Radial and elliptic flow at RHIC: further predictions

P.F. Kolb; P. Huovinen; P.V. Ruuskanen; S. Voloshin; U. Heinz

REVIEW

Radial and elliptic flow at RHIC: further predictions

P. Huovinen, P.F. Kolb, U. Heinz, P.V. Ruuskanen, S. Voloshin

High Energy Physics - Phenomenology · Submitted 12 Jan 2001 · 24 references

Pith's verdict: The numerical predictions are the real paper and they are sharp and testable; the analytic half has one claim you cannot check and one sign slip.

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arXiv IDhep-ph/0101136 (version 2)

Pith IDDW3DQPCP, Pith's permanent record of this paper and its review

CitationP.F. Kolb, P. Huovinen, P.V. Ruuskanen, S. Voloshin, U. Heinz. "Radial and elliptic flow at RHIC: further predictions." arXiv:hep-ph/0101136 (2001). https://pith.science/paper/DW3DQPCP

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Editor's note

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Short version: the numerical half of this is the real paper and it is worth your time; the analytic half has a claim you cannot verify from what is printed. Send it out, but ask for one paragraph of numbers first. What is new: they take the hydrodynamic machinery they had already fitted to SPS Pb+Pb and run it for identified hadrons at 130 A GeV. Table 1 gives pt-integrated v2 from pions through Omega, Figs. 3 to 5 give the pt-differential version by species and centrality. The result worth remembering is the one that looks contradictory at first: at fixed pt, v2 falls with mass, but the pt-averaged v2 rises with mass, because radial flow flattens the heavy-particle spectra and pushes spectral weight to high pt where v2 is large. That is a sharp, falsifiable statement, and it is exactly the kind of thing one run's worth of data settles. They also scan EOS and freeze-out temperature rather than quoting a single number, and they are upfront that hydro overshoots the measured charged-particle v2 at large b and high pt. Soft spot: the claim that Eq. (2) reproduces all relevant features of the full hydrodynamic results almost quantitatively. rho_0 and rho_a are tuned to the same numerical output, and neither the fitted values nor any residual is reported. Agreement could be 5 percent or 30 percent and the reader cannot tell. Since they explicitly offer Eq. (2) as a tool for extracting flow from non-central data, that gap matters. One paragraph with the fitted rho_0, rho_a and a couple of residuals would close it. Also: the mu term in Eq. (4) has the wrong sign. Expanding Eq. (3) for large arguments gives tanh[(kappa pt minus lambda mt)/2T minus mu/2], not plus mu/2. For the Fig. 7 parameters mu is about 0.13, so the offset is small, but it is a slip and should be fixed in proof. I would push back a little on the missing error bands. For a pre-data prediction paper the EOS and freeze-out scan is the relevant systematic; Gaussian bars on a hydrodynamic output would be false precision. A line on numerical resolution would be cheap, though. The SPS-fitted initial conditions are disclosed and are normal for an extrapolation paper, not a flaw. Who it is for: heavy-ion people who will compare species-resolved v2 to data, and anyone who wants a ready-made blast-wave fit with azimuthal modulation. I would cite Table 1 and the mass-ordering argument.

Referee report

Significance

The predictions are timely and genuinely falsifiable: they were made against data that were about to appear, and they specify the mass ordering, the pt shape, and the EOS and freeze-out-temperature sensitivities separately for several hadron species, which is exactly the kind of statement that can be confirmed or excluded. The analytic part is a real asset rather than decoration. Eq. (2) is a compact, physically transparent parametrization that experimentalists can fit directly, and the four-fireball model gives a clean and checkable explanation of both the mass ordering at fixed pt and the opposite Tf dependence of pion and proton v2. The paper is also explicit that its initial and freeze-out conditions are extrapolated from fits to SPS data, which is the honest framing for a prediction paper and is not a defect in itself.

