Space-time Evolution of Space-time Evolution of Bulk QCD Matter at RHICBulk QCD Matter at RHICSpace-time Evolution of Space-time Evolution of Bulk QCD Matter at RHICBulk QCD Matter at RHIC

HQ2006

Chiho NONAKAChiho NONAKANagoya UniversityNagoya University

In collaboration with Steffen A. Bass (Duke University & RIKEN BNL)In collaboration with Steffen A. Bass (Duke University & RIKEN BNL)

ContentsContents•IntroductionIntroduction

–Hydrodynamic models at RHICHydrodynamic models at RHIC–Freezeout process, finite state interactionsFreezeout process, finite state interactions

•3D hydro+UrQMD3D hydro+UrQMD•ResultsResults

–Single particle spectra, elliptic flowSingle particle spectra, elliptic flow•SummarySummary

Chiho NONAKA HQ2006

Hydrodynamic Models at RHICHydrodynamic Models at RHIC Hydrodynamic Models at RHICHydrodynamic Models at RHIC Success of Perfect Hydrodynami

c

Models at RHIC– Single particle spectra

Huovinen, Kolb, Heinz, Hirano, Teaney, Shuryak, Hama, Morita, …….

– Strong elliptic flow Strong coupled (correlated) QGP

at mid rapidityat mid rapidityHuovinen et.al, PLB503

Discrepancy at large : •Insufficient thermalization?•Viscosity effect?•Simple freezeout process?

•freezeoutfreezeout•viscosityviscosity

Hirano and Tsuda, PRC66

However….–Elliptic flow vs.

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Freezeout processFreezeout process in Hydro in HydroFreezeout processFreezeout process in Hydro in Hydro

– Difference between chemical and 　 thermal freezeout

Heinz,NPA

Possible solutions:– Partial chemical equilibrium (PCE) Hirano, Kolb, Rapp– Hydro + Micro Model Bass, Dumitru, Teaney, Shuryak

1. Single freezeout temperature?

• chemical freezeoutchemical freezeout statistical modelstatistical model TTchch ~170 MeV ~170 MeV

hadron ratiohadron ratio

• thermal freezeoutthermal freezeout hydro hydro TTff ~ 110~140 MeV ~ 110~140 MeV

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Final State InteractionsFinal State InteractionsFinal State InteractionsFinal State Interactions

Thermal model T = 177 MeV = 29 MeV

UrQMD

2. In UrQMD final state interactions are included correctly.

Markert @QM2004

3D-Hydro +UrQMD3D-Hydro +UrQMD

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– Hadron phase: viscosity effect– Freezeout process:

• Chemical freezeout & thermal freezeout• Final state interactions

3D-Hydro +UrQMD

Key:

Bass and Dumitru, PRC61,064909(2000)Teaney et al, nucl-th/0110037

• Treatment of freezeout is determined by mean free path.• Brake up thermalization: viscosity effect

3D-Hydro + UrQMD Model3D-Hydro + UrQMD Model3D-Hydro + UrQMD Model3D-Hydro + UrQMD Model

Full 3-d Hydrodynamics

• EoS :1st order phase transition QGP + excluded volume model

Cooper-Fryeformula

UrQMD

t fm/c

final stateinteractions

Monte Carlo

Hadronization

TC TSWTC:critical temperature TSW: Hydro UrQMD

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3-D Hydrodynamic Model 3-D Hydrodynamic Model 3-D Hydrodynamic Model 3-D Hydrodynamic Model Relativistic hydrodynamic equation

– Baryon number conservation

Coordinates

Lagrangian hydrodynamics– Tracing the adiabatic path of each volume element– Effects of phase transition on observables– Computational time– Easy application to LHC

Algorithm– Focusing on the conservation law

Flux of fluid

nucleus nucleus

energy momentum tensor

Lagrangian hydrodynamics

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ParametersParametersParametersParameters Initial Conditions

– Energy density

– Baryon number density

– Parameters

– Flow

Switching temperature

€

ε(x,y,η ) =εmaxW (x,y;b)H(η )

€

nB (x,y,η ) = nBmaxW (x,y;b)H(η )

TSW=150 [MeV]

vT=0vL= Bjorken’s solution);

Different from Pure Hydro !0=0.5 =1.5

εmax=40 GeV/fm3, nBmax=0.15 fm-3

0=0.6 fm/c

hydro Hydro+

UrQMD

0(fm) 0.6 0.6

εmax(GeV/fm3) 55 40

nBmax(fm-3) 0.15 0.15

0, 0.5, 1.5 0.5, 1.5

•longitudinal directionlongitudinal direction •transverse planetransverse plane

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PPTT spectra spectra PPTT spectra spectra PT spectra at central collisions

