QGP and Dynamics of
Relativistic Heavy Ion
Collisions
Tetsufumi Hirano
The University of Tokyo, Komaba
Thermal Quantum Field Theories and Their Applications
OUTLINE
•
Basic Checks
–
Energy density
–
Chemical and kinetic equilibrium
•
Dynamics of Heavy Ion Collisions
–
Elliptic Flow and Perfect Liquid!?
–
Recent Results from Hydro models
–
Some Comments on the Discovery
•
Summary and Outlook
My Charge: To interpret recent
experimental data at RHIC
from a QGP fluid dynamics point of view
Physics of the QGP
•
Matter governed by QCD, not QED
•
High energy density/temperature frontier
Toward an ultimate matter (Maximum energy
density/temperature)
•
Understanding the origin of matter which
evolves with our universe
•
Reproduction of QGP in H.I.C.
Reproduction of early universe on the Earth
Quark Gluon
Plasma
Hadronization
Nucleosynthesis
History of the Universe
~ History of Matter
QGP study
Understanding
early universe
Little Bang!
R
elativistic
H
eavy
I
on
C
ollider(2000

)
RHIC as a time machine!
100 GeV per nucleon
Au(197
×
100)+Au(197
×
100)
Collision energy
Multiple production
(N~5000)
Heat
side
view
front
view
STAR
STAR
BASIC CHECKS
Basic Checks (I): Energy Density
Bjorken energy density
t
: proper time
y: rapidity
R: effective transverse radius
m
T
: transverse mass
Bjorken(’83)
observables
Critical Energy Density from Lattice
Stolen from Karsch(PANIC05);
Note that recent results seem to be T
c
~190MeV
Centrality Dependence of Energy
Density
PHENIX(’
05
)
e
c
from lattice
Well above
e
c
from lattice
in central
collision at RHIC,
if assuming
t
=1fm/c.
CAVEATS (I)
•
Just a necessary condition in the sense
that temperature (or pressure) is not
measured.
•
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)
Basic Checks (II): Chemical Eq.
Two fitting parameters: T
ch
,
m
B
direct
Resonance decay
Amazing fit!
T=177MeV,
m
B
= 29 MeV
Close to T
c
from lattice
CAVEATS (II)
•
Even e
+
e

or pp data can be fitted well!
See, e.g., Becattini&Heinz(’97)
•
What is the meaning of fitting
parameters?
See, e.g., Rischke(’02),Koch(’03)
•
Why so close to T
c
?
No chemical eq. in hadron phase!?
Essentially dynamical problem!
Expansion rate
Scattering rate
(Process dependent)
see, e.g., U.Heinz, nucl

th/0407067
Basic Checks (III): Radial Flow
Spectrum for heavier particles
is a good place to see radial flow.
Blast wave model (thermal+boost)
Driving force of flow
pressure gradient
Inside: high pressure
Outside: vacuum (
p
=0)
Sollfrank et al.(’93)
Spectrum change is seen in AA!
O.Barannikova, talk at QM05
Power law in pp & dAu
Convex to Power law
in Au+Au
•
“Consistent” with
thermal + boost
picture
•
Large pressure
could be built up in
AA collisions
CAVEATS (III)
•
Not necessary to be thermalized completely
–
Results from hadronic cascade models.
•
How is radial flow generated dynamically?
•
Finite radial flow even in pp collisions?
–
(T,v
T
)~(140MeV,0.2)
–
Is blast wave reliable quantitatively?
•
Consistency?
–
Chi square minimum located a different point for
f
and
W
•
Flow profile? Freezeout hypersurface? Sudden
freezeout?
Basic Checks
Necessary
Conditions to Study QGP at RHIC
•
Energy density can be well above
e
c
.
–
Thermalized?
•
“Temperature” can be extracted.
–
Why freezeout happens so close to T
c
?
•
Pressure can be built up.
–
Completely equilibrated?
Importance of Systematic Study
based on Dynamical Framework
Dynamics of Heavy
Ion Collisions:
Elliptic Flow and Perfect Liquid
Dynamics of Heavy Ion Collisions
Time scale
10fm/c~10