Major objections (3)

[§3, Eq. (2) and the sentence introducing it] The text states: 'Making the Ansatz rho = rho_0 + rho_a cos(2 phi_s) we checked that, for a suitable choice of the average radial flow rapidity rho_0 and its azimuthal modulation amplitude rho_a, Eq. (2) reproduces all relevant features of the full hydrodynamic results almost quantitatively.' No values of rho_0 or rho_a are given, no residual or deviation measure is reported, and no pt or mass range is stated over which the agreement holds. This is load-bearing, because the same paragraph offers Eq. (2) as a tool 'to fit the spectra and elliptic flow from non-central collisions in order to extract also the average azimuthal flow modulation'; if the reproduction is only qualitative, the extracted modulation inherits that error. Please report the fitted (rho_0, rho_a) for each of the three parameter sets and quantify the agreement, for example by overlaying Eq. (2) on Fig. 3 or by tabulating the maximum deviation in v2 over the pt range shown. If the agreement is in fact qualitative, the sentence should be reworded accordingly.
[Table 1 and its caption] The table reports v2 for 'minimum bias Au+Au collisions', but the impact-parameter weighting used to perform the minimum-bias average is never specified. Because v2 is not linear in b and the hydrodynamic v2(b) saturates and then falls at large b (as the authors' own Fig. 5 and ref. [9] show), averaging with the number of participants, the number of binary collisions, or the charged multiplicity gives numerically different entries. The caption also says the pt-average 'was taken over the full spectrum' without stating the pt range, and it is not clear whether the early-freeze-out entries for the phi and Omega (Tf = 164 MeV) are averaged over their own, different spectra or over the same range as the other rows. Since Table 1 is the paper's headline prediction for identified hadrons, these definitions should be stated explicitly so that the numbers can be compared with the minimum-bias data they are meant to anticipate.
[§2, parameter sensitivity] The sensitivity study in §2 and Figs. 3-5 varies the equation of state and the freeze-out temperature, but not the initial energy density normalization or the formation time, which are precisely the quantities that are extrapolated from the SPS analysis of refs. [6,8,9] and which set the absolute scale of the radial flow. The absolute magnitudes in Table 1 and the spectral slopes in Figs. 1-2 depend on these, so a reader cannot judge how seriously to take the predicted numbers as opposed to the predicted trends. A short statement of the fractional change in the pt-averaged v2 and in the inverse slope parameter under a reasonable variation of the initial energy density (say plus or minus 20%) would make the extrapolation uncertainty explicit and would considerably strengthen the predictive claim.

Minor objections (7)

[§3, Eq. (4)] Expanding Eq. (3) for large arguments gives v2 approximately tanh[(1/2)((kappa pt - lambda mt)/T + ln(gamma_y v_y/(gamma_x v_x)))], whereas Eq. (4) prints + mu with mu = ln sqrt(gamma_x v_x/(gamma_y v_y)). The constant therefore appears with the opposite sign to the one obtained from the stated expansion. For the Fig. 7 parameters the offset is modest (mu is about 0.13), and Eq. (5) is unaffected because mu is temperature independent, but the sign should be corrected or the definition of mu adjusted.
[§3, sentence following Eq. (4)] The text quotes xi approximately 5 GeV for the Fig. 7 parameters. With T = 140 MeV, v_x = 0.6 and v_y = 0.5 one obtains gamma_x v_x = 0.75, gamma_y v_y = 0.577, hence kappa - lambda is about 0.077 and xi = (kappa - lambda)/(2T) is about 0.28 GeV^-1, which would place the turnover near pt of order 3.5 GeV, roughly consistent with the quoted 'pt > 2.5 GeV' but not with xi approximately 5. Please check the numerical value and state the units of xi explicitly.
[§3, Eq. (3)] The symbol E in the exponent exp[(E/T)(gamma_x - gamma_y)] is not defined. Presumably E = m_t at midrapidity, but this should be stated, together with the assumption that the four fireballs have equal volumes and that the two pairs are normalized equally.
[Fig. 1 and its caption] The UrQMD crosses shown for comparison are computed at sqrt(s) = 200 A GeV while the hydrodynamic curves are at 130 A GeV. The caption discloses this, but the statement in the text that the UrQMD spectra are 'slightly steeper than the measured spectra at SPS energies' rests on a cross-energy comparison and should be qualified as such.
[§2, parameter sets] The three parameter sets EOS Q(120), Q(140) and H(140) are defined only by reference to Table I of ref. [9], which is listed as in press. A one-sentence restatement of the relevant numbers (critical temperature, latent heat, freeze-out energy density) would make the present paper self-contained for a reader who wants to reproduce Table 1.
[Notation] The symbol v2 is used both for the pt-differential quantity v2(pt) and for the pt-averaged value, with the distinction carried only by context. A subscript or an explicit definition at first use in each section would remove the ambiguity, particularly in Table 1 and Fig. 5.
[Fig. 2 caption] The caption notes that the Omega distribution is also shown for Tf = 164 MeV, but does not say which centrality bin this additional curve belongs to or whether the factor-of-10 offsets between bins apply to it as well. Please clarify.

