Perfect Fluidity of QGP at RHIC?

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Perfect Fluidity of QGPat RHIC?

• Tetsufumi Hirano
• Institute of Physics
• University of Tokyo
• Komaba, Tokyo 153-8902, Japan

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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.
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OUTLINE

• RHIC serves the perfect liquid
• Elliptic flow
• Results from hydro cascade model
• Ratio of viscosity to entropy
• Summary

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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.
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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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Elliptic Flow from a Kinetic Theory
ideal hydro limit
Zhang et al.(99)
View from collision axis
Time evolution of v2
b 7.5fm
v2

• Gluons uniformly distributed
• in the overlap region
• dN/dy 300 for b 0 fm
• Thermal distribution with
• T 500 MeV

t(fm/c)
generated through secondary collisions
saturated in the early stage sensitive to cross
section (m.f.p.viscosity)
v2 is
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Hydro Meets Data for the First Time at RHIC
Current Three Pillars
THGyulassy(06),TH,Heinz,Kharzeev,Lacey,Nara(06)

• Perfect Fluid (s)QGP Core
• Ideal hydro description of the QGP phase
• Necessary to gain integrated v2
• Dissipative Hadronic Corona
• Boltzmann description of the hadron phase
• Necessary to gain enough radial flow
• Necessary to fix particle ratio dynamically
• Glauber Type Initial Condition
• Diffuseness of initial geometry

A Lack of each pillar leads to discrepancy!
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(CGC )QGP HydroHadronic Cascade
TH et al.(05-)
Hadronic Corona (Cascade, JAM)
t
sQGP core (Full 3D Ideal Hydro)
0.6fm/c
z
0
(Option) Color Glass Condensate
c.f. Similar approach by Nonaka and Bass
(DNP04,QM05)
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(1) Glauber and (2) CGC Hydro Initial Conditions
Which Clear the First Hurdle
Centrality dependence
Rapidity dependence

• Glauber model
• NpartNcoll 8515
• CGC model
• Matching I.C. via e(x,y,h)

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pT Spectra for identified hadronsfrom QGP
HydroHadronic Cascade
dN/dy and dN/dpT are o.k. by hydrocascade.
Caveat Other components such as recombination
and fragmentation should appear in the
intermediate-high pT regions.
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v2(Npart) from QGP Hydro Hadronic Cascade
TH et al.(06)

• 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
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Large Eccentricity from CGC Initial Condition
y
x
Pocket formula (ideal hydro) v2 0.2e _at_ RHIC
energies
Ollitrault(92)
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v2(pT) for identified hadrons
Glauber type initial condition
CGC initial condition
Mass dependence is o.k.
v2(model) gt v2(data)
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Viscosity and Entropy

• Reynolds number

Iso, Mori, Namiki (59)
Rgtgt1 ?Perfect fluid
where

• 11D 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.
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Why QGP Fluid Hadron Gas Works?
h shear viscosity, s entropy density
TH and Gyulassy (06)
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?!
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Digression
Pa N/m2
(Dynamical) Viscosity h 1.0x10-3 Pa s
(Water 20?) 1.8x10-5 Pa s (Air 20?)
Kinetic Viscosity nh/r 1.0x10-6 m2/s
(Water 20?) 1.5x10-5 m2/s (Air 20?)
hwater gt hair BUT nwater lt nair
Non-relativistic Navier-Stokes eq. (a simple form)
Neglecting external force and assuming
incompressibility.
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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
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Thank you!
THGyulassy(06)
QGP
mixed
hadron
Energy in (four-)velocity plane at midrapidity
Energy density in the transverse plane at
midrapidity
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Viscosity from a Kinetic Theory
See, e.g. DanielewiczGyulassy(85)
For ultra-relativistic particles, the shear
viscosity is
Ideal hydro l ? 0 shear viscosity ? 0
Transport cross section
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A Long Long Time Ago
we obtain the value R (Reynolds
number)110 Thus we may infer that the
assumption of the perfect fluid is not so good as
supposed by Landau.
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A Final Piece of RHIC Jigsaw Puzzle?
or
Glauber
CGC
Or any other possible scenarios based on
non-equilibrium models, instabilities, etc. for
thermalization / isotropization mechanism.
A much better understanding of initial condition
is desperately needed.
Distinguish via 3D jet tomography Adil, Gyulassy
and TH (06)
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Results from Hydro Cascade (III)
Glauber-BGK
CGC
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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
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Temperature Dependence of h/s

• Shear Viscosity in Hadron Gas

DanielewiczGyulassy(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

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Ideal QGP Fluid Dissipative Hadron Gas Models
(11)D with Bjorken flow (21)D with Bjorken flow Full (31)D
UrQMD A.Dumitru et al., PLB460,411(1999) PRC60,021902(1999)S.Bass and A.Dumitru, PRC61,064909(2000). N/A C.Nonaka and S.Bass, nucl-th/0510038.
RQMD N/A D.Teaney et al., PRL86,4783(2001), nucl-th/0110037 D.Teaney, nucl-th/0204023. N/A
JAM N/A N/A TH, U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara, PLB636299(2006).
hydro
cascade