Perfect Fluidity of the Quark Perfect Fluidity of the Quark Gluon Plasma in Relativistic Gluon Plasma in Relativistic

Heavy Ion CollisionsHeavy Ion Collisions

Tetsufumi HiranoTetsufumi HiranoDepartment of Physics, the University of TokyoDepartment of Physics, the University of Tokyo

hirano @ phys.s.u-tokyo.ac.jphirano @ phys.s.u-tokyo.ac.jphttp://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/

KEK-CPWS-HEAP2009KEK-CPWS-HEAP2009

OUTLINEOUTLINE IntroductionIntroduction

Quark gluon plasma and relativistic heavy ion collisionsQuark gluon plasma and relativistic heavy ion collisions Time evolution of heavy ion collisionsTime evolution of heavy ion collisions Transverse collective flow Transverse collective flow

Radial flowRadial flow Elliptic flowElliptic flow

Current status of dynamical modeling in heavy ion Current status of dynamical modeling in heavy ion collisionscollisions

Summary and OutlookSummary and Outlook

Where was the Quark Gluon Plasma?Where was the Quark Gluon Plasma?

History of the UniverseHistory of the Universe

History of the matterHistory of the matter

NucleosynthesisNucleosynthesis

HadronizationHadronization

Quark Gluon PlasmaQuark Gluon Plasma(after micro seconds of Big Bang)(after micro seconds of Big Bang)

Recipes for Quark Gluon PlasmaRecipes for Quark Gluon Plasma

CompressCompressHeat upHeat up hadronic many body systemhadronic many body system

Figure adopted fromFigure adopted fromhttp://www.bnl.gov/rhic/QGP.htmhttp://www.bnl.gov/rhic/QGP.htm

How are colored particles set free How are colored particles set free from confinement? from confinement?

Little Bang!Little Bang!Relativistic Heavy Ion Collider(2000-)

RHIC as a time machine!

100 GeV per nucleonAu(197×100)+Au(197×100)

Collision energy

Multiple production(N~5000)

Heat

sideview

frontview

STAR

STAR

Big Bang vs. Little BangBig Bang vs. Little Bang

Figure adopted fromFigure adopted fromhttp://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htmhttp://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm

3D Hubble expansion3D Hubble expansion

beam axisbeam axis

Nearly 1D Hubble expansion*Nearly 1D Hubble expansion*+ 2D transverse expansion + 2D transverse expansion

**Bjorken(’83)Bjorken(’83)

Big Bang vs. Little BangBig Bang vs. Little Bang

Collective flow is a key to check whether local thermalization is achieved.

Big BangBig Bang Little BangLittle Bang

Time ScaleTime Scale10-5 sec>>m.f.p./c

10-23 sec~m.f.p./c

Expansion RateExpansion Rate 105-6/sec 1022-23/sec

Local thermalization of the QGP is non-trivial in H.I.C.

SpectrumSpectrumRed-shifted

(CMB)Blue-shifted

(hadrons)

See, e.g., Yagi, Hatsuda, Miake, Quark-Gluon Plasma (Cambridge, 2005)

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact (two bunches of gluons)

Dynamics of Heavy Ion CollisionsDynamics of Heavy Ion Collisions

Time scale10fm/c~10-23sec

Temperature scale 100MeV~1012K

Jargon: CentralityJargon: Centrality

““Centrality” characterizes a collisionCentrality” characterizes a collisionand categorizes events.and categorizes events.

central eventcentral event peripheral eventperipheral event

Participant-Spectator picture is validParticipant-Spectator picture is valid

How to Quantify CentralityHow to Quantify Centrality

PHENIX: Correlation btw. BBC and ZDC signalsPHENIX: Correlation btw. BBC and ZDC signals

NNpartpart: The number of participants: The number of participantsNNcollcoll: The number of binary collisions: The number of binary collisionsNNpartpart and N and Ncollcoll as a function of as a function of impact parameterimpact parameter

197197Au+Au+197197AuAu

NNpartpart and N and Ncollcoll

Estimated Energy Density at RHICEstimated Energy Density at RHIC

PHENIX(’05)PHENIX(’05)

c from lattice

Well above Well above cc from lattice from lattice simulations in simulations in central collision central collision at RHICat RHIC