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The paper

The paper claims

A thermalized fireball explains how each hadron flows at RHIC, and why mass orders the flow.

The reading

The paper asks what a fully thermalized, hydrodynamically expanding fireball would predict for identified hadrons in gold-on-gold collisions at 130 GeV per nucleon pair, at a time when only the charged-particle elliptic flow had been measured. Its answer is a set of concrete predictions: transverse-momentum spectra for pions, kaons, protons and omega baryons at three centralities, and the elliptic flow coefficient $v_2$ both differentially in $p_t$ and averaged over the whole spectrum, for three combinations of equation of state and freeze-out temperature. The interesting structure is a split: at a fixed transverse momentum, heavier hadrons show smaller elliptic flow, while after averaging over the spectrum the heavier hadrons show larger elliptic flow. The paper then explains this split analytically, using a generalized blast-wave freeze-out formula and an even simpler four-fireball model, and uses the same machinery to show why raising the freeze-out temperature lowers the pion anisotropy while raising the proton one. If the predictions hold, a single thermalized source with a common flow velocity for all hadrons is the right picture at RHIC energies, and measured mass-dependent flow becomes a handle for extracting the freeze-out temperature and the stiffness of the equation of state.

What carries the argument

Two calculational devices carry the argument. The quantitative one is a generalized blast-wave freeze-out formula: a Cooper-Frye spectrum for a thin cylindrical shell with a boost-invariant longitudinal expansion and an azimuthally modulated radial flow rapidity $rho(phi_s) = rho_0 + rho_a cos(2 phi_s)$, which after integrating over the azimuthal emission angle gives $v_2(p_t)$ as a ratio of angular integrals of $I_2 K_1$ over $I_0 K_1$ (Eq. 2). The authors report that with suitable $rho_0$ and $rho_a$ this reproduces the full hydrodynamic results almost quantitatively, and it doubles as a fitting form for extracting average radial flow and its azimuthal modulation from data. The qualitative one is a toy source of four non-expanding fireballs moving in the transverse plane with $|v_x| > |v_y|$, which yields a closed expression (Eq. 3) in which the hadron mass enters only through a Boltzmann factor $e^{E(γ_x-γ_y)/T}$, making the mass ordering of $v_2$ at fixed $p_t$ transparent. Expanding that expression for large arguments gives the compact form $v_2(p_t) ≈ tanh((κ p_t - λ m_t)/2T + μ/2)$ with $κ = γ_x v_x - γ_y v_y$ and $λ = γ_x - γ_y$, which shows the crossover scale from quadratic to linear $p_t$ dependence is set by the rest mass, and whose temperature derivative (Eq. 5) changes sign between light and heavy particles.

Extended reading notes

Core claim

The paper's central claim is that a hydrodynamic model, with initial and freeze-out conditions carried over from an earlier analysis of lead-on-lead collisions at 17 GeV, makes sharp and internally consistent predictions for identified hadrons in gold-on-gold collisions at 130 GeV. Two of these predictions pull in opposite directions and are the paper's real content. At fixed transverse momentum, $v_2(p_t)$ falls as the hadron mass rises (Fig. 3), because radial flow depletes the low-$p_t$ part of a heavy particle's spectrum more strongly in the direction of larger radial velocity, eating into the azimuthal excess that produces $v_2$. But the $p_t$-averaged $v_2$ in Table 1 rises with mass, because radial flow flattens heavy-particle spectra and shifts their weight toward the high-$p_t$ region where the differential anisotropy is larger. The paper also reports that a stiffer equation of state gives larger $v_2$ at low $p_t$ and smaller $v_2$ at high $p_t$ for all species, while the freeze-out temperature moves pions and protons in opposite directions. The authors present the whole set as a discriminating test: forthcoming data should not only confirm or exclude the hydrodynamic picture but also select among the three parameter sets.

