7th Workshop on QCD and RHIC Physics

Xin-Nian WangLawrence Berkeley National Laboratory

Hard Probes at RHIC: a Theoretical Overview

Hefei, July 9-13, 2008

7th National Workshop on QCD and Relativistic Heavy-ion Collision Physics

Workshop on QCD and RHIC Physics, Wuhan, 2002

First meeting in 2001, CCAST, Beijing

Learning & exchange of ideas

Fun & friendship

New Discoveries

What has happened since then

Chinese STAR Collaboration: MPRC project for TOF

Chinese ALICE Collaboration

Major NSFC Project on RHIC Theory and Phenomenology

Empirical Evidence of sQGP at RHIC

Hydro-dynamics calc.

Pedestal&flow subtracted

A “Perfect Liquid” or sQGP?

Liquid, fluid and (strongly coupled) plasma

Characteristic of liquid orgas: pair correlation

Thoma’ 2006Yu, Xu, Liu & Liu, 2008

How small is the /s?

Room for some range of /s

Huovinen’08

C Geiner & Z. Xu’08

q-hat and Shear Viscosity

1

3 trsT

2 22 2 2

ˆ1 4 2

9tr T Ttr cm T

d qdq q

E dq T

33ˆ2

T

s q

Majumder, Muller and XNW’07

Shear viscosity

Jet quenching ˆ( ) q T ˆ( )q E

2ˆ 1 2 / 0.008 0.025q GeV fms

Jet transport in medium

Ap

0 y

Ap

qq

†( , ) ( ) ( ; ) ( ) ( ; ) |y

yW y y iD y g d y F y

L L

Jet Transport Operator

dpgF v

d

Classical correspondence:

…

(2)( , ) (0) (0; ,0 )exp[ ] ( ,0 ) ( )(4

,0 ) kq ixp yA

dyf x k e A y y kW Ay

L

Liang, XNW & Zhou’08

Maximal Two-gluon Correlation

†0

( ,0 ) ( ; ) ( ) ( ; )( ) |y

yW y g d yi y yD F

L L

22 (0) (0; ( )) ( )4

ni yk

n xpdyM e A y y AW y

L

1 2

4/31

2 1

2 2

(0) ( )

(

( ) ( )

() ) ( )qN N A N N

dy d d F F

d x G x

A y A

Af x A

( )( ( )( )0)D y Dd A y A Ayy

2 ( ) ( )( )

2

nnn A

AA N

yW dy N F dy y xF N G x

p

Medium Broadening

2

22

ˆ( , ) exp ( ) ( )4

( ) exp ( )

kq qA N N N

qN

f x k A d q f k

A k qd q f q

2 ˆ( )N Nk d q

Liang, XNW & Zhou’08Majumder & Muller’07Kovner & Wiedemann’01

2

02

4ˆ( ) ) ) |

1( (A N N x

s FN

c

C

Nxq xG

Jet transport parameter

( ) (0, ) ( )2

ixp AN

dxG x e N F F N

p

L

dpgF v

d

Solution of diffusion eq.

Jet transport parameter & Saturation

Gluon saturation2

2 202

4ˆ ( ) ( , ) |

1s A

A A sat A A N N sat xc

Cq L Q L xG x Q

N

Kochegov & Mueller’98McLerran & Venugapolan’95

2

2

4ˆ ( , ) )

1( ( )A N N

s FF N

c

Cq x

NxG x

Multi-gluon correlation:2 2ˆ( ) ( , )Nq Q xG x Q

Casalderrey-Salana, &XNW’07

q̂̂q

2sQ

DGLAP

Measuring qhat

Direct measurement:

or modified fragmentation function

Measuring parton energy loss

GW:Gyulassy & XNW’04BDMPS’96LCPI:Zakharov’96GLV: Gyulassy, Levai & Vitev’01ASW: Wiedemann’00HT: Guo & XNW’00AMY: Arnold, Moore & Yaffe’03

q

Apxp

xp

Ap

q

x1p+kT

Hadron suppression & medium properties

Bass et al’08

20 0ˆ 1 5 GeV /q fm

2ˆ 0.01 GeV /Nq fmCold nuclear matter in DIS

Wang & XNW’01

Majumder, Wang & XNW’07

OWWZ: Owen, Wang, XNW & Zhang’08

Gamma-jet: toward a true tomography

Isolated photons as tags:

