重イオン衝突物理でのジェットの理解へむけて
Nagoya University

Chiho Nonaka

July 10, 2009@第６回Heavy Ion Pub

Jet Quenching 1990– Jet Quenching in lepton nucleus sca@ering, Gyulassy and Plumer– Jets in heavy ion collisions, X‐N. Wang and Gyulassy

 RHIC– QM2001– Key issue– X‐N.Wang• Event generators –Quo Vadis?
• HIJING
Heavy Ion Pub @Osaka University
PerturbaRve QCD and Heavy Ion Collisions

RelaRvisRc Heavy Ion Collisions
 SchemaRc Sketcht

thermalizaRon hydrodynamicalexpansion

freeze‐outJet quenchingmechamism

Dynamics ofHot QCD ma@erJeon
Chiho Nonaka

hadronizaRon

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ

Chiho Nonaka

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ• hard sca@eringin medium• jet quenching

Chiho Nonaka

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ

Jeon
Chiho Nonaka

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ

Chiho Nonaka

Chujo@Nagoya

Chujo@Nagoya

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ

Chiho Nonaka

Phenomena
 Nuclear modiﬁcaRon factors
 Jets structure– Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φ ：Ridge

3<pt,trigger<4 GeV
Au+Au 0-10%pt,assoc.>2 GeVpreliminarySTAR

Chiho Nonaka

Phenomena Nuclear modiﬁcaRon factors  Jets structure – Azimuthal angle– 3 parRcle correlaRons– Δ η and Δ φRenk, Rupper, Nonaka, Bass, PRC75,031902(R),2007
Majumder, Nonaka, Bass, PRC76,041902(R),2007
Qin,Rupper,Turbide,Gale,Nonaka,Bass,PRC76,064907(2007)
Bass,Gale,Majumder,Nonaka,Qin,Renk,Ruppert, PRC79,024901(2009)

Chiho Nonaka

RelaRvisRc Heavy Ion Collisions
 SchemaRc Sketcht

thermalizaRon hydrodynamical
expansion

freeze‐outJet quenchingmechamism

Dynamics ofHot QCD ma@erJeon
Chiho NonakahadronizaRon

3D Hydro + UrQMD
 RelaRvisRc Heavy Ion Collisiont– SchemaRc sketch

thermalizaRon hydrodynamical hadronizaRon
freeze‐outexpansion
 3D Hydro + UrQMD
Success of hydrodynamic models at RHIC:
UrQMDFull 3‐d Hydrodynamics‐‐PT spectra, rapidity distribuRon, ellipRc ﬂow
Hadroniza;onLimitaRon of Hydro
Cooper‐FryeEx. EllipRc ﬂow at forward/backward rapidity,
HBTﬁnal state• EoS :1st order phase transiRonformulaExtension of HydrointeracRons
QGP + excluded volume model
Monte Carlo‐‐Viscosity eﬀect of hadron phase‐‐Final state interacRons
TTt fm/cC

Chiho NonakaSW

TC:criRcal temperature > TSW: Hydro  UrQMD

3‐D Hydrodynamic Model RelaRvisRc hydrodynamic equaRon– Baryon number conservaRon

energy momentum tensor

 Coordinates
 Lagrangian hydrodynamics– Tracing the adiabaRc path ofeach volume element– Eﬀects of phase transiRon on observables– ComputaRonal Rme– Easy applicaRon to LHC
 Algorithm– Base on the conservaRon law

Chiho Nonakanucleusnucleus

Lagrangian hydrodynamics
Flux ofﬂuidParameters
 IniRal CondiRons– Energy density
ε(x, y,η) =ε maxW (x, y;b)H(η)– Baryon number density
n B (x, y,η) = n BmaxW (x, y;b)H(η)€€– Parameters

τ0=0.6 fm/c
εmax=55 GeV/fm3, nBmax=0.15 fm‐3
η0=0.5 ση=1.5– Flow

vL=η (Bjorken’s soluRon); vT=0
 EquaRon of State
1st order phase transiRon, Tc=160 MeV
 Switching temperature
TSW=150 [MeV]

Chiho Nonaka

3D Ideal Hydrodynamic ModelRHIC•Chemical equilibriumfreezeout•Final state interacRonsare neglected.

