生成粒子の集団運動流（フロー）からみる高エネルギー原子核衝突
名古屋大学

野中 千穂

２００８年６月１６日＠第３回Heavy Ion Pub、名古屋

Introduc*on

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How to ﬁnd the QGP

Relativistic Heavy Ion Collision
Schematic sketchtcollision thermaliza:on hydrodynamic hadroniza:on freeze‐outexpansion

Difficulties•QGP signature ?
•Complicated process
hadron spectra
initial state
two particle correlationshydrodynamic expansion
hadronization? flow (radial, elliptic, direct)
fluctuation (charge, multiplicity)
freeze-out
electromagnetic probes…..
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Collec*ve Flowcollision axis

central collision

radialnon‐central collisiondN i  dN i  = N i0 (1+ 2v1 cos(φ − φ 0 ) + 2v 2 cos2(φ − φ 0 ) + …)
2dydφ  dydφd PT yφ€xdirected

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ellip:cHeavy Ion Pub

QGP on the EarthsNN

1987 BNL-AGS

Si51987 CERN-SPS S

20

1992 BNL-AGS

Au

4

1994 CERN-SPS Pb

17€2000 BNL-RHIC

Au 200+Au

2010 CERN-LHC Pb 5600+Pb

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RHIC Run History
run yearspecies

12000

Au+Au1302

2001/02

Au+Au200p+p200

d+Au

200

p+p200

Au+Au

200

Au+Au

62

p+p200Cu+Cu

200,62,22

p+p200345

2002/03
2003/04

2004/05

GeV

62006

p+p62

7

2006/07

Au+Au

200

8

2007/08

d+Au

200

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h=p://www.agsrhichome.bnl.gov/RHIC/Runs/

heavy ion collision• energy frontier• p+p : baseline• d+Au: initial vs. final• Cu+Cu: system size
• Energy dependence

PHENIX, STAR, PHOBOS,
BRAHMS

Heavy Ion Pub

Phenomenological Analyses
Experiments

QCD

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Phenomenological Models (I)collisionthermaliza:onhydrodynamic
expansiont

hadroniza:onfreeze‐out

Color Glass Condensate
Hydrodynamic Model
Cascade Model
Parton basedynamicalstatic
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Hadron base
Thermal ・Statistical Model
Heavy Ion Pub

Phenomenological Models (II)low PT

intermediate PThigh PT

2 < PT < 4~6 GeV

4~6 <PTGeV<2 GeV

Hydrodynamic ModelPT

Thermal・Statistical Model•Particle spectra•Hadron ratios•Collective flow?

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Recombination Model•Particle spectra•Hadron ratios•Collective flow
•Nuclear modification
factors

Perturbative QCD•Nuclear modification
factors•Jets in mediumHeavy Ion Pub

Collec*ve Flow at RHIC
Radial flow
Elliptic flow
Higher harmonics, v4, v6
Directed flow

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Heavy Ion Pub

Collec*ve Flow at RHIC
Radial flow
Elliptic flow
Higher harmonics, v4, v6
Directed flow

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Data
PT spectra, mT spectra
Models• Hydro inspired model
ex. blast wave model• Hydrodynamic model• Recombination model
Physics• Kinetic freezeout
temperature• Hadronization
mechanism
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Freezeout Temperature

Heinz,NPA

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Sta*s*cal‐Thermal Model−1

 −|S | E i − µ i Qi d pprim
N i = Vgi ∫dmi γ s i e T ± 1 BW (mi )3(2π )
ratios€"(1520)/"K */K &(1232)/p"/ !"/ !#-/!#+/!$+$/!$/ $%/K!-/!+
K -/K +p/p
K -/!p/!-3N i = N iprim + ∑ Br i→jN prim
jj

1

€10-1

FittedFitted-2

10!,K,p,",#,$,%!,K,p

10-3

STAR preliminary
0

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mT Distribu*ons

PHENI:X:PRC69(2004)03909

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Tchem ≠ Tkin<!>Radial transverse flow velocity
Chemical freezeout temperature

0.8
0.7
0.6T (GeV)

