Jet

Jet Tomography of Hot & Dense Matter

Xin-Nian WangLBNL, June 25, 2003

Equation of States

MeVTc 8170 3/ 3.06.0 fmGeVc

F. Karsch ‘2001

Hadrons:

0,

QGP:

Quarks(2x3x2x2)

Gluons(2x8)

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 gq

p q p qp q p q

F

xq

Fp q q

x

qpqxB

2

2

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

Dynamic System: Photon or dilepton emissionJ/ suppression

(talks by Averbeck, Sinha, Fries, Granier de Cassagnac)

Computed Tomography (CT)

Calibrated source

Absorption properties

Computerassisted correction

Image Jet Tomography: Using Parton Jets

Jets: Beams of quarks and gluons

2p p jets X

Jet Tomography

Au+Au

Talks by Jacobs, Bathe

EM Radiation

EM field carried by afast moving electronv

EM Radiation by scattering:Interference between initialand final state radiation

2

2

2 (1 )2 ln 1i f

BH

E v vdId m

Initial rad.

Final rad.

22 2

2

( )4

( )i f

fi

k k vk

d I ed

kvvk

dv

k

Electron Tomography

2 2 2( )

2

2 ( )4

i t k rd I e n n drd d

e

11

t( )

t

ii i

ii i

pv t t tEr t pv t t tE

ij

Classical radiation of a point charge (Jackson, p671)

(1 cos ) /i i fL L

(

22

1 )2

21

( ) ( )4

i ii i

i i i

i t k rk k v k k vd I ed d k

ev k v

2

2f Formation time

Two Limits2

2 21

21

/( ) ( )4

ij fii i

i i

L

i

k k v k k vd I ed d k v k

ev

Like a single scatteringFactorization Limit:22 2

12

1

( )( )4

N

N

k k vd I e k k vd d k v k v

f ijL

32 /

3,i ',j i

2Re ij fiLi i j

i

d I A A A ed k

2

BH

d I L dI Nd d

Bethe Heitler Limit:

f ijL

LPM Effect

BH coh

1( )

dI dId d N

Landau PomeranchuckMigdal

NcohNcoh Ncoh

Ncoh

2

2f

22

2cohqNE

2

coh 22 EN

q

radiation like from a single scatteringNcoh

coh coh fL N t

Radiation in QCD: Colors Make the Difference

pi pf

kac

k

pi pfpfpi

k

Gluon multiple scattering (BDMP’96)

accaS TTTTkkR

2

)1( 2

caS TTkq

kqR ,)(

)(22

)2(

dydN

y0

QCD

dydN

y0

QED

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 energy loss: A twisted story

e-

4

( , , ) () )( q h h

D

qh h twist

H x p qdW dW

dxd

f xz d

D zz

( ), () ( , ) q hq

hH x D zx px qfd

2 122

20 0

( , )2

QsT

g L AT

dz dz z z x R

Parton Energy Loss

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q Modified frag. function

HERMES data

2 20.00065 GeVsC

0.5 GeV/fmdEdx

in Au nuclei

Expanding Medium

0 0

2 2 2( ) ( ) )2 (R

g

R

a s dq d C

0

32l( ) 2ns

R

d EE C

(GVW, GOW,Wiedemann)

00( ) ( )R r

00

2

A

E ER

0EEnergy loss in a staticmedium with density 0

Single spectra in A+A collisions

0

0

0

1 0 0

( , , ) ( , , )L

d

dEE b r d b r ndx

1( ) ( )1 / 1 /

zD z DE E E E

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

A B a a b babcdT

d K d b d rd 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

Nuclear Modification Factor

NNAB

ABAB

NR

binary

)(2 bbTdN ABbin

pA

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

Fai, Papp, and Levai (02)

Vitev & Gyulassy (02)

Vitev (03)

Color dipole modelKopeliovich et al (02)

Alberto Accardi (01)LP model

Single hadron suppression

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

h AAAA AA

pp

K pR RK p

Talks by:Hwa,Bass,Greco,Molnar

Di-hadron Spectra2 2 2

1 2 1 22 21 2 21

( ) ( )2

ABA B

T T

d K d b d rd r t r t rdy d p dy d p

2 2/ 1 / 2( , , ) ( , , )a a b b a A a a b B b b

abcd

dx d k dx d k f x k r f x k r / 4/

2 2

ˆ( )

2( , ) ( , )h cab c c c h d d d

ci

d

d D z E D z Ez

ddt z

s p

cE

dE

Hadron-trigger fragmentation function:

1 2 11 1

1

/( , , )/

h h T TT T T

T

d dp d dpD z p pd dp

1,21

( | | )TT cut

T

pz y yp

Suppression of away-side jet

cE

dE

Azimuthal Anisotropy

dihadron

Single hadron

Azimuthal anisotropy II

Talk by R. Lacey, S Voloshin

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

Partonic Energy Loss 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 data of Au+Au Collisions

Initial Density about 30 times of that in a Cold Au Nucleus

Consistent with estimate of initial condition

Talks by Venugopalan, Bickley

Energy Loss Is Partonic!

Could it be caused by hadronic absorption or rescattering?

NO!Uncertainty principle:

f hErm

fm for E=10 GeV 7 ion0 pf

(1) Hadron formation time:h

Parton Energy Loss: 2

(2) Centrality dependence:

Parton energy loss: (3)

(3) PT Dependence:f h

Erm

Parton Energy Loss: (4)

• Large v2

Geometrical anisotropy is an early phenomenon!

early

late

Parton Energy Loss: (4)

(5) Same-side jet profile

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

PHENIX sees the same

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

Measuring Parton Energy Loss

ET

pTtrig

Partonic energy loss: (6) SPS

Summary

• Discovery of Jet Quenching proves that a strongly 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• Collective behavior: Hydrodyamic limit (talks by

Csernai,Huovinen, Nonaka)• It has to be QGP within QCD• Jet tomography become useful and power tool for

studying properties of dense matter

Hard Probes Collaboration

• Jet and high pt hadron• Quarkonium• Heavy Quarks• Direct Photons• DY

http://www-hpc.lbl.gov/

Hard Processes in p+p, p+A and A+A

Parton Shadowing in Nuclei

EMCshadowing

Energy Dependence

Thermal absorption important at lower E

Detailed balanceEnke Wang & XNWPRL87(01)142301

1.20

1

( / 1.6) /(7.5 / )d

dE E Edx

Medium Modified Fragmentation