Perfect Fluid QGP Perfect Fluid QGP or CGC? or CGC?

Tetsufumi Hirano*Tetsufumi Hirano*

Institute of Physics, University of Institute of Physics, University of TokyoTokyo

References:References:T.Hirano and M.Gyulassy, Nucl.Phys.A T.Hirano and M.Gyulassy, Nucl.Phys.A 769769(2006)71.(2006)71.T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636636 (2006)299; work in progress.(2006)299; work in progress.

““RHIC Physics in the Context of the Standard Model”RHIC Physics in the Context of the Standard Model”RBRC workshop on Heavy Ion PhysicsRBRC workshop on Heavy Ion Physics

* Visiting scientist at RBRC* Visiting scientist at RBRC

OUTLINEOUTLINE

• Dynamical modeling in heavy ion Dynamical modeling in heavy ion collisions based on ideal collisions based on ideal hydrodynamicshydrodynamics

• Elliptic flow and perfect fluidElliptic flow and perfect fluid

• Results from hydro modelsResults from hydro models– Dependence on freezeout prescriptionDependence on freezeout prescription– Dependence on initializationDependence on initialization

• Summary and OutlookSummary and Outlook

Why Hydrodynamics?Why Hydrodynamics?StaticStatic•EoS from Lattice QCDEoS from Lattice QCD•Finite Finite TT, , field theory field theory•Critical phenomenaCritical phenomena•Chiral property of hadronChiral property of hadron

Dynamic Phenomena in HICDynamic Phenomena in HIC•Expansion, FlowExpansion, Flow•Space-time evolution ofSpace-time evolution of thermodynamic variablesthermodynamic variables

Once one accepts localOnce one accepts localthermalization ansatz,thermalization ansatz,life becomes very easy.life becomes very easy.

A possible mechanism ofA possible mechanism ofapparent thermalizationapparent thermalization

Talk by Y.NaraTalk by Y.Nara

Energy-momentum:Energy-momentum:

Conserved number:Conserved number:

Three Inputs for Hydrodynamic Three Inputs for Hydrodynamic ModelsModels

Final stage:Free streaming particles Need decoupling prescription

Intermediate stage:Hydrodynamics can be validas far as local thermalization isachieved. Need EoS P(e,n)

Initial stage:Particle production,pre-thermalization, instability?Instead, initial conditions are put for hydro simulations.

Need modeling(1) EoS, (2) Initial cond., and (3) Decoupling

0z

t

Intermediate Stage: Equation Intermediate Stage: Equation of Stateof State

Latent heat

Lattice QCD predicts cross over phase transition.Nevertheless, energy density explosively increases in the vicinity of Tc. Looks like 1st order.

Lattice QCD simulationsLattice QCD simulations Typical EoS in hydro modelsTypical EoS in hydro models

H: resonance gas(RG)

p=e/3

Q: QGP+RG

F.Karsch

et a

l. (’00

)

P.K

olb

and

U.H

ein

z(’03)

Recent lattice results at finite T Talk by Y.Aoki

Initial Stage: Initial ConditionInitial Stage: Initial Condition

Transverse plane Reaction plane

Energy density distributionEnergy density distribution

Parameterization/model-calculation to reproduce (dN/d)/(Npart/2) and dN/d

Final Stage: FreezeoutFinal Stage: Freezeout(1) (1) Sudden freezeoutSudden freezeout (2) (2) Transport of hadronsTransport of hadrons

via Boltzman eq. (hybrid)via Boltzman eq. (hybrid)

Continuum approximation no Continuum approximation no longer valid at the late stagelonger valid at the late stageMolecular dynamic approach Molecular dynamic approach for hadrons (for hadrons (,K,p,…),K,p,…)

0z

t

0z

t

At At TT==TTff,,=0 (ideal fluid)=0 (ideal fluid) =infinity (free stream)=infinity (free stream)

T=Tf

QGP fluid

Hadron fluid

QGP fluid

Obviously, final results depend onObviously, final results depend onmodeling ofmodeling of

1.1.Equation of stateEquation of state2.2.Initial conditionInitial condition3.3.FreezeoutFreezeout

So it is indispensable to check sensitivitySo it is indispensable to check sensitivityof conclusion to model assumptions andof conclusion to model assumptions andtry to reduce model parameters.try to reduce model parameters.In this talk, I will cover 2 and 3.In this talk, I will cover 2 and 3.

