QGP at RHIC: Seen through Modified Jet Fragmentation

Jet

Xin-Nian Wang王新年LBNL

CCAST WorkshopAugust 10, 2004

My Collaborators

• China: – Enke Wang, Benwei Zhang, Hanzhong Zhang

• US:– X.F. Guo, J. Osborne, J. Owens, A. Majumder

Medium Response Function

41( ) (0) ( )4

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

1

2

2

2 2

( )

( )1

B

B

DISq qW g

q

p q p qp q p q

F

xq

Fp q q

x

qpqxB

2

2

Dynamic System: Photon or dilepton emission (space-like photon)J/ suppression

( ) ( )emj x j x QCD Response: Parton scattering & dE/dx

Jet Quenching & Modified Jet Fragmentation

How to measure dE/dx ?– Modification of fragmentation function

hadronsph

parton

E

)(0 zD ahare measured, and its QCD evolutiontested in e+e-, ep and pp collisions

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

),,()(0 EzDzD ahah

Suppression of leading particles (Huang, XNW’96)

Fragmentation Function

DIS off Nuclei

e-

, )) (( ,( )qh

q h hHdW

d f x p q Dxd

zz

x

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.

22 )(2)(21),,( xpqxpqpTreqpxH q

Parton Fragmentation Function

)()(0 zDzDdzd

hqhq

Sqhhq

zyiphhhq ySpSpTredyzzD hh 0)(,,)0(0

222)( /

q S

e+e- annihilation

DGLAP Evolution

z

zDzPzzDzP

zdzdzD h

hqqgqh

hqqgqz

Shhq

h

)1()(2

)(1

2

22

)1(23

)1(1)(

2

zzzCzP Fqgq Splitting function

DGLAP Evolution

z=0.9

0.75

0.5

0.35

0.25

0.15

0.075

Binnewies,Kniehl,Kramer1995

Multiple Parton Scattering

_2 1( )

4 1 1L Lix p y ix p y yS

T

e e

1f

Lx p

Formation time

2

2 (1 )T

Lx pq z z

[ , , ]Tzq

2 ~ 0x 2 Lx x

Modified Fragmentation

2 122

40

( , ) ( , )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

_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

Guo & XNW’00

Parton Energy Loss

2 1 22

2

2 2 20 0

( ,(1 )(

1 ))

Q Aqg L

AA s

gq

TcT T T

CzzT

d dzN

x xf xk

0

320( )( 2ln)a

R

A sEE C C d

BDPMGyulassy Vitev LevaiWang & WangWiedemann; Zakharov

2( , )~ 1 cos

( )( )

Aqg L

gAq f

gydy

T xy

xf x

Quark energy loss = energy carried by radiated gluon

HERMES data

2 20.00065 GeVsC 0.5 GeV/fmdEdx

in Au nuclei

E. Wang & XNWPRL 2000

High pT spectra in A+A collisions

0

0

0

1 0 0

( , , ) ( , , )L

d

dEE b r d b r ndx

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

2 2 2 2 21 2 1 22 ( ) ( )AB

A B a a b babcdT

d K d b d r d r t r t r dx d k dx d kdyd p

/ 1 // 2( , , ) 1 ( )( , , ) ab cda A a a b B b b h c c

c

df x k r f x k rd

D zzt

pQCD Parton Model

High pt spectra in pp collisions

H. ZhangJ. OwensE. WangXNW2004

High pt spectra in Au+Au

H. ZhangE. WangJ. OwensXNW2004, in preparation

Single hadron suppression

Suppression of away-side jet

cE

dE

Azimuthal anisotropy I

0 1 2(1 cos 2 cos 2 )chdN N v vd

Single hadron

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

DGLAP for Dihadron Fragmentation

2

1

1

1

2

2

2 11 2

1 222

21

2

( , , )( ) ( )

ln( , , )q

qh h

q q hgz z

h

D z z Q dyP z zD Qy y

y g h hQ y

h1h2

h1h2

h1

h2

1

1 2

222

121ˆ ( ) (( , )

1)

(,

)( )

1q

z

qz

hg hqgzD zD Q

ydy P y q g

yQ

y y

Comparison with Monte Carlo

Medium Modification

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

Modification due to recombination

21 2 1

01 2

22( , , ) ( , ) , ), ( h

q qq qqq h dz dz F zD z Q z zz P zQ

h h

2 2 21 2 1 2( , , ) ( , ) ( , )q qq q q q qF z z Q f z Q f z Q Hwa & Yang ?

h

2 2121 2

01 2( , ) ( , ) ( , , ) ) )( ( h

q h q q q qqh

ht

qfD z Q dz dz f z Q P z z zD zz

work in progress

Flavor of Jet Quenching

Parton recombination

Criteria for Discovery of QGP

• 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

Open system, expanding, short-lived, small volume

High density at RHIC

5.5 1.6E GeV for E=10 GeV

0

13.8 3.9 GeV/fmdEdx

cold matter

0.5 GeV/fmdEdx

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

1TdEdy R t

also consistent with hydrodynamic analysis of radial flow from

Thermalization

• Jet quenching– Single and dihadron suppression– Thermalization of hadrons in away-side jet

• Elliptic flow– Requires early thermalization– th<1 fm/c (U. Heinz)

• Good agreement with ideal fluid hydro• Hadron chemical composition

Partonic d.o.f. and Deconfinement

• Parton recombination effect– Reverse ordering of RAA and v2

– Qualitatively model independent• Deconfinement

– J/ suppression (sufficient?)

Summary

• Discovery of Jet Quenching at RHIC proves that a interacting dense matter is formed: Opaque to jets

• Jet quenching is caused by partonic energy loss• Dense matter at RHIC is 30 times higher than cold

nuclei, energy density is 100 times higher• Collective behavior: Hydrodyamic limit strongly

interactive QGP • Jet tomography become useful and power tool for

studying properties of dense matter

Future Perspective

• Beginning of jet tomography study– Details of modified fragmentation– Heavy quark fragmentation– Dihadron fragmentation– Jet-gamma events

• Measurements of rare events– J/ suppression– Dilepton and direct photon production

A Perfect Fluid ?

0T

Hydrodynamicmodel with

zero viscosity

14

String theoryAdS5/CFTPolicastro,Son,Starinets

Weakly coloredBound states

Bulk Elliptic Flow

)2cos2cos1( 210

vvNd

dNch

Hydro-dynamics calc.

2cos2 v

Pressure gradient anisotropy

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

Effect of Hadron Absorption

Uncertainty principle:

f hErm

fm for E=10 GeV 7 ion0 pf

Hadron formation time:

For protons fm for E=10 V0 Ge1 f

h

h

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