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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
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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
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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 %
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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)