1. Elliptic Flow from Hydro1. Elliptic Flow from Hydro(short review)(short review)

2. 2. Hydrodynamic Hydrodynamic afterburner for the CGC at afterburner for the CGC at

RHIC RHIC Tetsufumi Hirano

RIKEN BNL Research Center

Hot Quarks 2004Taos Valley, NM

Outline (part 1)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 FlowElliptic FlowHow does the system respond to initial spatial anisotropy?

Ollitrault (’92)

Hydrodynamic expansion

Initial spatial anisotropy

Final momentum anisotropy

INPUT

OUTPUT

Rescattering

dN/d

Free streaming

0 2

dN/d

0 2

2v2

x

y

Boltzmann to Hydro !?Boltzmann to Hydro !?Molnar and Huovinen (’04)

ela

stic cross se

ction

47mb ~ inelastic crosssection of pp at RHICenergy!?Still ~30% smaller thanhydro result!

Hydro (~0) is expected to gainmaximum v2 among transport theories. “hydrodynamic (maximum) limit”

Basics of hydrodynamicsBasics of hydrodynamicsHydrodynamic Equations

Energy-momentum conservation

Charge conservations (baryon, strangeness, etc…)

For perfect fluids (neglecting viscosity),

Energy density Pressure 4-velocity

Within ideal hydrodynamics, pressure gradient dP/dx is the drivingforce of collective flow. Collective flow is believed to reflect information about EoS! Phenomenon which connects 1st principle with experiment

Need equation of state(EoS)

P(e,nB)

to close the system of eqs. Hydro can be connecteddirectly with lattice QCD

Inputs for Hydrodynamic Inputs for Hydrodynamic SimulationsSimulations

Final stage:Free streaming particles Need decoupling prescription

Intermediate stage:Hydrodynamics can be appliedif thermalization is achieved. Need EoS

Initial stage:Particle production andpre-thermalizationbeyond hydrodynamicsInstead, initial conditions for hydro simulations

t

z

Main Ingredient: Equation Main Ingredient: Equation of Stateof State

Latent heat

One can test many kinds of EoS in hydrodynamics.

Typical EoS in hydro modelTypical EoS in hydro modelTypical EoS in hydro modelTypical EoS in hydro model

H: resonance gas(RG)

p=e/3

Q: QGP+RG

EoS with chemical freezeoutEoS with chemical freezeoutEoS with chemical freezeoutEoS with chemical freezeout

Kol

b an

d H

einz

(’0

3)

T.H

. an

d K

.Tsu

da(’0

2)

PCE:partial chemical equilibliumCFO:chemical freeze outCE: chemical equilibrium

Interface 1: Initial Interface 1: Initial ConditionCondition

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

•Parametrize initialhydrodynamic field

Initial time 0 ~ thermalization time

T.H

.(’0

2)

•Take initial distributionfrom other calculations

e or s proportional to part, coll or apart + bcoll

Energy density from NeXus.(Left) Average over 30 events(Right) Event-by-event basis

x

x x

yy

Interface 2: FreezeoutInterface 2: Freezeout

Tc

QG

P p

has

eH

ad

r on

ph a

s e

PartialChemicalEquilibrium

EOS

Hirano & Tsuda;Teaney;

Kolb & Rapp

Teaney, Lauret & Shuryak;

Bass & Dumitru

Tch

Tth

HadronicCascade

ChemicalEquilibrium

EOS

Tth

Kolb, Sollfrank,Huovinen & Heinz;

Hirano;…

Ideal hydrodynamics

Sudden freezeout: =0infinity

Cf.) Continuousparticleemissionby SPheRIOgroup

Hydrodynamic Results of Hydrodynamic Results of vv22

•Hydrodynamic response isconst. v2/ ~ 0.2 @ RHIC•Exp. data reach hydrodynamiclimit at RHIC for the first time.•Exp. line is expected to bendat higher collision energies.

(re

spo

nse

)=(o

utp

ut)/

(inp

ut)

Number density per unit transverse area

• Dimension• 2D+boost inv.

• Initial condition• Parametrization

• EoS• QGP + RG (chem. eq.)

• Decoupling• Sudden freezeout

STAR(’02)

LHC

?

Kolb, Sollfrank, Heinz (’00)

Hydrodynamic Results of Hydrodynamic Results of vv22((ppTT,,mm) )

• Dimension• 2D+boost inv.

• Initial condition• Parametrization

• EoS• QGP + RG (chem. eq.)

