Perfect Fluid QGP or CGC?

1
Perfect Fluid QGP or CGC?
RHIC Physics in the Context of the Standard
Model RBRC workshop on Heavy Ion Physics

• Tetsufumi Hirano
• Institute of Physics, University of Tokyo

Visiting scientist at RBRC
References T.Hirano and M.Gyulassy, Nucl.Phys.A
769(2006)71. T.Hirano, U.Heinz, D.Kharzeev,
R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299 work
in progress.
2
OUTLINE

• Dynamical modeling in heavy ion collisions based
  on ideal hydrodynamics
• Elliptic flow and perfect fluid
• Results from hydro models
• Dependence on freezeout prescription
• Dependence on initialization
• Summary and Outlook

3
Why Hydrodynamics?

• Static
• EoS from Lattice QCD
• Finite T, m field theory
• Critical phenomena
• Chiral property of hadron

Once one accepts local thermalization
ansatz, life becomes very easy.
Energy-momentum
Conserved number

• Dynamic Phenomena in HIC
• Expansion, Flow
• Space-time evolution of
• thermodynamic variables

A possible mechanism of apparent thermalization ?
Talk by Y.Nara
4
Three Inputs for Hydrodynamic Models
Final stage Free streaming particles ? Need
decoupling prescription
t
Intermediate stage Hydrodynamics can be valid as
far as local thermalization is achieved. ? Need
EoS P(e,n)
z

• Initial stage
• Particle production,
• pre-thermalization, instability?
• Instead, initial conditions
• are put for hydro simulations.

0
Need modeling (1) EoS, (2) Initial cond., and (3)
Decoupling
5
Intermediate Stage Equation of State
Typical EoS in hydro models
Lattice QCD simulations
H resonance gas(RG)
Q QGPRG
P.Kolb and U.Heinz(03)
F.Karsch et al. (00)
pe/3
Recent lattice results at finite T ? Talk by
Y.Aoki
Latent heat
Lattice QCD predicts cross over phase
transition. Nevertheless, energy density
explosively increases in the vicinity of Tc. ?
Looks like 1st order.
6
Initial Stage Initial Condition
Energy density distribution
Transverse plane
Reaction plane
Parameterization/model-calculation to reproduce
(dN/dh)/(Npart/2) and dN/dh
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Final Stage Freezeout
(1) Sudden freezeout
(2) Transport of hadrons via Boltzman eq. (hybrid)
TTf
t
t
Hadron fluid
QGP fluid
QGP fluid
z
z
0
0
Continuum approximation no longer valid at the
late stage ?Molecular dynamic approach for
hadrons (p,K,p,)
At TTf, l0 (ideal fluid) ? linfinity (free
stream)
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Caveats on Hydrodynamic Results

• Obviously, final results depend on
• modeling of
• Equation of state
• Initial condition
• Freezeout
• So it is indispensable to check sensitivity
• of conclusion to model assumptions and
• try to reduce model parameters.
• In this talk, I will cover 2 and 3.

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What is Elliptic Flow?
Ollitrault (92)
How does the system respond to spatial anisotropy?
Hydro behavior
No secondary interaction
y
f
x
INPUT
Spatial Anisotropy
2v2
Interaction among produced particles
dN/df
dN/df
OUTPUT
Momentum Anisotropy
f
0
2p
f
0
2p
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Elliptic Flow from a Kinetic Theory
ideal hydro limit
Zhang et al.(99)
View from collision axis
Time evolution of v2
b 7.5fm
v2

• Gluons uniformly distributed
• in the overlap region
• dN/dy 300 for b 0 fm
• Thermal distribution with
• T 500 MeV

t(fm/c)
generated through secondary collisions
saturated in the early stage sensitive to cross
section (m.f.p.viscosity)
v2 is
11
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Basis of the Announcement
PHENIX(03)
STAR(02)
pT dependence and mass ordering
Multiplicity dependence
Hydro results Huovinen, Kolb, Heinz,
13
Sensitivity to Different Assumptions in
Early/Late Stages
Glauber-type Color Glass Condensate
Sudden freezeout Discovery of Perfect Liquid ?
Hadronic rescattering ? ?
Initial Condition
Freezeout
14
Dependence on Freezeout Prescription
T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.
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Classification of Hydro Models
Model PCE Hirano, Teaney, Kolb
Model HC Teaney, Shuryak, Bass, Dumitru,
Model CE Kolb, Huovinen, Heinz, Hirano
T
1 fm/c
QGP phase
Perfect Fluid of QGP
Tc
3 fm/c
Partial Chemical Equilibrium EOS
Chemical Equilibrium EOS
Tch
Hadronic Cascade
Hadron phase
Tth
Tth
10-15 fm/c
t
ideal hydrodynamics
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v2(pT) for Different Freezeout Prescriptions
2000 (Heinz, Huovinen, Kolb) Ideal hydro w/
chem.eq.hadrons 2002 (TH,Teaney,Kolb) Chemical
freezeout 2002 (Teaney) Dissipation in hadron
phase 2005 (BNL) RHIC serves the perfect liquid.
20-30
Why so different/similar?
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Accidental Reproduction of v2(pT)
v2(pT)
v2(pT)
At hadronization
Chemical Eq.
v2
v2
freezeout
ltpTgt
ltpTgt
pT
pT
v2(pT)
Chemical F.O.
CE increase
CFO decrease
v2
ltpTgt
pT
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Why ltpTgt behaves differently?
Mean ET decreases due to pdV work