Chiho Nonaka

Parameters
 IniRal CondiRons– Energy density
ε(x, y,η) =ε maxW (x, y;b)H(η)– Baryon number densityn B (x, y,η) = n BmaxW (x, y;b)H(η)€€– Parameters

τ0=0.6 fm/c
εmax=40 GeV/fm3, nBmax=0.15 fm‐3
η0=0.5 ση=1.5– FlowvL=η (Bjorken’s soluRon); vT=0
 EquaRon of State
1st order phase transiRon, Tc=160 MeV
 Switching temperature
TSW=150 [MeV]

Chiho NonakahydroHydro+UrQMD

τ0(fm)

0.6

0.6εmax(GeV/fm3)

5540

nBmax(fm-3)

0.15

0.15

η0,ση0.5, 1.50.5, 1.5

3D Ideal Hydro+UrQMD

Chiho Nonaka

RelaRvisRc Heavy Ion Collisions
 SchemaRc Sketcht

thermalizaRon hydrodynamicalexpansion

freeze‐outJet quenchingmechamism

Dynamics ofHot QCD ma@erJeon
Chiho Nonaka

hadronizaRon

Energy LossQGP?

Jeon@Nagoya

ApplicaRon of Hydro InteracRons between jets and medium– Medium  Hydrodynamic Model SystemaRc Comparison of Jet Energy‐Loss Scheme– BDMPS/ASW: path integral approach to the opacity expansion– Higher Twist (HT)sou sector : Hydro– Arnold‐Moor‐Yaﬀe (AMY) : ﬁnite temperature ﬁeld theoryapproach– GLV: reacRon operator approach to the opacity expansion
Hirano and Nara,PRC69,034908(2004)

Chiho Nonaka

CalculaRon Scheme

Jeon@QM2009

Hadron ProducRond 2σ h1
dσ ab →cX D˜ c (z)AB= ∫ dx a ∫ dx b Ga ( x a )Gb (x b )2dyd pT πdtˆz€same iniRal state
G（x）：parton distribuRon funcRon: CTEQ5Vacuum fragmentaRon funcRons: KKP, AKP
diﬀerent in each energy loss scheme : ASW, HT, AMY
Dc(z): medium modiﬁed fragmentaRon funcRon

Chiho Nonaka

Energy Loss in Medium
 InformaRon of medium: thermodynamic values, velocity
 Hydrodynamic Models
 Transport coeﬃcients in each energy loss scheme– BDMPS/ASW
34qˆ (ξ ) = K ⋅ 2 ⋅ ε (ξ )ξ: trajectory of jets

– Higher Twist€γ ( r , τ )T 3 ( r , τ )qˆ ( r , τ ) = qˆ 0R(r,τ)+c(1−R(r, τ ))][ QGPHGQGPT03q０ at iniRal Rme( 0.6 fm/c), cHG hadron phase€– AMY: αs
CA g 2T ( r , τ ) mD2 q⊥max
qˆ ( r , τ ) =ln2πmD

Chiho Nonaka

RQGP: raRo of QGP phaseNuclear ModiﬁcaRon Factors•PredicRons:
PT dependence,centrality dependence•Very small diﬀerence
More sophisRcatedobservables are needed.

Parameters: ﬁxed in central collisions
ASWHT

K=3.5

q0=1.9 GeV2/fm αs=0.33

Chiho Nonaka

AMYScaling with the Medium
Possible choices of scalingqˆ ~ T 3€qˆ ~ ε 3 / 4 qˆ ~ sT ε, s: InformaRon of medium
Hydrodynamic model &EquaRon of states•Bjorken expansion
with Ideal QGP‐IdenRcal results•Hydro with realisRc equaRon ofstate‐diﬀerent Rme dependence
realisRc dynamical model,
proper medium scaling•Choice of cHG=0.2 mimics scaling withentropy density
PRC79,024901(2009)

Chiho Nonaka

QuanRtaRve Comparisonq̂(ξ) = q̂0 · Γ(ξ)Γ=ξ: trajectory of jets in medium!

