重イオン衝突実験で探る
QCD相図
名古屋大学

野中千穂

12月２６日＠九大若手研究会「量子力学の相構造研究の現状と展望」

The QCD Phase Diagram
高温

高密度

C.Nonaka

Phenomenology
experimentt

QCDtphenomenology•hydrodynamic models•event generators
C.Nonaka

Heavy Ion Collisions
Quark Gluon Plasmayearenergy1987

BNL-AGS

Si5

1987

CERN-SPS

Si

20

1992

BNL-AGS

Au

4

1994

CERN-SPS

Pb

17

2000

BNL-RHIC Au+Au

200

2009? CERN-LHC Pb+Pb

5600

C.NonakaQCD Phase Diagram

2000

1987
1987

C.NonakaRelativistic Heavy Ion Collider
Energy Frontier
PHOBOSSTAR

BRAHMSPHENIXS

C.Nonaka

New Discoveries at RHIC
A Case for the Strongly Interacting Quark-Gluon Plasma
RBRC Workshop 14-15 May, 2004
Lee, Ludlam, Gyulassy, McLerran, Shuryak, Mueller, Wang, Stocker, Blaizot, Gelis, Samios

Nuclear Physics A750(2005)

Abstract from T.D.Lee
At RHIC, recent experiments over the last two years
reveal a new state of nuclear matter, hitherto
Unknown to us. While the term “quark-gluonplasma (QGP)“ has been used in the past, thephysical picture was often modeled after the weaklyinteracting electron plasma, which is very different
from what has been discovered recently. At RHIC,
this new state of nuclear matter is found to interact
very strongly. Since it is composed of quarks andgluons, we may call this new state of nuclear mattersQGP, the strongly interacting quark-gluon plasma. !

C.Nonaka

sQGP
PHENIX, STAR, PHOBOS, BRAHMS

Key•relativistic hydrodynamic models•jet quenching•recombination models•color glass condensate

C.Nonaka

RHIC Physics
Collision processhydrodynamic hadronization
collisions thermalization
expansion

freezeout

Transverse momentum
low PT< 2 GeVhydrodynamicmodelintermediate PThigh PT

2 < PT < 4~6 GeV

4~6 GeV <recombination
modelPT

perturbative
QCD

C.NonakaSuccess of Hydro
Strong elliptic ﬂow at RHIC
ReactionplanePHENXzyx

C.Nonaka

Hydro at SPS
experiment

NA49:Pb+Pb

Minimum bias!

hydro model

17 GeV/A!

Kolb et al. PRC62(2000)
EoS: 1st order phase transition(2+1)-d hydroC.Nonaka

Success of Hydro
Strong elliptic ﬂow at RHIC
ReactionplanePHENXzyx

C.NonakaRelativistic Hydrodynamics
Relativistic hydro eq.

•equation of state∂ Tµν = 0energy momentum tensorµ νµνTµν = (! + p)u u − pg

QCD phase diagramµLocal thermodynamic equilibrium>>microscopic reaction rate
~ cross section x local particle density
macroscopic expansion rate
Collectivity
C.NonakaSuccess of Hydro
Collectivity•mass dependence of v

2PHENX

bulk collectivity•early thermalization
initial condition of hydro.
τ0 ∼ 0.6 fm

C.NonakaSuccess of Hydro
Collectivity

Caveat:PHENX•minimum bias
•mid rapidity•1st order phasetransition•chemical equilibrium•sudden freezeout

C.Nonaka

Recent Progress
Hydrodynamic modelhydrodynamic hadronization
collisions thermalization
expansion•!Color GlassCondensate•!Flux Tube•!Initial fluctuation!

•!Lattice QCD

freezeout!

viscous hydrodynamics

C.NonakaJet Quenching
Interactions between jets and medium
ex. nuclear modiﬁcation factors

soft sector:hydrodynamics

C.NonakaJet Energy Loss Scheme
ASW (Armesto, Salgado,Wiedemann)
Medium of heavy staUc scaVering centers w/Yukasa‐like potenUals
Parton picks up transverse kicks ~µ2
path integral over mulUple scaVerings in the medium

HT (higher Twist)
Few medium assumpUon: short color correlaUon lengthCalculates modiﬁcaUon of n‐hadron fragmentaUon funcUon due to mulUple scaVering in medium
ScaVering encoded as HT gluon‐gluon ﬁeld strength

AMY (Arnold, Moore Yaﬀe (AMY)
Thermalized partonic medium in HTL approximaUon
Hard parton comes on‐shell, receives hits of µ~gT
ResummaUon over mulUple scaVerings and absorpUonGLV
Renk, 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,arXiv:0808.0908(nucl‐th)C.Nonaka

Application of Hydro
Systematic comparison of jet energy loss scheme

soft sector:hydroC.Nonaka

RAA for In/Out of Plane!"#$!%$&'()*!
+)$&'()*!

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Recombination Model
Baryon puzzle

C.Nonaka

Nuclear Modiﬁcation factor

parton energy loss
in medium

no diﬀerence between
baryon and meson

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Baryon Puzzle
PHENIX

nucl-ex/0307022
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Baryon Puzzle

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Recombination Model
Recombination + Fragmentation
ReCofragmenting parton:ph = z p, z<1

recombining partons:
p1+p2=phFrag.

R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003)
R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 044902 (2003)
C. Nonaka, R.J. Fries & S.A. Bass, Phys. Lett. B583 73-78 (2004)
C. Nonaka, B. Mueller, M. Asakawa, S.A. Bass & R.J. Fries, PRC 69 031902 (2004)

C.Nonaka

Quark Number Scaling
Elliptic ﬂow of quarks
w ∝ 1 + 2v2,q (pT ) cos 2φReCofragmenting parton:ph = z p, z<1

recombining partons:
p1+p2=phElliptic ﬂow of hadrons

Frag.

