Anisotropic Flow; from the sQGP at RHIC towards the (s?)(w?)QGP at the LHC

Raimond SnellingsQGP Meeting, Variable Energy Cyclotron Centre, February 5, Kolkata, India

7/5/2005 2

Outline

Heavy Ion collisions and the Quark Gluon Plasma Probing the QGP: The azimuthal dependence of particle

production versus the reaction plane Measuring particle production versus the reaction plane The EOS of hot and dense QCD matter

magnitude of elliptic flow (v2) centrality dependence of elliptic flow v2(mass,pt), sensitivity to freeze-out and the QCD EoS

What have we learned so far? The magic of mid-rapidity and highest RHIC energy

elliptic flow versus energy and rapidity Other harmonics System size dependence and energy dependence What can we learn at the LHC with ALICE

7/5/2005 3

QCD at extreme conditions

Heavy-ion collisions provide experimental access to the properties of QCD matter at extreme temperature and density (the Equation of State at the QGP phase transition and in the QGP phase)

Better understand the evolution of our universe Deconfinement

The building blocks of QCD, quarks and gluons, become quasi free Approximate chiral symmetry restoration

The origin of our mass

Lattice QCD predicts a phase transition to a quark gluon plasma at energy densities of about 1 GeV/fm3 and at a temperature of about 170 MeV

The quark gluon plasma is a state of matter expected to have existed in the early universe about 1 microsecond after the Big Bang

7/5/2005 4

Phases of QCD matter:The Quark Gluon Plasma

Theory view of phases in QCD matter

B → 0 and high temperatures accessible in ultra relativistic heavy-ion collisions

Krishna Rajagopal and Frank Wilczek: Handbook of QCD

7/5/2005 5

Interpreting Heavy Ion Collisions

QGP properties are in principle calculable from the QCD Lagrangian using lattice QCD

Lattice QCD calculations are not yet advanced enough to form a solid basis for a quantitative comparison of experiment with theory → try to learn as much as possible from comparison to baseline data

A reference measurement is provided by elementary collisions p+p and p+A At the LHC p+A certainly not before 2010

Or by collision geometry Centrality dependence Azimuthal dependence

7/5/2005 6

Non-central A-A collisions

Non central collisions break the azimuthal symmetry!Observables, like collective motion and medium modification of jets, become azimuthally dependent.

7/5/2005 7

Jet Quenching: the initial color density

glueSglue

Debye

sRBDMS

q

vLqC

E

2

2

ˆ

~ˆ4

L

ELogrdCE jet

glueSRGLV 23 2

,

Thick plasma (Baier et al.):

Thin plasma (Gyulassy et al.):

Radiated gluons decohere due to multiple interactions with the mediumThis energy loss depends on the traversed path length and gluon density at the early phase

7/5/2005 8

v2(pt) for high pt particles (self normalizing tomography of dense matter)

M. Gyulassy, I. Vitev and X.N. Wang PRL 86 (2001) 2537

R.S, A.M. Poskanzer, S.A. Voloshin, STAR note, arXiv:nucl-ex/9904003

r

2 cos 2( )rv

http://www.lbl.gov/nsd/annual/rbf/nsd1998/rnc/RNC.htmEvent Anisotropy as a Probe of Jet Quenching R.S and X.-N. Wang

7/5/2005 9

The QCD Equation of State: pressure and nergy density

Large increase of degrees of freedom at Tc observed in quick change in energy density and pressure

Pressure gradient, dp/d generates collective flow

At the phase transition changes faster than p. Here dp/dhas its minimum, the so called softest point

F. Karsch, E. Laermann and A. Peikert, Phys. Lett. B 478 (2000) 447

30

3 2

freedom of degree44

N

T

p

T

7/5/2005 10

Collective motion:the velocity of sound

Velocity of sound Cs = (dp/d)1/2 different magnitude for system of quarks and gluons (1/3) and a hadronic system (0.2). Minimum in velocity of sound during phase transition so called softest point

Buildup of collective flow depends on the magnitude of the velocity of sound and the relative time spend in various phases

P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084

7/5/2005 11

Manifestations of Collective Flow (radial and anisotropic)

x

y

x

y

z

x

Only type of transverse flow in central collision (b=0) is radial flow Integrates pressure history over complete

expansion phase

Elliptic flow (v2) , hexadecupole flow (v4) , v6, … caused by anisotropic initial overlap region (b > 0) More weight towards early stage of

expansion.

