[Sec. IV B 3 and Sec. VI A] The justification for using the standard event-plane v2 throughout the identified-particle analysis rests on a nonflow check performed only for charged hadrons in the 20 to 60 percent centrality range (Fig. 20), yet the 10 percent systematic band in Fig. 33 is applied uniformly to pions, kaons, anti-protons, and Lambdas, which are measured with three different particle-identification techniques and have different residual backgrounds. Nonflow is expected to differ between mesons and baryons and between PID methods, and the baryon anchor of the scaling curve is the anti-proton sample, which the paper itself notes has a contamination problem and shows an anomalous negative v2 in central collisions (Fig. 7c). Please either repeat the modified event-plane comparison for at least one identified species, or state explicitly that species-dependent nonflow is assumed absent and quantify what size of species-dependent bias the scaling test could tolerate before the collapse would be destroyed.
[Sec. VI A, Table III, Eq. (14)] The measured v4/v2^2 ≈ 1.2 for charged hadrons and pions is in tension with the values 3/4 (meson) and 2/3 (baryon) that follow from the same coalescence framework combined with the parton relation v4^q = (v2^q)^2, and the paper resolves the tension by positing a proportionality constant of about 2 in Eq. (14). This matters for the interpretation of the v2/n scaling, because the two claims are presented as mutually supporting evidence for coalescence. Please state explicitly how strongly the v2/n scaling conclusion depends on the coalescence framework being correct in detail, and whether the v2 scaling survives as an empirical regularity if Eq. (14) is not assumed. A short paragraph separating the two claims would make the logic of Sec. VI A much easier to assess.
[Sec. VI D, Fig. 38] The Blast Wave parameters ρ2, ρ4, ε, ρ0, and T are plotted against centrality with no uncertainties, and the text states that ε comes out the same for the three data sets while the small differences in v2 are forced into ρ2. Without parameter errors or a covariance matrix the reader cannot judge whether the claimed maximum of ρ2 in the 30 to 60 percent centrality region is statistically meaningful, nor how strongly ρ2 and ε are anti-correlated. Please add fit uncertainties to Fig. 38 and, if available, the ρ2–ε correlation coefficient. The per-data-set χ2 values quoted in the text (14/6 for pions, 7/4 for kaons, 17/10 for protons) also deserve a sentence of interpretation, since the pion value corresponds to a fit quality that is marginal rather than good.

Minor objections (10)

[Abstract and Sec. V B] The abstract states that nonflow effects are extracted from the data, but Sec. V B concludes that either nonflow or flow fluctuations can explain the two-band structure and that most probably it is some of both. The abstract should be softened to reflect that the extraction is not unique, for example by saying that nonflow and fluctuation effects are bounded rather than extracted.
[Sec. IV B 1] The statement that adding the absolute value 0.0025 to the half-field v2 values brings them into agreement with the full-field data is unusual, since v2 is a ratio and an additive offset is not a natural form for a reconstruction systematic. Please justify this procedure or present the comparison in a form that makes the assumed systematic explicit.
[Fig. 33 caption and Sec. VI A text] The caption states that pions are not plotted in the top panel, while the text discusses the pion deviation in the ratio panel. Please make the caption and text consistent about which species appear in which panel, and state which species enter the polynomial fit.
[Sec. IV B 1 and Fig. 33] The text says only anti-protons are used at low pt because of proton contamination, but the figures and Table III are labeled p + pbar. Please state which sample actually enters Fig. 33 and Table III, and over what pt range the proton and anti-proton samples are combined.
[Sec. IV B 2, Fig. 17] The Monte Carlo test of the FTPC momentum resolution assumes an input v2(pt) shape at forward pseudorapidity. If that input shape was taken from mid-rapidity, the test cannot discriminate between a genuine change of shape at forward η and smearing. Please state what input shape was assumed and note the resulting limitation on the conclusion.
[Sec. V A] The relative systematic error of at least 2 percent attributed to different software implementations of the same method is quoted without saying how it was estimated. A sentence on the procedure would let the reader judge whether 2 percent is adequate.
[Table II] The multiplicity column is described as a mean with a standard deviation spread, but the symbol σ is also used elsewhere for resolution and for the nonflow width parameter. Please disambiguate the notation in the table caption.
[Figs. 22 and 24] Fig. 22 refers to surface shell Blast Wave fits while Fig. 24 refers to filled elliptic cylinder fits. Please state in each caption which Blast Wave variant is shown, since the two have different parameter sets and the parameters in Fig. 38 belong to one specific variant.
[Sec. III A, Eq. (2)] The notation for the first-order event planes (ΨFTPC11, ΨFTPC21, and later Ψa1, Ψb1) is not defined consistently. Please add one sentence fixing the superscript and subscript convention at first use.
[Sec. IV B 1, Fig. 9 inset] The inset shows neutral kaons slightly below charged kaons at low pt. Please state whether this difference is significant given the quoted systematic uncertainties on the two identification methods, since it bears on the species-dependent systematics relevant to the scaling analysis.

