Xin-Nian WangLBNL

First Workshop on Quark-Hadron Duality and the Transition to pQCDFrascati, June 6-9, 2005

Quark-hadron Duality of Hadronization in Nuclei

QCD

hadronsfrom Mars

quarksfrom Venus

Quark-hadron Duality

Quark scattering or hadron absorption?

e-

Quark propagation and scattering,

Hadronization outside the nuclei

Hadronization inside nuclei

Hadron absorption

Conclusions

• Never promise any great ideas!

Quark Fragmentation Function

Sqhhq

zyiphhhq ySpSpTre

dyzzD hh 0)(,,)0(0

222)( /

)()(0 zDzDdz

dhqhq

q S

e+e- annihilation

)(),(42

14

4

qWqpLq

e

shee

tot

4 4

4

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

Im 0 ( ), (0) 0

XX

iq y

W q J J q p

i d ye T J y J

X X

Collinear factorization

DGLAP Evolution

z

zDzP

z

zDzP

z

dzdzD h

hqqgqh

hqqgq

z

Shhq

h

)1()(2

)(1

2

22

)1(2

3

)1(

1)(

2

zz

zCzP Fqgq Splitting function

DIS off Nuclei

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

Multiple Parton Scattering

_2 1( )

41 1L Lix p y ix p y yS

T

e e

2

1 2 (1 )f

L T

q z z

x p

Formation time

h h

Erm

Multiple Parton Scattering

1 2( )21 2( , , ) ( ) ( )ik y yD D

T TW d k e H p q k A A y A y A

Generalized factorization:

(LQS’94)

22 )0,,(

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

TTD

k

TTD

kTD

TD

kkqpH

kkqpHkqpHkqpH

T

T

Collinear expansion:

Collinear approximation

AFFAkqpHW TD

kD

T

)0,,(2

Double scattering

22 )0,,(

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

TTD

k

TTD

kTD

TD

kkqpH

kkqpHkqpHkqpH

T

T

First term Eikonal

AzAdzigA

AAAzddzgAdzigA

)(exp)0(

2

1 2( )21 2( , , ) ( ) ( )ik y yD D

T TW d k e H p q k A A y A y A

Modified Fragmentation

2 122

40

( , ) ( , )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

Guo & XNW’00

_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

Twist Expansion

)(~)(2

)0(2

~222 BqsypixsS xAfAyAe

dy

d

dB

AyyFyFAedydydy

d

d yypixypixsD TB )()()(2

)0(222

~ 21)(21

4221

)()(~ 3/44 TTsBqs xGxxfA

])(1)[(~ 3/12222

TTS

BqsDS xGxAcxAf

d

d

d

d

3/1

22 LPM

A

Q 2

3/2

1Q

Ac

HERMES data

2 20.00065 GeVsC 0.5 GeV/fmdE

dx

in Au nuclei

E. Wang & XNWPRL 2000

Energy Dependence

Conclusions

• Never promise any great ideas!

• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering

Di-hadron fragmentation function

1 2 1 2 1 2 1 2( , ) 0 (0) , , ( ) 02q h h q h h h h q

S

D z z Tr p p S p p S y

h1 h2

jet

Majumder & XNW’04

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

Medium Modified Dihadron

D(z1,z2)/D(z1)Triggering h1

Higher orders or hadron absorption?

f h

Erm

Hadron formation time:

fm for E=10 GeV 70 pionf

protons fm for E=10 V0 Ge1 f

h

h

Conclusions

• Never promise any great ideas!

• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering

• Higher twists might be important

• Hadron absorption likely at lower energies

Angular distribution of radiative gluons

2

2 2

1 (1 ) 1

2g S

FT T

dN zC

dzdk z k

1gdN

d

max

(1 / )

2g

g

E

R

Radiation in vacuum

2

2 (1 )f

T

Ez z

k

2 2

2 2 2 2

2

1 (1 ) 1

( )1 fg A S

T c T

R

T

dN C zcmR

dzdk N ke

z k

Induced Bremsstrahlung:

Dihadron correlation in relative transverse momentum

Jet Quenching in Heavy-ion Collisions

Azimuthal asymmetry

jet1

jet2

Abnormal angular distribution

PHENIX STAR

Parton Energy Loss

2 1 22

2

2 2 20 0

( ,(1 )

(

1 )

)

Q Aqg L

AA s

gq

TcT T T

Czz

Td dz

N

x x

f xk

0

320( )(

2ln)a

R

A s

EE C C d

2( , )~ 1 cos

( )( )

Aqg L

gAq f

g

ydy

T xy

x

f x

Quark energy loss = energy carried by radiated gluon

0

13.8 3.9 GeV/fmdE

dx

cold matter

0.5 GeV/fmdE

dx

Conclusions

• Never promise any great ideas!

• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering

• Higher twists might be important

• Hadron absorption likely at lower energies

• Initial gluon density in Au+Au is about 30 times higher than cold nuclei

• Multiple hadron correlations critical measurements

Flavor of Jet Quenching

Parton recombination

A Perfect Fluid ?

0T

Hydrodynamicmodel with

zero viscosity

1

4

String theoryAdS5/CFTPolicastro,Son,Starinets

Weakly coloredBound states

Bulk Elliptic Flow

)2cos2cos1( 210

vvNd

dNch

Hydro-dynamics calc.

2cos2 v

Pressure gradient anisotropy

High 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 high pT data: single & di-hadron, v2

Initial (energy) density 30 (100) times of that in a Cold Au Nucleus

Consistent with estimate of initial condition 20

1TdE

dy R t

also consistent with hydrodynamic analysis of radial flow from

Parton Energy Loss

Same-side jet profile

Same-side jet cone remains the same as in pp collision

Hadron rescattering will change the correlation Between leading and sub-leading hadrons

Geometry of Heavy Ion Collisions

x

z

y

EZDC

ET

Centrality of the collisions

Impact Parameter (b)

EZDC

ET

NNAB

ABAB

NR

binary

)(2 bbTdN ABbin

No jet quenching in d+Au

Initial state effect: Shadowing & pt broadening: XNW, PRC61(00)064910

20-60%

STAR preliminary

20-60%

Azimuthal Anisotropy II

Azimuthal Mapping of jet quenching

out-plane

In-plane

High pT spectra in A+A collisions

0

0

0

1 0 0

( , , ) ( , , )L

d

dEE b r d b r n

dx

Modified fragmentation f( ) ( ) un cD z D z

2 2 2 2 21 2 1 22

( ) ( )ABA B a a b b

abcdT

dK d b d rd r t r t r dx d k dx d k

dyd p

/ 1 // 2( , , )1

( )( , , ) ab cda A a a b B b b h c c

c

df x k r f x k r

dD z

zt

pQCD Parton Model

Single hadron suppression

Comparison with Monte Carlo

Energy Loss of A Heavy Quark

2

1

1/ (1 ) / 2Hf

f z M zq

02 2 2 2

1

(1 )

dN

d z M

Dead cone effect

B. Zhang & XNW’03

Jet Quenching at RHIC

XNW’03

Mono-jet production

0

13.8 3.9 GeV/fmdE

dx

cold matter

0.5 GeV/fmdE

dx 0 0.2 fm/c

Suppression of away-side jet

20-60%

STAR preliminary

20-60%

Di-hadron invariant mass spectra