Directed flow (v1) , sensitive to earliest collision stage (b > 0) pre-equilibrium at forward rapidity, at

midrapidity perhaps different origin

7/5/2005 12

The magic of elliptic flow: self quenching, direct measure of multiple-interactions

P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084

The driving force of elliptic flow dominates at “early” times Coordinate space configuration anisotropic (almond shape)

however, initial momentum distribution isotropic (spherically symmetric)

Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in p+p)

Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow

7/5/2005 13

t(fm/c)

Main contribution to elliptic flow develops “early” in the collision

P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084 Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45

dimensional arguments: time proportional to size of the system, depends on centrality (“early” in peripheral, “late” in central collisions)

early depends on how long the system lives (timescales are of same order!)

Hydro

v2 v2

t(fm/c)

Zhang’s parton cascade

rn nv cos

7/5/2005 14

Measuring particle production versus the reaction plane

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Particle production versus the reaction plane: anisotropic flow

Phenomenological description of collective effects Natural in hydrodynamic language, however when we talk about flow

we do not necessary imply (ideal) hydrodynamic behavior Flow in cascade models: depends on constituent cross sections and

densities, partonic and/or hadronic (low-density mode) gave reasonable (better than ideal hydro) description at lower energies

Anisotropic flow ≡ correlation with the reaction plane Non-flow ≡ contribution to vn from correlations between particles not

due to their correlation with the reaction plane (HBT, resonances, jets, etc)

1

2

3

3

cos),(21dd

d

2

1

pd

d

nrtn

tt

nypvypp

NNE

rn nv cos

7/5/2005 16

Anisotropic flow is calculated using azimuthal correlations

)ψ( r)(cos inrn env

2 1 2 1 21 ( ) ( ) (( ) 2) ( ) ( {2})r r r rinn

in in in ine e e ee v

Assumption: all correlations between particles due to flow

Non flow correlation contribute order (1/N), problem if vn≈1/√N

1 2 3 4 3 4 3 21 2 1 4( ) ( ) ( )( ) ( ) 4( {4})in in inin in

n ve e e e e

Non flow correlation contribute order (1/N3), problem if vn≈1/N¾

N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906

Can be conveniently calculated using generating functions, extended to vn{∞} using Lee-Yang zeros, reliable vn>1/N

7/5/2005 17

Methods comparison (data)

Clearly needed to compare results from different methods Does not tell you what the underlying physics is which causes this difference Complete models should be able to reproduce all these correlations! Like to have different checks e.g. correlating signal between detectors with much

larger rapidity gap (like ZDC-SMD) For now: if physics conclusion depends on better than 10-20% agreement one

has to be very careful!

Aihong Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020, STAR PRL93 (2004) 252301; arXiv:nucl-ex/0409033

7/5/2005 18

non-flow or fluctuations?

1/ 6

36 4 2 212

1/ 4

2 2 2

22 42 2 2

22

2

2

4

{4}

{2}

{6} 12

2

9

v

v

v v v v v

v

v v

2 2

2 2

y x

y x

<v2n> ≠ <v2>n

Measuring the cumulants of different order provides constraints on both fluctuations and non-flow.(does not take into account PHOBOS part)

2v

M. Miller and RS, arXiv:nucl-ex/0312008

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The possible fluctuation contribution

“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities

M. Miller and RS, arXiv:nucl-ex/0312008

7/5/2005 20

Non-flow or fluctuations?

N

gvv 22

222 42

N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906

Non-flow should give a constant g2 which is not compatible with the data

N is number of clusters, could go like multiplicity, number of wounded nucleons, number of binary collisions, etc

M. Miller and RS, arXiv:nucl-ex/0312008

7/5/2005 21

Non-flow or fluctuations

UrQMD: Includes fluctuations and various non-flow contributions. In these calculations v2{4} reproduces true v2.

Non flow mechanisms ala Voloshin’s radial flow?

