Elliptic flow from two- and four-particle correlations in Au + Au collisions at sqrt{s_{NN}} = 130 GeV

STAR Collaboration

REVIEW

Elliptic flow from two- and four-particle correlations in Au + Au collisions at sqrt{s_{NN}} = 130 GeV

STAR collaboration

Nuclear Experiment · Submitted 3 Jun 2002 · 49 references

Pith's verdict: The method paper that made four-particle cumulants standard in flow analysis — the technique is solid, but the headline '15% non-flow' is an upper bound dressed as a measurement.

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CitationSTAR Collaboration. "Elliptic flow from two- and four-particle correlations in Au + Au collisions at sqrt{s_{NN}} = 130 GeV." arXiv:nucl-ex/0206001 (2002). https://pith.science/paper/IJZL43A3

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Editor's note

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Bottom line: this is the paper that put four-particle cumulants into routine use for elliptic flow, and the technique holds up. The number in the abstract — 'about 15%' non-flow — is softer than it reads, and the authors know it even if the abstract doesn't say so. Send it out; it will referee cleanly with a couple of pointed comments on Section V and the abstract wording. What is genuinely new here is the first application of the Borghini-Dinh-Ollitrault cumulant formalism to real flow data, plus the scalar-product pair method (Eq. 7) and the q-distribution fits. The cumulant algebra in Eqs. (10)-(15) and (21)-(27) is correct, and the MEVSIM studies in Figs. 9-12 are the real evidence: fixed input v2 = 0.10, embedded back-to-back pairs, four-particle clusters, varying opening angles, and the 4th-order cumulant recovers the input where the pair methods do not. That is a clean, independent validation of the separation technique, and it is the part of the paper I trust most. The soft spot is the quantitative attribution. The 15% is the difference between pair and cumulant v2, and Section V says plainly that event-by-event flow fluctuations produce the same difference — Eq. (29) puts sigma^2_{v^2} exactly where the non-flow term sits. The paper corrects only impact-parameter fluctuations within centrality bins and then asserts that fixed-b fluctuations are 'expected to be small' with no demonstration. So 15% is an upper bound on non-flow, and the cumulant v2 in Table I is correspondingly a lower bound on the true v2. The stress-test's flat-v example (ratio 1.5) is a worst case, not evidence the effect is large, but the point stands that it is unquantified. Two smaller things. The Section V correction is mildly circular — a0 through a6 are fit to the same eight v2(nch) points they then correct — but it only bites in the most central bin, where it sits inside the statistical error, so the physics conclusions are unaffected. And the pure four-particle non-flow estimate in Eqs. (16)-(17) is a model-dependent upper bound (M = 1000, perfect alignment); fine as an upper bound, but it is an estimate, not a measurement. The abstract's 'reliably separate' and 'about 15%' would read better with the upper-bound caveat the body already supplies. Who should read it: anyone doing flow analysis, and anyone working through the RHIC thermalization literature — the scalar-product method and the cumulant machinery are now standard and this is where they were introduced to data. Worth a serious referee.

Referee report

Significance

This is a methods paper that changed how the field reports anisotropic flow: the cumulant expansion, the scalar-product estimator, and the explicit demonstration that pair-correlation analyses absorb a non-flow component are all now standard tools, and the MEVSIM closure tests (Figs. 9-12) are a genuinely falsifiable validation of the technique against known inputs. The paper is also careful in a way that is unusual for the genre: it states its own soft spots (Section V on flow fluctuations, Section IV.A on the pure four-particle non-flow bound) rather than burying them. The physics payoff, v_2/epsilon reaching the hydrodynamic limit in central RHIC collisions while following a smooth density-scaling trend across beam energies, is a durable and much-quoted result. The methodological claim is well supported; the quantitative non-flow fraction is the part that needs qualification.