23
sec
Temperature scale
100MeV~10
12
K
Freezeout
“Re

confinement”
Expansion, cooling
Thermalization
First contact
(two bunches of gluons)
Why Hydrodynamics?
Static
•
EoS from Lattice QCD
•
Finite
T
,
m
field theory
•
Critical phenomena
•
Chiral property of hadron
Dynamic Phenomena in HIC
•
Expansion, Flow
•
Space

time evolution of
thermodynamic variables
Once one accepts local
thermalization ansatz,
life becomes very easy.
Energy

momentum:
Conserved number:
What is Elliptic Flow?
How does the system respond to spatial anisotropy?
Ollitrault (’92)
Hydro behavior
Spatial Anisotropy
Momentum Anisotropy
INPUT
OUTPUT
Interaction among
produced particles
dN
/
d
f
f
No secondary interaction
0
2
p
dN
/
d
f
f
0
2
p
2
v
2
x
y
f
QGP
mixed
hadron
Anisotropy of energy density distribution
Anisotropy of “Momentum” distribution
TH&Gyulassy(’06)
Time Evolution of a QGP Fluid
Time Evolution of v
2
from a Parton
Cascade Model
b
= 7.5fm
generated through secondary collisions
saturated in the early stage
sensitive to cross section (~1/m.f.p.~1/viscosity)
v
2
is
Zhang et al.(’99)
ideal hydro limit
t(fm/c)
v
2
: Ideal hydro
: strongly
interacting
system
Schematic Picture of Shear
Viscosity
See, e.g. Danielewicz&Gyulassy(’85)
Assuming relativistic particles,
Perfect fluid:
l=1/sr
0
shear viscosity
0
Shear flow
Smearing of flow
Next time step
Basis of the Announcement
PHENIX(’03)
STAR(’02)
Multiplicity dependence
p
T
dependence
and mass ordering
Hydro results: Huovinen, Kolb, Heinz,…
response =
(output)/(input)
“Hydro limit”
It is found that they reproduce v
2
(p
T
) data accidentally.
T.Hirano and M.Gyulassy,
Nucl.Phys.
A769
(
2006)71
.
Recent Hydro
Results
from Our Group
Centrality Dependence of v
2
Discovery of “Large” v
2
at RHIC
•
v
2
data are comparable with
hydro results.
•
Hadronic cascade cannot
reproduce data.
•
Note that, in v
2
data, there
exists eccentricity fluctuation
which is not considered in
model calculations.
Result from a hadronic cascade (JAM)
(Courtesy of M.Isse)
TH et al.
(
’
06
).
Pseudorapidity Dependence of v
2
h
=0
h
>0
h
<0
•
v
2
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
TH
(
’
02
); TH and K.Tsuda(’02);
TH et al.
(
’
06
).
QGP only
QGP+hadron
Hadron Gas Instead of Hadron Fluid
QGP core
A QGP fluid surrounded
by hadronic gas
QGP: Liquid (hydro picture)
Hadron: Gas (particle picture)
“Reynolds number”
Matter proper part:
(shear viscosity)
(entropy density)
big
in Hadron
small
in QGP
T.Hirano and M.Gyulassy,
Nucl.Phys.
A769
(
2006)71
.
See also talk/poster by Nonaka
Importance of Hadronic “Corona”
•
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!?
QGP only
QGP+hadron fluids
QGP fluid+hadron gas
T.Hirano et al.,
Phys.Lett.B
636
(2006)299
.
QGP Liquid + Hadron Gas Picture
Works Well
Mass dependence is o.k.
Note: First result was obtained
by Teaney et al.
20

30%
•
Centrality dependence is ok
•
Large reduction from pure
hydro in small multiplicity
events
T.Hirano et al.,
Phys.Lett.B
636
(2006)299
.
Some Comments
on the Discovery
1. Is mass ordering for v
2
(p
T
) a
signal of the perfect QGP fluid?
Mass dependence is o.k. from
hydro+cascade.
20