0.5

0.18

0.4

0.16

0.3

0.14

0.2

0.120.1

STAR Prelinimary

0.1

0100200300

400500

600

700

0.08

800
Nch

0.06
0.04

STAR Prelinimary

Kinetic freezeout temperature

0.02
0C.NONAKA

100200

300

400

500

600

700

800
Nch

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Mul* Strange Par*cles
π,K,p,Λ
Tchem=160~170 MeV
Tkin~100 MeV

STAR:PRL92(2004)182301

Multi strange particles
Tkin~170 MeV
Small cross section
Information just after
phase transition

Parameterization by a simple model
Detailed analyses: ex. Relativistic hydrodynamic model
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Collec*ve Flow at RHIC
Radial flow
Elliptic flow
Higher harmonics, v4, v6
Directed flow

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Data• elliptic flow
vs. PT, rapidity, multiplicity
system size, collisionenergy• fluctuations
Models• Hydrodynamic model• Recombination model

Heavy Ion Pub

Hydrodynamic Models
Assumptions (for multiple particle production)
Local thermalization
Mean free path ~ 0nucleusnucleusLandau(1956)

Bjorken(1986)

stopping

passing throughplateau

Relativistic
Hydrodynamic Equation
Equation of Stateenergy momentum tensor

Advantage: Phase transition
QGP phase
Hadron phase
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Success of Hydro at RHIC
Minimum bias

Huovinen et al.

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V2 vs mul*plicity

NA49:PRC68,034903(2003)
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ReCo+Fragmenta*on Model
ReCo vs. Fragmentation• phase space density of partons• shape of parton spectrum

gqq

ReCofragmen:ng parton:ph = z p, z<1
recombining partons:
p1+p2=phFrag.
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Quark Number Scaling
Elliptic flow v h ( P ) ≈ nv  1 P 2C.NONAKAT2nT

Heavy Ion Pub

New Discoveries at RHIC, April 2005

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Heavy Ion Pub

Collec*ve Flow at RHIC
Radial flow
Elliptic flow
Higher harmonics, v4, v6
Directed flow

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Data• elliptic flow
vs. PT, rapidity, multiplicity
system size, collision energy• fluctuations
Models• Hydrodynamic model• Recombination model
Physics• Early time thermalization• Equation of states• Initial conditions• Viscosity effect• Resonances, hadronstructure
Heavy Ion Pub

Hydrodynamic Model
Bulk QCD dynamics

collision

thermaliza:onhydrodynamical hadroniza:on
expansiontfreeze‐out

phase transi:on
QGP phase
Hadron phase

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Heavy Ion Pub

Success of Hydro at RHIC
✓Minimum bias

Initial time
τ=0.6 fm
Early time thermalization

Huovinen et al.

✓mid rapidity

2-D Hydrodynamics
Initial conditions
Glauber type:
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Centrality Dependence

peripheral

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centralHeavy Ion Pub

Rapidity Dependence

Hirano and Tsuda, PRC66

Forward/backward rapidity

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Freezeout & Final State Interac*ons
Bulk QCD dynamics

collision

thermaliza:ont

hydrodynamical hadroniza:on
expansion

freeze‐out

phase transi:on
QGP phase
Hadron phase
HydroHydrodynamics+Cascade Model

Bass,Dumitru, Shuryak, Teaney, Hirano, Nara, Nonaka….
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Rapidity Dependence

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Centrality Dependence

Viscosity Effect even in QGP phase?
Viscous relativistic hydrodynamic models
Incomplete equilibration: Bhalerao et al. PLB627(2005)
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Fluctua*ons

yAu+Au 200 AGeV PHOBOSε=€C.NONAKA

xy2 − x2
y2 + x2

Elliptic flowpressure gradient

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Perfect Fluid at RHIC?
Bulk QCD dynamics

collision

thermaliza:onhydrodynamical hadroniza:on
expansiontfreeze‐out

phase transi:on
QGP phase
Hadron phase

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Quark Number Scalingv 2 ( PT ) = cos 2Φ =Mesons