Major objections (2)

[Abstract [abstract:s4]; Section IV.E, Fig. 17; Section V, Eq. (29)] The abstract states without qualification that non-flow correlations 'account for on average about 15% of the observed second-harmonic azimuthal correlation', but Section V states explicitly that the same difference between the four-particle cumulant and twice the squared pair correlation can be produced by event-by-event flow fluctuations at fixed impact parameter, and that 'there is no way to calculate this effect, although it is expected to be small.' Eq. (29) makes the degeneracy concrete: sigma^2_{v^2} enters exactly where the non-flow term sits, and the paper's own flat-v illustration gives a pair-to-cumulant ratio of 5^{1/4} ~ 1.5, i.e. a 50% effect, far larger than 15%. The expectation that real fluctuations are small is asserted rather than demonstrated. This does not threaten the central methodological claim, which the MEVSIM studies (Figs. 9-12, fixed v_2 = 0.10 with no fluctuation) validate independently, but it does mean the 15% is an upper bound on non-flow rather than a measurement. I recommend the abstract and the Section IV.E/Fig. 17 discussion be reworded to say so, and that the flat-v bound be quoted explicitly as the scale of the systematic that remains unquantified.
[Section V, Eqs. (29)-(31) and Fig. 21] The fluctuation correction is obtained by fitting the polynomial v_2(b) of Eq. (30) to the same eight v_2(n_ch) measurements that Eq. (29) is then used to correct, and the paper states only that 'in principle, the final corrected v_2(n_ch) should be determined iteratively, but the result is stable on the first iteration.' That stability is not shown. Since the correction is a factor of two in the most central bin, and Table I gives v_2 = 0.012 +/- 0.015 there (consistent with zero), the one place where the correction matters is also the place where it is least testable. Please show the second iteration explicitly, and state how the result depends on the choice of polynomial order and on the constraint v_2(b_max) = 0 at b_max = 14.7 fm. If the corrected central value is stable to well within its 0.015 statistical error, a single sentence and a number would settle this.

Minor objections (11)

[Section IV.C, Eq. (22)] The text describes 'the term of order v_{2n}/M^2' as the contribution of the 2n higher harmonic, but the standard result is of order v_{2n}^2/M^2. Please check the exponent; as written the dimensional counting is inconsistent with the 1/M^3 term quoted alongside it.
[Section IV.D, discussion of Fig. 12] The cross-reference '(see also the end of section III.A)' is wrong: the estimate of the pure four-particle non-flow contribution is at the end of Section IV.A, Eqs. (16)-(17).
[Section IV.A, Eqs. (16)-(17)] The bound is evaluated at M = 1000, but Table I shows the observed multiplicity ranges from 534 to 4612 across the eight bins. Since the bound scales as 1/M^3, it would be helpful to state the range of the resulting delta-v over the actual multiplicities, so the reader can see that the conclusion of negligible four-particle non-flow holds in the peripheral bins as well as at mid-centrality.
[Section IV.C, Eq. (28) and the accompanying text] The statement that cumulants 'also correct for small anisotropies in the detector acceptance' is illustrated only with the second-order cumulant, Eq. (28). It would strengthen the paper to state explicitly whether the fourth-order generating-function cumulant used for the physics results retains the same protection against the sector-boundary structure visible in Fig. 1, or whether the check was done empirically by comparing with and without the shifting/reweighting compensation.
[Section IV.E, Fig. 13] The quarter-event prescription (same sign of charge, same sign of pseudorapidity, event plane from p_t < 0.5 GeV/c tracks) is introduced without justification. A sentence explaining what each of these three choices is intended to suppress would let the reader judge how much of the residual non-flow the crosses in Fig. 13 actually remove.
[Section IV.E, Fig. 13] The text does not state whether the generating-function cumulant (stars) and the four-subevent cumulant (squares) agree within errors. Since these are two independent implementations of the same quantity, an explicit statement of their consistency, or of the discrepancy, would be valuable.
[Section V, Eq. (30) and Fig. 21] The polynomial coefficients are quoted to three significant figures with no covariance information, and the dashed uncertainty band in Fig. 21 is described only as 'estimated'. Please state how that band was obtained (fit-parameter errors propagated, variation of fit order, or variation of b_max).
[Section VI, Fig. 22] The conversion dN/dy = 1.15 dN/deta is used without a reference. Please cite the source, or state that it is an estimate from the same HIJING sample used for the eccentricity calculation.
[Section V, notation] The expressions '<v4n> = sigma^2_{v2n} + <v2n>^2' and '<v2n> = sigma^2_{vn} + <vn>^2' are hard to parse because the harmonic index and the power are both written as superscripts. A short clarifying sentence, or a switch to bracket notation such as <v_n^4>, would help.
[References] Reference [37] ('STAR collaboration, R. Snellings et al., Quark Matter, (2001)') is incomplete: no proceedings volume or preprint number is given. Please supply the full citation.
[Section IV.A, Eq. (17)] Typographical: 'would drops very rapidly' should read 'would drop very rapidly'.

