To Those Who Perished in the 5.12 Earth Quake in China

Xin-Nian WangLBNL

4Th Electron-Ion Collider WorkshopHampton, May 19-23, 2008

Quark Propagation in a Nuclear Medium

Medium Response Function

41( ) (0) ( )4

iq x em emW q d xe A j j x A

1 22 2 2

1( ) ( )DIS B Bq q p q p qW g F x p q p q F x

q p q q q

qpqxB

2

2

Dynamic System: Photon or dilepton emission

J/ suppression

( ) ( )emj x j x QCD Response: Quark-medium scattering

Quark Propagation: Jet Quenching & Broadening

dE/dx modified frag. functions

hadronsph

parton

E

Dh/a(z)=dN/dz (z=ph/E)

),,()(0 EzDzD ahah

Suppression of leading particles

Fragmentation Function

Angular distributiondN/d2kT

<k2T> jet broadening

DIS off a large nucleus

[ ,0,0 ] momentum per nucleonp p

2[ , ,0 ], / 2B Bq x p q x q q p

1 ( ) ( ) ( )2 A NA

N p N pp

Loosely bound nucleus (p+, q- >> binding energy)

e-

Collinear Expansion

( ) 4 ˆTr ( )ni

i

W d k H k A A A A

p AAp

A

ˆ (0)ˆ ( ) ˆ( ) ( ) |k k xpk xpH k H kH

Collinear expansion:

Ward identities(1) (0)ˆ ˆ( ) ( )p H x H x

(0)

(1)ˆ ( ) ˆ ( , )

H xH x x

k

( )igA D

Collinear Expansion (cont’d)

(0) 4ˆ ( ) (0) (0, ) ( )ik yk d ye A L y y A

(0) 4(2)

2(0) (

40)1 ( )Tr[ ]

2 (ˆ ( ) ˆ (

2)

)dW d k H x kkd

‘Twist-2’ unintegrated quark distribution

q

xp

=

(1) 4 4(1, )(2)1

2 4 4 1,

' (1)' 1

1 ( )Tr[ ]2 (2 ) (

ˆ ( )2

ˆ ())

,,cc

c

L R

kdW d H x xk d k kd

k

1 1(1) 4 41 1 1 1 1

ˆ ( , ) (0) (0, ) ( ) ( , ) ( )ik y ik yk k d yd y e A L y D y L y y y A

‘Twist-3’ unintegrated quark distribution x1p

q

xp

TMD (unintegrated) quark distribution

(0)

2

2

1 ˆ( , ) [ ( ) ]2

( (0) ( )4

;(2 )

0 )

qA

ixp y ik y

f x k dk Tr k

d L yy d y e A y A

† †( ,0;0 ) (( ; ,0 )0; ,) ; )( L L yL L yy y

Longitudinal gauge link( , ; ) exp ( , )y

L y y P ig d A y

Belitsky, Ji & Yuan’970

( ; ,0 ) exp ( , )y

L y P ig d A

Transverse gauge link

Transport Operator

†(0, ) (0, ( ) ( ; ) ( ) ( ; )) |y

yy iD y g d L yi L y L F L yy

(2)( , ) (0) (0; , ( ,0 ) exp[ ] ( ,0 ) ( )4

0 )qA k

ixp y Wdyf x k e A L y y A ky

All in terms of collinear quark-gluon matrix elements

Liang, XNW & Zhou’08

2(2)

2 ( ) exp (0) ( )(2 )

ik yk y

d y e F y i F k

Taylor expansion

( , )W y y

Transport operator

Maximal Two-gluon Correlation

†0( ,0 ) ( ; ) ( ) ( ;( ) ) |

y

yW y g d L yi Fy LD y

22 (0) (0; ) ( )4

( )nn ixp y

kdyM e A L y W y y A

2

2( )

nn

A Nn A

AF N F xG xF N

p

1 2

4/31

2 1

2 2

(0) ( )

(

( ) ( )

() ) ( )qN N A N N

dy dy d F y F y

d x G

y A y A

Af xx A

1 2 12 (( ) ( ()0) )Ddy dy dy A y Ay D y A

Nuclear Broadening & Gluon Saturation

2(2)