• ET per particle increases
• in chemical equilibrium.
• ?This effect delays cooling of the system like a
  viscous fluid.
• Chemical equilibrium
• imitates viscosity
• at the cost of particle yield!
• ? HydroCascade is the only model to reproduce
  v2(pT)!!!

Chemical Freezeout
MASS energy KINETIC energy
Chemical Equilibrium
For a more rigorous discussion, see TH and
M.Gyulassy, NPA769(2006)71
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v2(pT) for identified hadronsfrom QGP Hydro
Hadronic Cascade
Pion
20-30
Proton
Mass dependence is o.k. Note First result was
obtained by Teaney et al.
Mass splitting/ordering comes from hadronic
rescattering. ?Not a direct signature of perfect
fluid QGP
20
v2(Npart) and v2(eta)
Significant Hadronic Viscous Effects at Small
Multiplicity!
21
Summary So Far

• When we employ Glauber-type initial conditions,
  hadronic dissipation is indispensable.
• Perfect fluid QGP core and dissipative hadronic
  corona

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Dependence on Initialization of Hydro
T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara,
Phys.Lett.B 636 (2006)299 work in progress.
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(1) Glauber and (2) CGC Hydro Initial Conditions
Which Clear the First Hurdle
Centrality dependence
Rapidity dependence

• Glauber model
• NpartNcoll 8515
• CGC model
• Matching I.C. via e(x,y,h)

Details on CGC ? Talk by K.Itakura
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v2(Npart) from QGP Hydro Hadronic Cascade
TH et al.(06)

• Glauber
• Early thermalization
• Mechanism?
• CGC
• No perfect fluid?
• Additional viscosity
• is required in QGP

Importance of better understanding of initial
condition
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Large Eccentricity from CGC Initial Condition
Hirano and Nara(04), Hirano et al.(06) Kuhlman
et al.(06), Drescher et al.(06)
y
x
Pocket formula (ideal hydro) v2 0.2e _at_ RHIC
energies
Ollitrault(92)
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v2(pT) and v2(eta) from CGC initial conditions
20-30
v2(model) gt v2(data)
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Summary and Outlook
FAKE!

• Much more studies needed for initial states
• Still further needed to investigate EOS
  dependence
• To be or not to be (consistent with hydro), that
  is the question!

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Acknowledgement
Miklos is supposed to attend this workshop but
cannot come. I really appreciate his
continuous encouragement to my work.
Get well soon completely, Miklos!
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Excitation Function of v2

• Hadronic Dissipation
• is huge at SPS.
• still affects v2 at RHIC.
• is almost negligible at LHC.

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Source Function from 3D Hydro Cascade
How much the source function differs from ideal
hydro in Configuration space?
Blink Ideal Hydro, Kolb and Heinz (2003) Caveat
No resonance decays in ideal hydro
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Non-Gaussian Source?
y
px 0.5GeV/c
x
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Viscosity from a Kinetic Theory
See, e.g. DanielewiczGyulassy(85)
For ultra-relativistic particles, the shear
viscosity is
Ideal hydro l ? 0 shear viscosity ? 0
Transport cross section
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Viscosity and Entropy

• Reynolds number

Iso, Mori, Namiki (59)
Rgtgt1 ?Perfect fluid
where

• 11D Bjorken flow Bjorken(83)
• Baym(84)Hosoya,Kajantie(85)Danielewicz,Gyulassy(
  85)Gavin(85)Akase et al.(89)Kouno et al.(90)

(Ideal)
(Viscous)
h shear viscosity (MeV/fm2), s entropy
density (1/fm3)
h/s is a good dimensionless measure (in the
natural unit) to see viscous effects.
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Why QGP Fluid Hadron Gas Works?
h shear viscosity, s entropy density
TH and Gyulassy (06)
Kovtun,Son,Starinets(05)

• Absolute value of viscosity

• Its ratio to entropy density

!
Rapid increase of entropy density can make hydro
work at RHIC. Deconfinement Signal?!
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Temperature Dependence of h/s

• Shear Viscosity in Hadron Gas

DanielewiczGyulassy(85)

• Assumption h/s at Tc in the sQGP is 1/4p

Kovtun, Son, Starinets(05)
No big jump in viscosity at Tc!