QGP from the 1QGP from the 1stst Principle Principle

Equation of state from lattice QCDEquation of state from lattice QCD•A large number of d.o.f. are freed around TA large number of d.o.f. are freed around Tcc..•Pseudo-critical temperature TPseudo-critical temperature Tcc: ~150-200 MeV: ~150-200 MeV•Typical energy density scale of transition : ~1 GeV/fmTypical energy density scale of transition : ~1 GeV/fm33

•Not available for time evolutionNot available for time evolution

M.Cheng et al., PRD77,014511 (’08)M.Cheng et al., PRD77,014511 (’08)

TransverseTransverse**

CollectiveCollectiveFlowFlow

* “Transverse”: a direction perpendicularto the collision axis.

Radial Flow (Azimuthally Averaged Radial Flow (Azimuthally Averaged Flow)Flow)

Blast wave model (thermal+boost)Driving force of flowpressure gradientIn general, flow is

sensitive to EOSInside: high pressure

Outside: vacuum (P=0)

Sollfrank et al.(’93)

Blue-Shifted SpectraBlue-Shifted SpectraO

.Bar

anni

kova

, tal

k at

QM

05

pp & dAu: Power-lawpp & dAu: Power-law

Au+Au: Convex to Au+Au: Convex to Power lawPower law

Consistent with the Consistent with the thermal+boost thermal+boost picturepicture

p

d Au

p

AuAu

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

Ollitrault (’92)Ollitrault (’92)

Hydro behavior

Spatial Anisotropy

Momentum Anisotropy

INPUTINPUT

OUTPUTOUTPUT

Interaction amongInteraction amongproduced particlesproduced particles

dN

/d

No secondary interaction

0 2

dN

/d

0 2

2v2

x

y

Time Evolution of vTime Evolution of v22 from a Parton from a Parton Cascade ModelCascade Model

b = 7.5fm

generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity)

v2 is

Zhang et al.(’99) ideal hydro limit

t(fm/c)

v 2 : Ideal hydro

: strongly interactingsystem

Arrival at Hydrodynamic LimitArrival at Hydrodynamic Limit

Experimental data reach Experimental data reach hydrodynamic limit curve hydrodynamic limit curve for the first time at RHIC.for the first time at RHIC.

xx

yy

Current Status ofCurrent Status ofDynamical ModelingDynamical ModelingIn Relativistic Heavy In Relativistic Heavy

Ion CollisionsIon Collisions

•Phenomenology (hydrodynamics) 　　　　

Complexity of QCDNon-linear interactions of gluons

Strong couplingMany body systemColor confinement

•Inputs to phenomenology (lattice QCD)

Strategy to Attack QGP ProblemStrategy to Attack QGP Problem•The first principle (QuantumChromo Dynamics)

•Experimental data @ Relativistic Heavy Ion Collider

200+ papers from 4 collaborationssince 2000

3D Ideal Hydro Simulation in 3D Ideal Hydro Simulation in Au+Au Au+Au Collisions with b=7.2fm @ 100 GeV/nCollisions with b=7.2fm @ 100 GeV/n

Higher quality animation is available at Caveat: Camera angle keeps changing.

Multi-Module Modeling (1)Multi-Module Modeling (1)

0collision axis

time

AuAu AuAu

QGP fluid

hadron gasInitial condition•Glauber•Color Glass Condensate•EPOS

0-10%

10-20%20-30%

…

H.J.Drescher and Y.Nara (2007), K.Werner et al.(2006)

Details of Initial ConditionsDetails of Initial ConditionsGlauber model•Conventional initialconditions•Announcement ofdiscovery was madein comparison ofresults from Glauberwith data.•Initial entropy distribution is prop. to Npart

Color Glass Condensate•Natural picture based on QCDat very high collisionenergies.

EPOS•Phenomenologicalimplication of partonladder ~ string. •Application to airshower simulation for high energy cosmic rays.