7/5/2005 22

Methods to determine vn

Non of the methods are perfect Presently still unclear how much is non-flow and how

much is fluctuations (in Cu+Cu, fluctuations and non-flow could be very important)

Important to have various methods to determine the reaction plane (and therefore flow)

Important to have various regions in phase space to determine the reaction plane

A reasonably safe estimate is that the real flow is in between (v2{2}+v2{4})/2 and v2{4}

Getting the reaction plane from v1 is an ideal cross check (ZDC-SMD)

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Integrated elliptic flow

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Excitation Function

Smooth increase as function of center of mass energy

At low energies negative elliptic flow due to shadowing of the spectator matter, “squeeze out”

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just 20k events

STAR Phys. Rev. Lett. 86, 402–407 (2001); Nucl. Phys. A698 (2002) 193

Charged particle elliptic flow at low pt; one of the first results from RHIC First time quantitative agreement with hydrodynamics ->

evidence of early pressure and approaching early thermalization

For peripheral collisions hydrodynamics breaks down

Charged particle elliptic flow (RHIC):It’s in the magnitude!

7/5/2005 26

Charged particle elliptic flow:It’s in the magnitude!

For mid-central collisions magnitude of the integrated charged particle elliptic flow well described by ideal hydrodynamics

Magnitude of integrated charged particle elliptic flow is a factor two bigger than expected in hadronic cascade calculations

Evidence for strongly interacting pre-hadronic phase!

v2{4} 130 GeV

Zhixu Liu

STAR Phys. Rev. Lett. 86, 402–407 (2001)

7/5/2005 27

Charged particle elliptic flow:Transverse momentum dependence

v2(pt) at top RHIC energies for charged particles disagrees with low density limit (LDL) and is consistent with hydrodynamics up to about 2 GeV/c

At lower energies the pt dependence of v2 is also not well described by LDL

P.F. Kolb et al., Phys.Lett.B500 232-240 (2001) 0012137

7/5/2005 28

v2(pt) and particle mass (the fine structure): some details

On what freeze-out variables does it depend (simplification)?The average velocity difference in and out

of plane (due to p)But also

The average freeze-out temperatureThe average transverse flowThe average spatial eccentricity

7/5/2005 29

Hydro Motivated Fit (blast-wave)

))(sinh()()( bf

tbt T

p ))(cosh()()( bf

tbt T

m

)2cos()( 0 bab

2

0 210

2

0 212

2

))2cos(21)(()(

))2cos(21)(()()2cos()(

bttb

bttbb

t

sKId

sKIdpv

STAR Phys. Rev. Lett. 87, 182301 (2001)

More recent and extended approach in: F. Retiere and M.A. Lisa Phys.Rev.C70:044907,2004

7/5/2005 30

The effect of freeze-out temperature and radial flow on v2

Light particle v2(pt) very sensitive to temperature Heavier particles v2(pt) more sensitive to transverse flow

T = 100 MeV, 2 =0.05

F. Retiere and M.A. Lisa, Phys.Rev.C70:044907,2004

0=0.9, 2 =0.05

7/5/2005 31

The effect of the azimuthal asymmetric flow velocity and shape

Larger value of the difference in collective velocity in and out of the reaction plane leads to larger slope of v2(pt) above ~ <pt> of the particle

Larger spatial anisotropy leads to larger v2 with little mass dependence (transverse flow boosts more particles in the reaction plane)

F. Retiere and M.A. Lisa, Phys.Rev.C70:044907,2004

T = 100 MeV, 0 =0.9

7/5/2005 32

Blast wave gives convenient summery of the data

Even these 4 parameters are a simplification The interplay of these can give quite complicated

behavior and interpreting the meaning is not straight forward

In a true dynamical model these parameters are connected

v2(mass,pt) reflects complete system evolution: the flow contributions from QGP phase, phase transition and hadron gas Ideal hydro, ideal hydro + cascade, parton cascade

+ coalescence, ideal + viscous, viscous + ideal + viscous, etc

7/5/2005 33

STAR QM2001

Mass dependence

Identified particle elliptic flow at low pt Mass dependence in accordance with collective flow. QGP

equation of state (phase transition) provides best description

Hydro calculation: P. Huovinen et. al.