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The paper

The paper claims

Four-particle cumulants can separate true elliptic flow from unrelated azimuthal correlations in STAR Au + Au data at $sqrt{s_{NN}}=130$ GeV.

The reading

The paper asks whether the elliptic flow signal in Au + Au collisions at $sqrt{s_{NN}}=130$ GeV can be cleaned of azimuthal correlations that have nothing to do with the reaction plane. Such non-flow correlations, from resonance decays, jets, quantum statistics, and final-state interactions, can inflate the standard two-particle flow measurement, and flow itself is a key readout of how quickly the collision thermalizes. Using STAR TPC data, the authors show that a four-particle cumulant analysis subtracts the pair-correlation background and leaves a flow term proportional to $-v_2^4$, while simulations with embedded back-to-back pairs recover the input flow. They report that non-flow accounts for about 15% of the observed second-harmonic correlation on average, with the largest relative contributions in the most peripheral and most central events, and they correct the most central bin for flow variations within the centrality bin.

What carries the argument

The load-bearing tool is the four-particle cumulant, written $langle langle u_1 u_2 u_3^* u_4^* rangle rangle = langle u_1 u_2 u_3^* u_4^* rangle - langle u_1 u_3^* rangle langle u_2 u_4^* rangle - langle u_1 u_4^* rangle langle u_2 u_3^* rangle$, where $u_i=e^{invarphi_i}$ is a unit flow vector for particle $i$. In the presence of flow this cumulant equals $-v_2^4$ plus small multiplicity-suppressed terms, while two-particle non-flow contributions are removed by construction. The cumulant generating function $langle G_n(z) rangle$ supplies a practical way to extract the cumulant from all particles in an event, and the four-subevent version provides a simpler cross-check. The scalar-product estimator $v_n=langle Q_n u_{n,i}^* rangle/(2sqrt{langle Q_n^a Q_n^{b*} rangle})$ is the paper's new two-particle alternative, weighting events by the flow-vector magnitude.

Extended reading notes

Core claim

The central claim is that four-particle correlations, organized as cumulants, can reliably separate collective elliptic flow from non-flow correlations in the first STAR Au + Au data at $sqrt{s_{NN}}=130$ GeV. The cumulant subtracts the products of two-particle correlations, so correlations from few-particle clusters cancel while the reaction-plane-correlated flow survives as a negative $v_2^4$ term. Applying this to data gives a non-flow correction of about 15% on average, largest in the most peripheral and most central bins; the most central bin also needs a factor-of-two correction for flow variations within the bin. The paper pairs this with a scalar-product two-particle method and a flow-vector-magnitude distribution analysis, both of which reproduce the conventional flow signal with smaller statistical errors or additional diagnostic power.

Load-bearing premise

The load-bearing premise is that the difference between the four-particle cumulant and twice the squared two-particle correlation is dominated by non-flow, with event-by-event flow fluctuations at fixed impact parameter small enough to neglect.

