QGP and Dynamics of

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Nov 16, 2013 (3 years and 10 months ago)

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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?