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The paper

The paper claims

Dividing flow by quark count collapses hadrons onto one curve

The reading

The STAR collaboration asks a deceptively simple question about gold-on-gold collisions at 200 GeV per nucleon pair: when the debris flies out preferentially in some azimuthal directions, does the pattern remember the quarks that made the hadrons? The paper's central answer is yes. Take the elliptic flow $v_2$ of a hadron, divide it by the number of constituent quarks $n$ in that hadron (two for mesons, three for baryons), and plot it against transverse momentum also divided by $n$. Charged and neutral kaons, anti-protons, and $Lambda+bar{Lambda}$ then fall on a single curve above $p_t/n approx 0.6$ GeV/$c$; only pions sit off it. If that collapse is real, hadrons in the intermediate momentum range are not produced by independent string fragmentation but by quarks recombining while they still carry the collective motion of the surrounding medium, which is a direct argument that the medium was deconfined. The paper also reports a companion regularity for the fourth harmonic, $v_4$ scaling as $v_2^2$ with a ratio near 1.2, and it compares analysis methods to argue that the residual non-flow correlations do not fake these patterns.

What carries the argument

The machinery is a comparison of many ways of measuring the same Fourier harmonics and then a rescaling by quark content. Event-plane methods correlate each particle with a plane reconstructed from the rest of the event, corrected for finite resolution; cumulant methods of order two, four and six subtract non-flow correlations order by order; the scalar-product and $q$-distribution methods provide independent handles, and the spread between two-particle and multi-particle results is used to bound the non-flow contamination $g_2 = N_{WN}(v_2^2{2} - v_2^2{4})$. On top of that sits the scaling ansatz: a hadron made of $n$ constituent quarks inherits $n$ times the quark anisotropy and $n$ times the quark momentum scale, so plotting $v_2/n$ versus $p_t/n$ should collapse mesons and baryons onto one curve if coalescence is the production mechanism. The same logic extended to the fourth harmonic yields relations between meson and baryon $v_4/v_2^2$ that the data can be checked against.

Extended reading notes

Core claim

The paper is a synthesis of STAR's azimuthal-anisotropy measurements in Au+Au at $sqrt{s_{NN}} = 200$ GeV, and its load-bearing claim is constituent-quark-number scaling. For identified particles from minimum-bias and mid-central collisions, the scaled quantity $v_2/n$ plotted against $p_t/n$ is described by one common curve above $p_t/n approx 0.6$ GeV/$c$ for $K^0_S$, $K^pm$, $p+bar{p}$, and $Lambda+bar{Lambda}$, while pions deviate. The authors read this as evidence that hadron formation at intermediate $p_t$ proceeds by coalescence of constituent quarks that already carry the anisotropic motion, which in turn supports the picture of a deconfined, collectively flowing partonic stage. A second regularity is reported: $v_4$ scales with $v_2^2$, with the ratio $v_4/v_2^2$ near 1.2 for charged hadrons and pions and roughly independent of $p_t$ (Table III). The paper is candid that this is larger than a simple coalescence estimate ($3/4$ for mesons, $2/3$ for baryons if $v_4^q = (v_2^q)^2$), so either the partonic relation needs a constant near 2 or the coalescence picture needs refinement. The paper also documents the supporting apparatus: directed flow $v_1$ from mixed-harmonic event planes, the sign of $v_2$ confirmed positive (in-plane), the bell-shaped fall-off of $v_2$ with pseudorapidity, high-$p_t$ $v_2$ and $v_4$ against jet-quenching models, a non-flow parameter $g_2$ extracted from the difference between two- and four-particle cumulants, and Blast Wave fits that reproduce spectra, $v_2$ and $v_4$ up to 1-2 GeV/$c$ with smoothly varying parameters.