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PPTT Spectra (Pure Hydro) Spectra (Pure Hydro)PPTT Spectra (Pure Hydro) Spectra (Pure Hydro)

Tf=110 MeVnormalization of K and p:ratio at Tchem

Heinz and Kolb, hep-ph/0204061

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Rapidity DistributionRapidity DistributionRapidity DistributionRapidity Distribution Impact parameter dependence of rapidity distributions

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Centrality DependenceCentrality DependenceCentrality DependenceCentrality Dependence Impact parameter dependence of PT

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PPT T Spectra for Strange ParticlesSpectra for Strange ParticlesPPT T Spectra for Strange ParticlesSpectra for Strange Particles

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Reaction Dynamics Reaction Dynamics Reaction Dynamics Reaction Dynamics At mid rapidity

decaydecay

•Slope becomes steeper

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Final State Interactions Final State Interactions Final State Interactions Final State Interactions

p, : flatter, pion wind: small cross section

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<P<PTT> vs mass> vs mass<P<PTT> vs mass> vs mass At mid rapidity

Hydrodynamic expansionHydrodynamic expansionfinal state interactionfinal state interaction

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vv22 in hadron phase ? in hadron phase ?vv22 in hadron phase ? in hadron phase ? Quark number scaling of v2

⎟⎠

⎞⎜⎝

⎛≈ TTh P

nnP

1)( 22 vv

vv22: early stage : early stage

of expansionof expansion

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Reaction Dynamics in vReaction Dynamics in v2 2 IIReaction Dynamics in vReaction Dynamics in v2 2 II

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Reaction Dynamics in vReaction Dynamics in v22 II IIReaction Dynamics in vReaction Dynamics in v22 II II

•Hydro+decayHydro+decay ~ Hydro@~ Hydro@TTSWSW

•vv22 grows in hadron grows in hadron

phase a bit.phase a bit.•vv22 builds up in QGP builds up in QGP

phase.phase.

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SummarySummarySummarySummary We present the 3-D hydrodynamic +cascade model 3-D Hydrodynamic Model

– Single particle distribution• Centrality dependence

– Elliptic flow– Low Tf : single spectra, elliptic flow, hadron ratios Necessity of improvement of freezeout process in Hydro

3-D Hydro + UrQMD – Single particle distribution

• Centrality dependence – Elliptic flow– Different initial conditions from pure Hydro– Hadron ratios Switching temperature from Hydro to UrQMD– Reaction dynamics in UrQMD

,small cross section, v2:improvement at forward/backward Work in progress

– EoS dependence: ex. lattice QCD– Switching temperature dependence

BackupBackupBackupBackup

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ParametersParametersParametersParameters Initial Conditions

– Energy density

– Baryon number density

– Parameters (pure hydro)

– Flow

Equation of State– 1st order phase transition Bag Model + Exclude volume model

Freezeout Temperature

€

ε(x,y,η ) =εmaxW (x,y;b)H(η )

€

nB (x,y,η ) = nBmaxW (x,y;b)H(η )

EOS(entropy density)

=0

€

B1

4 = 233 [MeV]

Tf=110 [MeV]

vT=0vL= Bjorken’s solution);

Different from hydo + UrQMD !0=0.5 =1.5

εmax=55 GeV/fm3, nBmax=0.15 fm-3

0=0.6 fm/c

•longitudinal directionlongitudinal direction •transverse planetransverse plane

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PPTT Spectra SpectraPPTT Spectra Spectra

Tf=110 MeVnormalization of K and p:ratio at Tchem

Heinz and Kolb, hep-ph/0204061

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Rapidity distributionRapidity distributionRapidity distributionRapidity distribution

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b dependence of Pb dependence of PTT spectra spectrab dependence of Pb dependence of PTT spectra spectra

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VV22 vs P vs PTTVV22 vs P vs PTT

Elliptic Flow

b=4.5 fm b=6.3 fm

•b=4.5 fm: consistent with experimental data•b=6.3 fm: proton overestimate

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vv22 vs vs vv22 vs vs

• Forward/backward rapidity: overestimate• Pure hydro is valid around mid rapidity.

