Perfect Fluid QGP or CGC?

1
Perfect Fluid QGP or CGC?

• Tetsufumi Hirano
• Institute of Physics, University of Tokyo

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.
Seminar_at_RCNP, 7/27/2006
2
OUTLINE

• Introduction
• Basic checks
• 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
Introduction
What is the matter where our building block plays
a fundamental role?
What is the origin of matter?
Confinement
Quark Gluon Plasma
Matter Particle quark Gauge Particle
gluon Dynamics QCD Matter form QGP
Quarks, Leptons Gauge particles
4
Two Faces of QCD
Strong coupling constant
q-qbar potential
F.Karsch and E.Laermann
S. Eidelman et al.
Color confinement
Asymptotic freedom
Low energy scale ?? High energy scale ??? ?
perturbation ? OK!
5
QGP Recipe

1. Adding pressure ? Pushing up chemical potential
   scale
2. Adding heat ? Pushing up temperature scale

6
QGP from 1st principle calculations

• Critical temperature
• Tc 170MeV 2x1012K !
• ec 0.3-1.3GeV/fm3
• Rapid increase around Tc

Karsch et al.
Normalized temperature
Stefan-Boltzmann law (energy density)?(d.o.f.)x(te
mperature)4 Hadron phase(p) 3 ?? QGP 37 (color,
flavor)
7
Matter Evolved with Our Universe
QGP Hadronization Nucleosynthesis
QGP study Understanding early universe
8
Little Bang!
Relativistic Heavy Ion Collider(2000-) RHIC as a
time machine!
front view
STAR
side view
STAR
Collision energy Multiple production Heat
100 GeV per nucleon Au(197100)Au(197100)
9
Physics of the QGP

• Matter governed by QCD, not QED
• High energy density/temperature frontier
• ?Toward an ultimate matter (Maximum energy
  density/temperature)
• Reproduction of QGP in H.I.C.
• ?Reproduction of early universe on the Earth
• Understanding the origin of matter which evolves
  with our universe

10
BASIC CHECKSAS AN INTRODUCTION
11
Basic Checks (I) Energy Density
Bjorken energy density
t proper time y rapidity R effective
transverse radius mT transverse mass
Bjorken(83)
12
Critical Energy Density from Lattice
Stolen from Karsch(PANIC05).
13
Centrality Dependence of Energy Density
Well above ec from lattice in central collision
at RHIC, if assuming t1fm/c.
ec from lattice
PHENIX(05)
14
CAVEATS (I)

• Just a necessary condition in the sense that
  temperature (or pressure) is not measured. (Just
  a firework?)
• How to estimate tau?
• If the system is thermalized, the actual energy
  density is larger due to pdV work.
• Boost invariant?
• Averaged over transverse area. Effect of
  thickness? How to estimate area?

Gyulassy, Matsui(84) Ruuskanen(84)
15
Basic Checks (II) Chemical Eq.
direct
Resonance decay
Two fitting parameters Tch, mB
16
Amazing fit!
T177MeV, mB 29 MeV
Close to Tc from lattice
17
CAVEATS (II)

• Even ee- or pp data can be fitted well!
• See, e.g., BecattiniHeinz(97)
• What is the meaning of fitting parameters?
  See, e.g., Rischke(02),Koch(03)
• Why so close to Tc?
• No chemical eq. in hadron phase!?
• Essentially dynamical problem!

Expansion rate ?? Scattering rate
(Process dependent)
see, e.g., U.Heinz, nucl-th/0407067
18
Statistical Model Fitting to eepp
BecattiniHeinz(97)
Phase space dominance? T prop to E/N?
See, e.g., Rischke(02),Koch(03)
19
Basic Checks (III) Radial Flow
Blast wave model (thermalboost)
Driving force of flow Inside high
pressure Outside vacuum (p0) ?pressure
gradient
Sollfrank et al.(93)
Spectrum for heavier particles is a good place to
see radial flow.
20
Spectrum change is seen in AA!
Power law in pp dAu
Convex to Power law in AuAu

• Consistent with thermal boost picture
• Pressure can be built up in AA

O.Barannikova, talk at QM05
21
CAVEATS (III)

• Finite radial flow even in pp collisions?
• (T,vT)(140MeV,0.2)
• Is blast wave reliable quantitatively?
• Not necessary to be thermalized completely
• Results from hadronic cascade models.
• How is radial flow generated dynamically?
• Consistency?
• Chi square minimum located a different point for
  f and W
• Separate f.o. due to strong expansion.
• Time scale micro sec. in early universe
• ?? 10-23 (10 yocto) sec. in H.I.C.
• Flow profile? Freezeout hypersurface? Sudden
  freezeout?

22
Basic Checks ? Necessary Conditions to Study QGP
at RHIC

• Energy density can be well above ec.
• tau? thermalized?
• Temperature can be extracted. (particle ratio)
• ee- and pp? Why freezeout happens so close to Tc
• Pressure can be built up. (pT spectra)
• Completely thermalized?

