Perfect Fluidity of the Quark Gluon Plasma in Relativistic Heavy Ion Collisions

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Perfect Fluidity of the Quark Gluon Plasma in
Relativistic Heavy Ion Collisions

• Tetsufumi Hirano
• Department of Physics, the University of Tokyo
• hirano _at_ phys.s.u-tokyo.ac.jp
• http//tkynt2.phys.s.u-tokyo.ac.jp/hirano/

KEK-CPWS-HEAP2009
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OUTLINE

• Introduction
• Quark gluon plasma and relativistic heavy ion
  collisions
• Time evolution of heavy ion collisions
• Transverse collective flow
• Radial flow
• Elliptic flow
• Current status of dynamical modeling in heavy ion
  collisions
• Summary and Outlook

3
Where was the Quark Gluon Plasma?
History of the Universe History of the matter
Nucleosynthesis Hadronization Quark Gluon
Plasma (after micro seconds of Big Bang)
4
Recipes for Quark Gluon Plasma
How are colored particles set free from
confinement?
Compress Heat up
hadronic many body system
Figure adopted from http//www.bnl.gov/rhic/QGP.ht
m
5
Little Bang!
front view
Relativistic Heavy Ion Collider(2000-) RHIC as a
time machine!
STAR
side view
STAR
Collision energy Multiple production (N5000) He
at
100 GeV per nucleon Au(197100)Au(197100)
6
Big Bang vs. Little Bang
beam axis
Nearly 1D Hubble expansion 2D transverse
expansion
3D Hubble expansion
Figure adopted from http//www-utap.phys.s.u-tokyo
.ac.jp/sato/index-j.htm
Bjorken(83)
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Big Bang vs. Little Bang
Big Bang Little Bang
Time Scale 10-5 sec gtgtm.f.p./c 10-23 sec m.f.p./c
Expansion Rate 105-6/sec 1022-23/sec
? Local thermalization of the QGP is non-trivial
in H.I.C.
Spectrum Red-shifted (CMB) Blue-shifted (hadrons)

• Collective flow is a key to check whether local
  thermalization is achieved.

See, e.g., Yagi, Hatsuda, Miake, Quark-Gluon
Plasma (Cambridge, 2005)
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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
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Jargon Centrality
Centrality characterizes a collision and
categorizes events.
central event
peripheral event
Participant-Spectator picture is valid
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How to Quantify Centrality
Npart and Ncoll
197Au197Au
Npart The number of participants Ncoll The
number of binary collisions Npart and Ncoll as a
function of impact parameter
PHENIX Correlation btw. BBC and ZDC signals
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Estimated Energy Density at RHIC
Well above ec from lattice simulations in central
collision at RHIC
ec from lattice
PHENIX(05)
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QGP from the 1st Principle
M.Cheng et al., PRD77,014511 (08)

• Equation of state from lattice QCD
• A large number of d.o.f. are freed around Tc.
• Pseudo-critical temperature Tc 150-200 MeV
• Typical energy density scale of transition 1
  GeV/fm3
• Not available for time evolution

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Transverse Collective Flow
Transverse a direction perpendicular to the
collision axis.
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Radial Flow (Azimuthally Averaged Flow)
Blast wave model (thermalboost)
Driving force of flow ?pressure gradient In
general, flow is sensitive to EOS Inside high
pressure Outside vacuum (P0)
Sollfrank et al.(93)
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Blue-Shifted Spectra
p
p
Au
d
Au
Au
pp dAu Power-law
AuAu Convex to Power law
O.Barannikova, talk at QM05
Consistent with the thermalboost picture
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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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Time Evolution of v2 from a Parton Cascade Model
Zhang et al.(99)
ideal hydro limit
v2
Ideal hydro
strongly interacting system
b 7.5fm
t(fm/c)
generated through secondary collisions
saturated in the early stage sensitive to cross
section (1/m.f.p.1/viscosity)
v2 is
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Arrival at Hydrodynamic Limit
y
x
Experimental data reach hydrodynamic limit curve
for the first time at RHIC.
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Current Status of Dynamical Modeling In
Relativistic Heavy Ion Collisions
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Strategy to Attack QGP Problem

