Transcript Perfect Fluidity of QGP at RHIC?

Perfect Fluidity of QGP
at RHIC?
Tetsufumi Hirano 平野哲文
Institute of Physics
University of Tokyo 东京大学
Komaba, Tokyo 153-8902, Japan
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.
OUTLINE
• “RHIC serves the perfect liquid”
• Elliptic flow
• Results from hydro + cascade model
• Ratio of viscosity to entropy
• Summary
What is “Perfect Liquid”?
A possibility of “Perfect Liquid
QGP” is intriguing. In this context,
a lot of people say,
“QGP viscosity is small”.
Viscosity is “small”
in comparison with …, what???
I will discuss this issue later.
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
Elliptic Flow from a Kinetic Theory
ideal hydro limit
Zhang et al.(’99)
v2
Time evolution of v2
View from collision axis
b = 7.5fm
t(fm/c)
• Gluons uniformly distributed
in the overlap region
• dN/dy ~ 300 for b = 0 fm
• Thermal distribution with
T = 500 MeV
generated through secondary collisions
v2 is saturated in the early stage
sensitive to cross section (~m.f.p.~viscosity)
TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)
Hydro Meets Data for the First Time at
RHIC: “Current” Three Pillars
1. Perfect Fluid (s)QGP Core
• Ideal hydro description of the QGP phase
• Necessary to gain integrated v2
2. Dissipative Hadronic Corona
• Boltzmann description of the hadron phase
• Necessary to gain enough radial flow
• Necessary to fix particle ratio dynamically
3. Glauber Type Initial Condition
• Diffuseness of initial geometry
A Lack of each pillar leads to discrepancy!
TH et al.(’05-)
(CGC +)QGP Hydro+Hadronic Cascade
Hadronic
Corona
(Cascade,
JAM)
t
0.6fm/c
z
0
c.f. Similar approach by Nonaka and Bass (DNP04,QM05)
sQGP core
(Full 3D
Ideal Hydro)
(Option)
Color Glass
Condensate
(1) Glauber and (2) CGC Hydro Initial
Conditions Which Clear the First Hurdle
Centrality dependence
Rapidity dependence
•Glauber model
Npart:Ncoll = 85%:15%
•CGC model
Matching I.C. via e(x,y,h)
pT Spectra for identified hadrons
from QGP Hydro+Hadronic Cascade
dN/dy and dN/dpT are o.k. by hydro+cascade.
Caveat: Other components such as recombination and
fragmentation should appear in the intermediate-high pT regions.
TH et al.(’06)
v2(Npart) from
QGP Hydro + Hadronic Cascade
Glauber:
 Early thermalization
 Mechanism?
CGC:
 No perfect fluid?
 Additional viscosity
is required in QGP
Result of JAM: Courtesy of M.Isse
Importance of better understanding of initial condition
Large Eccentricity from CGC Initial
Condition
y
x
Pocket formula (ideal hydro):
v2 ~ 0.2e @ RHIC energies
Ollitrault(’92)
v2(pT) for identified hadrons
Glauber type initial condition
Mass dependence is o.k.
CGC initial condition
v2(model) > v2(data)
Viscosity and Entropy
•Reynolds number
Iso, Mori, Namiki (’59)
R>>1
Perfect fluid
where
•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/fm2), s : entropy density (1/fm3)
h/s is a good dimensionless measure
(in the natural unit) to see viscous effects.
Why QGP Fluid + Hadron Gas Works?
TH and Gyulassy (’06)
h : shear viscosity, s : entropy density
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?!
Digression
[Pa] = [N/m2]
(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 [m2/s] (Water 20℃)
~1.5x10-5 [m2/s] (Air 20℃)
hwater > hair BUT nwater < nair
Non-relativistic Navier-Stokes eq. (a simple form)
Neglecting external force and assuming incompressibility.
Summary
• Perfect Fluid QGP + Dissipative Hadron +
Glauber initial conditions does a good job.
– Manifestation of deconfinement?
• CGC initial conditions spoil this agreement.
• Viscous QGP may compensate “CGC effect”.
• Importance of better understanding initial
conditions.
To be or not to be (consistent with hydro),
that is THE question.
--Anonymous
Thank you!
TH&Gyulassy(’06)
QGP
mixed
hadron
Energy density in the
transverse plane
at midrapidity
Energy in (four-)velocity plane
at midrapidity
Viscosity from a Kinetic Theory
See, e.g. Danielewicz&Gyulassy(’85)
For ultra-relativistic particles, the shear viscosity is
Ideal hydro:
l0
Transport cross section
shear viscosity  0
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.
A Final Piece of RHIC Jigsaw Puzzle?
or
Glauber
A much better understanding
of initial condition is
desperately needed.
Distinguish via 3D jet tomography
Adil, Gyulassy and TH (’06)
CGC
Or any other possible scenarios
based on non-equilibrium
models, instabilities, etc. for
thermalization / isotropization
mechanism.
Results from Hydro + Cascade (III)
Glauber-BGK
CGC
v2(pT) 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 v2(pT) slope
2005-2006(TH,Heinz,Nara,…)
+Color glass condensate
Future
“To be or not to be (consistent
with hydro), that is THE question”
-- anonymous
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?????????????????
20-30%
History of differential elliptic flow
~History of development of hydro
~History of removing ambiguity in hydro
Temperature Dependence of h/s
•Shear Viscosity in Hadron Gas
Danielewicz&Gyulassy(’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:
Ideal QGP Fluid
+ Dissipative Hadron Gas Models
hydro (1+1)D with
cascade
UrQMD
Bjorken flow
A.Dumitru et al.,
PLB460,411(1999);
PRC60,021902(1999);
S.Bass and A.Dumitru,
PRC61,064909(2000).
RQMD
N/A
JAM
N/A
(2+1)D with
Bjorken flow
N/A
D.Teaney et al.,
PRL86,4783(2001),
nucl-th/0110037;
D.Teaney,
nucl-th/0204023.
N/A
Full (3+1)D
C.Nonaka and S.Bass,
nucl-th/0510038.
N/A
TH, U.Heinz,
D.Kharzeev, R.Lacey,
and Y.Nara,
PLB636299(2006).