Caveats on Hydrodynamic Caveats on Hydrodynamic ResultsResults

What is Elliptic Flow?What is Elliptic Flow?How does the system respond to spatial anisotropy?How does the system respond to spatial anisotropy?

Ollitrault (’92)Ollitrault (’92)

Hydro behaviorHydro behavior

Spatial AnisotropySpatial Anisotropy

Momentum AnisotropyMomentum Anisotropy

INPUTINPUT

OUTPUTOUTPUT

Interaction amongInteraction amongproduced particlesproduced particles

dN

/d

No secondary interactionNo secondary interaction

0 2

dN

/d

0 2

2v2

x

y

Elliptic Flow from a Kinetic Elliptic Flow from a Kinetic TheoryTheory

b b = 7.5fm= 7.5fmTime evolution of Time evolution of vv22

generated through secondary collisionsgenerated through secondary collisions saturated in the early stage saturated in the early stage sensitive to cross section (~m.f.p.~viscosity)sensitive to cross section (~m.f.p.~viscosity)

• Gluons uniformly distributedGluons uniformly distributedin the overlap regionin the overlap region• dNdN//dy dy ~ 300 for ~ 300 for b b = 0 fm= 0 fm• Thermal distribution with Thermal distribution with T T = 500 MeV= 500 MeV

vv22 is is

Zhang et al.(’99)Zhang et al.(’99)View from collision axisView from collision axis

ideal hydro limitideal hydro limit

t(fm/c)

v2

Basis of the AnnouncementBasis of the AnnouncementPHENIX(’03)STAR(’02)

Multiplicity dependencepT dependenceand mass ordering

Hydro results: Huovinen, Kolb, Heinz,…

Sensitivity to Different Sensitivity to Different Assumptions in Early/Late Assumptions in Early/Late StagesStages

Glauber-typeGlauber-type Color Glass Color Glass CondensateCondensate

Sudden Sudden freezeoutfreezeout

Discovery ofDiscovery of

““Perfect Perfect Liquid”Liquid”

??Hadronic Hadronic

rescatteringrescattering ?? ??

InitialInitialConditionCondition

FreezeoutFreezeout

Dependence onDependence onFreezeout PrescriptionFreezeout Prescription

T.Hirano and M.Gyulassy, Nucl.Phys.A T.Hirano and M.Gyulassy, Nucl.Phys.A 769769(2006)71.(2006)71.

Classification of Hydro ModelsClassification of Hydro Models

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,…

Tch

Tth

Hadronic

Cascade

Chemical

Equilibrium

EOS

Tth

Model CE:Kolb, Huovinen,Heinz, Hirano…

Perfect Fluid of QGP

T

~1 fm/c

~3 fm/c

~10-15 fm/c

ideal hydrodynamics

vv22(p(pTT) for Different Freezeout ) for Different Freezeout Prescriptions Prescriptions

2000 (Heinz, Huovinen, Kolb…)2000 (Heinz, Huovinen, Kolb…)Ideal hydro w/ chem.eq.hadronsIdeal hydro w/ chem.eq.hadrons2002 (TH,Teaney,Kolb…)2002 (TH,Teaney,Kolb…)+Chemical freezeout+Chemical freezeout2002 (Teaney…)2002 (Teaney…)+Dissipation in hadron phase+Dissipation in hadron phase2005 (BNL)2005 (BNL)““RHIC serves the perfect liquid.”RHIC serves the perfect liquid.”

20-30%

Why so different/similar?

Accidental Reproduction of Accidental Reproduction of vv22(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

Why <pWhy <pTT> behaves > behaves differently?differently?ChemicalFreezeoutChemicalFreezeout

Chemical EquilibriumChemical

Equilibrium

Mean ET decreasesdue to pdV work

For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71

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! Hydro+Cascade is the only model to

reproduce v2(pT)!!!

vv22(p(pTT) for identified hadrons) for identified hadronsfrom QGP Hydro + Hadronic from QGP Hydro + Hadronic CascadeCascade

Mass dependence is o.k.Mass dependence is o.k.Note: First result was obtainedNote: First result was obtainedby Teaney et al.by Teaney et al.