Editorial extensions

If this is right

Pair-only analyses overstate elliptic flow by about 15% on average in this data set, with the largest relative overstatement in the most peripheral and most central collisions.
The fourth-order cumulant supplies non-flow-corrected $v_2$ versus pseudorapidity and transverse momentum, confirming that $v_2(p_t)$ flattens above about 2 GeV/$c$.
The corrected $v_2/epsilon$ follows a smooth rise with charged-particle density across AGS, SPS, and RHIC energies, with no obvious kink that would signal a softened equation of state.
The scalar-product method reduces statistical errors by 15–35% relative to the conventional event-plane method, with the largest gain in the most central and most peripheral events.
For future high-statistics central collisions, the factor-of-two correction from flow variations within the centrality bin must be applied to avoid a biased $v_2$.

Reading between the lines

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

Because the paper itself notes that event-by-event flow fluctuations enter the same cumulant difference as non-flow, a future measurement of fixed-impact-parameter $v_2$ fluctuations could turn the quoted 15% into an upper bound rather than a clean separation.
A sixth-order cumulant or a four-particle analysis with rapidity-separated subevents would test whether pure four-particle non-flow is truly negligible at the quoted precision.
The smooth $v_2/epsilon$ trend across AGS, SPS, and RHIC suggests that bulk elliptic flow changes gradually with charged-particle density; a beam-energy scan analyzed with the same cumulant method would test whether any sharp change is hidden by the present centrality binning.
The scalar-product estimator weights events by flow-vector magnitude, so comparing it with an unweighted event-plane analysis at higher statistics would show whether that weighting distorts the extracted $v_2$ when flow fluctuations are broad.

Original abstract

Elliptic flow holds much promise for studying the early-time thermalization attained in ultrarelativistic nuclear collisions. Flow measurements also provide a means of distinguishing between hydrodynamic models and calculations which approach the low density (dilute gas) limit. Among the effects that can complicate the interpretation of elliptic flow measurements are azimuthal correlations that are unrelated to the reaction plane (non-flow correlations). Using data for Au + Au collisions at sqrt{s_{NN}} = 130 GeV from the STAR TPC, it is found that four-particle correlation analyses can reliably separate flow and non-flow correlation signals. The latter account for on average about 15% of the observed second-harmonic azimuthal correlation, with the largest relative contribution for the most peripheral and the most central collisions. The results are also corrected for the effect of flow variations within centrality bins. This effect is negligible for all but the most central bin, where the correction to the elliptic flow is about a factor of two. A simple new method for two-particle flow analysis based on scalar products is described. An analysis based on the distribution of the magnitude of the flow vector is also described.

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, 6,871 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.69 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.53 · 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.

Elliptic flow holds much promise for studying the early-time thermalization attained in ultrarelativistic nuclear collisions. Flow measurements also provide a means of distinguishing between hydrodynamic models and calculations which approach the low density (dilute gas) limit. Among the effects that can complicate the interpretation of elliptic flow measurements are azimuthal correlations that are unrelated to the reaction plane (non-flow correlations). Using data for Au + Au collisions at sqrt{s_{NN}} = 130 GeV from the STAR TPC, it is found that four-particle correlation analyses can reliably separate flow and non-flow correlation signals. The latter account for on average about 15% of the observed second-harmonic azimuthal correlation, with the largest relative contribution for the most peripheral and the most central collisions. The results are also corrected for the effect of flow variations within centrality bins. This effect is negligible for all but the most central bin, where the correction to the elliptic flow is about a factor of two. A simple new method for two-particle flow analysis based on scalar products is described. An analysis based on the distribution of the magnitude of the flow vector is also described.

