Transcript Toward understanding the EOS of the QGP in relativistic

Perfect Fluidity of the Quark
Gluon Plasma in Relativistic
Heavy Ion Collisions
Tetsufumi Hirano
Department of Physics, the University of Tokyo
hirano @ phys.s.u-tokyo.ac.jp
http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/
KEK-CPWS-HEAP2009
OUTLINE

Introduction



Time evolution of heavy ion collisions
Transverse collective flow

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Quark gluon plasma and relativistic heavy ion collisions
Radial flow
Elliptic flow
Current status of dynamical modeling in heavy ion
collisions
Summary and Outlook
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)
Recipes for Quark Gluon Plasma
How are colored particles set free
from confinement?
Compress
hadronic many body system
Heat up
Figure adopted from
http://www.bnl.gov/rhic/QGP.htm
Little Bang!
front
view
Relativistic Heavy Ion Collider(2000-)
RHIC as a time machine!
STAR
side
view
STAR
Collision energy
100 GeV per nucleon
Au(197×100)+Au(197×100)
Multiple production
(N~5000)
Heat
Big Bang vs. Little Bang
beam axis
3D Hubble expansion
Nearly 1D Hubble expansion*
+ 2D transverse expansion
Figure adopted from
http://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm
*Bjorken(’83)
Big Bang vs. Little Bang
Big Bang
Little Bang
Time Scale
10-5 sec
>>m.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)
Dynamics of Heavy Ion Collisions
Freezeout
“Re-confinement”
Expansion, cooling
Thermalization
First contact
(two bunches of gluons)
Time scale
10fm/c~10-23sec
Temperature scale
100MeV~1012K
Jargon: Centrality
“Centrality” characterizes a collision
and categorizes events.
central event
peripheral event
Participant-Spectator picture is valid
How to Quantify Centrality
Npart and Ncoll
197Au+197Au
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
Estimated Energy Density at RHIC
ec from lattice
PHENIX(’05)
Well above ec
from lattice
simulations in
central collision
at RHIC
M.Cheng et al., PRD77,014511 (’08)
QGP from the 1st Principle
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
*
Transverse
Collective
Flow
*
“Transverse”: a direction perpendicular
to the collision axis.
Radial Flow (Azimuthally Averaged
Flow)
Driving force of flow
pressure gradient
In general, flow is
sensitive to EOS
Inside: high pressure
Outside: vacuum (P=0)
Blast wave model (thermal+boost)
Sollfrank et al.(’93)
p
Blue-Shifted Spectra
d
Au
p
Au
Au
O.Barannikova, talk at QM05
pp & dAu: Power-law
Au+Au: Convex to Power
law
Consistent with the
thermal+boost
picture
What is Elliptic Flow?
Ollitrault (’92)
How does the system respond to spatial anisotropy?
No secondary interaction
Hydro behavior
y
f
x
INPUT
Spatial Anisotropy
2v2
OUTPUT
dN/df
dN/df
Interaction among
produced particles
Momentum Anisotropy
0
f
2p
0
f
2p
Time Evolution of v2 from a Parton
Cascade Model
Zhang et al.(’99)
ideal hydro limit
v2
: Ideal hydro
b = 7.5fm
: strongly
interacting
system
t(fm/c)
v2 is
generated through secondary collisions
saturated in the early stage
sensitive to cross section (~1/m.f.p.~1/viscosity)
Arrival at Hydrodynamic Limit
y
x
Experimental data reach
hydrodynamic limit curve
for the first time at RHIC.
Current Status of
Dynamical Modeling
In Relativistic Heavy
Ion Collisions
Strategy to Attack QGP Problem
•The first principle (QuantumChromo Dynamics)
•Inputs to phenomenology (lattice QCD)
Complexity of QCD
Non-linear interactions of gluons
•Phenomenology
(hydrodynamics)
Strong coupling
Many body system
Color confinement
•Experimental data
@ Relativistic Heavy Ion Collider
200+ papers from 4 collaborations
since 2000
3D Ideal Hydro Simulation in Au+Au
Collisions with b=7.2fm @ 100 GeV/n
Higher quality animation is available at
Caveat: Camera angle keeps changing.
Multi-Module Modeling (1)
time
hadron gas
Initial condition
•Glauber
•Color Glass Condensate
•EPOS
QGP fluid
collision axis
Au
0-10%
Au
10-20%
20-30%
…
0
H.J.Drescher and Y.Nara (2007), K.Werner et al.(2006)
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.
Multi-Module Modeling (2)
time
hadron gas
QGP fluid
Ideal Hydrodynamics*
•Initial time 0.6fm/c
•Model EoS
•lattice-based#
•1st order
collision axis
0
Au
Au
*T.Hirano(2002), #Lattice
part : M.Cheng et al. (2008)
Relativistic Hydrodynamic Equations
for a Perfect Fluid
e : energy density,
Energy
Momentum
Baryon number
P : pressure,
: four velocity
Multi-Module Modeling (3)
time
hadron gas
QGP fluid
collision axis
0
Au
Au
Hadronic afterburner
•Hadronic transport
model (JAM, UrQMD)
•Kinetic theory of
hadron gases including
all resonances
•Switching temperature
T=160 MeV (169MeV)
Transverse Plane
Kinetic evolution
of hadron gas
y
x
Perfect fluid
evolution of QGP
Initial condition
QGP fluid surrounded
by hadron gas
pT Spectra for Pions and Protons
Glauber/CGC + Ideal Hydro + JAM
Hybrid model works well up to pT~1.5 GeV/c
(1st order, dotted) and 2-3 GeV/c (lattice-based, solid)
TH et al. (’06).
Centrality Dependence of Elliptic Flow
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)
TH et al, (in prepation)
Centrality Dependence of Elliptic Flow
197Au+197Au
63Cu+63Cu
Glauber/CGC + Ideal Hydro + JAM
•1st order phase transition is unlikely from data since
viscosity reduces v2 largely.
•How perfect?  Depends on initial model.
Effects of Viscosity
Glauber + Viscous Hydro
Figure taken from M.Luzum
and P.Romatschke, arXiv:0804.4015
•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.
Pseudorapidity Dependence of
Elliptic Flow Coefficient
QGP fluid+hadron gas
QGP+hadron fluids
QGP only
T.Hirano et al.,Phys.Lett.B636(2006)299.
Not boost invariant
Suppression in forward and backward rapidity
pT Dependence of Elliptic Flow
Au+Au 200 GeV
•Glauber+ Ideal hydro with
lattice(-motivated) EoS +
hadronic cascade
•Viscosity would be needed for
better description.
Results from EPOS Initial Conditions
K.Werner et al. (2009)
EPOS + Ideal Hydro + UrQMD
Reasonably reproduce rapidity dependence
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