22d
Φ
cos
2
ΦdN/
dPT
∫
22d
Φ
dN/
dPT
∫

• v2 baryon saturates at higher PT• at high PT: fragmenta:onv2 baryon ~ v2 meson• mass eﬀect ?
Hydrodynamical modelmφ ≈ mΛv 2φ ≈ v 2Λ• # of cons:tuent quarks ?
Baryons
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PLB587,73(2004)

Heavy Ion Pub

Quark Number Scaling
PHENIXPRL99(2007)052301

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v2 for Resonance Par*cles•QGP resonances:hadronizing QGP, no rescattering
K 0*

d , s quarks

n=2 scaling

K 0*

ds

•HG resonances:hadron final stage, h-h rescattering
K 0*

K + + π − → K 0*

n=4 scaling1 v 2h ( PT ) ≈ nv 2  PT n 

Key: v2 is additive for composite particles

Totalfullv2 = r ( PT ) v2QGP + (1 − rr((PPTT )))v2HGr ( PT ) is determined by experiments andK+

π − r ( PT ) : 0.7

Final Interactions
freeze-out processr ( PT ) : 0.7

related to width of particles and crosssection in the hadronic medium.
HeavyIon Pub
Hadron Structure : ExoticParticles
C.NONAKAn = 3± 2€
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Collec*ve Flow at RHIC
Radial flow
Data
Elliptic flow
• v4 vs. PT, centrality
Higher harmonics, v4, v6 • Models
Directed flow
• Hydrodynamic model• Recombination model
Physics• Equilibrium• Quark number scaling

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V4 as a func*on of PT

STAR:PRC75(2007)54906
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Equilibra*on, Recombina*on
Initial conditions
Kolb, PRC68(2003) 031902
Equilibration(deviation from ideal hydro)
Borghini, Ollitrault:PLB 642(2006)227> 0.5
Recombination
Texas group
Phys. Rev. C 69, 031901 (2004)
STAR:PRC75(2007)54906

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Heavy Ion Pub

Collec*ve Flow at RHIC
Radial flow
Elliptic flow
Higher harmonics, v4, v6
Directed flow

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Data• Directed flow
vs. rapidity, collisionenergyModels• Transport model• Hydrodynamic model
Physics• Stopping• Matter compressibility
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Directed Flowcharged hadrons
RHIC
10~70% centrality
Midrapidity
v1~0

STAR:PRL92(2004)062301,PRC72(2005)014904
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Forward/Backward η?
charged hadrons
Midrapidity
v1~0

PHOBOS:PRL97(206)01231

STARRHIC
10~70% centrality

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Background in Other Physical observables
HBT
Jet structure

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Summary
Success of(ideal) hydrodynamic model and recombination model
Strongly coupled (interacting) QGP

Perfect fluid at RHIC?
Thermalization, viscosity….
Models:Relativistic hydrodynamic model• Ini:al condi:ons, equa:on of states, freezeout process
Recombination model• Realis:c parton distribu:onC.NONAKA

Heavy Ion Pub

LHC
low PT

intermediate PThigh PT

RHIC<2 GeV

2 < PT < 4~6 GeV

4~6 <PTGeV

LHC< 4~5 GeV

5 < PT < 8~10 GeV

8~10 < PTPT

Hydrodynamic Model
Thermal・Statistical Model
Recombination Model
Perturbative QCD
Detailed analyses by hydrodynamic models and recombination models?

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RHIC

LHC

Heavy Ion Pub

Back upC.NONAKA

Heavy Ion PubQuark Recombina*on ModelMesons

1d 3N MµE 3 ∝ ∫ p dΣ µ ∫ dxw(r;xpT )w (r;(1− x) pT ) φ M (x)d pΣf02Baryons€

11−xd 3N Bµ
E 3 ∝ ∫ p dΣ µ ∫ dx ∫ dx'w(r;xpT )w(r;x' pT )w (r;(1− x − x') pT ) φ B (x, x')d p Σf002

