1. Elliptic Flow from Hydro (short review) 2. Hydrodynamic afterburner for the CGC at RHIC

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1. Elliptic Flow from Hydro(short review)2.
Hydrodynamic afterburner for the CGC at RHIC

• Tetsufumi Hirano
• RIKEN BNL Research Center

Hot Quarks 2004 Taos Valley, NM
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Outline (part 1)

• Apology Its hard to discuss
• all topics within 15-20 min
• I just pick up some results
• from hydro

• Elliptic flow
• Basics of hydrodynamics
• Results from hydrodynamic simulations
• Summary

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Elliptic Flow
Ollitrault (92)
How does the system respond to initial spatial
anisotropy?
Hydrodynamic expansion
y
f
x
INPUT
Initial spatial anisotropy
2v2
Rescattering
dN/df
OUTPUT
Final momentum anisotropy
f
0
2p
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Boltzmann to Hydro !?
Molnar and Huovinen (04)
47mb inelastic cross section of pp at
RHIC energy!? Still 30 smaller than hydro
result!
elastic cross section
Hydro (l0) is expected to gain maximum v2 among
transport theories. ? hydrodynamic (maximum)
limit
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Basics of hydrodynamics
Hydrodynamic Equations
Energy-momentum conservation
Charge conservations (baryon, strangeness, etc)
For perfect fluids (neglecting viscosity),
Need equation of state (EoS) P(e,nB) to close
the system of eqs. ? Hydro can be
connected directly with lattice QCD
Energy density
Pressure
4-velocity
Within ideal hydrodynamics, pressure gradient
dP/dx is the driving force of collective flow.
? Collective flow is believed to reflect
information about EoS! ? Phenomenon which
connects 1st principle with experiment
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Inputs for Hydrodynamic Simulations
Final stage Free streaming particles ? Need
decoupling prescription
t
Intermediate stage Hydrodynamics can be
applied if thermalization is achieved. ? Need EoS
z

• Initial stage
• Particle production and
• pre-thermalization
• beyond hydrodynamics
• Instead, initial conditions
• for hydro simulations

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Main Ingredient Equation of State
One can test many kinds of EoS in hydrodynamics.
Typical EoS in hydro model
EoS with chemical freezeout
H resonance gas(RG)
Q QGPRG
pe/3
Kolb and Heinz (03)
T.H. and K.Tsuda(02)
Latent heat
PCEpartial chemical equiliblium CFOchemical
freeze out CE chemical equilibrium
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Interface 1 Initial Condition

• Need initial conditions (energy density, flow
  velocity,)

Initial time t0 thermalization time

• Take initial distribution
• from other calculations

• Parametrize initial
• hydrodynamic field

y
y
T.H.(02)
x
x
x
Energy density from NeXus. (Left) Average over 30
events (Right) Event-by-event basis
e or s proportional to rpart, rcoll or arpart
brcoll
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Interface 2 Freezeout
Hirano Tsuda Teaney Kolb Rapp
Teaney, Lauret Shuryak Bass Dumitru
Kolb, Sollfrank, Huovinen Heinz Hirano
Ideal hydrodynamics
QGP phase
Tc
Partial Chemical Equilibrium EOS
Chemical Equilibrium EOS
Tch
Hadronic Cascade
Hadron phase
Cf.) Continuous particle emission by
SPheRIO group
Tth
Tth
t
Sudden freezeout l0?infinity
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Hydrodynamic Results of v2
Kolb, Sollfrank, Heinz (00)
STAR(02)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Sudden freezeout

LHC?
(response)(output)/(input)

• Hydrodynamic response is
• const. v2/e 0.2 _at_ RHIC
• Exp. data reach hydrodynamic
• limit at RHIC for the first time.
• Exp. line is expected to bend
• at higher collision energies.

Number density per unit transverse area
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Hydrodynamic Results of v2(pT,m)
PHENIX(03)

• Correct pT dependence
• up to pT1-1.5 GeV/c
• Mass ordering
• Deviation in intermediate
• high pT regions
• ? Other physics
• Jet quenching (Talk by Vitev)
• Recombination (Talk by Fries)
• Viscosity
• Not compatible with particle ratio
• Need chem. freezeout
• mechanism

Huovinen et al.(01)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Sudden freezeout

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Hydrodynamic Results of v2(h)

• Hydrodynamics works
• only at midrapidity?
• Forward rapidity at RHIC
• Midrapidity at SPS?
• Heinz and Kolb (04) Heinz,T.H. and Nara (in
  progress)

T.H. and K.Tsuda(02)

• Dimension
• Full 3D (t-h coordinate)
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• QGP RG (chem. frozen)
• Decoupling
• Sudden freezeout

