Theoretical Overview

1
Theoretical Overview
--Current status of perfect liquid--

• Tetsufumi Hirano
• Department of Physics
• The University of Tokyo

Homepage of Heavy Ion Café http//tkynt2.phys.s.u-
tokyo.ac.jp/hirano/hic/index.html
2
Outline

• My personal view of Perfect Liquid announcement
  and QM2006
• Whats Next?
• Systematic study based on the hybrid approach
  (base line argument)
• Initial condition mechanism of thermalization
• Improvement of current hydro models
• Utilizing outputs from hydro simulations

3
Elliptic Flow for Charged Particles
Roughly speaking, ideal hydro gives a good
description
P.Kolb et al.(01)
P.Huovinen(03)
T.H.(01)
TH, plenary talk _at_ QM2004
4
I did not make a conclusive statement _at_ QM2005
TH, plenary talk _at_ QM2004
5
An announcement was made on April 18, 2005
6
Behind the Press Release Room
TH, talk _at_ APS meeting, FL, 2005
Today, I wont discuss this particular topic any
more. See, TH and M.Gyulassy, NPA769,71(2006).
7
Mystery at QM2005, Budapest (Just 4 Months after
Press Release)
8 plenary talks from RHIC BRAHMS(1 talk),
PHENIX(3 talks), PHOBOS(1 talk), STAR(3 talks).
Nothing about press release nor perfect liquid
What happened to the press release on perfect
fluidity?
The press release was just a dream? Two Logos
(perfect liquid, sQGP) are enough?
TH, talk _at_ BNL, 11/04/2005
8
QM2006 _at_ Shanghai
24 plenary theory speakers 52 parallel theory
speakers (Impossible to cover all of them) Who
cares about perfect fluid in this conference?
9
Whats Next ?
TH, a slide prepared for YKIS06

• 1. Systematic studies based on
• the hybrid approach
• (Glauber I.C. perfect fluid QGP
• dissipative hadron gas).
• ? HBT, source functions
• System size, collision energy

• 3. Improvement of current
• hydro models
• ? Fluctuations
• ? Constraint of EOS
• (Causal) Viscosity
• Chemical non-equilibrium
• Mach cone

• 2. Initial condition mechanism
• of early thermalization
• ? CGC, Glasma
• Isotropization
• Instability
• Non-equilibrium field theory

• 4. Utilizing outputs from
• hydrodynamic simulations
• Jet quenching (q, Q, and g)
• J/Y transport
• EM radiation
• Recombination

10

• 1. Systematic studies based on
• the hybrid approach
• (Glauber I.C. perfect fluid QGP
• dissipative hadron gas).
• ? HBT, source functions
• System size, collision energy

• 3D Langrangean hydro UrQMD Jet Quenching
• C.Nonaka(plenary), S.Bass(parallel),
• 3D Eulerian Hydro JAM Jet Quenching
• TH(parallel), (Y.Nara),M.Isse(poster),

11
Current Status of HydroCascade
t
hadronic gas
QGP fluid
Perfect fluid QGP core Dissipative hadronic
corona TH and M.Gyulassy (2006)
z
0
12
Inputs of the Model
Solver Full 3D Eulerian ideal hydro JAM Initial
Condition Initial time t0 0.6fm/c Transverse
profile 0.85rpart0.15rcoll Longitudinal
profile BGK triangle
(Brodsky-Gunion-Kuhn) EoS Nf3 massless ideal QGP
gas Resonance gas (up to D(1232)) in partial
chemical equilibrium Critical temperature Tc
170MeV Chemical f.o. temperature Tch
170MeV Switching temperature Tsw 169MeV
13
pT Spectra from QGP Fluid Hadron Gas Model
A hybrid model works well up to
pT1.5GeV/c. Other components (reco/frag) would
appear above.
14
Elliptic Flow from QGP Fluid Hadron Gas Model
Good agreement for bulk (pTlt1.5GeV/c)
15
PID v2(pT) at midrapidity
?Presumably due to fluctuation
MillerSnellings(03)
O.K. in semicentral collisions
16
Hydro cascade at work in forward
Adapted from S.J.Sanders (BRAHMS) _at_ QM2006
17
A Probable Scenario
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?!
18
Other systems?
Kapusta, talk _at_ QM2006 Csernai,Kapusta,
McLerran(06)
Something happens at Tc Not driven by entropy
jump
19