7/5/2005 34

Mass dependence

pions to Cascade follow the mass dependence at low-pt

Ideal hydro provides a reasonable description (common velocity and common freeze-out!)

7/5/2005 35

Mass dependence

At larger transverse momenta the v2(pt) start to deviate from hydro

The mass dependence breaks down, in fact the various particle species cross

7/5/2005 36

Charged particle elliptic flow at higher pt

Exceeds extreme jet quenching (surface emission) break down from ideal

hydro but it needs an extra contribution

E. Shuryak: nucl-th/0112042

7/5/2005 37

Identified particle elliptic flow at higher pt one of the surprises at RHIC

D. Molnar and S. Voloshin, Phys.Rev.Lett. 91 (2003) 092301

Baryon/meson scaling at intermediate transverse momenta: fits in coalescence picture, mass effect opposite to expectations from hydrodynamics

Explains the larger than expected elliptic flow at intermediate pt Why does this simple picture work so well?

Elliptic flow of particles unaffected by the hadronic phase (lucky windows at intermediate pt)?

What about space momentum correlations? Could this mechanism be an alternative for ideal hydro behavior?

7/5/2005 38

Charged particle elliptic flow at higher pt

v2 measured in region where coalescence contribution is expected to diminish

However, due to non-flow uncertainties no detailed conclusions can be drawn so far

STAR PRL93 (2004) 252301; arXiv:nucl-ex/0409033

7/5/2005 39

Experimental summary of the first 3 years and the BNL statement

RHIC Scientists Serve Up “Perfect” LiquidNew state of matter more remarkable than predicted -- raising many new questionsApril 18, 2005

7/5/2005 40

Main arguments for the ideal fluid-like behavior

Large elliptic flow, strongly interacting system which approaches ideal hydrodynamics Inconsistent with conventional hadronic approaches A more complete description of ideal hydro + hadron cascade shows

that at top RHIC energies v2 is dominated by the ideal hydro contribution (for real detailed comparison hadron cascade is needed)

Magnitude of mass scaling of elliptic flow (the fine structure) is consistent with Hydrodynamics Particles exhibit common flow velocity (if strange and multistrange

particles deviate, it must be in the details of the fine structure) Hydro is constrained at RHIC

Initial conditions in hydro consistent with densities obtained from jet quenching and estimates from CGC

EoS used in hydro consistent with lattice QCD calculations (more on that next)

Viscous correction quickly destroy agreement with data (D. Teany)

7/5/2005 41

In the press

7/5/2005 42

AdS/CFT

November, 2005 Scientific American “The Illusion of Gravity” J. Maldacena

A test of this prediction comes from the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory, which has been colliding gold nuclei at very high energies. A preliminary analysis of these experiments indicates the collisions are creating a fluid with very low viscosity. Even though Son and his co-workers studied a simplified version of chromodynamics, they seem to have come up with a property that is shared by the real world. Does this mean that RHIC is creating small five-dimensional black holes? It is really too early to tell, both experimentally and theoretically.

7/5/2005 43

Dependence on the EOS!

Test the effect of four different EoS; qp is lattice inspired, Q has first order phase transition, H is hadron gas with no phase transition and T a smooth parameterization between hadron and QGP phase

Remember C2s= dp/d closely related to acceleration p/(+p)

Pasi Huovinen, arXiv:nucl-th/0505036

7/5/2005 44

Dependence on the EOS!

Integrated charged particle flow not so sensitive to the EoS (due to spectra constraint in ideal hydro?)

Pasi Huovinen, arXiv:nucl-th/0505036

7/5/2005 45

Dependence on the EOS!

EoS Q and EoS T (both have significant softening) do provide the best description of the magnitude of the mass scaling in v2(pt)

The lattice inspired EoS (EoS qp) in ideal hydro does as poorly as a hadron gas EoS!