30%
Proton
Pion
Mass ordering comes from
rescattering effect. Interplay
btw. radial and elliptic flows
Not a direct sign of the
perfect QGP fluid
2. Is viscosity really small in QGP?
•
1+1D 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/fm
2
),
s
: entropy density (1/fm
3
)
h
/
s
is a good dimensionless measure
(in the natural unit) to see viscous effects.
Shear viscosity is small
in comparison with
entropy density!
A Probable Scenario
TH and Gyulassy (’06)
!
•
Absolute value of viscosity
•
Its ratio to entropy density
Rapid increase of entropy density can
make hydro work at RHIC.
Deconfinement Signal?!
h
: shear viscosity,
s
: entropy density
Kovtun,Son,Starinets(’05)
Digression
(Dynamical) Viscosity
h
:
~1.0x10

3
[Pa s] (Water
20
℃
)
~1.8x10

5
[Pa s] (Air 20
℃
)
Kinetic Viscosity
n=h/r
:
~1.0x10

6
[m
2
/s] (Water
20
℃
)
~1.5x10

5
[m
2
/s] (Air
20
℃
)
[Pa] = [N/m
2
]
Non

relativistic Navier

Stokes eq. (a simple form)
Neglecting external force and assuming incompressibility.
h
water
>
h
air
BUT
n
water
<
n
air
3. Is
h
/s enough?
•
Reynolds number
Iso, Mori, Namiki (’59)
R
>>1
Perfect fluid
•
Need to solve viscous fluid dynamics in (3+1)D
Cool! But, tough!
Causality problem (talk by Kunihiro, talk/poster by Muroya)
•
(1+1)D Bjorken solution
4. Boltzmann at work?
s
~ 15 *
s
pert
!
Caveat 1: Where is the “dilute” approximation in Boltzmann
simulation? Is
l
~0.1fm o.k. for the Boltzmann description?
Caveat 2: Differential v
2
is tricky. dv
2
/dp
T
~v
2
/<p
T
>.
Difference of v
2
is amplified by the difference of <p
T
>.
Caveat 3: Hadronization/Freezeout are different.
25

30%
reduction
Molnar&Gyulassy(’00)
Molnar&Huovinen(’04)
gluonic
fluid
5. Does v
2
(p
T
) really tell us
smallness of
h
/s in the QGP phase?
•
Not a result from dynamical calculation, but a “fitting” to data.
•
No QGP in the model
•
t
0
is not a initial time, but a freeze

out time.
•
G
s
/
t
0
is not equal to
h
/s, but to 3
h
/4sT
0
t
0
(in 1+1D).
•
Being smaller T
0
from p
T
dist.,
t
0 should be larger (~10fm/c).
D.Teaney(’03)
6. Is there model dependence in
hydro calculations?
Novel initial conditions
from Color Glass Condensate
lead to large eccentricity.
For CGC, see also
talk/poster by Itakura
Need viscosity even in QGP!
Hirano and Nara(’04), Hirano et al.(’06)
Kuhlman et al.(’06), Drescher et al.(’06)
Summary and Outlook
•
We have discovered “something” really
intriguing at RHIC
–
Perfect QGP fluid and dissipative hadron gas
–
Hydro at work as a signal of deconfinement(?)
–
Large cross section among partons is needed.
•
Still a lot of work needed
–
Initial stage, thermalization time, …
–
h
and
h
/s are not sufficient to discuss viscous aspects
in H.I.C. (“Perfect fluid” is a dynamic concept.)
–
Beyond Boltzmann/ideal hydro approach?
–
Success and challenge of hydrodynamics
Hadron Gas instead of Hadron Fluid
0
z
t
(Option)
Color Glass
Condensate
sQGP core
(Full 3D
Hydro)
Hadronic
Corona
(Cascade,
JAM)
Glauber

BGK and CGC Initial Conditions
Which Clear the First Hurdle
Glauber

BGK
•
Glauber model
N
part
:N
coll
= 85%:15%
•
CGC model
Matching I.C. via e(x,y,
h
)
Centrality dependence
Rapidity dependence
CGC
p
T
Spectra for identified hadrons
from QGP Hydro+Hadronic Cascade
Caveat: Other components such as recombination and
fragmentation should appear in the intermediate

high p
T
regions.
dN/dy and dN/dp
T
are o.k. by hydro+cascade.
Results from Hydro + Cascade
Glauber

BGK
CGC
v
2
(p
T
) from Hydro: Past, Present
and Future
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.”
2004