• 2. Initial condition mechanism
• of early thermalization
• ? CGC, Glasma
• Isotropization
• Instability
• Non-equilibrium field theory

• Plenary
• F.Gelis, QCD at small x
• M.Strickland, Thermalization via instabilities
• Parallel
• R.Venugopalan, Multiple production to NLO in AA
  collisions
• M.Asakawa, Anomalous viscosity of an expanding
  quark-gluon plasma
• R.Fries, Early time evolution of high energy
  heavy ion collisions
• Z.Xu, Parton Thermalization and Energy Loss in
  U.R.H.I.C within a P.C.
• X.-M.Xu, Thermalization of Quark-Gluon Matter

20
How Do Partons Get Longitudinal Momentum to
Thermalize?
Free Streaming etay
Sheet etaconst
dN/dy
dN/dy
yh
yh
Sum of delta function
Width ?Thermal fluctuation
21
2?2 Collisions Do Not Help!
Only 2?2 collisions, partons are still in
a transverse sheet etayconst. 2?3 may help.
Xu and Greiner, hep-ph/0406278
22
Time Scale of Equilibration
Adapted from Z.Xu, Talk _at_ QM2006 Do we really
need ltpz2gtltpx2gt?
q(t) gives the timescale of kinetic equilibration.
23
Caveat on Kinetic Equilibration
Static medium ?Expanding medium
(11)D Bjorken case
Do we need complete isotropy? Shear viscosity
allows small deviation from isotropic distribution
24
Interplay btw. Expansion and Instability
Adapted from M.Strickland, Talk _at_ QM2006
25
Instability
Adapted from M.Strickland, Talk _at_ QM2006
26

• 3. Improvement of current
• hydro models
• ? Fluctuations
• ? Constraint of EOS
• (Causal) Viscosity
• Chemical non-equilibrium
• Mach cone

• Plenary
• D.T.Son, AdS/CFT and QGP
• D.Teaney, Experimental evidence of perfect
  fluididty at RHIC
• J.Kapusta, The strongly interacting low viscosity
  matter
• J.Casalderrey-Solana, Mach Cone in QGP
• P.Levai, Viscosity in the strongly interacting
  quark matter around Tc
• C.M.Ko, Parton transport description of heavy ion
  collisions
• Parallel
• T.Renk, Mach cone and dijets
• G.L.Ma, Two- and Three-particle Correlations in a
  P.C.
• S.Gavin, Measuring Shear Viscosity Using pT
  Correlations
• S.Mrowczynski, Chromo-hydrodynamics of the
  unstable QGP
• R.S.Bhalerao, Eccentricity fluctuations and
  elliptic flow at RHIC
• D.Molnar, Why even a small viscosity matters at
  RHIC
• T.Kodama, New Formulation of Dissipative
  Relativistic Hydrodynamics

27
Importance of Relaxation Time
cf.)????????(2002?8??)

• Non-rela. (Cattaneo (48))