Load-bearing premise

The scaling claim rests on the assumption that below about 2 GeV/$c$ the simple event-plane measurement is clean enough of non-flow correlations for every identified species and centrality, an assumption the paper justifies only with charged-hadron comparisons in the 20-60% centrality range.

Editorial extensions

If this is right

If quark-number scaling holds, the anisotropy measured in hadrons is a direct readout of the momentum anisotropy of quarks before hadronization, giving an experimental window on the partonic stage rather than only on the final hadron gas.
The observed crossover at intermediate $p_t$, where three-quark baryons overtake two-quark mesons in $v_2$, becomes a signature of a change in hadron production mechanism rather than a smooth hydrodynamic mass ordering.
The measured $v_4/v_2^2 approx 1.2$ sets a quantitative target that any coalescence or hydrodynamic calculation must hit, and the paper notes hydrodynamic predictions near 0.3-0.7 fall short.
The extracted non-flow parameter $g_2$ falling by roughly a factor of three from central to peripheral collisions favours eccentricity-fluctuation explanations over a constant non-flow term, which changes how two-particle flow measurements should be interpreted.
Blast Wave parameters ($T$, $rho_0$, $rho_2$, $rho_4$, eccentricity) varying smoothly with centrality give a compact, reusable characterisation of a large body of spectra and flow data below 1-2 GeV/$c$.

Reading between the lines

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

The scaling test is done with two-particle-dominated measurements, and the paper itself estimates those may be 10-20% high; a species-dependent non-flow bias could mimic or mask a collapse, so a four-particle cumulant version of the same plot for identified kaons, protons and Lambdas would be the decisive version of this figure.
The pion deviation is attributed partly to resonance-decay feed-down and partly to the pion's small mass relative to constituent-quark masses; if the feed-down explanation is right, removing decay pions from the sample should move them toward the universal curve, which is a checkable prediction the paper does not perform.
The factor-of-about-two mismatch between the measured $v_4/v_2^2$ and the simple coalescence estimate suggests the partonic anisotropy itself is not simply quadratic in $v_2$; a measurement of $v_6$ scaling in the same framework would discriminate between a modified coalescence relation and a genuine higher-harmonic component in the initial geometry.
The unexplained half-field discrepancy at low $p_t$, which the authors flag as not understood, is a reminder that track-merging systematics can produce negative non-flow; the same effect, if present at reduced magnitude in full-field data, would bias the low-$p_t$ end of the scaling curve.

Original abstract

The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a Blast Wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v_2, scaling with the number of constituent quarks and parton coalescence is discussed. For v_4, scaling with v_2^2 and quark coalescence is discussed.

The compiled record

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

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,275 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a Blast Wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v_2, scaling with the number of constituent quarks and parton coalescence is discussed. For v_4, scaling with v_2^2 and quark coalescence is discussed.

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	The results from the STAR Collaboration on directed flow (v_1), elliptic flow (v_2), and the fourth harmonic (v_4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at sqrtsNN = 200 GeV are summarized and compared with results from other experiments and theoretical models.	contribution 0.97	0.80	0.16	asserted 0.86
s1	Results for identified particles are presented and fit with a Blast Wave model.	method 0.71	0.86	0.05	asserted 0.98
s2	Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data.	method 0.89	0.86	0.06	asserted 0.96
s3	For v_2, scaling with the number of constituent quarks and parton coalescence is discussed.	interpretation 0.86	0.55	0.10	unclear 0.61
s4	For v_4, scaling with v_2^2 and quark coalescence is discussed.	interpretation 0.80	0.57	0.09	unclear 0.60

What kind of paper the classifier reports this is: empirical study 0.77 · evidence from observation or experiment 0.58.