Load-bearing premise

The load-bearing premise, stated in the Introduction, is that the initial conditions and the constant-energy-density freeze-out surface with its temperatures of roughly 120 and 140 MeV can be carried over unchanged from lead-on-lead collisions at 17 GeV to gold-on-gold collisions at 130 GeV; every absolute number in the tables and figures inherits that extrapolation.

Editorial extensions

If this is right

Measuring $v_2(p_t)$ for pions, kaons and protons separately at 130 GeV should show the predicted ordering: lower anisotropy for heavier species at fixed $p_t$, higher anisotropy for heavier species once averaged over the spectrum.
The sign of the freeze-out-temperature dependence differs between pions and protons, so a measured $v_2(p_t)$ for both species constrains the freeze-out temperature without needing to fix the equation of state first.
The equation of state leaves a characteristic shape change rather than a pure rescaling: a stiffer equation of state raises $v_2$ at low $p_t$ and lowers it at high $p_t$, which is distinguishable from a shift in freeze-out temperature.
The omega baryon is predicted to be strongly affected by hadronic rescattering after hadronization, so comparing its flow and spectral slope under late versus early freeze-out tests how much flow is generated in the hadronic stage.
The generalized blast-wave formula offers a two-parameter fit (average radial flow rapidity and its azimuthal modulation) that can be applied directly to non-central collision data to extract both quantities at once.

Reading between the lines

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

If the predicted mass ordering survives but the absolute magnitudes do not, that pattern would point to a changed freeze-out energy density or incomplete thermalization at the higher collision energy rather than to a failure of the hydrodynamic framework itself, which makes the mass ordering a more robust diagnostic than any single normalization.
The negative low-$p_t$ dip in $v_2$ that the toy model produces for protons, and that the authors note is washed out once a realistic radial velocity profile replaces the constant-velocity shell, suggests looking for that dip as a signature of an unusually narrow radial velocity distribution rather than of strong radial flow in general.
Because the analytic formula ties the crossover momentum between quadratic and linear $p_t$ dependence to the rest mass times a flow-dependent prefactor, the position of that crossover across several hadron species could serve as an independent estimate of the average radial flow velocity, separate from the usual spectral-slope fits.
The paper's own framing invites a joint fit: spectra fix temperature and average radial flow, while the azimuthal modulation of $v_2(p_t)$ fixes the anisotropy, so the two together over-determine the freeze-out surface and give an internal consistency check on the assumption of a single common flow velocity for all hadrons.

Original abstract

Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at sqrt(s) = 130 A GeV. The dependence of the differential and p_t-integrated elliptic flow on the hadron mass, equation of state and freeze-out temperature is studied both numerically and analytically.

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, 2,344 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.08 · 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.

Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at sqrt(s) = 130 A GeV. The dependence of the differential and p_t-integrated elliptic flow on the hadron mass, equation of state and freeze-out temperature is studied both numerically and analytically.

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	Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at sqrt(s) = 130 A GeV.	contribution 0.93	0.93	0.17	asserted 0.94
s1	The dependence of the differential and p_t-integrated elliptic flow on the hadron mass, equation of state and freeze-out temperature is studied both numerically and analytically.	contribution 0.93	0.90	0.13	asserted 0.96

What kind of paper the classifier reports this is: simulation study 0.69 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
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relations to other papers

levels run

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T body sentences
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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.** shows mt-spectra for pions, kaons, protons and Ω hyperons at different collision centralities. For peripheral collisions the spectra get steeper, due to a decrease of the average radial flow velocity hv⊥i as a result of a lower initial energy density and a shorter lifetime of the reaction zone. The comparison between theory and experiment will be particularly interesting in the region of large impact parameters where the measured elliptic flow [1] lags behind the hydrodynamical results [9]. As discussed in the Introduction, the single-particle spectra may help to understand whether…

**Figure 4.** FIG. 4. The effect of the EOS and the freeze-out tem

**Figure 6.** FIG. 6. Simple source of four fireballs.

**Figure 7.** FIG. 7. Transverse momentum dependence of elliptic flow

Showing 4 of the paper's 7 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0101136 by the authors.