2005 (TH,Gyulassy)
Mechanism of v
2
(p
T
) slope
2005

2006(TH,Heinz,Nara,…)
+Color glass condensate
Future
“To be or not to be (consistent
with hydro), that is THE question”

anonymous
History of differential elliptic flow
~History of development of hydro
~History of removing ambiguity in hydro
20

30%
XXXXXXXXXXXXXX
?????????????????
XXXXXXXXXXXXXX
Temperature Dependence of
h
/s
•
We propose a possible scenario:
Kovtun, Son, Starinets(‘05)
Danielewicz&Gyulassy(’85)
•
Shear Viscosity in Hadron Gas
•
Assumption:
h
/s at T
c
in the sQGP is 1/4
p
No big jump in viscosity at T
c
!
Viscosity from a Kinetic Theory
See, e.g. Danielewicz&Gyulassy(’85)
For ultra

relativistic particles, the shear viscosity is
Ideal
hydro:
l
0
shear viscosity
0
Transport cross section
Schematic Picture of Shear
Viscosity
See, e.g. Danielewicz&Gyulassy(’85)
Assuming relativistic particles,
Perfect fluid:
l=1/sr
0
shear viscosity
0
Shear flow
Smearing of flow
Next time step
A Long Long Time Ago…
…we obtain the value
R
(Reynolds number)=1~10…
Thus we may infer that
the assumption of the
perfect fluid is not so good as supposed by Landau
.
h
/s from Lattice
A.Nakamura and S.Sakai,PRL94,072305(2005).
Shear viscosity to
entropy ratio from
lattice (pure gauge)
+ an assumption
of spectral function
eta/s < 1
is one of the
promising results of
applicability for
hydro at RHIC
Challenging calculation!
I love to
see this
region!!
Navier

Stokes Eq. and Relaxation
Time
•
Non

rela. (Cattaneo (’48))
t
0: Fourier law
t
: relaxation time
Heat Eq. (Hyperbolic Eq.)
Finite relaxation time
Telegraph Eq.(Parabolic Eq.)
Balance Eq.
Constitutive Eq.
Violation of
causality
cf.)
杉山勝、数理科学
(2002
年８月号）
Novel Viscous Fluid Dynamics
How to get constitutive eqs.?
2
nd
thermodynamic law
Balance Eqs
Constitutive
Eq.
Mueller,Israel,Stewart,…
1
st
order
2
nd
order
Toward determination of transport
coefficient of the QGP
(Linear Response)
＝
(Transport Coefficient)
x (Thermodynamic Force)
bulk, shear, heat conductivity
Lattice QCD + Kubo formula
Relaxation for viscosity
：
It can be obtain from a comp. btw. Boltzmann
Eq. and visc. fluid dynamics.
Higher order moment for n(1
±
n)
Can it be obtained from Lattice?
•
Navier

Stokes eq. (1
st
order)
•
Novel rela. visc. fluid dynamics (2
nd
order)
Israel,Stewart
Nakamura,Sakai
How Do Partons Get Longitudinal
Momentum in Comoving System?
Free Streaming eta=y
dN/dy
y
dN/dy
y
Sum of delta function
Width
“Thermal” fluctuation
Sheet:
eta=const
2
2 Collisions Do Not Help!
Xu and Greiner, hep

ph/0406278
Only 2
2 collisions,
partons are still in a
transverse sheet
eta~y~const.
2
3 may help.
h
/s from MD simulations
Y.Akimura et al., nucl

th/0511019
eta/s has a minimum
in the vicinity of T
c
!
No thermal qqbar
production
Preliminary
result
Statistical Model Fitting to ee&pp
Becattini&Heinz(’97)
Phase space dominance?
“T” prop to E/N?
See, e.g., Rischke(’02),Koch(’03)
Hadron phase below T
ch
in H.I.C.
•
“chemically frozen”
Themalization can be
maintained through elastic scattering.
•
There still exit “quasi

elastic” collisions, e.g.
•
The numbers of short

lived resonances can be
varied. (Acquirement of chemical potential)
•
Recent data suggests importance of (process
dependent) hadronic rescattering
–
Hard to describe this by hydro.
A Closer Look Reveals Details of
Hadronic Matter
Stolen from M.Bleicher (The Berkeley School)
How Reliable Quantitatively?
Radial flow in pp collisions?
f, W?
Small
rescattering
System
expands
like this
trajectory?
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