What was examined, and what was not

sources read

arXiv listing abstract v3

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: (color online). The event plane resolutions as a func

**Figure 2.** FIG. 2: (color online). Directed flow of charged hadrons

**Figure 3.** FIG. 3: (color online). The product of

**Figure 13.** FIG. 13: (color online). The top panel shows the charged

**Figure 14.** FIG. 14: (color online). The ratio of the scalar product

**Figure 15.** FIG. 15: (color online). Charged hadron

**Figure 16.** FIG. 16: (color online). Charged hadron

**Figure 22.** FIG. 22: (color online). Graphs of

**Figure 23.** FIG. 23: (color online). A polar graph of the distribution

**Figure 26.** FIG. 26: (color online). The ratio

**Figure 28.** FIG. 28: (color online). High

**Figure 31.** FIG. 31: (color online). The nonflow parameter,

**Figure 32.** FIG. 32: (color online). Upper panel: The ratio

**Figure 33.** FIG. 33: (color online). Top panel: Identified particle

**Figure 34.** FIG. 34: (color online). Top panels: The

**Figure 36.** shows the centrality dependence of pion and anti-proton v2 compared with hydrodynamic results [61]. The three centrality bins shown are described in Table II. Systematic uncertainties, such as the matching of the centralities, are not included. Also, from the

**Figure 37.** FIG. 37: (color online). Schematic illustration of an ellip

**Figure 38.** FIG. 38: (color online). The Blast Wave parameters

**Figure 39.** FIG. 39: (color online). For centrality 20–30% we show

Showing 30 of the paper's 39 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:nucl-ex/0409033 by the authors.

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Forward citations

Cited by 41 Pith papers

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

Thermal and geometric normal modes of spectral fluctuations in heavy-ion collisions
nucl-th 2026-04 unverdicted novelty 7.0 of 10

Rotated PCA of simulated Pb+Pb spectra separates spectral fluctuations into a coherent thermal mode that fully explains v0(pT) and a double-node geometric mode that drives the low-pT sign change of v02(pT).
QCD Shear Viscosity at (almost) NLO
hep-ph 2018-02 conditional novelty 7.0 of 10

Including next-to-leading order corrections in the strong coupling lowers the perturbative QCD shear-viscosity-to-entropy ratio by a factor of three to five, with most of the shift coming from the transverse momentum ...
Charmed baryon-to-meson ratios inside jets as a discriminator of hadronization mechanisms: from color reconnection in p+p to coalescence in Pb+Pb
hep-ph 2026-10 conditional novelty 6.0 of 10

The in-jet Λc+/D0 ratio is predicted to be enhanced by color reconnection in p+p and suppressed by thermal coalescence in Pb+Pb, providing a jet-based discriminator of hadronization mechanisms.
Constraining Light and Strange Flavor Equilibration in Relativistic Heavy-Ion Collisions
hep-ph 2026-08 accept novelty 6.0 of 10

A Bayesian analysis of Au+Au collisions shows that strange quarks in the quark-gluon plasma are initially less abundant than light quarks and approach chemical equilibrium more slowly.
Longitudinal Dynamics of Large and Small Systems from a 3D Bayesian Calibration of RHIC Top-energy Collision Data
nucl-ex 2026-01 conditional novelty 6.0 of 10

A 3D Bayesian calibration of RHIC Au-Au and d-Au data constrains the longitudinal initial state and QGP viscosity, and its posterior predicts p-Au and 3He-Au flow measurements.

Show 36 more citing papers

From hydro to jet quenching, coalescence and hadron cascade: a coupled approach to solving the $R_{AA}\otimes v_2$ puzzle
hep-ph 2021-03 conditional novelty 6.0 of 10

A coupled hydrodynamics, jet-quenching, coalescence, and hadron-cascade simulation reproduces hadron suppression and elliptic flow together across all transverse momenta in Pb+Pb collisions.
Phenomenological constraints on the transport properties of QCD matter with data-driven model averaging
hep-ph 2020-10 conditional novelty 6.0 of 10

Bayesian model averaging over three hadronization prescriptions gives shear viscosity to entropy density near 0.1 and bulk viscosity to entropy density near 0.05 to 0.1 for quark-gluon plasma at 150 to 250 MeV, with n...
Magnetic fields in heavy ion collisions: flow and charge transport
hep-ph 2019-08 conditional novelty 6.0 of 10