References

Works cited (24)

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Simulating elliptic flow with viscous hydrodynamics
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Viscous corrections to the particle distribution function, not the modified flow, dominate the change in high-pT elliptic flow, and the auxiliary stress tensor stops tracking the Navier-Stokes gradient form above eta/...
Bulk viscosity of QCD matter near the critical temperature
hep-ph 2007-05 conditional novelty 6.0 of 10

Bulk viscosity of hot QCD matter rises to zeta/s about 1 near the deconfinement temperature, according to a low-energy-theorem sum rule combined with lattice data.
Characteristic form of boost-invariant and cylindrically non-symmetric hydrodynamic equations
nucl-th 2006-03 conditional novelty 6.0 of 10

A boost-invariant, cylindrically non-symmetric perfect-fluid system is written in Riemann variables and reduced to two coupled equations for a combined wave amplitude and the flow angle.
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.
Flow analysis from multiparticle azimuthal correlations
nucl-th 2001-05 accept novelty 6.0 of 10

A generating-function cumulant expansion of multiparticle azimuthal correlations yields flow estimates that are insensitive to lower-order nonflow correlations and correctable for detector acceptance.
Elliptic flow in an expanding and rotating fireball
nucl-th 2026-09 conditional novelty 5.0 of 10

In a rotating blast-wave fireball model, spin from the orbital angular momentum of off-central heavy-ion collisions adds roughly 2 to 10 percent to elliptic flow, with anisotropic expansion remaining the dominant source.
(3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density
nucl-th 2019-06 conditional novelty 5.0 of 10

BEShydro is a new open-source (3+1)-dimensional relativistic hydrodynamics code that evolves net baryon density and diffusion alongside shear and bulk viscosity, validated against semi-analytic solutions and against MUSIC.
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...
Resolution Effects in the Hybrid Strong/Weak Coupling Model
hep-ph 2017-07 conditional novelty 5.0 of 10

Giving the quark-gluon plasma a finite spatial resolution length in the hybrid strong/weak coupling jet-quenching model produces only small changes to jet shapes, fragmentation functions, and missing-pT observables.
New theories of relativistic hydrodynamics in the LHC era
hep-ph 2017-07 accept novelty 5.0 of 10

The hydrodynamic gradient expansion is an asymptotic series whose large-order factorial growth encodes the transient, nonhydrodynamic modes of the underlying plasma.
Collectivity and electromagnetic radiation in small systems
nucl-th 2016-09 conditional novelty 5.0 of 10

A hydrodynamics plus hadron-cascade model reproduces measured collective flow in small collision systems and predicts a factor-of-two thermal photon excess at low transverse momentum in central p+Pb and (p,d,3He)+Au c...
Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p-Pb collisions at $\mathbf{\sqrt{{\textit s}_{\rm NN}}}$ = 5.02 TeV
nucl-ex 2016-01 accept novelty 5.0 of 10

In proton-lead collisions at 5.02 TeV, the proton-to-pion ratio rises with event multiplicity at 2 to 10 GeV/c while the kaon-to-pion ratio stays flat, and protons alone show a Cronin-like nuclear enhancement.
Viscous Effects on the Mapping of the Initial to Final State in Heavy Ion Collisions
nucl-th 2014-11 conditional novelty 5.0 of 10

In viscous hydrodynamic simulations of heavy ion collisions, initial eccentricities predict elliptic and triangular flow well, but directed, quadrangular, and pentagonal flow require nonlinear eccentricity combination...
Bulk viscous evolution within anisotropic hydrodynamics
hep-ph 2014-05 conditional novelty 5.0 of 10

Adding an explicit bulk-pressure degree of freedom to anisotropic hydrodynamics improves agreement with the exact Boltzmann solution for the bulk pressure of a massive gas, at a small cost to the pressure anisotropy.
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.
Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
nucl-th 2012-04 conditional novelty 5.0 of 10