#$2!
"%p &d NMPTT∝ 1 + 2v2,qcos 2φ ∼ 1 + 2 × 2v2,qcos 2φdφdPT PT
222Quark number scaling""!
!
PTPTv2,M (PT ) ∼ 2v2,qv2,B (PT ) ∼ 3v2,q2
3
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Quark Number Scaling
Meson
v2,M (PT ) ∼ 2v2,qBaryonv2,B (PT ) ∼ 3v2,q!
!

PT2"

PT3"

C.NonakaStrong correlated(interacting) matteris created at RHIC!

QCD Phase Diagram

LHC

C.NonakaLarge Hadron Collider
CMSLHC-bALICEATLAS

C.NonakaQCD Phase Diagram

LHC

energy survey

C.Nonaka

QCP Search
Can we discover
the QCD critical point at RHIC?
BNL, March 9-10, 2006

ScienceC.Nonaka

QCP Searchttenergy scantfocusing.

MM.
Stephanov,andE.Shuryak,
E.Shuryak,
Stephanov, K.Rajagopal,
K. Rajagopal, andPRL81 (1998) 4816
PRL81(1998)4816

C.Nonaka

Where is the QCP?
Eﬀective models, Lattice QCD

Stephanov, hep-lat/0701002

Stephanov,hep-lat/0701002

experiments and phenomenological analyses
C.Nonaka

Toward Quantitative Analyses
Realistic dynamical model
3D Hydro+UrQMD Model
Equation of state with the QCD critical point
focusing eﬀect near the QCD critical point inisentropic trajectories on the T − µB planeEmission time dependencehigh PT particles emit at earlier time

Asakawa, Bass, Mueller, Nonaka
PRL101:122302(2008), Phys.Rev.C71:044904(2005)
PRC75:014902(2007)

C.Nonaka

EOS with QCD Critical Point
Singular part near QCP + non singular partnon-singular part: QGP phase and hadron phasesingular part:3d Ising Model!
r=T ! TCTCh : extermal magnetic field

Same Universality Class(T, µB )( r , h)mapping (r, h) → (T, µB )matching with QGP and!
hadronic entropy density
thermodynamic quantities!, p, nB

QCD
T , µBQGPT!

r h
Hadronicµ!"C.Nonaka

Focusing Eﬀect
Isentropic trajectories in the QCD diagramnB /s = const. in ideal hydrodynamic expansion
with QCP

without QCP(Bag Model)

focusednot focused
C.Nonaka

Emission Time Dependence
UrQMD (hadron base event generator)(µB , T ) = (406, 145)

emission time(µB , T ) = (4anti-p/p ratio

C.NonakaDemonstration•Location of QCP(µB , T ) = (550, 159)

QCPCF

•Critical Region•Chemical freezeout point(µB , T ) = (406, 145)

C.NonakaCritical Region
tanh[ Sc (T, µB )]

QCP

0.8

CF

QGP phase!

CFT

-0.8

hadron phaseµB

11
Sreal (T, µB ) = {1" tanh[Sc (T, µB )]}S H (T, µB ) + {1+ tanh[Sc (T, µB ) ]}SQ (T, µB )2
2

C.Nonaka

EOS with QCP(µB , T ) = (550, 159)

entropy density

isentropic trajectories

C.NonakaIsentropic TrajectoriesHadronization
occurs from thephase boundary
to the chemical
freezeout pointµBT!

cross overﬁrst order

FO, COQCPp̄p!

!

2µB∼ exp −T""

ratio
C.NonakaSignature of QCPxpbar/p ratiop̄p!

!

2µB∼ exp −
TCO, FO
QCP""

steeper pbar spectra at high PT
C.NonakaSignature of QCP
NA49 PRC73(2006)

C.NonakaQuantitative Analyses
3D Hydro + UrQMD

Nonaka, Bass, PRC75:014902(2007)

hydrodynamic hadronization
collisions thermalization
expansion

freezeout

Full 3-d Hydrodynamics

UrQMD

HadronizationEoS :1st order phase transition
Cooper-Frye
QGP + excluded volume model
formulafinal stateinteractions

Monte CarloTCTSWt fm/c

TC:critical temperature > TSW: Hydro ! UrQMD

C.NonakaInitial Condition
Initial conditions

QCP: TE = 159 MeV, µ! E = 550 MeV

energy density!(x, y, η) = !max W (x, y; b)H(η)

baryon number density
nB (x, y, η) = nB max W (x, y; b)H(η)
parameters !
ﬂowvL = η

τ0 = 0.6 fm/c
η0 = 0.5, ση = 1.5

TC=170 MeV

210vT = 0

EOS: with the QCD critical point
Switching temperature: 150 MeV
C.NonakaIsentropic Trajectory

QCP

UrQMD

C.Nonaka

PT Spectra!!Narrow collision energy window is needed. " NA49: anti-p spectra•!Careful choice for initial condition of hydro calculation

C.NonakaSummarysQGP is created at RHIC.
success of hydrodynamic models
jet quenching
recombination models
The QCD critical point searchanti proton/proton ratio

LHC, RHIC, FAIR,
Phenomenological Analyses
C.Nonaka

Back UpEOS of 3D Ising Model
Parametric Representation

T − Tcr=Tcexternal magnetic ﬁeldh:β M = M0 R θ
h = h0 Rβ h̃(θ) = hR0βδ (θ − 0.76201θ3 + 0.00804θ5 )β = 0.326
r = R(1 − θ2 )(R ≥ 0, −1.154 ≤ θ ≤ 1.154)
δ = 4.8

Guida and Zinn-Justin NPB,97

Mapping

QCD

Thrµ!"

order parameterM ↔ "q̄q#

C.Nonaka