φM,φB:light‐cone wave func:on€Equal momentum fraction(x=1/2,x=x’=1/3)
d 3N M
d 3N B2E 3 ≅ CM w ( pT /2), E 3 ≅ CB w 3 ( pT /3)
d pd pCM,CB:coalescence probabili:es€

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Ellip*c FlowHadrons <- Quarks
v2,q:Ellip:c ﬂow of quarks

w ∝1+ 2v 2,q cos2φ

Mesons2d NM∝[1+ 2v 2,q cos2φ ]2 ≅ 1+ 4 2,q cos2φ
dφdpT pT€v 2,M ( pT ) ≅ 2v 2,q ( pT /2),v 2,B ( pT ) ≅ 3v 2,q ( pT /3)

Quark number scaling€€€
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3‐D Hydrodynamic Model
Relativistic hydrodynamic equationenergy momentum tensor
Baryon number conservation
Coordinates
Lagrangian hydrodynamics
Tracing the adiabatic path ofeach volume element
Effects of phase transition on observables nucleus
nucleus
Computational time
Lagrangian hydrodynamics
Easy application to LHC
Algorithm
Focusing on the conservation law
Flux ofﬂuid

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Heavy Ion PubTrajectories on the phase diagram
Lagrangian hydrodynamics
temperature and chemical
poten:al of volume elementof ﬂuid

Eﬀect ofphase transi:on

C.N et al., Eur. Phys.J C17,663(2000)
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PT Distribu*ons• Low PT<2 GeV:thermal
1 dN≈ exp(−PT /T)
PT dPT€• High PT>5~6 GeV: pQCD
1 dN
≈ PT−nPT dPT€

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Hadron ra*os

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<PT> vs mass

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Tfo and βTSTARDiﬀerent Tfo and βT for Strange baryons ?
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C.NONAKA

Heavy Ion PubTransverse ﬂow

Decay の取り扱いに依存
C.NONAKAC.NONAKAPHENIX
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Baryon Puzzle at RHIC 1
1. Large p/π ratio at high PT(PHENIX:nucl‐ex/0307022)
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Baryon Puzzle at RHIC
1. Large p/π ratio at high PTqqg1dNdz E dN aE 3h =∫ 2Dα →h ( z )d P 0 z z d 3 (P / z )Da→h (z ) : fragmenta:on func:ons(PHENIX:nucl‐ex/0307022)• p/π ra:o ~ 1 (PT>2 GeV)
in central collisions

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Baryon Puzzle at RHIC
2. Difference in baryon and meson jet-suppression
RCP

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Baryon Puzzle at RHIC
2. Difference in baryon and meson jet-suppression• Parton energy loss at high PT• hard sca=eringin medium• jet quenching• Suppression in RCPbaryon occurs athigher PT than RCPmeson

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Baryon Puzzle at RHIC
3.Difference in baryon and meson elliptic flow
STAR Preliminary (Au+Au; 200 GeV; |y|<1.0)

0.3

h +h2!+!

-Hydro calculations
"Kp!

0.2

Anisotropy Parameter v 2+0KS

0.1

002

4

6

Transverse Momentum p T (GeV/c)(STAR : PRL91 (2004) 052302）
00.3

KS

C.NONAKAHydro calculations"KdN≈ v0 (1 + 2v1 cos(ϕ ) + 2v 2 cos(2ϕ ))dϕ!+!
Heavy Ion Pub

Baryon Puzzle at RHIC
3.Difference in baryon and meson elliptic flow
STAR Preliminary (Au+Au; 200 GeV; |y|<1.0)

0.3

h +h2!+!

-v 2 ( PT ) = cos 2Φ =Hydro calculations
"Kp!

0.2

Anisotropy Parameter v 2+0KS

22d
Φ
cos2
Φd
N/dPT
∫
22dΦ
dN/dPT
∫

0.1

0024

6

Transverse Momentum p T (GeV/c)• Satura:onin v2baryon occurs
0K S P than v !meson+ !.
athigherT2
0.3

Hydro calculations"K
0.2
p
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0.1

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PHENIXPRL99(2007)052301

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PHENIXPRL98(2007)162301

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Eﬀect of Phase Transi*on

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Rischke ‘95

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