TH(’02); TH and K.Tsuda(’02); TH et
al. (’06).
Pseudorapidity Dependence of v2
QGP+hadron
QGP only
h<0
h=0
h>0
•v2 data are comparable with
hydro results again around h=0
•Not a QGP gas  sQGP
•Nevertheless, large
discrepancy in
forward/backward rapidity
See next slides
T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.
Hadron Gas Instead of Hadron Fluid
A QGP fluid surrounded
by hadronic gas
QGP core
QGP: Liquid (hydro picture)
Hadron: Gas (particle picture)
“Reynolds number”
Matter proper part:
(shear viscosity)
(entropy density)
big
small
in Hadron
in QGP
Importance of Hadronic “Corona”
QGP fluid+hadron gas
QGP+hadron fluids
QGP only
•Boltzmann Eq. for hadrons
instead of hydrodynamics
•Including viscosity through
finite mean free path
•Suggesting rapid increase of
entropy density
•Deconfinement makes hydro
work at RHIC!?
 Signal of QGP!?
T.Hirano et al.,Phys.Lett.B636(2006)299.
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!
How to Quantify Centrality
y
Thickness function:
Woods-Saxon nuclear density:
# of binary collisions
sin = 42mb @200GeV
Gold nucleus:
r0=0.17 fm-3
R=1.12A1/3-0.86A-1/3
d=0.54 fm
# of participants
1－（survival probability）
x
Parton Distribution in Proton
at Small x
x 20!!
•Gluons are dominant at
small x.
•Small x = High energy
•Hadron/Nucleus as a
bunch of gluons at high
energy
Bjorken x ~ Fraction of longitudinal momentum
in proton
Kinematics in gg g
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)
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.
“Phase Diagram” of hadrons
non-perturbative region
CGC
•Onset of CGC at RHIC
•Some evidences exist.
•Test of CGC at LHC
•How to describe
perturbative CGC to
non-perturbative QGP?
BFKL
dilute parton
DGLAP
0
Onset of CGC in d+Au Collisions
at RHIC
forward rapidity
theory (CGC)
data
midrapidity
BRAHMS Collaboration, white paper
D.Kharzeev et al., PRD68,094013(’03).
y=0,1,2,3
H.Fujii, talk at RCNP workshop(’07)