• We propose a possible scenario

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Digression
Pa N/m2
(Dynamical) Viscosity h 1.0x10-3 Pa s
(Water 20?) 1.8x10-5 Pa s (Air 20?)
Kinetic Viscosity nh/r 1.0x10-6 m2/s
(Water 20?) 1.5x10-5 m2/s (Air 20?)
hwater gt hair BUT nwater lt nair
Non-relativistic Navier-Stokes eq. (a simple form)
Neglecting external force and assuming
incompressibility.
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A Bigger Picture in Heavy Ion Collisions
Before collisions
Geometric Scaling
CGC
DGLAP region
Parton production Pre- equilibrium
Transverse momentum
Shattering CGC
(N)LOpQCD
Instability? Equilibration?

• Parton energy loss
• Inelastic
• Elastic

Interaction
Perfect fluid QGP or GP

• Hydrodynamics
• viscosity?
• non chem. eq.?

Recombination Coalescence
Dissipative hadron gas
Hadronic cascade
Fragmentation
Proper time
Low pT
High pT
Intermediate pT
38
Differential Elliptic Flow Developsin the Hadron
Phase?
Kolb and Heinz(04)
Is v2(pT) really sensitive to the late dynamics?
100MeV
T.H. and K.Tsuda (02)
140MeV
0.8
1.0
0.4
0.6
0.2
0
0.8
0.4
0.6
0.2
0


transverse momentum (GeV/c)
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Mean pT is the Key
Generic feature!
t
t
Slope of v2(pT) v2/ltpTgt
Response to decreasing Tth (or increasing t)
v2
v2/ltpTgt
ltpTgt
CE
PCE
t
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(CGC )QGP HydroHadronic Cascade
TH et al.(05-)
Hadronic Corona (Cascade, JAM)
t
sQGP core (Full 3D Ideal Hydro)
z
0
(Option) Color Glass Condensate
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Ideal QGP Fluid Dissipative Hadron Gas Models
(11)D with Bjorken flow (21)D with Bjorken flow Full (31)D
UrQMD A.Dumitru et al., PLB460,411(1999) PRC60,021902(1999)S.Bass and A.Dumitru, PRC61,064909(2000). N/A C.Nonaka and S.Bass, nucl-th/0510038.
RQMD N/A D.Teaney et al., PRL86,4783(2001), nucl-th/0110037 D.Teaney, nucl-th/0204023. N/A
JAM N/A N/A TH, U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara, PLB636,299(2006).
hydro
cascade
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Hydro Meets Data for the First Time at RHIC
Current Three Pillars
THGyulassy(06),TH,Heinz,Kharzeev,Lacey,Nara(06)

• Perfect Fluid (s)QGP Core
• Ideal hydro description of the QGP phase
• Necessary to gain integrated v2
• Dissipative Hadronic Corona
• Boltzmann description of the hadron phase
• Necessary to gain enough radial flow
• Necessary to fix particle ratio dynamically
• Glauber Type Initial Condition
• Diffuseness of initial geometry

A Lack of each pillar leads to discrepancy!
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pT Spectra for identified hadronsfrom QGP
HydroHadronic Cascade
dN/dy and dN/dpT are o.k. by hydrocascade.
Caveat Other components such as recombination
and fragmentation should appear in the
intermediate-high pT regions.
44
Discussions Hadronic Dissipation

• Hybrid Model
• QGP Fluid Hadronic Gas Glauber I.C.
• Hydro Model
• QGP Fluid Hadronic Fluid Glauber I.C.

Comparison?Try to draw information on hadron gas

• Key technique in hydro
• Partial chemical equilibrium in hadron phase
• Particle ratio fixed at Tch
• Chemical equilibrium changes dynamics.
• TH and K.Tsuda(02),TH
  and M.Gyulassy(06)

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Hadronic Dissipation Suppresses Differential
Elliptic Flow
Difference comes from dissipation only in the
hadron phase

• Relevant parameter Gs/t
• Teaney(03)
• Dissipative effect is not so
• large due to small expansion
• rate (1/tau 0.05-0.1 fm-1)

Caveat Chemically frozen hadronic fluid is
essential in differential elliptic flow. (TH and
M.Gyulassy (06))