Enke Wang (Institute of Particle Physics, Huazhong Normal University)

I. Jet Quenching in QCD-based Model

II. Jet Quenching in High-Twist pQCD

III. Jet Tomography of Hot and Cold Strong Interaction Matter

IV. Modification of Dihadron Frag. Function

Modified Fragmentation Function in Strong Interaction Matter

hadrons

q

q

hadrons

leadingparticle

leading particle

p-p collision

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressedA-A collision

Jet Quenching:

EEE '

E

Fragmentation Function:

p

hp

S~

q

),( 2QzD hhq DGLAP Equation

p

pz h

h

hhh zzz

),(),(),(~ 222 QzDQzDQzD hhhqhhq

I. Jet Quenching in QCD-based Model

G-W (M. Gyulassy, X. –N. Wang) Model:

Static Color-Screened Yukawa Potential

Feynman Rule:

q

p

p-q )2()2( 00 qpiqpiD

ip

ipi

2)(

p

pp+k

,)2( ckpigs

cTc

k

ik

gikig

2)(

0

k-q,a k,c

q,b })]()[(

)()]([{0

00

kqkg

qkgqkqgf abc

Opacity Expansion Formulism (GLV)

Double Born Scattering

GLV, Phys. Rev. Lett. 85 (2000) 5535; Nucl. Phys. B594 (2001) 371

Elastic Scattering

Assumption

• The distance between the source and the scattering center are large compaired to the interaction range:

• The packet j(p) varies slowly over the range of the momentum transfer supplied by the potential:

•The targets are distributed with the density:

Opacity: Mean number of the collision in the medium

1

0 zzi

)()( qpjpj

),,,(),,,( 2121 NN zzzA

Nxxx

)(/

121 )(

)(),,,( NLz

e

jN

jN

ejeNL

zzzz

jjj zzz 1

1)(

N

LNLe

el 1

A

NLn el

First Order in opacity Correction

First Order in opacity Correction

Medium-induced radiation intensity distribution:

Induced radiative energy loss:

Induced gluon number distribution:

)cos(1)2)(( 111122

22

)1(

zBCqvqdLC

kdxd

dNx

g

sR

Non-Abelian LPM Effect

2)1( LE LE )1(

QCD:

QED:

Higher order in Opacity

Reaction Operator Approach: (GLV)

Induced gluon number distribution:Non-Abelian LPM Effect

Radiated Energy Loss vs. Opacity

First order in opacity correction is dominant!

Detailed Balance Formulism (WW)

E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001) 142301

k

x0 p

k

x0 p

Stimulated Emission Thermal Absorption

B-E Enhancement Factor

1+N(k)

Thermal Distribution Func.

N(k)

Final-state Radiation

k

x0 p

k

x0 p

Energy loss induced by thermal medium:

0

)0()0(

)0(

T

abs d

dp

d

dpdE

22

2 )2('62

4ln

3

E

FsET

E

TC=

Net contribution: Energy gain

Stimulated emission increase E loss Thermal absorption decrease E loss

First Order in Opacity Correction

Single direct rescattering:

k

y0 y1 p

k

y0 y1 p

y0 y1 p

k

Double Born virtual interaction:

k

y0 y1 y1 p

y0 y1 y1 p

k

k

y0 y1 y1 p

y0 y1 y1 p

k

Key Point: Non-Abelian LPM Effect—destructive Interference!

Energy Loss in First Order of Opacity

Energy loss induced by rescattering in thermal medium: )1()1()1(

absradEEE

Take limit:

1EL E LT 2

Zero Temperature Part:

0

)0(

)1(

T

rad d

dpdE

048.0

2ln

4 2

2

L

EC

g

Fs

L2

GLV ResultTemperature-dependent Part:

0

)1()1(

)1(

T

abs d

dp

d

dpdE

2

22 )2('61ln

3

E

g

Fs

T

L

E

LTC

Energy gain

Numerical Result for Energy Loss

3.0S

)1()1()0(

radabsabsEEEE

• Intemediate large E, absorption is important

•Energy dependence becomes strong

•Very high energy E, net energy gain can be neglected

Parameterization of Jet Quenching with Detailed Balance Effect

)/5.7/()6.1/( 02.1

001

EEdL

dE

d

Average parton energy loss in medium at formation time:

Energy loss parameter proportional to the initial gluon density 2

00

1

ARd

dN

Modified Fragmentation Function (FF)

),(

)],(/),()[1(),,(

2'0/

/

2'0/

'2'0

/

'/2

/

cchL

gghc

gcch

c

cLccch

zDe

zDz

zLzD

z

zeEzD

(X. -N. Wang , PRC70(2004)031901)

,//),/( ''cTgcTcTc EpLzEppz

Comparison with PHENIX Data

PHENIX,

Nucl. Phys. A757 (2005) 184

DGLAP Equation at Finite TemperatureJ. A. Osborne, E. Wang, X.-N. Wang, Phys. Rev. D67 (2003) 094022

DGLAP Equation at Finite Temperature

Splitting function at finite temperature:

Quark Energy Loss from Splitting Function

The minus sign indicates that the absorptive processes

in the plasma overcome the emissive processes.

The net Contribution is energy loss!

II. Jet Quenching in High-Twist pQCD

e-

, )) (( ,( )qh

q h hHdW

d f x p q Dxd

zz

x

pypedy

xf yixpBq )()0(

2

1

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.