• The first principle (QuantumChromo Dynamics)

• Inputs to phenomenology (lattice QCD)

Complexity of QCD Non-linear interactions of
gluons Strong coupling Many body system Color
confinement

• Phenomenology (hydrodynamics)

• Experimental data
• _at_ Relativistic Heavy Ion Collider
• 200 papers from 4 collaborations
• since 2000

22
3D Ideal Hydro Simulation in AuAu Collisions
with b7.2fm _at_ 100 GeV/n
Higher quality animation is available at
Caveat Camera angle keeps changing.
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Multi-Module Modeling (1)
hadron gas

• Initial condition
• Glauber
• Color Glass Condensate
• EPOS

time
QGP fluid
collision axis
0
Au
Au
H.J.Drescher and Y.Nara (2007), K.Werner et
al.(2006)
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Details of Initial Conditions

• Glauber model
• Conventional initial
• conditions
• Announcement of
• discovery was made
• in comparison of
• results from Glauber
• with data.
• Initial entropy
• distribution is prop.
• to Npart

• Color Glass
• Condensate
• Natural picture
• based on QCD
• at very high collision
• energies.

• EPOS
• Phenomenological
• implication of parton
• ladder string.
• Application to air
• shower simulation
• for high energy
• cosmic rays.

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Multi-Module Modeling (2)
hadron gas

• Ideal Hydrodynamics
• Initial time 0.6fm/c
• Model EoS
• lattice-based
• 1st order

time
QGP fluid
collision axis
0
Au
Au
T.Hirano(2002), Lattice part M.Cheng et al.
(2008)
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Relativistic Hydrodynamic Equations for a Perfect
Fluid
e energy density,
P pressure,
four velocity
Energy
Momentum
Baryon number
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Multi-Module Modeling (3)
hadron gas

• Hadronic afterburner
• Hadronic transport
• model (JAM, UrQMD)
• Kinetic theory of
• hadron gases including
• all resonances
• Switching temperature
• T160 MeV (169MeV)

time
QGP fluid
collision axis
0
Au
Au
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Transverse Plane
Kinetic evolution of hadron gas
y
x
Perfect fluid evolution of QGP
Initial condition
QGP fluid surrounded by hadron gas
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pT Spectra for Pions and Protons
Glauber/CGC Ideal Hydro JAM
Hybrid model works well up to pT1.5 GeV/c (1st
order, dotted) and 2-3 GeV/c (lattice-based,
solid)
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Centrality Dependence of Elliptic Flow
TH et al. (06).

• Discovery of Large v2 at RHIC
• v2 data are comparable with (naive) hydro
  results for the first time.
• Hadronic cascade models cannot reproduce data.
• This is the first time for ideal
• hydro at work in H.I.C.
• ? Strong motivation to develop hydro-based
  analysis tools.

Glauber Ideal Hydro
Result from a hadronic cascade (JAM) (Courtesy of
M.Isse)
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Centrality Dependence of Elliptic Flow
TH et al, (in prepation)
197Au197Au
63Cu63Cu
Glauber/CGC Ideal Hydro JAM

• 1st order phase transition is unlikely from data
  since
• viscosity reduces v2 largely.
• How perfect? ? Depends on initial model.

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Effects of Viscosity

• A tiny kinetic viscosity
• leads to large reduction
• of elliptic flow coefficients.
• Elliptic flow is sufficiently
• sensitive to constrain EoS,
• transport coefficients, and
• initial conditions.