The authors derive and numerically solve (2+1)-dimensional anisotropic hydrodynamics with a hard-scale-proportional relaxation rate, finding agreement with second-order viscous hydrodynamics at small shear viscosity a...
Non-boost-invariant anisotropic dynamics
nucl-th 2010-11 conditional novelty 5.0 of 10

Three coupled partial differential equations describe the non-boost-invariant evolution of an anisotropically expanding quark-gluon plasma, recovering Bjorken boost-invariant expansion as a limiting case.
An expanding spherical fireball model for light hadron production at RHIC ($\sqrt{s_{\rm NN}}=7.7$--$39$ GeV)
nucl-th 2026-07 conditional novelty 4.0 of 10

An expanding spherical fireball model with Cooper–Frye freeze-out describes STAR pT spectra of π±, K±, p, p̄ at √sNN=7.7–39 GeV and predicts Gaussian rapidity distributions.
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.
Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
nucl-th 2017-05 conditional novelty 4.0 of 10

Quasiparticle anisotropic hydrodynamics with three momentum-anisotropy parameters and anisotropic freeze-out describes ALICE Pb-Pb spectra, elliptic flow, and HBT radii using three fitted parameters.
Spectra and elliptic flow of light hadrons in an expanding fire-cylinder model for the RHIC Beam Energy Scan
nucl-th 2026-02 unverdicted novelty 3.0 of 10

An expanding fire-cylinder model fitted to pion pT spectra describes spectra of other light hadrons and qualitatively matches their elliptic flow in peripheral Au+Au collisions at BES energies.
Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
nucl-th 2017-12 accept novelty 3.0 of 10

The gradient expansion of relativistic hydrodynamics diverges but is Borel-resummable, and the resulting non-equilibrium attractor explains why low-order viscous hydrodynamics describes heavy-ion collision data far be...
Relativistic anisotropic hydrodynamics
nucl-th 2017-12 accept novelty 3.0 of 10

Anisotropic hydrodynamics, which deforms the particle distribution function rather than linearizing around equilibrium, reproduces exact Boltzmann solutions better than second- and third-order viscous hydrodynamics in...
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.
Viscous Hydrodynamics and the Quark Gluon Plasma
nucl-th 2009-05 accept novelty 3.0 of 10

Combining elliptic flow measurements with viscous hydrodynamic and kinetic theory models bounds the quark gluon plasma shear viscosity to entropy ratio at eta/s < 0.4, with a preferred range of roughly (1 to 3) times 1/4 pi.
Jet quenching and medium response in high-energy heavy-ion collisions: a review
hep-ph 2020-02 accept novelty 2.0 of 10

Jet-induced medium response, the recoil partons and hydrodynamic wake left behind a quenching jet, is required to describe soft hadrons, jet shapes, jet masses and cone-size dependence of jet suppression in heavy-ion ...
Anisotropic Hydrodynamics: Three lectures
nucl-th 2014-10 conditional novelty 2.0 of 10

Anisotropic hydrodynamics extends relativistic fluid modeling to far-from-equilibrium heavy-ion systems by promoting momentum-space anisotropy to a leading-order dynamical variable, and it outperforms standard second-...
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...
Quarkonia in the Quark Gluon Plasma
hep-ph 2013-02 conditional novelty 2.0 of 10

Quarkonium melting in the quark-gluon plasma is governed by a complex-valued heavy-quark potential whose imaginary part produces in-medium widths of 20 to 100 MeV, blurring the sharp dissociation temperatures of the o...
Hydrodynamic Modeling of Heavy-Ion Collisions
nucl-th 2013-01 accept novelty 2.0 of 10

Event-by-event viscous hydrodynamics with fluctuating initial conditions reproduces measured flow harmonics at RHIC and LHC, which supports extracting the quark-gluon plasma shear viscosity to entropy density ratio fr...
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).
Collective phenomena in non-central nuclear collisions
nucl-ex 2008-09 accept novelty 2.0 of 10

Anisotropic flow measurements from AGS to RHIC energies support the picture of a strongly coupled, early-thermalizing medium, with multiparticle cumulants providing the cleanest access to reaction-plane elliptic flow.
Physics of Strongly coupled Quark-Gluon Plasma
hep-ph 2008-07 conditional novelty 2.0 of 10

The review synthesizes evidence that the quark-gluon plasma near the QCD transition is a strongly coupled near-perfect liquid, with hydrodynamics, a magnetic monopole plasma, and AdS/CFT offering complementary descriptions.

