1

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

I. Introduction

II. Modification of Frag. Func. in Cold Nucleus

III. Modification of Frag. Func. in QGP Medium

IV. Summary

Collaborators: X.-N. Wang, B.-W. Zhang

Modification of Fragmentation Function in Strong Interacting Medium

2

I. IntroductionRutherford experiment atom discovery of nucleus

SLAC DIS experiment e proton discovery of quarks

A-A collisions: Naturally provides jet and the QGP

Jet (hard probe) created by parton scattering before QGP is formed

– high transverse momentum

– calculable in pQCD

penetrating beam (jet) absorption or scattering pattern

QGP

Hard Probes of Quark Matter:

3

Jet quenching and Observation

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

A-A collision

Jet Quenching:

EEE '

E

Modification of Fragmentation Function:

),( 20 QzD hhq

hh zzz ')1(

),(),(),(~ 2202 QzDQzDQzD hhhqhhq

hqABT

AA

Dtd

dPDFsT

dydp

d ~

ˆ2

Particle Production:

hp

S~

'pp

)'

',(

p

pz

p

pz h

hh

h

4

Light Quark Energy Loss

PHENIX,

Nucl. Phys. A757 (2005) 184

Theoretical results from the light quark energy loss is consistent with the experimental data

5

Heavy quark energy loss: Early Expectations

k

E

M

dP

k

dkkdCdP Fs

,

)/1()(

0

2220

022

022

22

B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301 Y. Dokshitzer & D. Kharzeev PLB 519(2001)199

Heavy quark has less dE/dx due to suppression of small angle gluon radiation

“Dead Cone” effect

J. Adams et. al, PRL 91(2003)072304M. Djordjevic, et. al.

PRL 94(2005)112301

6

STARSTAR

No Significant Difference BetweenHeavy Quark Jet and Light Quark Jet

Non-photonic electrons from heavy quark decays

Charged hadrons fromLight quark fragmentation

7

Question: Heavy Quark Energy Loss?

Theoretical Calculation

How Reasonable?

)1

(1

1),(

~ 0

z

zD

zEzD ahah

Energy loss fraction

8

II. Modification of Frag. Func. in Cold Nucleus

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

e-A DIS:

9

Modified Fragmentation Function

Fragmentation function in vacuum

X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591

),(),(),(~ 2202 QzDQzDQzD hhqhhqh

pQCDhq

Modification term

10

Modified Frag. Function in Cold Nuclear Medium

2 122

40

( , ) ( , )2

h

QS h

q 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

11

Rescaling of Modified Fragmentation Function

),1

(1

1),(

~ 202 Qz

zD

zQzD

effhq

eff

rescalinghq

zzeff 6.0

zSolid curve:

Dashed curve:

),(

),(~

20

2

QzD

QzD

hq

pQCDhq

),(

),(~

20

2

QzD

QzD

hq

rescalinghq

12

Comparison with HERMES Data

22 0060.0)(~

GeVQC 33.0)( 2 Qs 22 3GeVQ , ,

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

13

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

Mass effects:

1) Formation time of gluon radiation 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

14

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

15

III. Modification of Frag. Func. in QGP Medium

Cold Nucleus Medium QGP Medium

A| Akykfk

kd||),(

2)2( 23

3

k k

16

Same Framework for Light and Heavy Quark

),(),(),(~ 2202 QzDQzDQzD hhh

pQCD

Light quark:

0M),(),( 2020 QzDQzD hhqh

Heavy quark:

0M)()( 0

,0

hhQnph zDzD

Peterson form

17

Generalized Jet Transport Parameter

Unintegrated gluon distribution function:

Average tranverse momentum broading:

averaged transverse momentum transfer squared per unit distanceRq̂

),,(),0,(ˆ nrbyEq gR

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Jet Energy Loss

),0,(ˆ])1([

)1(64222

422 yEq

Mzl

lzdzdldy

E

ER

T

TT

s

])1(4

))1(([sin),,(

22222

1 zEz

MzlyMlza T

T

LPM effect

19

Modified Frag. Function in QGP Medium

Modified splitting functions

])([)2(2

),( 01

0 2

2

2

22

2

z

zD

l

dl

z

dzqdQzD h

qgqz

Q

T

TTsh

h

)(])1([

2

)(

),,,(

)1(

14222

622

virtualMzlN

lC

xf

qMxxT

z

z

Tc

TAsA

q

TLA

qgqgq

Parameters:

fm

MeVT

fmGeVq

1.0

600

/0.1ˆ

0

0

20

20

Modification of Frag. Func. for light quark in QGP

z

)(

)(~

0 zD

zD

Solid Curve:

can be

approached by

)(~

zD pQCDhq

)1

(1

1

)(~

0

effhq

eff

rescalinghq

z

zD

z

zD

Dashed curve:),(

),(~

20

2

QzD

QzD

hq

pQCDhq

),(

),(~

20

2

QzD

QzD

hq

rescalinghq

zzeff 65.0

21

Modified Frag. Func. for heavy quark in QGP

c quark:

can be approached by)(~

zD pQCDHQ

)1

(1

1)(

~ 0

effHQ

eff

rescalingHQ z

zD

zzD

zzeff 9.0

vacuum

medium

rescaling

medium/vacuum

rescaling/vacuum

E=10GeV E=50GeV

vacuum

medium

rescaling

medium/vacuum

rescaling/vacuum

z z

22

b quark:

can be approached by)(~

zD pQCDHQ

)1

(1

1)(

~ 0

effHQ

eff

rescalingHQ z

zD

zzD

zzeff 9.0

vacuum

medium

rescaling

medium/vacuum

rescaling/vacuum

E=10GeV

vacuum

medium

rescaling

medium/vacuum

rescaling/vacuum

E=50GeV

zz

23

Ratio of energy loss between heavy and light quark in QGP

q

Q

z

z

Solid Curve:

Dashed curve:

qeff

Qeff

z

z

qpQCD

QpQCD

z

z

E1) In the intermediate jet energy region the ratio increase

rapidly with increasing energy.

2) In the very high jet energy region the effective energy loss of heavy quark is larger than one of light quark

c

b

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IV. Summary

1) The modified fragmentation function in strong interacting medium (cold nucleus and QGP) has been calculated in pQCD.

2) The modified fragmentation function in QGP medium can be approached by rescaling fragmentation function with effective energy loss fraction . For light quark , for heavy quark .

3)The different effective energy fraction shift of the fragmentation function for light and heavy quark will help us to understand the different behavior of the light and heavy quark jet.

effz zzeff 65.0zzeff 9.0

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Thank YouThank You

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