Transcript 1. Elliptic Flow from Hydro (short review) 2. Hydrodynamic afterburner for the

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
Outline (part 1)
Apology: It’s 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
Elliptic Flow
Ollitrault (’92)
How does the system respond to initial spatial anisotropy?
Free streaming
Hydrodynamic expansion
y
f
x
INPUT
Rescattering
OUTPUT
0
f
2p
Final momentum
anisotropy
2v2
dN/df
dN/df
Initial spatial
anisotropy
0
f
Boltzmann to Hydro !?
Molnar and Huovinen (’04)
elastic cross section
47mb ~ inelastic cross
section of pp at RHIC
energy!?
Still ~30% smaller than
hydro result!
Hydro (l~0) is expected to gain
maximum v2 among transport theories.
 “hydrodynamic (maximum) limit”
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)
Energy density
Pressure
4-velocity
to close the system of eqs.
 Hydro can be connected
directly with lattice QCD
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
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
Main Ingredient: Equation of State
One can test many kinds of EoS in hydrodynamics.
H: resonance gas(RG)
Q: QGP+RG
EoS with chemical freezeout
T.H. and K.Tsuda(’02)
Kolb and Heinz (’03)
Typical EoS in hydro model
Latent heat
PCE:partial chemical equiliblium
CFO:chemical freeze out
CE: chemical equilibrium
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
T.H.(’02)
y
x
x
e or s proportional to
rpart, rcoll or arpart + brcoll
Energy density from NeXus.
(Left) Average over 30 events
(Right) Event-by-event basis
x
Interface 2: Freezeout
QGP phase
Tc
Kolb, Sollfrank,
Huovinen & Heinz;
Hirano;…
Hirano & Tsuda;
Teaney;
Kolb & Rapp
Teaney, Lauret
& Shuryak;
Bass & Dumitru
Ideal hydrodynamics
Chemical
Equilibrium
EOS
t
Tth
Tch Partial
Chemical
Equilibrium
EOS
Tth
Sudden freezeout: l=0infinity
Hadronic
Cascade
Cf.)
Continuous
particle
emission
by SPheRIO
group
Hydrodynamic Results of v2
Kolb, Sollfrank, Heinz (’00)
LHC?
(response)=(output)/(input)
STAR(’02)
Number density per
unit transverse area
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• QGP + RG (chem. eq.)
• Decoupling
• Sudden freezeout
•Hydrodynamic response is
const. v2/e ~ 0.2 @ RHIC
•Exp. data reach hydrodynamic
limit at RHIC for the first time.
•Exp. line is expected to bend
at higher collision energies.
Hydrodynamic Results of v2(pT,m)
PHENIX(’03)
Huovinen et al.(’01)
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• QGP + RG (chem. eq.)
• Decoupling
• Sudden freezeout
• Correct pT dependence
up to pT=1-1.5 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
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
1. QGP + RG (chem. eq.)
2. QGP + RG (chem. frozen)
• Decoupling
• Sudden freezeout
Hydrodynamic Results of v2 (again)
Teaney, Lauret, Shuryak(’01)
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• Parametrized by latent heat
(LH8, LH16, LH-infinity)
• RG
• QGP+RG (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)
Summary of Results
Models for
Hadron
Phase
Chemical
Equilibrium
Partial
Chemical
Equilibrium
Hadronic
Cascade
Excitation
v2(pT,m)
function
Yes
No
Yield
or ratio
No*
Yes/
Y
es
No* N/A
Viscous
effect
No
Currently
Yes
Yes
Yes
No
Caveat
* P (Pbar) yields
<< exp. data
* Tth dependence
is currently not
understood well.
How do we treat
boundary
es
between hydro
and cascade
Through
Boltzmann eq. correctly?
Y
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: Don’t forget HBT puzzle! Hydro+cascade?
– Need further systematic studies, e.g., hydro+cascade in
forward rapidity region, more realistic EoS, unified
treatment, viscosity, etc.
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)
• CGC+hydro+jet model (CHJ model)
• Toward a unified dynamical description for
relativistic heavy ion collisions
CGC, hydrodynamics,
and jet quenchingNuclear modification
Centrality dependence
of dN/dh/(Npart/2)
factor RAA
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?
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:
Nuclear wave
function
Parton
distribution
CGC+Hydro+Jet (CHJ) model
(a la KLN)
(CTEQ)
Transverse momentum
Shattering CGC
Parton
production
LOpQCD
(kT factorization)
Hydrodynamics
(full 3D hydro)
Proper time
Hadron QGP
gas
Collinear factorized
Parton distribution
CGC
(PYTHIA)
Jet quenching
Freezeout
(a la Gyulassy-Levai-Vitev)
Fragmentation
(chemical & thermal)
Low pT
Parton energy loss
Intermediate pT
High pT
dN/dh from a Saturation Model
Kharzeev and Levin (’01)
ggg
f
Parton-hadron duality
~1/as
0
Qs2
k T2
CGC works well for rapidity and centrality dependences!
Clearly, one needs final state interaction!