Pasi Huovinen, arXiv:nucl-th/0505036

Detailed agreement between ideal hydro and measured v2(mass,pt) an accident? (Hirano and Gyulassy arXiv:nucl-th/0506049)

7/5/2005 46

Charged particle elliptic flow:The centrality dependence

Different centrality dependence between hydro (proportional to and peaks around b=12 fm) and low density limit (peaks around b=8 fm)

Data peaks around b ≈10 fm (in between LDL and hydrodynamics) Slightly shifting to larger b for 200 GeV compared to 62

However not corrected for non-flow yet which (can) shift it to smaller b

pions: 0.2 < pt <0.7

Adapted from S.A. Voloshin and A.M. Poskanzer, Phys.Lett.B474 27-32 (2000) 9906075

STAR preliminary

Yuting Bai

7/5/2005 47

v2/ versus multiplicity density

STAR Phys. Rev. C 66, 034904 (2002)

v2 scales monotonic with the particle density from AGS to RHIC

The “physics” does not change from AGS to RHIC !?!?

v2 reaches the hydro limit for the more central collisions at the highest RHIC energies

What will happen at the LHC ?

7/5/2005 48

QGPQGP

QGPQGP

QGP

Wanna see this?

Fine-tune the “hadronic” focus!

focus:

hadron corona

LDL or hadronic corona

From T. Hirano

7/5/2005 49

Beam energy dependence

energy dependence only described by hybrid models (or phenomenological scaling) non-ideal component more important at lower energies

(and at forward rapidities). What will happen at the LHC?

D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).

7/5/2005 50

3D-Hydro

Incomplete thermalization away from mid-rapidity Connected to energy dependence?

Hirano: Nucl Phys A715 821 824 2003; Heinz and Kolb: J. Phys. G Nucl. Part. Phys. 30 S1229

7/5/2005 51

Energy and dependence of v2

PHOBOS Phys. Rev. Lett. 94, 122303 (2005)

no boost invariance and monotonic dependence on energy

7/5/2005 52

What about the eccentricity()?

7/5/2005 53

Top RHIC energies at dip in v2

Hydro prediction for lower energies v2 increases?

the radial flow <v> increases monotonically with beam energy (pion multiplicity at fixed impact parameter), is the slope of v2(pt) expected to increase for ideal hydro?

Where are the 62 GeV calculations?

Adapted from P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084

Energy dependence of v2(pt)

Is the slope of v2(pt) more sensitive to the energy dependence?

7/5/2005 54

v2/<pt> energy dependence

Slope of v2(pt) seems to saturate How significant is it, does it signal softening of the

EOS? Need quantitative model calculations

K. Paech, H. Stocker, A. Dumitru: Phys. Rev. C 68, 044907 (2003) ; PHENIX arXiv:nucl-ex/0411040

7/5/2005 55

Energy dependence of v2(pt)

For charged particles PHENIX observes similar v2(pt) at 62 and 200 GeV while the difference with 17 GeV (CERES) is much bigger

PHENIX

What is the reason for this similar behavior?

Are the individual contributions from the different particles also so similar (naïve expectations are somewhat larger flow and different relative contribution from the various (mass) particles as function of pt)?

PHENIX arXiv:nucl-ex/0411040

7/5/2005 56

Lower energies: identified particles

Identified particles are to first order very similar at 62 and 200 GeV ReCo works also well at intermediate transverse momenta at 62 GeV Can it be an alternative for ideal hydro: LDL plus coalescence?

STAR preliminary

Xin Dong

STAR preliminary

Yuting Bai

7/5/2005 57

What about higher harmonics?

Higher harmonics are natural but are expect to be small v4 - a small, but sensitive observable for heavy ion collisions

(Peter Kolb, PRC 68, 031902) v4 - magnitude sensitive to ideal hydro behavior (Borghini and

Ollitrault, arXiv:nucl-th/0506045) Ideal hydro v4/v2

2 = 0.5

-0.04

-0.02

0.02

0.04

0

7/5/2005 58

pion v4 at 62 and 200 GeV

Measured relative to the 2nd order event plane

v4 for pions is positive and similar at 62 and 200 GeV over large range in pt

STAR preliminary

Yuting Bai

7/5/2005 59

v4 scaling with v22

Even in detail at low-pt v4 is within uncertainties the same at 62 and 200 GeV and the scaling with v2