20-30%

Proton

Pion

Mass splitting/ordering comesMass splitting/ordering comesfrom hadronic rescattering.from hadronic rescattering.Not a direct signature ofNot a direct signature ofperfect fluid QGPperfect fluid QGP

vv22(N(Npartpart) and v) and v22(eta)(eta)

Significant Hadronic Viscous EffectsSignificant Hadronic Viscous Effects at Small Multiplicityat Small Multiplicity!

Summary So FarSummary So Far

• When we employ Glauber-type initial When we employ Glauber-type initial conditions, hadronic dissipation is conditions, hadronic dissipation is indispensable.indispensable.

• Perfect fluid QGP core and dissipative Perfect fluid QGP core and dissipative hadronic coronahadronic corona

Dependence onDependence onInitialization of HydroInitialization of Hydro

T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B Y.Nara, Phys.Lett.B 636636 (2006)299; work (2006)299; work in progress.in progress.

(1) Glauber and (2) CGC Hydro (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the Initial Conditions Which Clear the First Hurdle First Hurdle

•Glauber modelGlauber model NNpartpart:N:Ncollcoll = 85%:15% = 85%:15%•CGC modelCGC model Matching I.C. via e(x,y,Matching I.C. via e(x,y,))

Centrality dependenceCentrality dependence Rapidity dependenceRapidity dependence

Details on CGC Talk by K.Itakura

vv22(N(Npartpart) from ) from QGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

GlauberGlauber:: Early thermalizationEarly thermalization Mechanism? Mechanism? CGCCGC:: No perfect fluid?No perfect fluid? Additional viscosity Additional viscosity

is required in QGPis required in QGP

Importance of better understanding of initial Importance of better understanding of initial conditioncondition

TH et al.(’06)TH et al.(’06)

Large Eccentricity from CGC Initial Large Eccentricity from CGC Initial ConditionCondition

xx

yy

Pocket formula (ideal hydro):Pocket formula (ideal hydro): vv22 ~ 0.2 ~ 0.2 @ RHIC energies @ RHIC energies

Ollitrault(’92)Ollitrault(’92)

Hirano and Nara(’04), Hirano et al.(’06)Hirano and Nara(’04), Hirano et al.(’06)Kuhlman et al.(’06), Drescher et al.(’06)Kuhlman et al.(’06), Drescher et al.(’06)

vv22(p(pTT) and v) and v22(eta) from CGC (eta) from CGC initial conditionsinitial conditions

vv22(model) > v(model) > v22(data)(data)

20-30%

Summary and OutlookSummary and Outlook

• Much more studies needed for initial Much more studies needed for initial statesstates

• Still further needed to investigate EOS Still further needed to investigate EOS dependencedependence

• To be or not to be (consistent with hydro), To be or not to be (consistent with hydro), that is the question!that is the question!

FAKE!FAKE!

AcknowledgementAcknowledgementMiklos is supposedto attend thisworkshop but cannot come.I really appreciatehis continuousencouragementto my work.

Get well soon completely, Miklos!

Excitation Function of v2Excitation Function of v2

Hadronic DissipationHadronic Dissipation•is huge at SPS.is huge at SPS.•still affects v2 at RHIC.still affects v2 at RHIC.•is almost negligible at LHC.is almost negligible at LHC.

Source Function from 3D Hydro Source Function from 3D Hydro + Cascade+ Cascade

Blink: Ideal Hydro, Kolb and Heinz (2003)Caveat: No resonance decays in ideal hydro

How much the source functionHow much the source functiondiffers from ideal hydrodiffers from ideal hydroin Configuration space?in Configuration space?

Non-Gaussian Source?Non-Gaussian Source?

x

y

px=0.5GeV/c

Viscosity from a Kinetic Viscosity from a Kinetic TheoryTheory

See, e.g. Danielewicz&Gyulassy(’85)See, e.g. Danielewicz&Gyulassy(’85)

For ultra-relativistic particles, the shear viscosity isFor ultra-relativistic particles, the shear viscosity is

IdealIdeal hydro: hydro: 00

shear viscosity shear viscosity 0 0Transport cross sectionTransport cross section

Viscosity and EntropyViscosity and Entropy

•1+1D Bjorken flow 1+1D Bjorken flow Bjorken(’83)Bjorken(’83) Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…

(Ideal)(Ideal)

(Viscous)(Viscous)

•Reynolds numberReynolds number

: shear viscosity (MeV/fm: shear viscosity (MeV/fm22), ), s s : entropy density : entropy density (1/fm(1/fm33))

wherewhere

//ss is a good dimensionless measure is a good dimensionless measure(in the natural unit) to see viscous effects.(in the natural unit) to see viscous effects.