• Decoupling• Sudden freezeout

PHENIX(’03)

• 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

Huovinen et al.(’01)

Hydrodynamic Results of Hydrodynamic Results of vv22(())

• Dimension• Full 3D ( coordinate)

• Initial condition• Parametrization

• EoS1. QGP + RG (chem. eq.)2. QGP + RG (chem. frozen)

• Decoupling• Sudden freezeout

•Hydrodynamics worksonly 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)

Hydrodynamic Results of Hydrodynamic Results of vv22 (again)(again)

• 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)

Teaney, Lauret, Shuryak(’01)

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

Summary of ResultsSummary of ResultsModels for

Hadron

Phase

v2(pT,m)Excitation

function

Yield

or ratio

Viscous

effectCaveat

Chemical

Equilibrium Yes No No* No* P (Pbar) yields

<< exp. data

Partial

Chemical

Equilibrium

Yes/No*

Currently

N/A Yes No

* Tth dependence is currently not understood well.

Hadronic Cascade Yes Yes Yes

YesThrough

Boltzmann eq.

How do we treat boundary between hydro and cascade correctly?

Summary for Part 1Summary 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 Hydrodynamic afterburner for the CGC at RHICfor the CGC at RHIC

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

In collaboration with Y.Nara

CGC, hydrodynamics,CGC, hydrodynamics, and jet quenching and jet quenching

Centrality dependenceof dN/d/(Npart/2)

Kharzeev, Levin, Nardi (KLN)… Vitev, Gyulassy, Levai,

Wang, Wang, …

Nuclear modificationfactor RAA

These three physics related with each other?

v2(pT)

Kolb, Heinz, HuovinenT.H., Teaney, Shuryak,…

Dense Matter at RHICDense Matter at RHICCGC

Hydrodynamics

Jet quenching

Mean free path is assumed to be very small:

Gluon multiplicity (QS: saturation scale)

Opacity is large:

CGC+Hydro+Jet (CHJ) CGC+Hydro+Jet (CHJ) modelmodel

Pro

per

time

Transverse momentum

CGCCGC(a la KLN)(a la KLN)

Shattering CGCShattering CGC(k(kTT factorization) factorization)

HydrodynamicsHydrodynamics(full 3D hydro)(full 3D hydro)

Parton energy lossParton energy loss(a la Gyulassy-Levai-Vitev)(a la Gyulassy-Levai-Vitev)

Low pLow pTT High pHigh pTT

Collinear factorizedCollinear factorizedParton distributionParton distribution(CTEQ)(CTEQ)

LOpQCDLOpQCD(PYTHIA)(PYTHIA)

Nuc

lear

wav

efu

nctio

nP

arto

n di

strib

utio

n

Par

ton

prod

uctio

nQ

GP

Had

ron

gas

FragmentationFragmentationFreezeoutFreezeout(chemical & thermal)(chemical & thermal)

Jet quenchingJet quenching

Intermediate pIntermediate pTT

I do not discuss high pT physics today.

dN/d from a Saturation Model

Qs2

kT20

gggggg

Kharzeev and Levin (’01)

Parton-hadron dualityParton-hadron duality

s

CGC works well for rapidity and centrality dependences!Clearly, one needs final state interaction!

Initial Condition from CGCSaturation scale at a transverse position:

Momentum rapidity y space time rapidity s

Input for hydrodynamicsimulations

wherewhere

Unintegrated gluon distribution can be written

Three parameters: K, , More realistic wave function can be used.

Example of a SimulationExample of a SimulationSpace-time evolution of energy density in

sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm

Results from CHJ modelResults from CHJ modelPseudorapidity dist.

pT spectrumH

ydro

Que

nche

d je

t

Centrality and rapidity dependencesare well described by CH(J) model. What is the role of hydro incomparison with KLN approach?

Mean pT

How How EETT//NN (energy/entropy) (energy/entropy) evolves in CHJ model?evolves in CHJ model?

Gluons produced fromtwo CGC collisions

ET/N ~ 1.6 GeV

Initial conditionof hydrodynamicsimulations

ET/N ~ 1.0 GeV ET/N ~ 0.55 GeV Consistent withclassical Yang Millson 2D lattice

Consistent withexp. data ~0.6 GeV

Final (psuedo)rapidityspectra of all hadrons

This should be obtained through non-equilibrium processes.

Production of entropy

Hydrodynamic evolution“PdV work” reduces ET/N.

Toward a Unified ModelToward a Unified ModelP

rope

r tim

e

Transverse momentum

CGCCGC(a la KLN)(a la KLN)

Color QuantumColor QuantumFluidFluid(Q(QSS

22<k<kTT22<Q<QSS

44//22))((xx-evolution eq.)-evolution eq.)

Shattering CGCShattering CGC(k(kTT factorization) factorization)

HydrodynamicsHydrodynamics(full 3D hydro)(full 3D hydro)

Parton energy lossParton energy loss(a la Gyulassy-Levai-Vitev)(a la Gyulassy-Levai-Vitev)

HadronicHadroniccascadecascade(JAM)(JAM)

Low pLow pTT High pHigh pTT

RecombinationRecombination(via string fragmentation)(via string fragmentation)

Collinear factorizedCollinear factorizedParton distributionParton distribution(CTEQ)(CTEQ)

LOpQCDLOpQCD(PYTHIA)(PYTHIA)

Nuc

lear

wav

efu

nctio

nP

arto

n di

strib

utio

n

Par

ton

prod

uctio

n(d

issi

pativ

epr

oces

s?)

