What can we learn What can we learn from hydrodynamic from hydrodynamic analysis of elliptic analysis of elliptic

flow?flow?Tetsufumi HiranoTetsufumi Hirano

Dept. of Physics, Columbia Dept. of Physics, Columbia Univ.Univ.

T.H. and M.Gyulassy, nucl-th/0506049T.H. and M.Gyulassy, nucl-th/0506049T.H., Y.Nara T.H., Y.Nara et alet al., work in progress.., work in progress.

Quark Matter 2005, August 4-9, Budapest, HungaryQuark Matter 2005, August 4-9, Budapest, Hungary

OutlineOutline

1.1. Perfect fluidity of sQGP core and Perfect fluidity of sQGP core and highly dissipative hadronic coronahighly dissipative hadronic corona

2.2. CGC + full 3D hydro + cascadeCGC + full 3D hydro + cascade

3.3. Hydrodynamic analysis suggests Hydrodynamic analysis suggests even a signal ofeven a signal of

DECONFINEMENT?!DECONFINEMENT?!

Bases of the DiscoveryBases of the Discovery

Integrated elliptic flow

NA49(’03)

PHENIX white paper

Differential elliptic flow

Our claims:Our claims:1.1. Ideal hydrodynamics Ideal hydrodynamics

accidentally accidentally reproduces these reproduces these

data!data!2.2. Nevertheless, Nevertheless,

“perfect fluidity of the “perfect fluidity of the sQGP” statement and sQGP” statement and early thermalization early thermalization

still hold. still hold.

WHY!!!???WHY!!!???

Classification of Hydro Classification of Hydro ModelsModels

Tc

QG

P p

has

eH

ad

r on

ph a

s e

Partial

Chemical

Equilibrium

EOS

Model PCE:Hirano & Tsuda;

Teaney;Kolb & Rapp…

Model HC:Teaney, Lauret

& Shuryak;Bass & Dumitru…

Tch

Tth

Hadronic

Cascade

Chemical

Equilibrium

EOS

Tth

Model CE:Kolb, Sollfrank,

Huovinen & Heinz;Hirano;…

Perfect Fluid of QGP

T

~1 fm/c

~3 fm/c

~10-15 fm/c

ideal hydrodynamics

PH

EN

IX w

hite

pa

per, N

PA

757

,184

(200

5)

Are hydro results consistent?If not, what does it mean?

elliptic flow

pT spectra

p

PartialCEPartialCE

Chem.Eq.Chem.Eq.

HadronicCascadeHadronicCascade

Differential Elliptic Flow Differential Elliptic Flow DevelopsDevelops

in the Hadron Phase?in the Hadron Phase?

T.H

. and K.T

suda (’02)

Ko

lb a

nd

Hei

nz(

’04)

0.4 0.6 0.80.20 0.4 0.6 0.80.20 1.0

140MeV

100MeV

transverse momentum (GeV/c)

Mean pT is the Key

Response to decreasing Tth (or increasing )v2

PCE

CE

v2/<pT><pT>

Cancel between vCancel between v22 and and <p<pTT> >

pT

v2(p

T)

<pT>

v2

pT

v2(p

T)

v2

<pT>

pT

v2(p

T)

v2

<pT>

Chemical Eq.

Chemical F.O.

At hadronization

CE: increase

CFO: decrease

freezeout

1.Why mean pT behaves so differently?2. Why CE result ~ HC result?

PartialCEPartialCE

Chem.Eq.Chem.Eq.

HadronicCascadeHadronicCascade

PH

EN

IX w

hite

pa

per,

NP

A75

7,1

84

(20

05

)

Intuitive PictureIntuitive Picture

ChemicalFreezeoutChemicalFreezeout

Chemical EquilibriumChemical

Equilibrium

Mean ET decreasesdue to pdV work

For a more rigorous discussion, see T.H. and M.Gyulassy, nucl-th/0506049

MASS energy

KINETICenergy

ET per particle increases in chemical equilibrium.

This effect delays cooling of the system like a viscous fluid.

Chemical equilibrium imitates viscosity

at the cost of particle yield!!!

Summary of Hydro Summary of Hydro ResultsResults

Models for

Hadron

Phasev2(pT,m)

pT

spectra

Yield

or ratio

Viscous

effectCaveat

Chemical

Equilibrium Yes Yes* No No

* P (Pbar) yields

<< exp. data

Partial

Chemical

EquilibriumNo Yes* Yes No

*Only low pT for pions

Hadronic Cascade Yes Yes Yes Yes*

*Kinetic approach•Boundary

(QGPhadron)

“No-Go theorem”Ruled out!

WINNER for hydro race at RHIC ! Hybrid model (Ideal QGP fluid + dissipative hadron gas)

CGC + Full 3D Hydro + CGC + Full 3D Hydro + CascadeCascade

0z

t

ColorGlassCondensate

sQGP core(Full 3DHydro)

HadronicCorona(Cascade)

CGC + Full 3D Hydro CGC + Full 3D Hydro + Hadronic Cascade+ Hadronic Cascade

PHOBOS data:“Triangle shape”prop. to dN/dTth=100MeV:“Trapezoidal shape”Typical hydro resultTth=169MeV:Triangle shape!Just after hadronization

CGC+hydro+cascade:Good agreement!

Perfect fluid sQGP core +dissipative hadronic corona picture

works as well in forward region!

What Have We Learned?What Have We Learned?T

.H. a

nd

M.G

yula

ssy

(’05

)

!•Absolute value of viscosity •Its ratio to entropy density

What makes this sudden behavior?