Ideal MHD simulations of heavy-ion collisions find that a chiral magnetic field encoded in the initial conditions is transported by the expanding plasma into a late-time electric charge dipole perpendicular to the rea...
Normalized symmetric cumulants as a measure of QCD phase transition: a viscous hydrodynamic study
hep-ph 2019-08 conditional novelty 6.0 of 10

A viscous hydrodynamic study shows that normalized symmetric cumulants of flow harmonics can discriminate a crossover QCD equation of state from a first-order one at 62.4 GeV Au+Au collisions.
Chemical Equilibration in Hadronic Collisions
hep-ph 2018-11 conditional novelty 6.0 of 10

Full QCD effective kinetic theory shows chemical equilibration in an expanding quark-gluon plasma occurs after hydrodynamization but before thermalization, implying collisions with dN_ch/deta greater than about 100 re...
Charge-dependent Flow Induced by Magnetic and Electric Fields in Heavy Ion Collisions
hep-ph 2018-06 conditional novelty 6.0 of 10

Electromagnetic fields in heavy-ion collisions generate charge-dependent flow: rapidity-odd Delta v1 and Delta v3 from Faraday, Lorentz and spectator Coulomb forces, and rapidity-even Delta v2 and Delta <pT> from the ...
Elliptic flow of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
nucl-ex 2014-05 accept novelty 6.0 of 10

Identified hadrons in Pb-Pb collisions at 2.76 TeV show mass-ordered elliptic flow at low momentum and only approximate number-of-constituent-quark scaling, with ±20% deviations above 3 GeV/c.
Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV
nucl-ex 2013-10 accept novelty 6.0 of 10

CMS measured the n = 3 to 6 azimuthal anisotropy harmonics of charged particles in 2.76 TeV PbPb collisions with three independent analysis methods, finding a pattern consistent with a strongly coupled fluid whose ini...
Long-range angular correlations of $\rm \pi$, K and p in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV
nucl-ex 2013-07 accept novelty 6.0 of 10

In proton-lead collisions at 5.02 TeV, the second-order azimuthal coefficient v2 is smaller for protons than for pions below about 2 GeV/c and larger above it, a mass ordering that resembles heavy-ion elliptic flow.
Measurement of the distributions of event-by-event flow harmonics in lead--lead collisions at sqrt(s_NN)=2.76 TeV with the ATLAS detector at the LHC
hep-ex 2013-05 accept novelty 6.0 of 10

Unfolded event-by-event distributions of v2, v3 and v4 in 2.76 TeV Pb+Pb collisions show non-Gaussian elliptic-flow fluctuations that multi-particle cumulants cannot resolve at present precision.
Third Harmonic Flow of Charged Particles in Au+Au Collisions at sqrtsNN = 200 GeV
nucl-ex 2013-01 accept novelty 6.0 of 10

In 200 GeV Au+Au collisions, triangular flow v3 falls steadily with increasing pseudorapidity separation between the correlated particles and shows no plateau anywhere inside the STAR acceptance.
Ultra-relativistic nuclear collisions: event shape engineering
nucl-ex 2012-08 conditional novelty 6.0 of 10

Cutting on the reduced flow-vector magnitude q_n in one subevent selects collisions with a specific initial geometry, and the resulting flow distributions in a second subevent remain well described by a Bessel-Gaussian form.
Determining initial-state fluctuations from flow measurements in heavy-ion collisions
nucl-th 2011-04 accept novelty 6.0 of 10

Ratios of mixed-harmonic flow correlations cancel the hydrodynamic response coefficients, leaving quantities that measure the initial-state geometry of a heavy-ion collision directly.
QCD Equation of State and Hadron Resonance Gas
hep-ph 2009-12 conditional novelty 6.0 of 10

Most of the discrepancy between lattice QCD thermodynamics and the hadron resonance gas is explained by lattice cutoff and quark-mass shifts in the hadron spectrum, and the authors release a matched equation of state ...
Long range rapidity correlations and jet production in high energy nuclear collisions
nucl-ex 2009-09 accept novelty 6.0 of 10

In central Au+Au collisions at 200 GeV, a narrow-in-azimuth, long-in-rapidity correlated yield (the ridge) persists for trigger pT above 6 GeV/c and has a transverse-momentum spectrum similar to bulk hadrons, unlike t...
The Importance of Correlations and Fluctuations on the Initial Source Eccentricity in High-Energy Nucleus-Nucleus Collisions
nucl-ex 2007-11 accept novelty 6.0 of 10