3-15 %3-15 %15-25 %15-25 %

Step2. 3-D Hydro + UrQMDStep2. 3-D Hydro + UrQMDStep2. 3-D Hydro + UrQMDStep2. 3-D Hydro + UrQMD

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vv22 vs P vs PTTvv22 vs P vs PTT

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vv22 vs vs vv22 vs vs

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Relativistic Heavy Ion Collision & Hydrodynamic models– Schematic sketch

initial conditionsinitial conditions•parametrization parametrization •color glass color glass condensate…condensate…

equation of statesequation of states•bag modelbag model•lattice QCD…lattice QCD…

freezeout processfreezeout process•chemical equilibriumchemical equilibrium•partial chemical partial chemical equilibriumequilibrium•cascade model…cascade model…

Hydrodynamic Model at RHICHydrodynamic Model at RHICHydrodynamic Model at RHICHydrodynamic Model at RHIC

t

QGP production hadron phasephase transition

hydrodynamical expansion

freeze-outhadronizationthermalizationcollision

HydroHydro Model Model

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Introduction 1 Introduction 1 Introduction 1 Introduction 1 Success of Ideal Hydrodynamic Models at RHIC

– Strong elliptic flow• strong coupled QGP

Huovinen et.al, PLB503

–Single particle spectra PT spectra up to ~ 2GeV Huovinen, Kolb, Heinz, Hirano, Teaney, Shuryak, Hama, Morita, …….

Nonaka and BassNonaka and Bass

))2cos(2)cos(21( 210 ϕϕϕ

vv ++≈ vd

dN

at mid rapidityat mid rapidity

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Introduction 2 Introduction 2 Introduction 2 Introduction 2 Success of Ideal Hydrodynamic Models at RHIC

Discrepancy at large : •Insufficient thermalization?•Mean free path•Viscosity effect?

However…–Elliptic flow as a function of

Hirano and Tsuda, PRC66

•freezeoutfreezeout•viscosityviscosity

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V2 vs multiplicity V2 vs multiplicity V2 vs multiplicity V2 vs multiplicity

NA49:PRC68,034903(2003)

SPSSPS

RHICRHIC

sQGPsQGP

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Hydrodynamic ModelsHydrodynamic ModelsHydrodynamic ModelsHydrodynamic Models

PT spectraPHENIX:Nucl.Phys. A757 (2005) 184Au + Au GeV

• hadron ratiohadron ratio CECE 　　 　　 PCE PCE RQMDRQMD

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Hydrodynamic ModelsHydrodynamic ModelsHydrodynamic ModelsHydrodynamic Models

Elliptic Flow

PHENIX:Nucl.Phys. A757 (2005) 184Au + Au GeV

CECE 　　 　　 PCE PCE RQMDRQMD

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Hydrodynamic ModelsHydrodynamic ModelsHydrodynamic ModelsHydrodynamic Models

PT spectra Elliptic Flow

PHENIX:Nucl.Phys. A757 (2005) 184Au + Au GeV

Ref. Initial Cond. ε(GeV/fm3)or s(fm-3)

fm/c Latent heat(GeV/fm3)

Hadronic stage Tf (MeV)

[1] 23(ε)(eWN) 0.6 1.15 CE 120[2] 110(s)(0.75sWN+0.25sBC) 0.6 1.15 PCE 100[3] 35(ε)(eBC) 0.6 1.7 PCE 100,120,140

[4] 16.7(ε)(sWN) 1.0 0.8 RQMD ~100[1]Huovinen et.al., PLB(130) [2]Kolb et.al. PRC, [3]Hirano et.al.PRC(130), [4]Teaney et al.

Initial Conditions EoS Freeze-out

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Trajectories on the Phase DiagramTrajectories on the Phase DiagramTrajectories on the Phase DiagramTrajectories on the Phase Diagram Lagrangian hydrodynamics

　　　　

C.N et al., Eur. Phys.J C17,663(2000)

(ix,iy,iz)(ix,iy,iz)

effect of phase transition

xx

yy

transverse planetransverse plane

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( )∑=

Δ+−Δ+∂+Δ∂+=Δ+3

1

),(),()()(),()(n

nnnn

tt

mm ittXittXivtivitvttv

Numerical Calculation Numerical Calculation Numerical Calculation Numerical Calculation Step 1.

Step 2.

Step 3.

titu

ituitXittX

t

mmm Δ+=Δ+

),(),(

),(),(

ATns

Tsn

itTittT BB

ns B ⎭⎬⎫

⎩⎨⎧

∂∂

−∂∂

Δ+=Δ+ ),(),(

1),(),(

,

ATnT

sTs

T

nititt B

B

ns B⎭⎬⎫

⎩⎨⎧

∂∂

−∂∂

Δ+=Δ+ ),(),(

1),(),(

,

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂∂

∂−

∂∂

∂∂

=ΔT

TnTsTn

T

Ts BBns B

),(),(),(),(,

μ

μ

μ

μ

μμ

1),(),(

),(),(−

Δ+Δ+=

ittdittuitditu

A tt

tt

Coordinates move in parallel with baryon number current and entropy density current.

local velocity: )( ttvm Δ+

from hydro eq.

temperature and chemical potential

0},({ = ∂ uTs )

∂ { ( , }n T uB ) = 0

CPU time is almost proportional of # of lattice points.