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	Elliptic flow holds much promise for studying the early-time thermalization attained in ultrarelativistic nuclear collisions.	background 1.00	0.05	0.04	hedged possibility 0.75
s1	Flow measurements also provide a means of distinguishing between hydrodynamic models and calculations which approach the low density (dilute gas) limit.	background 1.00	0.06	0.03	asserted 0.72
s2	Among the effects that can complicate the interpretation of elliptic flow measurements are azimuthal correlations that are unrelated to the reaction plane (non-flow correlations).	background 0.97	0.07	0.03	asserted 0.73
s3	Using data for Au + Au collisions at sqrt{s_{NN}} = 130 GeV from the STAR TPC, it is found that four-particle correlation analyses can reliably separate flow and non-flow correlation signals.	result 0.83	0.96	0.76	asserted 1.00
s4	The latter account for on average about 15% of the observed second-harmonic azimuthal correlation, with the largest relative contribution for the most peripheral and the most central collisions.	result 1.00	0.94	0.18	asserted 1.00
s5	The results are also corrected for the effect of flow variations within centrality bins.	method 0.85	0.89	0.05	asserted 0.99
s6	This effect is negligible for all but the most central bin, where the correction to the elliptic flow is about a factor of two.	result 0.96	0.90	0.06	asserted 1.00
s7	A simple new method for two-particle flow analysis based on scalar products is described.	method 0.81	0.87	0.04	asserted 0.96
s8	An analysis based on the distribution of the magnitude of the flow vector is also described.	method 0.89	0.85	0.03	asserted 0.95

What kind of paper the classifier reports this is: empirical study 0.83 · evidence from analysis of existing data 0.64.

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 azimuthal angle distribution of tracks from

**Figure 2.** FIG. 2: Correlation between the event plane angles deter

**Figure 3.** FIG. 3: The event plane resolution for full events as a func

**Figure 5.** FIG. 5: The upper panel shows

**Figure 7.** FIG. 7: Reduced flow vector distributions for centrality bin

**Figure 8.** FIG. 8: Elliptic flow as determined from the fits to the

**Figure 11.** FIG. 11: Elliptic flow from the conventional method (circles

**Figure 12.** FIG. 12: Elliptic flow from the conventional method (cir

**Figure 13.** FIG. 13: Measured elliptic flow versus centrality for Au +

**Figure 16.** FIG. 16: Elliptic flow versus pseudorapidity from the conven

**Figure 20.** FIG. 20: The upper panel shows measured

**Figure 22.** presents Au + Au data from AGS/E877 [45], from NA49 [43], as well as the current STAR measurements based on 4th-order cumulants, corrected for fluctuations as detailed in Section IV. Alternative forms of the centrality dependence readily can be generated using the tabulated quantities presented in Table I. Generally, the current STAR results underline the need for much increased statistics, particularly for the most central collisions. Within the uncertainties, a smooth trend of increasing v2/ε with increasing centrality (larger (dN/dy)/S) is observed, without the obvious kink…

Showing 16 of the paper's 22 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:nucl-ex/0206001 by the authors.

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A detailed description of the detector in its year- one conﬁguration can be found elsewhere [22]. The main feature of the STAR TPC relevant to this analysis is its full azimuthal coverage (see Fig. 1). The analysis is based on 170000 events corresponding to a minimum bias trigger. Events with a primary vertex beyond 1 cm radially from the beam or 75 cm lo...

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Forward citations

Cited by 35 Pith papers

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

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Measurement of prompt $\mathrm{D}^0$ and $\overline{\mathrm{D}}^0$ meson azimuthal asymmetry and search for strong electric fields in PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV
hep-ex 2020-09 accept novelty 6.0 of 10

The first measurement of the rapidity-dependent v2 difference between D0 and Dbar0 mesons in 5.02 TeV PbPb collisions is consistent with zero: 0.001 ± 0.001 (stat) ± 0.003 (syst).
Fluctuations of anisotropic flow in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector
nucl-ex 2019-04 accept novelty 6.0 of 10

Four-particle cumulants of dipolar flow are nonzero in Pb+Pb collisions, and multi-particle flow cumulants change sign in ultra-central events, with the pattern depending on which observable defines centrality.