2 (the dashed lines) holds for both energies

Ratio approximately unity which according to Borghini and Ollitrault is inconsistent with ideal hydrodynamics

See no obvious change as function of collision energy

Lines v22

STAR preliminary

Yuting Bai

7/5/2005 60

Smaller systems

Too early do draw conclusions, large differences between methods in Cu+Cu

7/5/2005 61

Summary Elliptic flow is a very powerful observable

Its magnitude in agreement with prediction from ideal hydrodynamics and ideal hydro + hadron cascade

Mass dependence of elliptic flow in agreement with common collective velocity and favors soft effective EOS

The basis of the ideal fluid statement

The break down of hydro behavior at more peripheral collisions higher transverse momenta and away from midrapidity can be understood and was qualitatively predicted in hydro+hadron cascade calculations (Teany and Shuryak)

However, the observed monotonic behavior also naturally expected in scaling with dN/dy. Would like to see at least some change in slope of energy dependence v2/ (slope of v2(pt) perhaps more sensitive?)

What about v4? Still a lot to do and understand (both at RHIC and at the LHC)

7/5/2005 62

The LHC accelerator

7/5/2005 63ALICE Set-up

HMPID

Muon Arm

TRD

PHOS

PMD

ITS

TOF

TPC

Size: 16 x 26 m

Weight: 10,000 tons

7/5/2005 64

The perfect fluid at RHIC, the wQGP at the LHC?

Less flow at higher energies?

Remember the predictions for RHIC!

7/5/2005 65

Past experiences, no guarantee for the future?

7/5/2005 66

Elliptic flow at LHC energies from ideal hydrodynamics

Whatever the outcome will be it is a day 1 measurement at the LHC with very likely similar impact as at RHIC

From Heinz, Kolb, Sollfrank

7/5/2005 67

The End

7/5/2005 68

Velocity of sound from Lattice

Minimum in velocity of sound Cs = (dp/d)1/2

Buildup of collective flow depends on the magnitude of the velocity of sound and the relative time spend in various phases

Need sensitivity to (integrals of) p/ during different parts of the system evolution!

F. Karsch and E. Laermann, arXiv:hep-lat/0305025

7/5/2005 69

In what direction is RHIC flowing?

Spectra and v2 of multistrange particles and phi meson promise an additional handle on the pre-hadronic dynamics What is the accuracy needed? What is the guidance from theory calculations?

The radial and anisotropic flow of charm Partial charm quark thermalization constraint for

thermalization light quarks? Increase the energy density: U+U collisions? What do we expect at higher energies?

7/5/2005 70

Mean Free Path & Viscosity

For ultra-relativistic particles, the shear viscosity is

Ideal hydro: 0 shear viscosity 0

Transport cross section

7/5/2005 71

Jet quenching: it’s a final state phenomena!

Strong suppression (5x) in the inclusive hadron yields and the away-side azimuthal correlation while no suppression in d+Au: jet-quenching clearly final state phenomenon

7/5/2005 72

High-pt suppression: big effect!

D. d’Enterria

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

High-pt hadron yields are suppressed by a factor 5!

7/5/2005 73

The initial color density is large!

Medium induced radiative energy loss (jet quenching) is the only currently known physical mechanism that can consistently explain the high-pt suppression

Within such models, initial gluon densities of about dng/dy~1000 are obtained. This corresponds to an initial energy density ~15 GeV/fm3 (more than 50X cold nuclear matter gluon density) Consistent with simple Bjorken estimates from dET/d Consistent with input initial conditions in hydrodynamic models

Does the system strongly re-interact and does it approach thermalization?

7/5/2005 74

ALICE

7/5/2005 75

v4 scaling with v22

Calculations from Huovinen with ideal hydro with freeze-out conditions matching the inclusive spectra, do however match the v4 measurements (EoS dependent)

Pasi Huovinen, arXiv:nucl-th/0505036

7/5/2005 76

The “perfect” liquid at RHIC

Nature Vol. 430 page 499 (2004)

Sometimes theorist do get their feet wet and experimentally test fluid behavior

When physicist talk about a perfect liquid, they don’t mean the best glass of champagne they ever tasted. The word “perfect” refers to the liquid’s viscosity