Multi-Module Modeling (2)Multi-Module Modeling (2)

0collision axis

time

AuAu AuAu

QGP fluid

hadron gasIdeal Hydrodynamics*•Initial time 0.6fm/c•Model EoS

•lattice-based#

•1st order

*T.Hirano(2002), #Lattice part : M.Cheng et al. (2008)

Relativistic Hydrodynamic Equations Relativistic Hydrodynamic Equations for a Perfect Fluidfor a Perfect Fluid

Baryon number

Energy

Momentum

e : energy density, P : pressure, : four velocity

Multi-Module Modeling (3)Multi-Module Modeling (3)

0collision axis

time

AuAu AuAu

QGP fluid

hadron gas

Hadronic afterburner•Hadronic transportmodel (JAM, UrQMD)•Kinetic theory of hadron gases includingall resonances•Switching temperatureT=160 MeV (169MeV)

Transverse PlaneTransverse Plane

QGP fluid surrounded QGP fluid surrounded by hadron gasby hadron gas

Initial conditionInitial condition

Perfect fluidPerfect fluidevolution of QGPevolution of QGP

Kinetic evolutionKinetic evolutionof hadron gasof hadron gas

xx

yy

ppTT Spectra for Pions and Protons Spectra for Pions and Protons

Hybrid model works well up to pT~1.5 GeV/c(1st order, dotted) and 2-3 GeV/c (lattice-based, solid)

Glauber/CGC + Ideal Hydro + JAM

Centrality Dependence of Elliptic FlowCentrality Dependence of Elliptic FlowDiscovery of “Large” v2 at RHIC• v2 data are comparable with (naive) hydro results for the first time.• Hadronic cascade models cannot reproduce data.

This is the first time for idealhydro at work in H.I.C. Strong motivation to develop hydro-based analysis tools.

Result from a hadronic cascade (JAM)(Courtesy of M.Isse)

TH et al. (’06).

Glauber + Ideal Hydro

Centrality Dependence of Elliptic Flow Centrality Dependence of Elliptic Flow

•1st order phase transition is unlikely from data since viscosity reduces v2 largely.•How perfect? Depends on initial model.

197Au+197Au 63Cu+63Cu

Glauber/CGC + Ideal Hydro + JAM

TH et al, (in prepation)

Effects of ViscosityEffects of Viscosity•A tiny kinetic viscosityleads to large reductionof elliptic flow coefficients.•Elliptic flow is sufficiently sensitive to constrain EoS,transport coefficients, andinitial conditions.

Figure taken from M.Luzumand P.Romatschke, arXiv:0804.4015

Glauber + Viscous Hydro

Pseudorapidity Dependence of Pseudorapidity Dependence of Elliptic Flow CoefficientElliptic Flow Coefficient

QGP only QGP+hadron fluids

QGP fluid+hadron gas

T.Hirano et al.,Phys.Lett.B636(2006)299.

Not boost invariantNot boost invariantSuppression in forward and backward rapiditySuppression in forward and backward rapidity

ppTT Dependence of Elliptic Flow Dependence of Elliptic FlowAu+Au 200 GeV

•Glauber+ Ideal hydro withlattice(-motivated) EoS +hadronic cascade•Viscosity would be needed forbetter description.

Results from EPOS Initial ConditionsResults from EPOS Initial Conditions

EPOS + Ideal Hydro + UrQMD

Reasonably reproduce rapidity dependence

K.Werner et al. (2009)

Summary & OutlookSummary & Outlook Elliptic flow pattern observed at RHIC is Elliptic flow pattern observed at RHIC is

described reasonably well by hydro-based described reasonably well by hydro-based models.models. Hydro model at work for the first time in H.I.C.Hydro model at work for the first time in H.I.C. Hadron-based kinetic theory cannot reproduce Hadron-based kinetic theory cannot reproduce

flow pattern.flow pattern. Systematic studies are undergoing:Systematic studies are undergoing:

Effects of viscosity Effects of viscosity Constraint of EOS and transport Constraint of EOS and transport coefficientscoefficients

Understanding of initial pre-thermalization stage Understanding of initial pre-thermalization stage