Show 30 more citing papers

Anisotropic flow in Xe-Xe collisions at $\mathbf{\sqrt{s_{\rm{NN}}} = 5.44}$ TeV
nucl-ex 2018-05 accept novelty 6.0 of 10

Xe-Xe flow harmonics at 5.44 TeV are measured for the first time; elliptic flow is lower than Pb-Pb in mid-central collisions and higher in central ones, and triangular flow is generally larger.
Measurement of prompt D$^0$ meson azimuthal anisotropy in PbPb collisions at $\sqrt{s_\mathrm{NN}} = $5.02 TeV
nucl-ex 2017-08 accept novelty 6.0 of 10

Prompt D0 mesons in PbPb collisions show positive elliptic flow across 1 to 40 GeV/c and, for the first time, a triangular flow coefficient peaking near 0.07 at about 4 GeV/c.
Azimuthal anisotropy of charged particles with transverse momentum up to 100 GeV in PbPb collisions at sqrt(s[NN]) = 5.02 TeV
hep-ex 2017-02 conditional novelty 6.0 of 10

Charged-particle azimuthal anisotropy in PbPb collisions at 5.02 TeV persists to transverse momenta of 60-80 GeV/c, and its centrality pattern matches a model in which jet energy loss scales linearly with the path len...
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 event-plane correlations in sqrt(s_NN)=2.76 TeV lead-lead collisions with the ATLAS detector
hep-ex 2014-03 accept novelty 6.0 of 10

Fourteen two- and three-plane correlation observables in Pb+Pb collisions show centrality trends that a pure Glauber geometry model cannot reproduce, while hydrodynamic and transport models can.
Generic framework for anisotropic flow analyses with multi-particle azimuthal correlations
nucl-ex 2013-12 accept novelty 6.0 of 10

A general Q-vector formalism computes any m-particle azimuthal correlator exactly in a single pass, with recursive algorithms for high orders and explicit corrections for acceptance, reconstruction efficiency, and fin...
D meson elliptic flow in non-central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76TeV
nucl-ex 2013-05 accept novelty 6.0 of 10

D mesons in 30-50% central Pb-Pb collisions at 2.76 TeV show positive elliptic flow, averaging 0.204 in 2 < pT < 6 GeV/c, comparable in magnitude to light-flavour hadrons.
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.
Exploring the origin of D$^0$ meson elliptic flow in PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV using event shape engineering
nucl-ex 2026-07 accept novelty 5.5 of 10

Prompt D0 v2 is strongly linearly correlated with low-pT charged-particle v2 across q2-selected event classes, indicating initial-state geometry dominates charm-hadron elliptic flow in PbPb collisions.
Cumulants of mean transverse momentum and elliptic flow in the hydrodynamic model of heavy-ion collisions
nucl-th 2026-05 unverdicted novelty 5.0 of 10

Hydrodynamic simulations of heavy-ion collisions demonstrate that cumulants linking mean pT and elliptic flow quantitatively match relations derived from initial-state entropy predictors and moments of harmonic flow.
Flow in small systems in the EPOS4 approach for high-energy scatterings
hep-ph 2025-08 conditional novelty 5.0 of 10

In the EPOS4 framework, a symmetric initial parton distribution cannot reproduce the flat elliptic flow versus multiplicity seen in high-multiplicity pp collisions, whereas a two-center 'dipole' proton shape can.
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.
Anisotropic flow of identified particles in Pb-Pb collisions at $\mathbf{\sqrt{{\textit s}_{\rm NN}}}=5.02$ TeV
nucl-ex 2018-05 accept novelty 5.0 of 10

Identified hadrons in Pb-Pb collisions at 5.02 TeV show mass-ordered flow below 3 GeV/c and meson-versus-baryon grouping at intermediate momentum, with the phi meson tracking protons at low momentum and pions at highe...
Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at $\mathbf{\sqrt{{\textit s}_\text{NN}}} = \mathbf{5.02}$ and $\mathbf{2.76}$ TeV
nucl-ex 2018-04 accept novelty 5.0 of 10

Anisotropic flow harmonics up to v6 rise by 2 to 10 percent between 2.76 and 5.02 TeV, follow an approximate pT^(n/3) scaling at low momentum, and show a small, centrality-dependent negative skewness in the event-by-e...
Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76$ TeV
nucl-ex 2017-09 conditional novelty 5.0 of 10