Balance Eq.
Constitutive Eq.
t?0 Fourier law
t relaxation time
Heat Eq. (Parabolic Eq.) Finite
relaxation time Telegraph Eq.(Hyperbolic Eq.)
Violation of causality
28
Solution of Viscous Fluids
Adapted from D.Teaney, Talk _at_ QM2006
29
Be Cautious about Corrections
Adapted from D.Teaney, Talk _at_ QM2006
30
Summary by Teaney
Adapted from D.Teaney, Talk _at_ QM2006
31
Comarison btw. Hydro and Cascade
Adapted from D.Molnar, Talk _at_ QM2006 Many caveats
in this kind of comparisons!
32
Boltzmann at work?
MolnarGyulassy(00)
MolnarHuovinen(04)
25-30 reduction
gluonic fluid
s 15 spert !
Caveat 1 Where is the dilute approximation in
Boltzmann simulation? Is l0.1fm o.k. for the
Boltzmann description? Caveat 2 Differential v2
is tricky. dv2/dpTv2/ltpTgt. Difference of v2 is
amplified by the difference of ltpTgt. Caveat 3
Hadronization/Freezeout are different.
33
Schematic Picture of Shear Viscosity
See, e.g. DanielewiczGyulassy(85)
Assuming relativistic particles,
Perfect fluid l1/sr ? 0 shear viscosity ? 0
Gradient of flow
Smearing of flow
Next time step
34
A New Channel to Measure Viscosity
Adapted from S.Gavin, Talk _at_ QM2006 Remember
shear viscosity causes diffusion of flow
35
Correlation is broadened
36
Correlation fn. of pT
Adapted from S.Gavin, Talk _at_ QM2006
37
Turbulent Leads Perfect Fluid?
Adapted from M.Asakawa, Talk _at_ QM2006
38
Anomalously Small Viscosity
Adapted from M.Asakawa, Talk _at_ QM2006
39
Mach Angle
Adapted from J. Casalderrey-Solana, Talk _at_ QM2006
40
Mach Emission Angle? Sound Velocity
Adapted from H.Stöcker, Talk _at_ Xian workshop
41
Dissipation Destroys Mach Cone?
Following figures taken from a talk by
Stöcker Viscous hydro simulations by Brazil
group See also, T.Kodama, talk _at_QM2006
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Mach Emission Angle80 Deg.?
Adapted from H.Stöcker, Talk _at_ Xian workshop
52
Current Data Consistent with Soft EoS (on
average)!?
Adapted from H.Stöcker, Talk _at_ Xian workshop
53
3-Particle Correlation
Adapted from G.-L. Ma, Talk _at_ QM2006
54
Mach Cone in AMPT?
Adapted from G.-L. Ma, Talk _at_ QM2006
55
Hadronic Rescattering is not enough?
Adapted from G.-L. Ma, Talk _at_ QM2006 Caveat AMPT
does not reproduce RAA
56

• 4. Utilizing outputs from
• hydrodynamic simulations
• Jet quenching (q, Q, and g)
• J/Y transport
• EM radiation
• Recombination

• Plenary
• P.F.Zhuang, J/Y suppression and regeneration
• Parallel
• J.-e Alam, Thermal Radiation at RHIC
• S.Turbide, High Momentum Dilepton Production From
  Jets in a QGP
• J.Long, Photons and Evolution of chemically
  equilibrating and expanding QGP at finite baryon
  density
• Poster
• M.Isse, Jet-fluid string formation and decay in
  high energy H.I.C.

57
J/Y transport in QGP fluids
21D Boltzmann suppression regeneration
Adapted from P.F.Zhuang, Talk _at_ QM2006
58
J/Y transport in QGP fluids (contd.)
Adapted from P.F.Zhuang, Talk _at_ QM2006
59
RAA for J/Y
Adapted from P.F.Zhuang, Talk _at_ QM2006
60
Hydro Data Available
http//tkynt2.phys.s.u-tokyo.ac.jp/hirano/parevo/
parevo.html
61
Summary

• Agreement btw. hydrocascade and data indicates
  Perfect Liquid.
• It is worth following up the analysis.
• Important to understand initial conditions.
• Viscous hydro as an applicable condition
• Consistency among models ? Utilize the hydro
  data.

62
Whats Next ?

• 1. Systematic studies based on
• the hybrid approach
• (Glauber I.C. perfect fluid QGP
• dissipative hadron gas).
• ? HBT, source functions
• System size, collision energy

• 3. Improvement of current
• hydro models
• ? Fluctuations
• ? Constraint of EOS
• (Causal) Viscosity
• Chemical non-equilibrium
• Mach cone

• 2. Initial condition mechanism
• of early thermalization
• ? CGC, Glasma
• Isotropization
• Instability
• Non-equilibrium field theory

• 4. Utilizing outputs from
• hydrodynamic simulations
• Jet quenching (q, Q, and g)
• J/Y transport
• EM radiation
• Recombination

63
BGK triangle
Adapted from A.Adil, Talk _at_ QM2006
64
Two-Particle Correlation Function
C2
F
fitting?
pair wave fn. (FSI? Coulomb?)
relative distance dist.
normalized source fn.
hydro, blast-wave, cascade,
65
Source Function from 3D Hydro Cascade
How much the source function differs from ideal
hydro in Configuration space?
Blink Ideal Hydro, Kolb and Heinz (2003) Caveat
No resonance decays in ideal hydro
66
Non-Gaussian Source?
y
px 0.5GeV/c
x