RR>>1 >>1 Perfect fluidPerfect fluid

Iso, Mori, Namiki (’59)Iso, Mori, Namiki (’59)

Why QGP Fluid + Hadron Gas Works?Why QGP Fluid + Hadron Gas Works?T

H a

nd

Gyu

lass

y (’

06)

TH

an

d G

yula

ssy

(’0

6)

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

Rapid increase of entropy density Rapid increase of entropy density cancan

make hydro work at RHIC.make hydro work at RHIC.Deconfinement Signal?!Deconfinement Signal?!

: shear viscosity, : shear viscosity, s s : entropy density: entropy density

Kovtun,Son,Starinets(’05)Kovtun,Son,Starinets(’05)

Temperature Dependence Temperature Dependence ofof /s/s

•We propose a possible scenario:We propose a possible scenario:

Kovtun, Son, Starinets(‘05)Kovtun, Son, Starinets(‘05)

Danielewicz&Gyulassy(’85)Danielewicz&Gyulassy(’85)•Shear Viscosity in Hadron GasShear Viscosity in Hadron Gas

•Assumption:Assumption: /s at T/s at Tcc in the sQGP is 1/4 in the sQGP is 1/4

No big jump in viscosity at Tc!

DigressionDigression(Dynamical) Viscosity (Dynamical) Viscosity :: ~1.0x10~1.0x10-3-3 [Pa s] (Water [Pa s] (Water 20℃)20℃) ~1.8x10~1.8x10-5-5 [Pa s] (Air 20℃) [Pa s] (Air 20℃) Kinetic Viscosity Kinetic Viscosity :: ~1.0x10~1.0x10-6-6 [m [m22/s] (Water/s] (Water 20℃)20℃) ~1.5x10~1.5x10-5-5 [m [m22/s] (Air/s] (Air 20℃) 20℃)

[Pa] = [N/m[Pa] = [N/m22]]

Non-relativistic Navier-Stokes eq. (a simple form)Non-relativistic Navier-Stokes eq. (a simple form)

Neglecting external force and assuming incompressibility.Neglecting external force and assuming incompressibility.

waterwater > > airair BUT BUT waterwater < < airair

A Bigger Picture in Heavy Ion A Bigger Picture in Heavy Ion CollisionsCollisions

Pro

per

time

Pro

per

time

Transverse momentumTransverse momentum

CGCCGC Geometric ScalingGeometric Scaling

Shattering CGCShattering CGC

HydrodynamicsHydrodynamics•viscosity?viscosity?•non chem. eq.?non chem. eq.?

Parton energy lossParton energy loss•InelasticInelastic•ElasticElastic

HadronicHadroniccascadecascade

Low pLow pTT High pHigh pTT

RecombinationRecombinationCoalescenceCoalescence

““DGLAP region”DGLAP region”

(N)LOpQCD(N)LOpQCD

Bef

ore

Bef

ore

colli

sion

sco

llisi

ons

Par

ton

Par

ton

prod

uctio

npr

oduc

tion

Pre

-P

re-

equi

libriu

meq

uilib

rium

““ Per

fect

” flu

idP

erfe

ct”

fluid

QG

P o

r G

PQ

GP

or

GP

Dis

sipa

tive

Dis

sipa

tive

hadr

onha

dron

gas

gas

FragmentationFragmentation

InteractionInteraction

Intermediate pIntermediate pTT

Instability?Instability?Equilibration?Equilibration?

Differential Elliptic Flow Differential Elliptic Flow DevelopsDevelopsin 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 pMean pTT is the Key is the Key

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

(or increasing )vv22

PCEPCE

CECE

vv22/</<ppTT>><<ppTT>>

Generic Generic feature!feature!