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Hydrodynamic Results of v2 (again)
Teaney, Lauret, Shuryak(01)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• Parametrized by latent heat
• (LH8, LH16, LH-infinity)
• RG
• QGPRG (chem. eq.)
• Decoupling
• Hadronic cascade (RQMD)

• Large gap (50 reduction) at SPS comes
• from finite l or viscosity.
• Latent heat 0.8 GeV/fm3 is favored.
• Hadronic afterburner explains forward rapidity?
• (T.H. and
  Y.Nara, in progress)

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Summary of Results
Models for Hadron Phase v2(pT,m) Excitation function Yield or ratio Viscous effect Caveat
Chemical Equilibrium Yes No No No P (Pbar) yields ltlt exp. data
Partial Chemical Equilibrium Yes/No Currently N/A Yes No Tth dependence is currently not understood well.
Hadronic Cascade Yes Yes Yes Yes Through Boltzmann eq. How do we treat boundary between hydro and cascade correctly?
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Summary for Part 1

• Hydrodynamics works well at RHIC?
• Perhaps promising
• Caveat 1 Hadron phase should be described by
  viscous fluid/hadronic cascade. Realistic
  treatments of boundary is also mandatory.
• Caveat 2 Dont forget HBT puzzle! Hydrocascade?
• Need further systematic studies, e.g.,
  hydrocascade in forward rapidity region, more
  realistic EoS, unified treatment, viscosity, etc.

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Hydrodynamic afterburner for the CGC at RHIC
In collaboration with Y.Nara

• Outline (part 2)
• Three key topics at RHIC
• Hydrodynamics
• Jet quenching
• Color Glass Condensate (CGC)
• CGChydrojet model (CHJ model)
• Toward a unified dynamical description for
  relativistic heavy ion collisions

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CGC, hydrodynamics, and jet quenching
Nuclear modification factor RAA
Centrality dependence of dN/dh/(Npart/2)
v2(pT)
Kharzeev, Levin, Nardi (KLN)
Vitev, Gyulassy, Levai, Wang, Wang,
Kolb, Heinz, Huovinen T.H., Teaney, Shuryak,
These three physics related with each other?
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Dense Matter at RHIC
CGC
Gluon multiplicity (QS saturation scale)
Hydrodynamics
Mean free path is assumed to be very small
Jet quenching
Opacity is large
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CGCHydroJet (CHJ) model
Nuclear wave function Parton distribution
CGC (a la KLN)
Collinear factorized Parton distribution (CTEQ)
Transverse momentum
Shattering CGC (kT factorization)
LOpQCD (PYTHIA)
Parton production
I do not discuss high pT physics today.
Hydrodynamics (full 3D hydro)
Parton energy loss (a la Gyulassy-Levai-Vitev)
Jet quenching
QGP
Hadron gas
Freezeout (chemical thermal)
Fragmentation
Proper time
Low pT
High pT
Intermediate pT
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dN/dh from a Saturation Model
Kharzeev and Levin (01)
gg?g
Parton-hadron duality
f
1/as
Qs2
kT2
0
CGC works well for rapidity and centrality
dependences! Clearly, one needs final state
interaction!
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Initial Condition from CGC
Saturation scale at a transverse position
where
Unintegrated gluon distribution can be written
Momentum rapidity y ? space time rapidity hs
Input for hydrodynamic simulations
Three parameters K, l, k ? More realistic wave
function can be used.
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Example of a Simulation
Space-time evolution of energy density in
sqrt(sNN)200 GeV AuAu collision at b7.2fm
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Results from CHJ model
Pseudorapidity dist.
pT spectrum
Quenched jet
Hydro
Mean pT
Centrality and rapidity dependences are well
described by CH(J) model. ? What is the role of
hydro in comparison with KLN approach?
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How ET/N (energy/entropy) evolves in CHJ model?
Initial condition of hydrodynamic simulations
Gluons produced from two CGC collisions
Final (psuedo)rapidity spectra of all hadrons
ET/N 1.6 GeV
ET/N 1.0 GeV
ET/N 0.55 GeV
? Consistent with classical Yang Mills on 2D
lattice
? Consistent with exp. data 0.6 GeV
This should be obtained through non-equilibrium
processes. ? Production of entropy
Hydrodynamic evolution ?PdV work reduces ET/N.
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Toward a Unified Model
Nuclear wave function Parton distribution
CGC (a la KLN)
Color Quantum Fluid(QS2ltkT2ltQS4/L2) (x-evolution
eq.)
Collinear factorized Parton distribution (CTEQ)
(classical Yang-Mills on 2D lattice)
Transverse momentum
Parton production (dissipative process?)
Shattering CGC (kT factorization)
LOpQCD (PYTHIA)
(classical Yang-Mills on 2D lattice)
important in forward region
Hydrodynamics (full 3D hydro)
Parton energy loss (a la Gyulassy-Levai-Vitev)
Jet quenching
QGP
Recombination (via string fragmentation)
Hadron gas
Hadronic cascade (JAM)
Freezeout (chemical thermal)
Fragmentation
Proper time
Low pT
High pT
Intermediate pT
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Summary and Outlook for Part 2