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.
Example of a Simulation
Space-time evolution of energy density in
sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm
Results from CHJ model
Pseudorapidity dist.
Quenched
jet
Hydro
pT spectrum
Centrality and rapidity dependences
are well described by CH(J) model.
 What is the role of hydro in
comparison with KLN approach?
Mean pT
How ET/N (energy/entropy) evolves
in CHJ model?
Gluons produced from
two CGC collisions
Initial condition
of hydrodynamic
simulations
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
This should be obtained through
non-equilibrium processes.
 Production of entropy
 Consistent with
exp. data ~0.6 GeV
Hydrodynamic evolution
“PdV work” reduces ET/N.
Nuclear wave
function
Parton
distribution
Parton
production
(dissipative
process?)
CGC
(a la KLN)
(classical Yang-Mills
on 2D lattice)
Collinear factorized
Color Quantum
Fluid(QS2<kT2<QS4/L2) Parton distribution
(x-evolution eq.)
(CTEQ)
Transverse momentum
Shattering CGC
LOpQCD
(kT factorization)
(classical Yang-Mills
on 2D lattice)
Hydrodynamics
(full 3D hydro)
Proper time
Hadron QGP
gas
Toward a Unified Model
(PYTHIA)
Jet quenching
Hadronic
Freezeout
cascade
Recombination
Low pT
Intermediate pT
Parton energy loss
(a la Gyulassy-Levai-Vitev)
(via string fragmentation)
Fragmentation
(chemical
(JAM) & thermal)
High pT
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!
SPARE SLIDES
Kolb and Heinz (’03)
Elliptic Flow Generated
in Early Stage
“Elliptic flow” is believed to be sensitive
to the early dynamics.
Wait! Is the momentum anisotropy ep observable ?
EoS dependence of v2(pT)
 Pion elliptic flow is insensitive
to EoS.
Pressure
 What makes a difference
of proton elliptic flow?
0
RG+QGP
“hard” EoS
Resonance Gas (RG)
“soft” EoS
20 e (GeV/fm3)
y
Anisotropic Flow
f
x
z
x
Transverse plane
Reaction plane
A.Poskanzer & S.Voloshin (’98)
0th: azimuthally averaged dist.  radial flow
1st harmonics: directed flow
2nd harmonics: elliptic flow
…
“Flow” is not a good terminology
especially in high pT regions
due to jet quenching.
Large radial flow reduces v2 for
protons
High pT
protons
Low pT
protons
•Radial flow pushes protons to high
pT regions
•Low pT protons are likely to come
from fluid elements with small
radial flow
Even for positive elliptic flow of matter,
v2 for heavy particles can be negative
in low pT regions!
v2(pT,m) from hydro(+cascade)
pion v2/e
Results from
(1) partial chemical equilibrium EoS
proton v2/e
Results from
(1) chemical equilibrium EoS
or
(2) resonance gas EoS (no QGP)
or
(3) hydro+RQMD
Compiled by C.Ogilvie
pT distribution from PCE
P.Kolb and R.Rapp(’03)
Dashed line: Initial transverse kick
Solid line: a=0
•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…
v2(pT) Stalls in Hadron Phase?
Hadronic rescattering via RQMD
does not change v2(pT) for p !
D.Teaney(’02)
Pb+Pb, SPS 17 GeV, b=6 fm
Solid lines are guide to eyes
Mechanism for stalling v2(pT)
•Hydro (chem. eq.):
Pion dominance
Effect of EoS
•Hydro+RQMD:
Effective viscosity
Effect of finite l
How ep is distributed to hadrons?
Chemical
Equilibrium
Partial
Chemical
Equilibrium
T.H. and K.Tsuda (’02)
p
K
p
CE
ep
pions
kaons
protons
Tth
radial flow
Proton v2(pT)
Pions v2(pT)
PCE
ep
PCE leads to
overestimation
of v2(pT) for p
when radial flow
is large enough
to reproduce
pT distribution.
pions
kaons
protons
Comparison of CE with PCE
EOS
Time Evolution
Comparison CE with PCE (contd.)
Tth dependence
pT
v2(pT)
CE
sensitive
insensitive
PCE
insensitive
sensitive
Hadronic Cascade Will Help?
STAR (’02)
T.H.(’01)
Forward rapidity at RHIC
~ Midrapidity at SPS?
“Thermalization coeff.”?
Hydro: P.Kolb et al.(’00)
Sensitivity to Freezeout (contd.)
Soff, Bass, Dumitru (’01)
• Dimension
Hydro+cascade 200
1D+boost inv. + cylindrical sym.
Hydro 160
• Initial condition
Parametrization
• EoS
Hydro+cascade 160
QGP + RG (chem. eq.)
Hydro 200
• Decoupling
Hadronic afterburner by UrQMD
STAR
PHENIX
Taken from D. Magestro, talk @ QM04
HBT radii from continuous
particle emission model?
•It is getting better in low pT
region for Tc=160 MeV case
by smearing through cascade.
Still something is missing
to interpret the data.
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.