QG

PH

adro

nga

s

FragmentationFragmentationFreezeoutFreezeout(chemical & thermal)(chemical & thermal)

(classical Yang-Mills(classical Yang-Millson 2D lattice)on 2D lattice)

(classical Yang-Mills(classical Yang-Millson 2D lattice)on 2D lattice)

Jet quenchingJet quenching

Intermediate pIntermediate pTT

important in forward region

Summary and Outlook Summary and Outlook for Part 2for 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 onthermalization remains!

SPARE SLIDESSPARE SLIDES

Elliptic Flow GeneratedElliptic Flow Generatedin Early Stagein Early Stage

“Elliptic flow” is believed to be sensitive to the early dynamics.Wait! Is the momentum anisotropy p observable ?

Kol

b an

d H

einz

(’0

3)

EoS dependence of vEoS dependence of v22(p(pTT))

What makes a differenceof proton elliptic flow?

e (GeV/fm3)20

Pre

ssur

e

Ultrar

elat

ivist

ic pi

on g

as

Resonance Gas (RG)“soft” EoS

RG+QGP“hard” EoS

Rescale

0

Pion elliptic flow is insensitive to EoS.

Anisotropic FlowAnisotropic Flow

A.Poskanzer & S.Voloshin (’98)

z

x

x

y

Transverse plane Reaction plane

0th: azimuthally averaged dist. radial flow1st harmonics: directed flow2nd harmonics: elliptic flow…

“Flow” is not a good terminologyespecially in high pT regions

due to jet quenching.

Large radial flow reduces Large radial flow reduces vv22 for protonsfor 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 negativein low pT regions!

High pTprotons

Low pTprotons

vv22((ppTT,,mm) from ) from hydro(+cascade)hydro(+cascade)

pion

v2/

prot

on v

2/

Results from(1) partial chemical equilibrium EoS

Results from(1) chemical equilibrium EoSor(2) resonance gas EoS (no QGP)or(3) hydro+RQMD

Compiled by C.Ogilvie

ppTT distribution from PCE distribution from PCE

P.K

olb and R.R

app(’03)

Dashed line: Initial transverse kick

Solid line: =0

•Up to what pT do weneed to reproduce databy hydro?

•Recombination?•Baryon junction?

•What is initial collectiveflow?

•Classical YM onlattice may help…

vv22((ppTT) Stalls in Hadron ) Stalls in Hadron Phase?Phase?

D.T

eaney(’02)

Pb+Pb, SPS 17 GeV, b=6 fm

Hadronic rescattering via RQMDdoes not change v2(pT) for !

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

How How pp is distributed to is distributed to hadrons?hadrons?

ChemicalEquilibrium

PartialChemical

Equilibrium

K

p

p

pionskaonsprotons

p

pions

kaons

protons

CECE PCEPCE

T.H

. and K.T

suda (’02)

Tth

Proton v2(pT)

Pions v2(pT)

radial flow

PCE leads tooverestimationof v2(pT) for when radial flowis large enoughto reproducepT distribution.

Comparison of CE with Comparison of CE with PCEPCE

EOS Time Evolution

Comparison CE with PCE Comparison CE with PCE (contd.)(contd.)

pT v2(pT)

CE sensitive insensitive

PCE insensitive sensitive

Tth dependence

Hadronic Cascade Will Hadronic Cascade Will Help?Help?

ST

AR

(’02)

Hydro: P.Kolb et al.(’00)

T.H

.(’01)

Forward rapidity at RHIC~ Midrapidity at SPS?“Thermalization coeff.”?

Sensitivity to Freezeout Sensitivity to Freezeout (contd.)(contd.)

HBT radii from continuousparticle emission model?

• Dimension1D+boost inv. + cylindrical sym.

• Initial conditionParametrization

• EoSQGP + RG (chem. eq.)

• DecouplingHadronic afterburner by UrQMD

•It is getting better in low pT region for Tc=160 MeV caseby smearing through cascade.Still something is missingto interpret the data.

STARPHENIX

Taken from D. Magestro, talk @ QM04

Hydro 200

Hydro 160

Hydro+cascade 200

Hydro+cascade 160

Soff, Bass, Dumitru (’01)

Hydro + Rate Eq. in QGP phase

Including ggqqbar and ggggg

Collision term:

T.S.Biro et al.,Phys.Rev.C48(’93)1275.

Assuming “multiplicative” fugacity, EoS is unchanged.