(CGC +)QGP Hydro+Hadronic (CGC +)QGP Hydro+Hadronic CascadeCascade

0z

t

(Option)(Option)Color GlassColor GlassCondensateCondensate

sQGP coresQGP core(Full 3D(Full 3DIdeal Hydro)Ideal Hydro)

HadronicHadronicCoronaCorona(Cascade, (Cascade, JAM)JAM)

TH et al.(’05-)TH et al.(’05-)

Ideal QGP Fluid Ideal QGP Fluid + Dissipative Hadron Gas + Dissipative Hadron Gas ModelsModels

(1+1)D with(1+1)D with

Bjorken flowBjorken flow(2+1)D with(2+1)D with

Bjorken flowBjorken flowFull (3+1)DFull (3+1)D

UrQMUrQMDD

A.Dumitru et al., A.Dumitru et al., PLB460,411(1999); PLB460,411(1999); PRC60,021902(199PRC60,021902(1999);S.Bass and 9);S.Bass and A.Dumitru, A.Dumitru, PRC61,064909(200PRC61,064909(2000).0).

N/AN/A

C.Nonaka and C.Nonaka and S.Bass, S.Bass,

nucl-th/0510038nucl-th/0510038..

RQMDRQMD

N/AN/A

D.Teaney et al., D.Teaney et al., PRL86,4783(2001), PRL86,4783(2001), nucl-th/0110037nucl-th/0110037;;

D.Teaney, D.Teaney, nucl-th/0204023nucl-th/0204023..

N/AN/A

JAMJAMN/AN/A N/AN/A

TH, U.Heinz, TH, U.Heinz, D.Kharzeev, D.Kharzeev, R.Lacey, and R.Lacey, and Y.Nara, Y.Nara, PLB636,299(2006).PLB636,299(2006).

hydrohydro

cascadecascade

Hydro Meets Data for the First Time Hydro Meets Data for the First Time at RHIC: “Current” Three Pillarsat RHIC: “Current” Three Pillars

1.1. Perfect Fluid (s)QGP CorePerfect Fluid (s)QGP Core• Ideal hydro description of the QGP phaseIdeal hydro description of the QGP phase• Necessary to gain integrated vNecessary to gain integrated v22

2.2. Dissipative Hadronic CoronaDissipative Hadronic Corona• Boltzmann description of the hadron phaseBoltzmann description of the hadron phase• Necessary to gain enough radial flowNecessary to gain enough radial flow• Necessary to fix particle ratio dynamicallyNecessary to fix particle ratio dynamically

3.3. Glauber Type Initial ConditionGlauber Type Initial Condition• Diffuseness of initial geometryDiffuseness of initial geometry

TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)

A Lack of each pillar leads to discrepancy!A Lack of each pillar leads to discrepancy!

ppTT Spectra for identified Spectra for identified hadronshadronsfrom QGP Hydro+Hadronic from QGP Hydro+Hadronic CascadeCascade

Caveat: Other components such as recombination and Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high pfragmentation should appear in the intermediate-high pTT regions. regions.

dN/dy and dN/dpdN/dy and dN/dpTT are o.k. by hydro+cascade. are o.k. by hydro+cascade.

Discussions: Hadronic Discussions: Hadronic DissipationDissipation• Hybrid Model:Hybrid Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic GasGas + Glauber I.C. + Glauber I.C.

• Hydro Model:Hydro Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic FluidFluid + Glauber I.C. + Glauber I.C.

ComparisonComparisonTry to drawTry to drawinformation on hadron gasinformation on hadron gas

Key technique in hydroKey technique in hydro: : •Partial chemical equilibrium in hadron phasePartial chemical equilibrium in hadron phase•Particle ratio fixed at TParticle ratio fixed at Tchch

Chemical equilibrium changes dynamics. Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06)TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

Hadronic Dissipation Hadronic Dissipation Suppresses Differential Elliptic Suppresses Differential Elliptic FlowFlow

Difference comes Difference comes from dissipation from dissipation only in the hadron only in the hadron phase phase

Caveat: Chemically frozen hadronic fluid is Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and essential in differential elliptic flow. (TH and M.Gyulassy (’06))M.Gyulassy (’06))

•Relevant parameter: Relevant parameter: ss Teaney(’03)Teaney(’03)•Dissipative effect is not soDissipative effect is not solarge due to small expansion large due to small expansion rate (1/tau ~ 0.05-0.1 fmrate (1/tau ~ 0.05-0.1 fm-1-1))