Importance of Systematic Study based on
Dynamical Framework
23
Dynamics of Heavy Ion Collisions
Freezeout Re-confinement Expansion,
cooling Thermalization First contact (two
bunches of gluons)
Temperature scale 100MeV1012K
Time scale 10fm/c10-23sec
24
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

25
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
26
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
Latent heat
Lattice QCD predicts cross over phase
transition. Nevertheless, energy density
explosively increases in the vicinity of Tc. ?
Looks like 1st order.
27
Initial Stage Initial Condition
Energy density distribution
Transverse plane
Reaction plane
Parameterization/model-calculation to reproduce
(dN/dh)/(Npart/2) and dN/dh
28
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)
29
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.

30
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
31
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
32
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33
Basis of the Announcement
PHENIX(03)
STAR(02)
response (output)/(input)
pT dependence and mass ordering
Multiplicity dependence
Hydro results Huovinen, Kolb, Heinz,
34
Sensitivity to Different Assumptions in
Early/Late Stages
Glauber-type Color Glass Condensate
Sudden freezeout Discovery of Perfect Liquid ?
Hadronic rescattering ? ?
Initial Condition
Freezeout
35
Dependence on Freezeout Prescription
T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.
36
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
37
Chemically Frozen Hadron Phase

• Statistical model
• TchgtTth
• (conventional) hydro
• TchTth

• No reproduction
• of ratio and spectra
• simultaneously

Chemical parameters ? particle ratio Thermal
parameters ? pt spectra
38
Nobody knows this fact
P.Huovinen, QM2002 proceedings
39
Extension of Phase Diagram

• Single Tf in hydro
• Hydro works?
• Both ratio and
• spectra?

Introduction of chemical potential for each
hadron!
mi
40
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?
41
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)
42
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
43
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
44
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
45
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 nucl-th/0607018
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
46
(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
47
v2(pT) for identified hadronsfrom QGP Hydro
Hadronic Cascade
20-30
Mass dependence is o.k. Note First result was
obtained by Teaney et al.
48
v2(Npart) and v2(eta)
Significant Hadronic Viscous Effects at Small
Multiplicity!
49
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.
50
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?!
51
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.
52
Taken from Csernai-Kapusta-McLerran paper
53
Summary So Far

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

54
Dependence on Initialization of Hydro
T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara,
Phys.Lett.B 636 (2006)299 work in progress.
55
(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)

56
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
57
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)
58
v2(pT) and v2(eta) from CGC initial conditions
20-30
v2(model) gt v2(data)
59
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!

60
Experimental Facts
Explosive increase! Hadron and nucleus as a bunch
of gluons
What happens eventually? Unitarity? Froissart
bound?
61
Interplay between Emission and Recombination
Small x gluons come from large x partons (linear
effect)
Fusion of two gluons (non-linear effect)
Figures from Iancu and Venugopalan, QGP3
62
Phase Diagram of Hadron
Q2 Size of a probe (resolution) x Momentum
fraction
CGC
geometrical scaling
BFKL
non-perturbative region

• Linear region(s)
• dilute parton
• geometrical scaling
• Non-linear region
• CGC

dilute parton
DGLAP
0
63
Color Glass Condensate (CGC)

• Color Gluons are colored
• Glass The strong analogy to actual glasses.
• Disorder
• Evolve slowly due to Lorentz time duration
• Condensate High density of massless gluons
• Density r 1/asgtgt1
• Coherence
• Characteristic momentum
• a.k.a. saturation scale

saturation
Gribov, Levin Ryskin (83) Mueller, Qiu
(86) Blaizot, Mueller (87)
64
A Saturation Model
Z1/mx
BFKL eq.linear ?Non-linear evolution
is important in high density.
65
Gluon Production from a Saturation Model
A la Karzeev and Levin
f
1/Qs
saturation scale
Qs2
kT2
0
Mueller diagram
gg?g
66
Results from Kharzeev Levin
Unintegrated gluon dist.
dilute
dense
Parton-hadron duality (gluon dist. ? pion dist.)
67
A Closer Look Reveals Details of Hadronic Matter
Stolen from M.Bleicher (The Berkeley School)
68
How Reliable Quantitatively?
f, W? Small rescattering
peripheral
System expands like this trajectory?
central
Radial flow in pp collisions?
69
Excitation Function of v2

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

70
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
71
Phi meson as a direct messenger of QGP
hadronization
VERY PRELIMINARY
Final v2
Just after hadronization
Violation of mass ordering in low pT region!
Tiny splitting
72
Phi spectra
VERY PRELIMINARY
What happens above pT1.5GeV/c?
73
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
74
Non-Gaussian Source?
y
px 0.5GeV/c
x
75
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
76
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

77
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
78
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.
79
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)

80
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))