Spatial correlations among participating nucleons make the fourth-order participant eccentricity cumulant deviate from the smooth-matter eccentricity by almost a factor of two in Cu+Cu collisions, breaking a widely us...
How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
hep-ph 2004-12 conditional novelty 6.0 of 10

Heavy-quark diffusion in the quark-gluon plasma is computed from perturbative QCD and propagated through a hydrodynamic simulation, yielding charm R_AA and elliptic flow as functions of a single transport coefficient.
Elliptic flow of $\phi$ and $\Omega$ via quark recombination mechanism in relativistic heavy-ion collisions
nucl-th 2026-11 conditional novelty 5.0 of 10

A quark recombination model with viscous corrections describes phi and Omega elliptic flow from RHIC to LHC energies, and extracts the strange quark elliptic flow.
Constraining the $f_0(980)$ Structure and Formation Dynamics via Anisotropy-Response Scaling
nucl-ex 2026-09 conditional novelty 5.0 of 10

Anisotropy-response scaling shows the f0(980) in p+Pb collisions behaves like a single meson with weak final-state sensitivity, distinct from a K Kbar molecular benchmark, indicating a compact structure.
Exploring Data-Driven Corrections for $\phi$-Meson Global Spin Alignment Measurements
nucl-ex 2025-08 unverdicted novelty 5.0 of 10

A data-driven correction built from combinatorial kaon pairs inside the phi mass window is tested with toy Monte Carlo, showing partial success and clear shortcomings.
Impact of Tracking Resolutions on $\phi$-Meson Spin Alignment Measurement
physics.data-an 2025-02 conditional novelty 5.0 of 10

Track angular and momentum resolutions shift the extracted phi-meson spin alignment parameter rho_00 by less than 0.0005 in STAR-like toy-model simulations, though the invariant-mass method's conversion formula is wrong.
Multi-system Bayesian constraints on the transport coefficients of QCD matter
hep-ph 2020-11 conditional novelty 5.0 of 10

Combined Bayesian calibration to LHC and RHIC hadronic data constrains the quark-gluon plasma shear and bulk viscosities near 150 to 250 MeV, but the constraints weaken above 250 MeV and shift with the choice of parti...
Measurement of the azimuthal anisotropy of charged particles produced in $\sqrt{s_\mathrm{NN}} = 5.02$ TeV Pb+Pb collisions with the ATLAS detector
nucl-ex 2018-08 accept novelty 5.0 of 10

ATLAS reports flow harmonics v2 through v7 in 5.02 TeV lead-lead collisions, and finds that the transverse-momentum shape of v2 and v3 is the same across centralities once each curve is rescaled.
Event-by-event fluctuations in perturbative QCD + saturation + hydro model: pinning down QCD matter shear viscosity in ultrarelativistic heavy-ion collisions
hep-ph 2015-05 conditional novelty 5.0 of 10

An event-by-event pQCD plus saturation plus viscous hydro model reproduces LHC and RHIC bulk observables and favors a small, mildly rising shear viscosity in the quark-gluon plasma with a small hadronic value, though ...
Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics
nucl-th 2012-05 conditional novelty 5.0 of 10

Initial flow velocity fluctuations in event-by-event (3+1)D ideal hydrodynamics harden hadron pT spectra, and longitudinal rapidity fluctuations reduce elliptic flow at large pT.
Elliptic Flow and Fixed p_T Suppression in a Final State Interaction Model
hep-ph 2006-02 conditional novelty 5.0 of 10

A final state interaction model with a 1.3 mb cross-section tuned to pion suppression also reproduces the measured elliptic flow v2 in Au+Au collisions at RHIC from soft to high pT.
Thermal Radiation from an Analytic Hydrodynamic Model with Hadronic and QGP Sources in Heavy-Ion Collisions
hep-ph 2025-07 unverdicted novelty 4.0 of 10

An analytic hydrodynamic model with QGP and hadronic photon sources reproduces measured non-prompt direct photon spectra in 200 GeV Au+Au collisions and extracts centrality-dependent initial temperatures.
Study of the hottest droplet of fluid through correlations and fluctuations of collective variables
nucl-th 2025-05 conditional novelty 4.0 of 10

