Perfect Fluidity of QGPPerfect Fluidity of QGPat RHIC?at RHIC?

Tetsufumi HiranoTetsufumi HiranoInstitute of PhysicsInstitute of PhysicsUniversity of TokyoUniversity of Tokyo

Komaba, Tokyo 153-8902, JapanKomaba, Tokyo 153-8902, Japan

平野哲文平野哲文

东京大学东京大学

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.(2006)299.

OUTLINEOUTLINE• ““RHIC serves the perfect liquid”RHIC serves the perfect liquid”• Elliptic flowElliptic flow• Results from hydro + cascade modelResults from hydro + cascade model• Ratio of viscosity to entropyRatio of viscosity to entropy• Summary Summary

What is “Perfect Liquid”?What is “Perfect Liquid”?A possibility of “Perfect LiquidA possibility of “Perfect LiquidQGP” is intriguing. In this context,QGP” is intriguing. In this context,a lot of people say, a lot of people say,

“ “QGP viscosity is small”.QGP viscosity is small”.

Viscosity is “small”Viscosity is “small”in comparison with …, what???in comparison with …, what???I will discuss this issue later.I will discuss this issue later.

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)

v 2

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!

(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)

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

TH et al.(’05-)TH et al.(’05-)

0.6fm/c0.6fm/c

(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

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.

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

Result of JAM: Courtesy of M.IsseResult of JAM: Courtesy of M.Isse

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(Ollitrault(’’92)92)

vv22(p(pTT) for identified hadrons) for identified hadronsGlauber type initial conditionGlauber type initial condition CGC initial conditionCGC initial condition

Mass dependence is o.k.Mass dependence is o.k. vv22(model) > v(model) > v22(data)(data)

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?TH

and

Gyu

lass

y (’0

6)TH

and

Gyu

lass

y (’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)

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

SummarySummary• Perfect Fluid QGP + Dissipative Perfect Fluid QGP + Dissipative

Hadron + Glauber initial conditions Hadron + Glauber initial conditions does a good job.does a good job.– Manifestation of deconfinement?Manifestation of deconfinement?

• CGC initial conditions spoil this CGC initial conditions spoil this agreement.agreement.

• Viscous QGP may compensate “CGC Viscous QGP may compensate “CGC effect”.effect”.

• Importance of better understanding Importance of better understanding initial conditions. initial conditions. To be or not to be (consistent To be or not to be (consistent

with hydro),with hydro),that is THE question. --that is THE question. --

AnonymousAnonymous

QGPmixedhadronEnergy density in the Energy density in the transverse planetransverse planeat midrapidityat midrapidity

Energy in (four-)velocity Energy in (four-)velocity planeplaneat midrapidityat midrapidity

Thank you!Thank you!TH&Gyulassy(’06)TH&Gyulassy(’06)

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

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.

A Final Piece of RHIC Jigsaw A Final Piece of RHIC Jigsaw Puzzle?Puzzle?

A much better understandingA much better understanding of initial condition isof initial condition is desperately needed. desperately needed.

GlauberGlauber

oror

CGCCGC

Or any other possible Or any other possible scenarios based on non-scenarios based on non-equilibrium models, equilibrium models, instabilities, etc. for instabilities, etc. for thermalization / thermalization / isotropization mechanism.isotropization mechanism.Distinguish via 3D jet tomographyDistinguish via 3D jet tomography

Adil, Gyulassy and TH (’06)Adil, Gyulassy and TH (’06)

Results from Hydro + Cascade Results from Hydro + Cascade (III)(III)

Glauber-BGK CGC

vv22(p(pTT) from Hydro: Past, ) from Hydro: Past, Present and FuturePresent and Future

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.”2004-2005 (TH,Gyulassy)2004-2005 (TH,Gyulassy)Mechanism of vMechanism of v22(p(pTT) slope) slope2005-2006(TH,Heinz,Nara,…)2005-2006(TH,Heinz,Nara,…)+Color glass condensate+Color glass condensateFutureFuture““To be or not to be (consistentTo be or not to be (consistentwith hydro), that is THE question”with hydro), that is THE question” -- anonymous-- anonymous

History of differential elliptic flowHistory of differential elliptic flow~History of development of hydro~History of development of hydro~History of removing ambiguity in hydro~History of removing ambiguity in hydro

20-30%

XXXXXXXXXXXXXXXXXXXXXXXXXXXX

??????????????????????????????????

XXXXXXXXXXXXXXXXXXXXXXXXXXXX

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!

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 withBjorken flowBjorken flow

Full (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/AC.Nonaka and C.Nonaka and S.Bass, S.Bass, nucl-th/0510038nucl-th/0510038..

RQMDRQMDN/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/AJAMJAM

N/AN/A N/AN/ATH, U.Heinz, TH, U.Heinz, D.Kharzeev, D.Kharzeev, R.Lacey, and R.Lacey, and Y.Nara, Y.Nara, PLB636299(2006).PLB636299(2006).

hydrohydro

cascadecascade