2

ˆ( , ) ( ) exp ( ) ( )4

1 ( ) exp

kq qA N N N

qN

f x k Af x d q k

kAf x

2 ˆ( )N Nk d q

2

02

4ˆ( ) ) ) |1

( (A N N xs F

Nc

CN

xq xG

Quark jet transport parameter

22 2

02

4ˆ ( ) ( ) ( , ) |1

s Asat A N A N N sat x

c

CQ q xG x QN

Liang, XNW & Zhou’08

Coherence effect correlation between different nucleons

Gluon saturationKochegov & Mueller’98

McLerran & Venugapolan’95

SIDIS off Nuclei

e-

(0) ( ),) (( , ) q h hqh

f x H xdW

dxdz

p Dq z

pypedyxf yixpBq )()0(

21

2)(

/( ) 0 (0) , , ( ) 02 2 2

h hip y zhq h h q h h q

S

z dyD z e Tr p S p S y

Frag. Func.

(0) 2 21( , , ) ( ) 2 ( )2qH x p q e Tr p q xp q xp

DGLAP Evolution

z

zDzPzzDzP

zdzdzD h

hqqgqh

hqqgqz

Shhq

h

)1()(2

)(1

2

22

)1(23

)1(1)(

2

zzzCzP Fqgq Splitting function

q

p

k1 k2

p

q

Induced gluon emission in twist expansionq

Apxp

xp

Ap

q

x1p+kT

1 2(1 2

)2 ( , , ) ( ) ( )ik y yDTT

DH p q kW d A y A yk e A A

2 2( , , ) ( , ,0)( , ,0) ( , ,0)TT

D D DT Tkk

DTH p q k H p q H p H p qq k k

Collinear expansion:

AFFAkqpHW TD

kD

T

)0,,(2

Double scattering

LPM Interference

[ , , ]Tzq

2 0x B Lx x2 Lx xBx

2

2 (1 )

TLx

p q z z

_2 1

2( )2 (0

0

2

4) 1

(1 )( , , ) | 1 1L L

T

ix p y ix p y yDk

s

TkH p q k H e ez

z

1f

Lx p Formation

time

2

2 (1 )T

Lx pq z z

222

4

1 ( )(1 )

N sqg L N L

T

zd x G x dzdz

Modified Fragmentation2 12

24

0

( , ) ( , )2

h

QS h

q h h L q hz

zd dzD z Q z x Dz z

2 ( , ) 21( , ) (virtual)(1 ) ( )

Aqg L A S

L Aq c

T x x Czz xz f x N

Modified splitting functions

Guo & XNW’00

_2 1(

1 22

)

1( , ) (0) ( )2 2

1

( ) ( )

1

B

L Lix p y ix p

ix p yAqg L

y y

F y F ydyT x x dy dy A A

e

e

e

y

Two-parton correlation:

ˆ ˆ( ,0) (( , )

1 cos(2( )

, ))A

qg LsN N

c qL NN LA

T x xd

N fq

xx pq x

1/3AR A

Quadratic Nuclear Size Dependence

02 2~ ( )qs

N Bd Af xd

1 2

2

1 22 4( )1 2~ (0) ( )

2 2( ) (

2)

2B Tix p y ix psD y ydyd Fd y F yy dy e A y

dA

2

04/3

4~ [ ( )]( )T

qN B

sT N T xx G xA f x

1/32 2

02 2~ ( )[1 ( ) ) ](SD

T Ts

q Bd c A x G xd fd

A xd

3/1

22 LPM

AQ

2

3/2

1QAc

HERMES data

2ˆ 0.01 GeV / fmq 0.5 GeV/fmdEdx

in Au nuclei

E. Wang & XNWPRL 2000

Energy Dependence

Jet quenching in heavy-ion collisionCentral Au+Au

single hadron

dihadron

2ˆ 1 2 GeV / fmq 2ˆ 0.01 GeV / fmq in cold nucleiin hot matter

Summary

• Quark transverse momentum distribution can be expressed in term collinear quark-gluon matrix elements

• quark propagation in nuclei leads to kT broadening gluon correlation function

• Jet transport parameter qhat saturation scale Qsat

2

• Modified fragmentation function qhat~0.01 GeV^2/fm in HERMES at HERA versus qhat~ 1-2 GeV^2/fm in QGP at RHIC

• qhat at small x and large Q^2 can reveal gluon dynamics (correlation, saturation) in nuclei