Glauber Viscous Hydro
Figure taken from M.Luzum and P.Romatschke,
arXiv0804.4015
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Pseudorapidity Dependence of Elliptic Flow
Coefficient
QGP fluidhadron gas
QGPhadron fluids
QGP only
T.Hirano et al.,Phys.Lett.B636(2006)299.
Not boost invariant Suppression in forward and
backward rapidity
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pT Dependence of Elliptic Flow
AuAu 200 GeV

• Glauber Ideal hydro with
• lattice(-motivated) EoS
• hadronic cascade
• Viscosity would be needed for
• better description.

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Results from EPOS Initial Conditions
K.Werner et al. (2009)
EPOS Ideal Hydro UrQMD
Reasonably reproduce rapidity dependence
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Summary Outlook

• Elliptic flow pattern observed at RHIC is
  described reasonably well by hydro-based models.
• Hydro model at work for the first time in H.I.C.
• Hadron-based kinetic theory cannot reproduce flow
  pattern.
• Systematic studies are undergoing
• Effects of viscosity ? Constraint of EOS and
  transport coefficients
• Understanding of initial pre-thermalization stage

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Pseudorapidity Dependence of v2
TH(02) TH and K.Tsuda(02) TH et al. (06).
QGPhadron

• v2 data are comparable with hydro results again
  around h0
• Not a QGP gas ? sQGP
• Nevertheless, large discrepancy in
  forward/backward rapidity
• ?See next slides

QGP only
h0
hlt0
hgt0
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Hadron Gas Instead of Hadron Fluid
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
A QGP fluid surrounded by hadronic gas
Reynolds number
QGP core
Matter proper part (shear viscosity) (entropy
density)
big in Hadron
small in QGP
QGP Liquid (hydro picture) Hadron Gas (particle
picture)
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Importance of Hadronic Corona

• Boltzmann Eq. for hadrons instead of
  hydrodynamics
• Including viscosity through finite mean free path

QGP fluidhadron gas
QGPhadron fluids
QGP only

• Suggesting rapid increase of entropy density
• Deconfinement makes hydro work at RHIC!?
• ? Signal of QGP!?

T.Hirano et al.,Phys.Lett.B636(2006)299.
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Sensitivity to Initial Conditions
Novel initial conditions from Color Glass
Condensate lead to large eccentricity.
Hirano and Nara(04), Hirano et al.(06) Kuhlman
et al.(06), Drescher et al.(06)
Need viscosity even in QGP!
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How to Quantify Centrality
y
Thickness function
Gold nucleus r00.17 fm-3 R1.12A1/3-0.86A-1/3 d
0.54 fm
x
Woods-Saxon nuclear density
of binary collisions
of participants
sin 42mb _at_200GeV
1-(survival probability)
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Parton Distribution in Proton at Small x

• Gluons are dominant at small x.
• Small x High energy
• Hadron/Nucleus as a bunch of gluons at high energy

x 20!!
Bjorken x Fraction of longitudinal momentum in
proton Kinematics in gg? g
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Interplay btw. Emission and Recombination at
Small x
Linear effect (BFKL)
Non-linear effect
Figures adopted from E.Iancu and R.Venugopalan,
in Quark Gluon Plasma 3 (world scientific)
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Non-Linear Evolution and Color Glass Condensate
(CGC)
Rate eq.
small x high energy
More sophisticated equation (BK or JIMWLK) based
on QCD is solved.
Figures adopted from K.Itakura, talk at QM2005.
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Phase Diagram of hadrons

• Onset of CGC at RHIC
• Some evidences exist.
• Test of CGC at LHC
• How to describe
• perturbative CGC to
• non-perturbative QGP?

CGC
geometrical scaling
BFKL
non-perturbative region
LHC
RHIC
dilute parton
DGLAP
0
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Onset of CGC in dAu Collisions at RHIC
midrapidity
forward rapidity
data
BRAHMS Collaboration, white paper
y0,1,2,3
theory (CGC)
H.Fujii, talk at RCNP workshop(07)
D.Kharzeev et al., PRD68,094013(03).