Event-shape-selected Pb-Pb data show the charge-dependent three-particle correlator scales with elliptic flow, capping the Chiral Magnetic Effect contribution at 26-33% (95% CL) in 10-50% centrality.
Temperature dependence of shear viscosity of $SU(3)$--gluodynamics within lattice simulation
hep-lat 2017-01 conditional novelty 5.0 of 10

Shear viscosity of SU(3) gluodynamics stays small across the confinement transition, with eta/s between roughly 0.15 and 0.57 over T/Tc from 0.9 to 1.5.
$v_4$, $v_5$, $v_6$, $v_7$: nonlinear hydrodynamic response versus LHC data
nucl-th 2015-02 conditional novelty 5.0 of 10

Higher flow harmonics v4 through v7 decompose into linear and nonlinear hydrodynamic response, and the nonlinear coefficients extracted from LHC data agree with viscous hydrodynamic calculations.
Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV with the ATLAS detector
hep-ex 2014-08 accept novelty 5.0 of 10

Four-particle and higher cumulants of charged-particle azimuthal correlations in Pb+Pb collisions at 2.76 TeV give flow harmonics well below the two-particle values, and the derived fluctuation measure F(vn) is not re...
Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions
nucl-ex 2012-09 accept novelty 5.0 of 10

Flow-fluctuation bias in event-plane measurements of mixed-harmonic correlations can reach a factor of two, and a scalar-product estimator removes it without changing the physics target.
Does stability of relativistic dissipative fluid dynamics imply causality?
hep-ph 2009-07 conditional novelty 5.0 of 10

Second-order relativistic fluid dynamics with shear viscosity is stable and causal only if the shear relaxation time exceeds a fixed multiple of the sound attenuation length, even though the group velocity is superlum...
Scaling of soft QGP signatures in relativistic lead, xenon and oxygen collisions in EPOS4
hep-ph 2026-08 conditional novelty 4.0 of 10

EPOS4 with UrQMD reproduces bulk yields, spectra, pT fluctuations and flow in Pb-Pb and Xe-Xe collisions, and predicts sizable elliptic flow in O-O collisions.
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.
Chiral Magnetic Effect Task Force Report
nucl-th 2016-08 conditional novelty 4.0 of 10

Colliding same-mass, different-charge nuclei at RHIC can isolate the magnetic-field-dependent part of charge separation and test the chiral magnetic effect.
Causal Viscous Hydrodynamics for Relativistic Heavy Ion Collisions
nucl-th 2009-08 conditional novelty 4.0 of 10

Causal viscous hydrodynamics in 2+1 dimensions with shear viscosity near the KSS bound suppresses elliptic flow by roughly 30%, making v2 a sensitive diagnostic of the quark-gluon plasma shear viscosity to entropy ratio.
Elliptic flow in the Gaussian model of eccentricity fluctuations
nucl-th 2007-08 accept novelty 4.0 of 10

In a Gaussian model of eccentricity fluctuations, elliptic flow from four-particle cumulants exactly equals the mean reaction-plane flow, and all higher cumulants collapse to the same value.
Novel Collective Phenomena in High-Energy Proton-Proton and Proton-Nucleus Collisions
nucl-ex 2015-09 accept novelty 3.0 of 10

High-multiplicity proton-proton and proton-lead collisions show heavy-ion-like long-range azimuthal correlations, and neither hydrodynamic nor Color Glass Condensate explanations is yet ruled out by the data.
What is the Quark-Gluon Plasma made of?
nucl-th 2025-06 accept novelty 2.0 of 10

The quark-gluon plasma is best described as a strongly coupled liquid of massive, very short-lived quark and gluon quasiparticles, with sound (phonon) modes becoming the most well-defined collective excitation at low momenta.
The Hot QCD White Paper: Exploring the Phases of QCD at RHIC and the LHC
nucl-ex 2015-02 conditional novelty 2.0 of 10

The white paper consolidates evidence that quark-gluon plasma is a strongly coupled liquid with the smallest specific viscosity measured, and lays out the measurements and facilities needed to pin down its temperature...
Initial State Fluctuations and Final State Correlations in Relativistic Heavy-Ion Collisions
nucl-th 2013-12 accept novelty 2.0 of 10

Fluctuations in the transverse energy distribution of a heavy-ion collision generate the full set of observed flow harmonics, with linear hydrodynamic response holding for harmonics two and three and nonlinear mode mi...