: shear viscosity, s : entropy density

ConclusionConclusionCritical data harvested at RHICCritical data harvested at RHIC1.1.Particle ratio (Particle yield)Particle ratio (Particle yield)2.2.ppT T spectraspectra3.3.vv22, v, v22(p(pTT), and v), and v22(())

Nearly perfect fluidity of the sQGP coreNearly perfect fluidity of the sQGP coreANDAND

Highly dissipative hadronic coronaHighly dissipative hadronic corona DECONFINEMENT!?DECONFINEMENT!?

Hydrodynamic analysesHydrodynamic analyses

BONUS SLIDES!BONUS SLIDES!

Tth<Tch

Chemical parameters particle ratioThermal parameters pt spectra

•Statistical modelTch>Tth

•(conventional) hydroTch=Tth

• No reproductionof ratio and spectrasimultaneously

Many people don’t know this…

P.Huovinen, QM2002 proceedings

Extension of Parameter Space

i Introduction of chemical potentialfor each hadron!

•Single Tf in hydro•Hydro works?•Both ratio andspectra?

Chemical Potential & Chemical Potential & EoSEoS

EOS

Example of chem. potential

Partial chemical equilibrium (PCE)

Expansion dynamics is changed(or not)?

T.H

. an

d K

.Tsu

da(

’02)

Does Dynamics change?

Model PCE

Model CE

Contour(T=const.)

T() at origin

T.H

. an

d K

.Tsu

da(

’02)

<vr>(Tth)

pT Spectra

•How to fix Tth in conventional hydro

• Response to pT slope• Spectrum harder with decreasing Tth

• Up to how large pT?

•Tth independence of slope in chemically frozen hydro

• No way to fix Tth

• Suggests necessity of (semi)hard components

Charged hadrons in AuAu 130AGeV

Chemical

Equilibrium

Partial

Chemical

EquilibriumT.H

. an

d K

.Tsu

da (

’02)

Why <pT> behaves differently?Simplest case: Pion gasLongitudinal expansion

pdV work!

dET/dy should decrease with decreasing Tth. <ET>dN/dy should so.

CFO: dS/dy = const. dN/dy = const. <pT> MUST decreases

CE: dS/dy = const.dN/dy decreases (mass effect)<pT> can increase as long as <ET>dN/dy decreases.

Result from the 1st law of thermodynamics &

Bjorken flow

dET/d

y

proper time

ideal hydro

QGPQGP

Fuzzy imageif focus is not adjusted yet.

QGPQGP

QGP Wanna see this?

Fine-tune the “hadronic” focus!

focus:

hadron coronaThe importance of the dissipative

hadronic corona to understand“perfect fluid” sQGP core!

The End of 50-Year-OldThe End of 50-Year-Old Ideal, Chem. Eq. Hadronic Ideal, Chem. Eq. Hadronic

FluidFluidAfter the famous Landau’s paper (1953), ideal and chemical equilibrium hadronic hydrodynamics has been exploited for along time. However, the model may notbe used when chemical freezeout happens earlier than thermal freezeoutsince it accidentally reproduces pT spectra and v2(pT)at the cost of particle yields.

A Long Long Time Ago…A Long Long Time Ago…

…we obtain the value R (Reynolds number)=1~10…Thus we may infer that the assumption of theperfect fluid is not so good as supposed by Landau.

Digression

1. Ideal hydrodynamics reproduce v2(pT) remarkably well, but not HBT radii.

TRUEFALSE

2. v2(pT) is not sensitive to the late hadronic stage. TRUE

FALSE

TRUE: Ideal Hydrodynamics reproduces neither v2(pT) nor HBT radii at RHIC.

TRUE: v2(pT) depends on thermal equilibrium, chemicalequilibrium, and viscous effects in the hadron phase.

Check Sheet for Prevailing Check Sheet for Prevailing OpinionOpinion

X

X

FAQFAQ1. We cannot say “Hydro works very well at RHIC”anymore?

Yes/No. Only a hydro+cascade model does a good job.Nevertheless, HBT puzzle!QGP as a perfect fluid. Hadron as a viscous fluid.

2. Why ideal hydro can be used for chemically frozenhydro?

We can show from AND .One has to distinguish “chemical freeze out” from “chemical non-equilibrium”.

Finite Mean Free Path & Finite Mean Free Path & ViscosityViscosity

See, e.g. Danielewicz&Gyulassy(1985)

For ultra-relativistic particles, the shear viscosity is

Ideal hydro: 0 shear viscosity 0

Transport cross section

Toward a Unified Model in Toward a Unified Model in H.I.C.H.I.C.

T.H. and Y.Nara (’02-)T.H. and Y.Nara (’02-)P

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

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

FragmentationFragmentation

(MV model(MV modelon 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?Not

cov

ered

in thi

s ta

lk

Not

cov

ered

in thi

s ta

lk

Importance of Importance of Thermalization Stage at Thermalization Stage at

RHICRHIC

•CGC + hydro + cascade agreement only up to 15~20% centrality(impact parameter ~5fm)•Centrality dependenceof thermalization time

Semi-central to peripheral collisions:Not interpreted only by hadronic dissipationImportant to understand pre-thermalization stage

Initial EccentricityInitial Eccentricity

CGC initial conditiongives ~25% largerinitial eccentricitythan participant orbinary collision scaling.

Viscosity and EntropyViscosity and Entropy

•1+1D Bjorken flow(Ideal)

(Viscous)

•Reynolds number

: shear viscosity (MeV/fm2)s : entropy density (1/fm3)

where

/s is a good dimensionless measureto see viscous effects.

R>>1 Perfect fluid

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 negative in low pT regions!

High pTprotons

Low pTprotons

xy

pT

Blast wave peak depends on

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.): Cancellation betweenv2 and <pT>Effect of EoS

•Hydro+RQMD: Effective viscosity

Effect of finite