22 )(2)(2

1),,( xpqxpqpTreqpxH q

Modified Fragmentation Function

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q

Cold nuclear matter or hot QGP medium lead to the modification of fragmentation function

Jet Quenching in e-A DISX.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591

e-

Modified Frag. Function in Cold Nuclear Matter

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q 2 12

24

0

( , ) ( , )2

h

Q

S hq h h L q h

z

zd dzD z Q z x D

z z

2 ( , ) 21( , ) (virtual)

(1 ) ( )

Aqg L A S

L Aq c

T x x Czz x

z f x N

Modified splitting functions

_2 1(

1 2 1 2

2)

1

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

( ) ( )1 1

B

L Lix p y ix

ix p yA

y

g

y

q L

pe

dyT x x dy dy e A F y F y y A

y y ye

Two-parton correlation:

LPM

Modified Frag. Function in Cold Nuclear Matter

hadrons

ph

parton

E

),,()(0 EzDzD ahah

)(0 zDah

are measured, and its QCD evolutiontested in e+e-, ep and pp collisions

Suppression of leading particles

Fragmentation function without medium effect:

Fragmentation function with medium effect:

),1

(1

1),( 0

z

zD

zEzD ahah

Heavy Quark Energy Loss in Nuclear MediumB. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493

Mass effects:

1) Formation time of gluon radiation time become shorter

222 )1(

)1(2

Mzl

qzz

T

f

LPM effect is significantly reduced for heavy quark

2) Induced gluon spectra from heavy quark is suppressed by

“dead cone” effect

4

2

2

04

222

2

/]1[][

Mzl

lf

T

T

qQ

zq

l

q

M

T

0

Dead cone Suppresses gluon radiation amplitude at 0

Heavy Quark Energy Loss in Nuclear Medium

)]},,(),,()[1(),,(2

1{

~)~~(~

)1(

1~

),(

22

2

22

1

/~22

3

4

2~

~

1

0

2

2

2

2

22

MlzcMlzceMlzc

x

xxxd

zz

zdz

xQN

xCCQxz

TT

xx

T

L

ML

x

xL

Ac

BsA

B

Q

g

AL

M

LPM Effect

,~~

2

2

Qx

Mx

x

x

A

B

A

L

AN

A Rmx

1

1) Larg or small :

Bx

2Q

A

A

B

c

SAQ

gR

Qx

x

N

CCz

2

2~~

2) Larg or small :2Q

2

22

2~~

A

A

B

c

SAQ

gR

Qx

x

N

CCz

Bx

Heavy Quark Energy Loss in Nuclear Medium

The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

2Q

The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

Bx

III. Jet Tomography of Hot and Cold Strong Interaction Matter

E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301

2 21 1 22 2

22 2 2 2

0 0 0 0

1 (1 )( ,

()

, )

( )2

Q Qs A sT

g L T

Aqg

T cT T T

L

Aq

Cd zz dz z z x d dz

Nk

T x x

f x

Cold Nuclear Matter:Quark energy loss = energy carried by radiated gluon

2 2 13ln

2A

s N Ac B

CE C m R

N x

Energy loss

3/2AE

Comparison with HERMES Data

HERMES Data: Eur. Phys. J. C20 (2001) 479

22 0060.0)(~

GeVQC 33.0)( 2 Qs 22 3GeVQ , ,

Expanding Hot Quark Gluon Medium

_2 1(

1 2 1 2

2)

1

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

( ) ( )1 1

B

L Lix p y ix

ix p yA

y

g

y

q L

pe

dyT x x dy dy e A F y F y y A

y y ye

2( , )~ ( ) 1 cos

( )

Aqg L

gAq f

T x x ydy y

f x

0

32

( )2

lnR

s dE

E

R. Baier et al

Initial Parton Density and Energy Loss

jet1

jet2

0

32

2( ) ln

R

s

EE d

00( ) ( )R r

01 0

2d

A

E ER

Initial energy loss in a static medium with density 0

:0E

0 0.1 fm 015

2AR

1

0.5 GeV/fmd

dE

dx

6.140

dx

dEGeV/fm

Initial parton density (Energy loss ) is 15~30 times that in cold Au nuclei !

Comparison with STAR data

STAR, Phys. Rev. Lett. 91 (2003) 172302

d-Au Result

理论预言

实验结果

E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301

STAR, Phys. Rev. Lett. 91(2003) 072304

IV. Modification of Dihadron Frag. Function

h1 h2

jet

A. Majumder, Enke Wang, X. –N. Wang, Phys. Rev. Lett. 99 (2007) 152301

Dihadron fragmentation:

h1

h2

DGLAP for Dihadron Fragmentation

2

1

1

1

2

2

2 11 2

1 222

21

2

( , , )( ) ( )

ln( , , )q

qh h

q q hg

z z

h

D z z Q dyP

z zD Q

y yy g h h

Q y

h1h2

h1h2

h1

h2

1

1 2

2

22

121ˆ ( ) (( , )

1)

(,

)( )

1q

z

q

z

hg hqgz

Dz

D Qy

dyP y q g

yQ

y y

Evolution of Dihadron Frag. Function

Evolution of Dihadron Frag. Function

)()(),( 21212121 zDzDzzD h

qhq

hhq

Medium Modi. of Dihadron Frag. Function

Nuclear Modification of Dihadron Frag. Func.

)(

)()(

212

2222 zN

zNzR

h

Ah

h

e-A DIS

Hot Medium Modification

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