What can we learn from What can we learn from hydrodynamic analysishydrodynamic analysis

at RHIC? at RHIC?

Tetsufumi HiranoTetsufumi Hirano

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

Workshop on Quark-Gluon-Plasma Thermalization Workshop on Quark-Gluon-Plasma Thermalization August 10-12, TU Wien, Vienna, AustriaAugust 10-12, TU Wien, Vienna, Austria

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., in preparation.., in preparation.

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?!

Basis of the Basis of the AnnouncementAnnouncement

Integrated elliptic flow

NA49(’03)

PHENIX white paper

Differential elliptic flowCommon initial time in hydro ~ 0.6-1.0 fm/c

A big surprise!

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 “perfect fluidity of

the sQGP” statement the sQGP” statement still holds. still holds.

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, Teaney;

Kolb…

Model HC:Teaney, Shuryak,

Bass, Dumitru,Nonaka…

Tch

Tth

Hadronic

Cascade

Chemical

Equilibrium

EOS

Tth

Model CE:Kolb, HuovinenHeinz, 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)

Is v2(pT) really sensitiveto the late dynamics?

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

Slope of v2(pT) ~ v2/<pT> Response to decreasing Tth

(or increasing )v2

PCE

CE

v2/<pT><pT>

Generic Generic feature!feature!

Accidental Reproduction Accidental Reproduction of vof v22(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!!!

Chem. Eq. Imitates Viscosity!

Model PCE

Model CE

Contour(T=const.)

T() at origin

T.H

. an

d K

.Tsu

da(

’02)

<vr>(Tth)

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)by Teaney, Lauret, and Shuryak

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 in a way thatit imitates viscosity.

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

Summary 1Summary 1Critical data harvested at RHICCritical data harvested at RHIC1.1.Particle ratio (Particle yield)Particle ratio (Particle yield)2.2.ppT T spectraspectra3.3.vv22 AND v AND v22(p(pTT))

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

Highly dissipative hadronic coronaHighly dissipative hadronic corona

Hydrodynamic analysesHydrodynamic analyses

Results from CGC + full 3DResults from CGC + full 3Dhydro + hadronic cascadehydro + hadronic cascade

Part 2Part 2Part 2Part 2

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

Pro

per

time

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

T.H. and Y.Nara, PRC66(’02)041901, 68(’03)064902, 69(’04)034908, PRL91(’03)082301, NPA743(’04)305

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

0z

t

ColorGlassCondensate

sQGP core(Full 3DHydro)

HadronicCorona(Cascade, JAM)

c.f. Recent similar approach by Nonaka and Bass (DNP04,QM05)

vv22(() from CGC + Full 3D ) from CGC + Full 3D Hydro Hydro

+ Hadronic Cascade+ Hadronic CascadePHOBOS 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 in forward region!

CGC+Hydro+Cascade CGC+Hydro+Cascade in Cu+Cu Collisionsin Cu+Cu Collisions

The effect of rescatteringis seen especiallynear midrapidity.

Predictions for LHCPredictions for LHCfrom CGC+Hydro+Cascadefrom CGC+Hydro+Cascade

•No jet components•Need to estimate systematic error from Cooper-Frye formula•Monotonic increase is consistent with previous work by Teaney et al.

Early Thermalization in Early Thermalization in Peripheral Collisions at Peripheral Collisions at

RHIC?RHIC?•CGC + hydro + cascade agreement only up to 15~20% centrality(impact parameter ~5fm)•Centrality dependenceof thermalization time?Common 0=0.6fm/c

Semi-central to peripheral collisions:Not interpreted only by hadronic dissipationImportant to understand pre-thermalization stageImcomplete thermalization? (Talk by Borghini)

Does the hydrodynamic Does the hydrodynamic agreement with experimentalagreement with experimentaldata suggest evendata suggest even DECONFINEMENT?!DECONFINEMENT?!

hydro+cascadePart 3Part 3Part 3Part 3

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

Iso, Mori, Namiki (1959)

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

Summary

• The sQGP core + the dissipative hadronic corona picture can be established through careful comparison of current hydro results with high precision RHIC data.• This picture is confirmed in forward rapidity region by using a “cutting edge” hybrid model (CGC + full 3D hydro + hadronic cascade).• This picture is manifestation of the sudden change of entropy density at Tc, namely deconfinement!