Pseudorapidity Dependence of vPseudorapidity Dependence of v22

=0 >0<0

•v2 data are comparable with hydro results again around =0•Not a QGP gas sQGP•Nevertheless, large discrepancy in forward/backward rapiditySee next slides

TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

QGP onlyQGP+hadron

Hadron Gas Instead of Hadron FluidHadron Gas Instead of Hadron Fluid

QGP coreQGP core

A QGP fluid surrounded by hadronic gas

QGP: Liquid (hydro picture)Hadron: Gas (particle picture)

“Reynolds number”

Matter proper part: (shear viscosity)(entropy density)

bigin Hadron

smallin QGP

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

Importance of Hadronic “Corona”Importance of Hadronic “Corona”

•Boltzmann Eq. for hadrons instead of hydrodynamics•Including viscosity through finite mean free path

•Suggesting rapid increase of entropy density•Deconfinement makes hydro work at RHIC!? Signal of QGP!?

QGP only QGP+hadron fluids

QGP fluid+hadron gas

T.Hirano et al.,Phys.Lett.B636(2006)299.

Sensitivity to Initial ConditionsSensitivity to Initial Conditions

Novel initial conditionsfrom “Color Glass Condensate”lead to large eccentricity.

Need viscosity even in QGP!

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

# of binary collisions# of binary collisions

x

yThickness function:Thickness function:

Woods-Saxon nuclear density:Woods-Saxon nuclear density:Gold nucleus:Gold nucleus:00=0.17 fm=0.17 fm-3-3

RR=1.12=1.12AA1/31/3-0.86-0.86AA-1/3-1/3

=0.54 fm=0.54 fm

n n = 42mb @200GeV= 42mb @200GeV

# of participants# of participants

11 －（－（ survival probabilitysurvival probability ））

How to Quantify CentralityHow to Quantify Centrality

Parton Distribution in Proton Parton Distribution in Proton at Small xat Small x

x 20!!x 20!!

•Gluons are dominant at Gluons are dominant at small x.small x.•Small x = High energySmall x = High energy•Hadron/Nucleus as a Hadron/Nucleus as a bunch of gluons at high bunch of gluons at high energyenergy

Bjorken x ~ Fraction of longitudinal momentum Bjorken x ~ Fraction of longitudinal momentum in protonin protonKinematics in ggKinematics in gg g g

Interplay btw. Emission and Interplay btw. Emission and Recombination at Small xRecombination at Small x

Linear effect (BFKL)Linear effect (BFKL)

Non-linear effectNon-linear effect

Figures adopted from Figures adopted from E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)

Non-Linear Evolution and Non-Linear Evolution and Color Glass Condensate (CGC)Color Glass Condensate (CGC)

Rate eq.*Rate eq.*

Figures adopted from K.Itakura, talk at QM2005.Figures adopted from K.Itakura, talk at QM2005.**More sophisticated equation (BK or JIMWLK) based on QCD is solved.More sophisticated equation (BK or JIMWLK) based on QCD is solved.

small xsmall xhigh energyhigh energy

““Phase Diagram” of hadronsPhase Diagram” of hadrons

0

non

-pe

rtu

rba

tive

regi

on

dilute parton

CGC

geometrical s

calin

g

DGLAP

BFKL•Onset of CGC at RHICOnset of CGC at RHIC

•Some evidences exist.Some evidences exist.•Test of CGC at LHCTest of CGC at LHC

•How to describe How to describe perturbative CGC toperturbative CGC tonon-perturbative QGP?non-perturbative QGP?RHIC

RHIC

LHCLHC

Onset of CGC in d+Au Collisions Onset of CGC in d+Au Collisions at RHICat RHIC

BRAHMS Collaboration, white paperBRAHMS Collaboration, white paper

midrapiditymidrapidity forward rapidityforward rapidity

data

data

theo

ry (C

GC)

theo

ry (C

GC)

D.Kharzeev et al., PRD68,094013(’03).D.Kharzeev et al., PRD68,094013(’03).

y=0,1,2,3

H.Fujii, talk at RCNP workshop(’07)H.Fujii, talk at RCNP workshop(’07)