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Summary 1Summary 1Summary 1Summary 1 Pure hydro with single freezeout temperature

Hadron ratio

Elliptic flow at forward/backward rapidity

Improvement of freezeout processImprovement of freezeout process

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Distribution of # of CollisionsDistribution of # of CollisionsDistribution of # of CollisionsDistribution of # of Collisions

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ff distribution distributionff distribution distribution

==00 ==2.22.2 ==3.23.2

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ff distribution distributionff distribution distribution

b=2.4 b=2.4 fmfm b=4.5 b=4.5 fmfm b=6.3 b=6.3 fmfm

at mid rapidityat mid rapidity

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Distribution of # of CollisionsDistribution of # of CollisionsDistribution of # of CollisionsDistribution of # of Collisions

finite b:finite b:• dN/ndN/ncollcoll becomes small becomes small• steep dropsteep drop

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ff distribution distributionff distribution distribution

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Reaction Dynamics in Reaction Dynamics in f f (M)(M)Reaction Dynamics in Reaction Dynamics in f f (M)(M)

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Reaction Dynamics in Reaction Dynamics in f f (B)(B)Reaction Dynamics in Reaction Dynamics in f f (B)(B)

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xxf f Distribution Distribution xxf f Distribution Distribution

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Reaction Dynamics IReaction Dynamics IReaction Dynamics IReaction Dynamics I

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Reaction Dynamics IIReaction Dynamics IIReaction Dynamics IIReaction Dynamics II

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Reaction Dynamics IVReaction Dynamics IVReaction Dynamics IVReaction Dynamics IV

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xxf f Distribution IIDistribution IIxxf f Distribution IIDistribution II

HBT analysesHBT analyses

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Future taskFuture taskFuture taskFuture taskModel : Initial conditions

– Realistic initial conditions• Early thermalization < 1 fm/c• From color field

Hard sector– Dynamical effect on jets– Jet correlations

Observables: Electromagnetic probe

– NA60 In + In collisions• Hadronic states in medium• Chiral symmetry restoration and deconfinement

HBT puzzle ?– The 3-D hydro + cascade model provides a possible solution?

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Soft + HardSoft + HardSoft + HardSoft + Hard Soft

Hard

• Full 3-d Hydrodynamic Model• QGP formation, EoS

• Micro. transport (PCM)• Hard scattering & jet production• Propagation of jet in medium, energy loss

• First schematic attempt

t fm/c

coupled hydro + PCM calculation

Hirano & NaraPRC66:041901,2002, PRL91:082301,2003

Hadronization

Fragmentation

Improved Cooper-Fryeformula (Reco)

FinalInteractions

• Dynamical effect on jets• Jet correlations

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NA60(QM2005) 1NA60(QM2005) 1NA60(QM2005) 1NA60(QM2005) 1

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NA60(QM2005) 2NA60(QM2005) 2NA60(QM2005) 2NA60(QM2005) 2

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HBT Puzzle HBT Puzzle HBT Puzzle HBT Puzzle

1/ ≈sideout RR

Heinz and Kolb, hep-ph/0204061

Morita, Muroya, Nonaka and Hirano,Phys.Rev.C66:054904,2002

Experimental data:

Expansion time is very short & Flash like particle emission

1/ >sideout RR

1/ ≈sideout RR

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Possible Solution to HBT PuzzlePossible Solution to HBT PuzzlePossible Solution to HBT PuzzlePossible Solution to HBT Puzzle

Super Cooling ? Csernai et al, PLB551(2003)121

Viscosity ? Teaney, nucl-th/0301099

x-t correlation ? Lin @Collective Flow and QGP properties

AMPT(a multi-phase transport model): strong and positive xout-t correlation term Hydro: initial negative xout-t correlation

Fromhydro model

1/ >sideout RR 1/ ≈sideout RRHydro:Hydro: Data:Data:

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Hydro vs. Hydro + UrQMDHydro vs. Hydro + UrQMDHydro vs. Hydro + UrQMDHydro vs. Hydro + UrQMD Hadron Interactions

K+

p

<PT>

y• decrease• K,p increase• proton earn large PT

<PT>

K++

p

BRAHMS 0-5 %

y

<PT>

TSW (MeV)

p

K+

• <PT> increases as TSW

increases

Hydro + UrQMD • Large <PT> Low v2

(hadron interactions)