The thesis uses event-by-event fluctuations and correlations of collective flow and mean transverse momentum to propose new probes of the initial state, explain the ATLAS [pT]-variance fall, and constrain nuclear deformation.
An Experimental Exploration of the QCD Phase Diagram: The Search for the Critical Point and the Onset of De-confinement
nucl-ex 2010-07 conditional novelty 4.0 of 10

STAR proposes a RHIC beam energy scan from 5 to 39 GeV, with event-count targets for critical-point and deconfinement measurements and test-run evidence that the detector performs at those energies.
Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
nucl-ex 2005-01 accept novelty 4.0 of 10

Three years of RHIC gold-gold data are consistent with a thermalized, deconfined quark-gluon plasma, but the STAR Collaboration judges the evidence short of proof and lists the measurements still needed.
Few is different: deciphering many-body dynamics in mesoscopic quantum gases
cond-mat.quant-gas 2025-09 unverdicted novelty 3.0 of 10

A workshop report mapping the size, equilibrium, and interaction frontiers of hydrodynamic behavior in mesoscopic quantum systems, connecting few-atom Fermi gases and high-energy small collision systems.
Hot QCD White Paper
nucl-ex 2023-03 accept novelty 2.0 of 10

A community roadmap arguing that hot QCD has matured into precision science and recommending continued RHIC operation, deeper US participation in the LHC heavy-ion program, and sustained theory and computing support.
Experimental overview on small collision systems at the LHC
nucl-ex 2016-02 accept novelty 2.0 of 10

High-multiplicity proton-proton and proton-lead collisions at the LHC reproduce nearly every bulk observable associated with collective flow in lead-lead collisions, and no single framework yet explains all of them.
Properties of hot and dense matter from relativistic heavy ion collisions
nucl-th 2015-10 accept novelty 2.0 of 10

Collisions of heavy nuclei at RHIC and the LHC produce a locally thermalized, nearly perfect fluid whose equation of state, transport coefficients, and freeze-out conditions can be read off bulk observables.
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
hep-th 2011-01 accept novelty 2.0 of 10

The review synthesizes a decade of work showing that strongly coupled plasma calculations from gauge/string duality give a coherent, quantitatively useful picture of hot QCD matter and heavy ion observables.
Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
hep-ph 2009-04 accept novelty 2.0 of 10

Superfluid helium, ultracold Fermi gases, and the quark-gluon plasma all reach a shear viscosity to entropy ratio within a factor of a few of the conjectured quantum bound 1/(4 pi).

How later papers used it

115 later papers cite it

Evidence: substantial. 110 of the citing papers share no author with it, and 40 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 157 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: 6 used its data or values and 3 compared their own results with it. 1 more paper by the same authors is listed: 1 used its data or values.

Uses its data or values 7 of 22 papers with this label · 1 by the same authors

Selected this paper's v_n measurements for n = 2 to ensure compatibility with its viscous hydrodynamical calculations.

Acoustic scaling of anisotropic flow in shape-engineered events: implications for extraction of the specific shear viscosity of the quark gluon plasma (2013) · 1.00 · paraphrased: the licence does not allow quoting
Showed this paper's published data for the various methods in a figure.

Effect of flow fluctuations and nonflow on elliptic flow methods (2009) · 0.90 · paraphrased: the licence does not allow quoting
Showed this paper's published data for the various methods in a figure.

Effect of nonflow and flow fluctuations on elliptic flow methods (2009) · 0.89 · paraphrased: the licence does not allow quoting
Evaluated values for Var(v_2^2) and √(c_k)/⟨p_T⟩ from the experimental data published in this paper and another work, shown as hatched bands.

Model study of the energy dependence of the correlation between anisotropic flow and the mean transverse momentum in Au+Au collisions (2021) · 0.86 · paraphrased: the licence does not allow quoting
Took its v_2{4} data for Au+Au collisions at √(s_NN)=200 GeV from this paper.

Temperature dependence of $\eta/s$: uncertainties from the equation of state (2018) · 1.00 · paraphrased: the licence does not allow quoting
Took v̅_2(p_⊥) from this paper to estimate v̅_2 in that p_⊥ range.