"3 ! "3/4 ! "T!
s,,T0!0s0q̂(ξ) = q̂0 :iniRal· Γ(ξ)maximum value‐BDMPS/ASW
34qˆ (ξ ) = K ⋅ 2 ⋅ ε (ξ )‐Higher Twist€γ ( r , τ )T 3 ( r , τ )qˆ ( r , τ ) = qˆ 0R(r,τ)+c(1−R(r, τ ))][QGPHG
QGP
T03

q０ at iniRal Rme( 0.6 fm/c), cHG hadron phase

€

‐AMY
CA g 2T ( r , τ ) mD2 q⊥maxqˆ ( r , τ ) =ln2πmD

RQGP: raRo of QGP phaseNuclear ModiﬁcaRon Factors•PredicRons:
PT dependence,centrality dependence•Very small diﬀerence
More sophisRcatedobservables are needed.

Parameters: ﬁxed in central collisions
ASWHT

K=3.5

q0=1.9 GeV2/fm αs=0.33

Chiho Nonaka

AMYScaling with the Medium
Possible choices of scalingqˆ ~ T 3€qˆ ~ ε 3 / 4 qˆ ~ sT ε, s: InformaRon of medium
Hydrodynamic model &EquaRon of states•Bjorken expansion
with Ideal QGP‐IdenRcal results•Hydro with realisRc equaRon ofstate‐diﬀerent Rme dependence
realisRc dynamical model,proper medium scaling•Choice of cHG=0.2 mimics scaling withentropy density
PRC79,024901(2009)

Chiho NonakaAzimuthal angle dependence

20‐30 % centrality

Chiho Nonaka

RAA for In/Out of planeout of planein plane

Temperature proﬁle in 3D hydroT (GeV)
20‐30 % centrality•AMY & HT: same azimuthal spread,but diﬀerence in magnitude

Chiho NonakaAzimuthal Spread
b=7.5 fmout of planein plane

b=7.5 fm

•ASW shows a signiﬁcantly stronger
azimuthal dependence of RAA than
AMY & HT

Chiho Nonaka

Nuclear ModiﬁcaRon Factor
HTreacRon plane•Three approaches agree with each otherSame suppression factorx

RAA is anRcorrelated with <ρL>

Chiho Nonaka

Survival probability P(x,y)

Summary Sou sector: 3D Hydro + UrQMD Model– Success at RHIC: PT spectra, rapidity distribuRon, ellipRc ﬂow

 Jets in medium– Jet quenching mechanisms: BDMPS /ASW, higher twist and AMY– Nuclear modiﬁcaRon factors• Transport coeﬃcients

Chiho Nonaka

TECHQM
 h@ps://wiki.bnl.gov/TECHQM/index.php/Main_Page

Working Groups: partonic energy loss
bulk evoluRon

Event Generators

Joen@QM2009

Mach Cone InteracRons between medium and jets

B.Betz et al. 0812.4401

Neufeld and Mueller 0902.2950

AdS/CFTChiho Nonaka

Possible SoluRon to Ridge
 Brazil group
IniRal condiRons
Nexus

Hydro
SPheRIO

HadonizaRon
Cooper‐FryeAveraged iniRal condiRons

Flux tube+ﬂuctuaRons

Challenge
Theory: Towards quanRtaRve calculaRons– Dynamical model– Jet quenching mechanism

Phenomena:
 Azimuthal angle distribuRon– ReacRon plane dependence?
– EllipRc ﬂow?

 Collisions energy dependence?

Esumi‐san’s talk!

Toward More RealisRc Dynamical Model Based on hydrodynamic models: MulR Module ModelingthermalizaRon hydrodynamicalexpansion
IniRal CondiRons• Event by event ﬂuctuaRon
ellipRc ﬂow vs Npart
Hirano and Nara
Ridge
Brazil group
Chiho Nonaka

hadronizaRon

freeze‐out

Hydrodynamics
Freezeout process•Viscosity•HadronizaRon –RecombinaRon
shear, bulk
•Final state interacRons•EquaRon of state
QCD criRcal point?