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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
7/5/2005 15
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
7/5/2005 19
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)
7/5/2005 23
Integrated elliptic flow
7/5/2005 24
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”
7/5/2005 25
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