• First step toward a unified and dynamical
  approach to relativistic heavy ion collisions
  (CHJ model)
• Each component can be improved.
• CGC Realistic wave function, classical YM on
  lattice,
• Hydro Realistic EoS from lattice QCD, rate eq.
  for QGP,
• Jet Species dependent energy loss, fluctuations,
  
• Another idea can be plugged in this approach.
• Hadronic cascade
• Recombination
• Etc.

A big problem on thermalization remains!
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SPARE SLIDES
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Elliptic Flow Generatedin Early Stage
Kolb and Heinz (03)
Elliptic flow is believed to be sensitive to
the early dynamics. Wait! Is the momentum
anisotropy ep observable ?
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EoS dependence of v2(pT)
? Pion elliptic flow is insensitive to EoS.
? What makes a difference of proton elliptic
flow?
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Anisotropic Flow
y
f
x
z
x
Transverse plane
Reaction plane
A.Poskanzer S.Voloshin (98)
Flow is not a good terminology especially in
high pT regions due to jet quenching.
0th azimuthally averaged dist. ? radial flow 1st
harmonics directed flow 2nd harmonics elliptic
flow
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Large radial flow reduces v2 for protons
High pT protons

• Radial flow pushes protons to high pT regions
• Low pT protons are likely to come from fluid
  elements with small radial flow

Low pT protons
Even for positive elliptic flow of matter, v2 for
heavy particles can be negative in low pT regions!
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v2(pT,m) from hydro(cascade)
Results from (1) partial chemical equilibrium EoS
Results from (1) chemical equilibrium EoS or (2)
resonance gas EoS (no QGP) or (3) hydroRQMD
pion v2/e
proton v2/e
Compiled by C.Ogilvie
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pT distribution from PCE

• Up to what pT do we
• need to reproduce data
• by hydro?
• Recombination?
• Baryon junction?
• What is initial collective
• flow?
• Classical YM on
• lattice may help

P.Kolb and R.Rapp(03)
Dashed line Initial transverse kick
Solid line a0
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v2(pT) Stalls in Hadron Phase?
Hadronic rescattering via RQMD does not change
v2(pT) for p !

• Mechanism for stalling v2(pT)
• Hydro (chem. eq.)
• Pion dominance
• ?Effect of EoS
• HydroRQMD
• Effective viscosity
• ?Effect of finite l

D.Teaney(02)
PbPb, SPS 17 GeV, b6 fm
Solid lines are guide to eyes
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How ep is distributed to hadrons?
Partial Chemical Equilibrium
Chemical Equilibrium
p
Tth
PCE leads to overestimation of v2(pT) for p when
radial flow is large enough to reproduce pT
distribution.
radial flow
K
T.H. and K.Tsuda (02)
Proton v2(pT)
p
Pions v2(pT)
pions
pions
CE
PCE
ep
ep
kaons
kaons
protons
protons
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Comparison of CE with PCE
EOS
Time Evolution
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Comparison CE with PCE (contd.)
Tth dependence
pT v2(pT)
CE sensitive insensitive
PCE insensitive sensitive
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Hadronic Cascade Will Help?
T.H.(01)
STAR (02)
Forward rapidity at RHIC Midrapidity at
SPS? Thermalization coeff.?
Hydro P.Kolb et al.(00)
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Sensitivity to Freezeout (contd.)
Soff, Bass, Dumitru (01)

• Dimension
• 1Dboost inv. cylindrical sym.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Hadronic afterburner by UrQMD

Hydrocascade 200
Hydro 160
Hydrocascade 160
Hydro 200
STAR
PHENIX

• It is getting better in low pT
• region for Tc160 MeV case
• by smearing through cascade.
• Still something is missing
• to interpret the data.

Taken from D. Magestro, talk _at_ QM04
HBT radii from continuous particle emission model?
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Hydro Rate Eq. in QGP phase
T.S.Biro et al.,Phys.Rev.C48(93)1275.
Including gg??qqbar and gg??ggg
Collision term
Assuming multiplicative fugacity, EoS is
unchanged.