HSW’96, OWWZ’08

Huang, Sarcevic & XNW’96

Volume emission for small zT Surface emission for large zT>1

Jet Quenching phenomenology

2 -fit to single hadron Raa in Au+Au at all centralities at RHIC energy

0

0

0

1 0 0

( , , )L

qd

g b rE ndE

ddL

Phenix’08, see Nagle’s talkOWWZ’08

TECHQM

Theoretical improvements

2

9 (3)ln

2 11rad c

sel

E N ELLT

E

Elastic vs radiative: for finite E & L Qin, et al ‘’08

22

2

ˆ ˆ ˆ( ) ( ,0) ( , ) 2 ( ,0 ( ))gL L

dNc x q q x q

d d Qz

O

Recoil in radiative process:

2

2( )QOQuark-annihilation

Flavor changing process

q

Ap Ap

qNLO corrections to LO collinearfactorized contribution

Mass correction for heavy quarks2

2( )QM

QO

Heavy Quarks

Eel for heavy quark is larger than light quarks

D

dpp

dt

Langevin Eq. for v<<1 Moore & Teaney’05

22 logD s

D

T T

M

pQCD

2

2D

T

M

Strong coupling SYM

Casalderrey-Solana & Teaney’06Gubser’06, Herzog et al’06

Rcb Ratio

Horowitz & Gyulassy’08

Wicks et al’06,Djordjevic et al’06

Armesto, et al’08

Inclusion of multiple gluon emission

2 22

( , ) gdNP z

dzd

Modified DGLAP Evolution Eq. Guo & XNW’00q

Ap Ap

q

22 2

2

( , )( ) ( , ) ( , )

log 2sD z Q dy y

P y P y Q D Qd Q y z

Renk’08

Effects of hydrodynamics

0ˆ( , )E d q r n

0r

n

1D vs. 2+1D

Faster decrease in but increased duration

Gyulassy, et al’02

Viscous hydro, 3-D haydro: effects are expected to be small

Some decrease in anisotropy of E in 1+2D without effect of flow

Gyulassy, et al’02

00

ˆ ˆu p

q qp

Effect of flow

ˆ0.9

ˆflow

no flow

q

q

Baier, Mueller &Schiff’06

Liu, Rajagopal & Wiedemann’06

Azimuthal anisotropy

234.6partN 166.6partN

114.2partN 74.4partN

45.5partN 25.7partN

GeVpT 85

OWWZ’ 2008 Bass et al’08

20-30%

1+1D Bjorken1+2D hydro

Medium response to jets

Sonic mach cones induced by propagating jetsStocker’05, Casaderrey-Solana, Shuryak & Teaney’05 c

cos sc

c

v Mach cone angle:

Sound attenuation with of the cone structure:sT

Neufeld, Muller & Ruppert’08

pQCD/s=1/4

Chesler & Yaffe;07Fries et al’07

SYM

Cone & ridge in parton cascade

Double peak structure was seen in AMPT simulation Ma, et al ‘06

pT=0~1GeV/c

Soft hadrons associated with a jet Minimum distance required

Ridge along tangential jetspunch-through jets

tangential jets

Longitudinal flow (Armesto et al’05)Longitudinal field (Majumder et al’07)Recombination (Hwa’05, Wong’ 07)

Summary

• sQGP still needs to be quantified• Jet transverse momentum broadening provides a

lot of information about the medium: gluon density, gluon correlations, etc, all characterized by jet transport parameter qhat

• Jet quenching provided an indirect measurement of qhat

• Jet quenching phenomenology has advanced to more quantitative analysis

• More exclusive studies such as gamma-jet and medium excitation are necessary