How later papers used it

92 later papers cite it

Evidence: some. 91 of the citing papers share no author with it, and 46 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 122 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

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

Uses its method or tool 3 of 45 papers with this label

The event shape selection is performed as in [ref] based on the magnitude of the second-order reduced flow vector, $q_2$ [ref] , defined as

Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76$ TeV (2017) · Introduction · 1.00
Furthermore, the inclusive photon elliptic flow is measured with the Scalar Product method [ref] , using a pseudorapidity gap of $|Δη| > 0.9$ between the photon and the reference flow particles.

Direct photon elliptic flow in Pb-Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}}=2.76$ TeV (2018) · Analysis method · 1.00
Made event-shape selections via selections on the magnitude of the second-order reduced flow vector q2 from this paper.

Collision system and beam energy dependence of anisotropic flow fluctuations (2018) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

77 arXiv papers cite this in 105 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Results from four-particle correlation analysis, which can filter out contributions to the flow signal from correlations unrelated to the event reaction plane (``non-flow''), are presented and compared to the conventional method, in which non-flow effects are treated as part of the systematic uncertainty.

Flow and non-flow correlations from four-particle multiplets in STAR · 0.82

Papers citing it · 44 sentences without a confident label

Uses its method or tool 42 papers

The event shape selection is performed as in [ref] based on the magnitude of the second-order reduced flow vector, $q_2$ [ref] , defined as

Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76$ TeV · Introduction · 1.00
The coefficients are obtained using the scalar product (SP) method [ref] .

J/$\psi$ elliptic and triangular flow in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV · Data analysis · 1.00
The dimuon $v_2$ is measured using the scalar product method [ref] , correlating the reconstructed dimuons with the second-order harmonic event flow vector $Q_2^SPD$ [ref] calculated from the azimuthal distribution of the reconstructed SPD tracklets

Measurement of $\Upsilon(1{\rm S})$ elliptic flow at forward rapidity in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV · Introduction · 1.00

Compares with it 2 papers

We note that the behaviors of $v_2{2}$ and $v_2{4}$ are consistent with those reported in Ref. [ref] .

Effectiveness of nonflow suppression using multi-particle correlators · Non-flow suppression in toy model I · 0.89
The measurements in both centrality classes are compatible within uncertainties with the $$-meson $v_2$ measured with the Scalar Product (SP) method [ref] by the CMS Collaboration in $|y|<1$ [ref] .

Event-shape engineering for the D-meson elliptic flow in mid-central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV · Results · 0.92

Cites it as background 6 papers

In heavy-ion collisions, two-particle correlations () in relative azimuthal angle with large pseudorapidity [ref] separation show distinct long-range correlations [ref] .

Measurement of the Sensitivity of Two-Particle Correlations in $pp$ Collisions to the Presence of Hard Scatterings · Introduction · 0.87
One of the major discoveries at the RHIC is large azimuthal anisotropy [ref] , which is comparable with the results from relativistic hydrodynamic models [ref] .

New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids · Introduction · 0.86
The most studied Fourier component is $V_2Δ$ [ref] , corresponding to elliptic flow [ref] .

Directed flow at midrapidity in sqrt(s_NN)=2.76 TeV Pb+Pb collisions · Introduction · 0.97

Discussion

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A detailed description of the detector in its year- one conﬁguration can be found elsewhere [22]. The main feature of the STAR TPC relevant to this analysis is its full azimuthal coverage (see Fig. 1). The analysis is based on 170000 events corresponding to a minimum bias trigger. Events with a primary vertex beyond 1 cm radially from the beam or 75 cm lo...

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