Weihai, 2004

QCD and Heavy-ion Collisions

王新年

LBNL

相对论重离子碰撞与低能强子物理讨论会

威海 , 2004 年 8 月报 3-7 日

Weihai, 2004Heavy-ion Collisions

RHIC BNL

Au+Au up to 200 GeV/n

Weihai, 2004QCD Theory

• (approx.)Chiral symmetry and its spontaneous breaking• Goldstone boson and chiral condensate

• Scale and UA(1) anomaly

• SU(3) gauge symmetry (non-Abelian)• Confinement at long distance

• Asymptotic freedom at short distance

• ….

,1

1( )

2 4

fna

QCD a a af a

L i gA m F F

Weihai, 2004Chiral Symmetry

Chirality of massless quarks: 5

1(1 )

2L 5

1(1 )

2R

Chiral symmetry: LiL Le

Ri

R Re

Conserved currents: 2a

aV 5 2

aaA

Spontaneously broken: 0

Goldstone bosons (,K,)(3) (3) (3)L RSU SU SU

Or alternatively: 5 / 2/ 2 , iiV AU e U e

Weihai, 2004Chiral symmetry restoration

Restoration at high temperature

F. Karsch ‘2001

MeVTc 8170

Brown-Rho postulation:( )( )

(0) (0)

TM T

M

Weihai, 2004UA(1) Anomaly

U(1) and UA(1) Symmetry:5, ii

AU e U e

(Classically) conserved current:0V 0 5A

Spontaneous chiral symmetry breaking 9th Goldstone boson (0)

A0 not a conserved current UA(1) is broken in

quantum theory: Chiral anomaly0

2

16f a

s a

nA F F

Alder&Jackiw

0

22 4

2

20 | ( ), (0) | 0

16f s

YM

nm i d x T FF x FF

f

Topological susceptibility2

YM

Weihai, 2004Partial restoration of UA(1)

Z. Huang & XNW

UA(1) restored phase could lead to false vacuum 0 Massive parity violation Kharzeev & Pisarski

Weihai, 2004Running of s(Q)

S Bethke J.Phys. G26 (2000) R27

22 2 23

4( )

(11 ) ln( / )sf QCD

Qn Q

Gross,Wilczek;Politzer (73)

SU(3) Gauge SymmetryNon-abelian interaction

Anti-screening of color

Asymptotic freedom

Weihai, 2004Ideal Gas Approximation

• Leading orders inperturbation (Kapusta)

• Failure of simple perturbation: (non-convergenceg g~1)(Arnold & Zhai ’94)

– Expand contributions from soft modes k~ gT in terms of g.

1/3

0

[ ]exp ( )T

Z d d d xL

)4

151(

3016 4

2

sT

g

ssfqq TTn

2

184

1

21

501

120

76

2

4224

2

432

0 2ln013.0007.0ln09.012.0095.01 g

TgggPP

Weihai, 2004Resummation of HTL

• Resummation of Hard Thermal Loops (Braaten & Pisarski)

– Effective theory integrating out “hard” (k~T) loops

– Resummation of HTP

)(

)(

)(

)()(

22 pp

pe

pp

pepD

HTLL

LHTLT

T

xix

xxxD

HTLL 21

1ln

21)1( 22

)1(41

1ln)1(

4222

22 xxi

x

xx

xxD

HTLT

(Weldon’94)

p

px 0

= + + …

222 )6/1( Tgn fD

Debye mass

Weihai, 2004

Quasi-partciles & Self-consistent Resummation

• Quasi-particles with dispersion given by HTL

• Self-consistentresummation:

• Dyson’s equation

-1 -10 0 0

1 1Tr lnD Tr ln D

2 2HTL THL

)(10

1 DDD

Weihai, 2004Scale Anomaly

• Scale invariance (massless quarks)

• QCD interaction renormalization of g()

– Break scale invariance scale anomaly

3/ 2( ) ( )

( ) ( )

x x

A x A x

( ) ( )scaleJ x x T x

( ) ( ) 0scaleJ x T x

Classically conserved dilation current

12as

aT F F

BFF aas 4

12

2 40.015 GeVs F

Gluon condensate

0 0, PB B

Bag constant

Weihai, 2004QCD Phase transition

• Ideal quark and gluon gas

• Massless pion gas

• First order phase transition:

2416

30T

g

247

6120q q fn T

243

30T

3

P

( ) ( )q g c cP T P T

1/ 40.72cT B ( 0)

P

T4

T4

4B

Tc4

Tc4

,q g B ,

1

3 q gP B

Weihai, 2004Lattice QCD results

MeVTc 8170 3/ 3.06.0 fmGeVc

F. Karsch ‘2001

Weihai, 2004Confinement-deconfinement

Karsch, Laermann and Peikert 2001

( ) + V r rr

SU(3) non-Abelian gauge interaction confinement

Heavy quark potential:

J/ suppression

Weihai, 2004QGP in AA Collision?

• Criteria:– High density: >>c

– Large volume: V>> (mean-free-path)

– Long life-time: t>>– Local thermal equilibration (interaction): approximately

– parton degrees of freedom

– Debye screening of strong interaction: deconfinement

Expanding, short-lived, small volume QGP?

Weihai, 2004Energy Loss & Jet Quenching

0

320( )(

2ln)a

R

A s

EE C C d

BDPMGyulassy Vitev LevaiWang & WangWiedemann; Zakharov

e-

20 0 for ( )E L

Weihai, 2004Single hadron suppression

NLO calc.H.-Z. Zhang

Weihai, 2004Suppression of away-side jet

cE

dE

Weihai, 2004Azimuthal anisotropy I

0 1 2(1 cos 2 cos 2 )chdNN v v

d

Single hadron

Weihai, 2004dE/dx and gluon density at RHIC

5.5 1.6E GeV for E=10 GeV

0

13.8 3.9 GeV/fmdE

dx

cold matter

0.5 GeV/fmdE

dx

0 0.2 fm/c

From RHIC data of Au+Au Collisions

Initial Density about 30 times of that in a Cold Au Nucleus

Consistent with estimate of initial condition2

1dN

dy R t

Weihai, 2004Elliptic Flow

py

px

Coordinate space: initial asymmetry

Momentum space: final asymmetry

)2cos2cos1( 210

vvNd

dNch

2cos2 v Pressure gradient diff

Hydro-dynamics calc.

Weihai, 2004Early Thermalization

1 fm/cth Constraint on thermalization time

U. Heinz nucl-th/0407067

Weihai, 2004Flavor of Jet Quenching

Parton recombination -> Partonic degrees of freedom

Weihai, 2004Summary

• Heavy-ion collisions can test many properties of QCD– Deconfinement phase transition– Chiral symmetry restoration

• Current RHIC data indicate formation of QGP– High energy density 20 GeV/fm (t0=1 fm/c)

from jet quenching, dN/dy, radial flow– Jet quenching Strong parton interaction

thermalizationv2 early thermalization

– Parton recombination partonic matter• More experimental studies to come

– Heavy-quark energy loss (B.-W. Zhang)