Realistic Implementation of Chiral Magnetic Wave in Heavy Ion Collisions (2013) · 0.99 · paraphrased: the licence does not allow quoting

By the same authors

Modeled the background using v_2 values from separate flow measurements in this paper.

Azimuthal di-hadron correlations in d+Au and Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV from STAR (2010) (same authors) · 0.82 · paraphrased: the licence does not allow quoting

Compares with it 3 of 18 papers with this label

Compared its own minimum bias v_2(p_T) results for pions in Au+Au collisions at RHIC with this paper's RHIC data.

Elliptic flow in nuclear collisions at the Large Hadron Collider (2008) · 0.97 · paraphrased: the licence does not allow quoting
Said that its model clearly overshoots this paper's proton v_2 data.

Elliptic flow from pQCD + saturation + hydro model (2007) · 0.92 · paraphrased: the licence does not allow quoting
Finally, Fig. [ref] shows our model predicts a larger differential elliptic flow for identified particles than what was measured in Au+Au collisions at STAR [ref] .

Comparisons and Predictions for Collisions of deformed $^{238}$U nuclei at $\sqrt{s_{NN}} = 193$ GeV (2023) · Differential flow · 1.00

How the literature uses it

94 arXiv papers cite this in 129 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 · 74 sentences without a confident label

Uses its method or tool 1 paper

By carrying out the modified reaction-plane (MRP) method [ref] as employed by the STAR collaboration, particle pairs with $| Δη| <$ 0.5 are excluded from the construction of the event planes.

Event-plane dependent di-hadron correlations with harmonic $v_n$ subtraction in a hydrodynamic model · Event plane dependence of di-hadron correlations · 1.00

Uses its data or values 20 papers

The data employed in this work are taken from measurements by the ALICE and CMS collaborations for Pb+Pb collisions at $√(s_NN)$ = 2.76 TeV [ref] , as well as measurements by the STAR collaboration for Au+Au collisions at $√(s_NN)= 200$ GeV [ref] .

Acoustic scaling of anisotropic flow in shape-engineered events: implications for extraction of the specific shear viscosity of the quark gluon plasma · Introduction · 1.00
The eccentricity $ϵ$ is chosen to fit the observed centrality dependence of elliptic flow $v_2$ in 62 and 200 GeV Au+Au collisions and 2.76 TeV Pb+Pb collisions [ref] .

Fluctuation Probes of Early-Time Correlations in Nuclear Collisions · Glasma Fluctuations · 0.88
The published STAR data [ref] for the various methods are shown in Fig. [ref].

Effect of flow fluctuations and nonflow on elliptic flow methods · Glauber fluctuations · 0.90

Compares with it 12 papers

Figure 6 shows our results for the minimum bias $v_2(p_T)$ of pions in Au+Au collisions at RHIC (thin lines), compared with the RHIC data from STAR [ref] and PHENIX [ref] .

Elliptic flow in nuclear collisions at the Large Hadron Collider · Results for RHIC · 0.97
They also indicate similar patterns to the data reported by the STAR experiment [ref] (solid points).

Beam Energy Dependence of the Linear and Mode-Coupled Flow Harmonics Using the A Multi-Phase Transport Model · Results and discussion · 0.94
RHIC results are compared with STAR [ref] and PHENIX [ref] data.

Elliptic flow from pQCD + saturation + hydro model · Introduction · 0.97

Cites it as background 14 papers

Experiments carried out at the relativistic heavy ion collider (RHIC) have demonstrated that the quark gluon plasma is a very good fluid [ref] .

Elliptic flow and nearly perfect fluidity in dilute Fermi gases · Introduction · 0.84
One of the most interesting and unique features of ultrarelativistic heavy-ion collisions is the collective flow of the final state particles [ref] .

Study of the hottest droplet of fluid through correlations and fluctuations of collective variables · Collective flow and fluctuations · 0.90
This was typically interpreted to arise naturally in hadronization scenarios based on quark coalescence in which the flow of bound mesons and baryons depends solely on the collective flow of light and strange quarks (assumed to be identical) and the number of valence quarks [ref] .

J/$\psi$ elliptic and triangular flow in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV · Results and discussions · 0.91

Discussion

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

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