How later papers used it

137 later papers cite it

Evidence: substantial. 133 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 175 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

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 4 papers with this label

The azimuthal asymmetry can be parameterized by modulation in the velocity profile $ρ=ρ_0+ρ_a cos(2ϕ_s)$, where $ϕ_s$ is the azimuthal angle in relation to reaction plane, as proposed by Huovinen et al [ref] .

Study of the azimuthal asymmetry in heavy ion collisions combining initial state momentum orientation and final state collective effects (2023) · Theoretical framework and main predictions · 0.87

How the literature uses it

121 arXiv papers cite this in 156 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 · 106 sentences without a confident label

Uses its method or tool 4 papers

To understand how flow modifies local correlations we first model the average anisotropic expansion of the system with a blast wave model [ref] .

Flow Fluctuations from Early-Time Correlations in Nuclear Collisions · Flow Fluctuations from Glasma and Transverse Expansion · 0.99
The azimuthal asymmetry can be parameterized by modulation in the velocity profile $ρ=ρ_0+ρ_a cos(2ϕ_s)$, where $ϕ_s$ is the azimuthal angle in relation to reaction plane, as proposed by Huovinen et al [ref] .

Study of the azimuthal asymmetry in heavy ion collisions combining initial state momentum orientation and final state collective effects · Theoretical framework and main predictions · 0.87
A different way to obtain an analytic expression which explains the negative $v_2$ is to consider only the in-plane ($ϕ=0$) and out-of-plane ($ϕ=π/2$) directions (similar to the analysis performed in [ref] ).

Decreasing elliptic flow at the LHC: Calculations in a parton recombination approach · Introduction · 0.96

Compares with it 3 papers

The STAR formula provides a better fit to the data than the formula of Ref. [ref] .

Blast-wave description of $\Upsilon$ elliptic flow at energies available at the CERN Large Hadron Collider · Blast-wave model with elliptical freeze-out hyper-surface · 0.95
In general, the centrality dependence of the thermal parameters $T_eq$ and $β_s$ appearing in Tab. [ref] has the opposite behavior compared to the BGBW approaches [ref] .

Study of the azimuthal asymmetry in heavy ion collisions combining initial state momentum orientation and final state collective effects · Results and discussion · 0.99
Figure [ref] (top panel) also shows results for bulk ($π, K, p$) and for singly strange particles ($K_S^0, Λ$), and hydrodynamic model calculations [ref] .

Systematics of Identified Particle Production in pp, dAu and Au-Au Collisions at RHIC Energies · Elliptic flow · 0.81

Cites it as support 5 papers

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

Collective phenomena in the early stages of relativistic heavy-ion collisions · Evidence for early thermalization · 0.97
Hydrodynamic models could naturally explain the unexpectedly large elliptic flow at RHIC compared to that at SPS [ref] .

Evaluating Results from the Relativistic Heavy Ion Collider with Perturbative QCD and Hydrodynamics · Success of Hydrodynamic Models at RHIC · 0.97
Although there is no experimental information on the nucleon $v_2^$ at very low $p_T^$ region, hydrodynamic model studies [ref] show that the nucleon $v_2^$ produced in heavy ion collisions at RHIC has non-negative values [ref] .

Elliptic flow of deuterons in relativistic heavy-ion collisions · Nucleon spectrum and elliptic flow · 0.97

Cites it as background 35 papers

The approaches used for this purpose have included relativistic ideal hydrodynamics [ref] , second-order viscous hydrodynamics [ref] , and, most recently, anisotropic hydrodynamics [ref] .

Anisotropic hydrodynamics for conformal Gubser flow · Introduction · 0.99
As the QGP evolves, it cools and the systems forms hadrons (and a relatively small number of light nuclei) that eventually freeze out and stream to the detectors [ref] .

The Hypertriton Puzzle in Relativistic Heavy-Ion Collisions · The puzzle · 0.96
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

Discussion

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