Single & Dihadron Suppression at RHIC and LHC

Xin-Nian WangLawrence Berkeley National Laboratory

Last call for prediction for LHC, CERN, May 29-June 2,2007

Collaborators: J. Owens, E. Wang, Z. Zhang, Phys. Rev. Lett. 98, 21230 (2007) [nucl-th/0701045]

Outline

• Jet quenching in twist expansion framework

• Single and dihadron suppression at RHIC and LHC

• A roadmap for jet study at LHC

Jet Quenching in A+A Collisions

hadrons

q

q

hadrons

leadingparticle

leading particle

N-N collision

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

A-A collision

Alphabets of jet quenching

• Gyulassy-Levai-Vitev (GLV)– (Djordjevic, Wicks, Horowitz, …)

• Armesto-Salgado-Wiedeman (ASW)– (Dainess et al, Arleo, Renk, Eskola, …)

• Arnold-Moore-Yaffe (AMY)• High-Twist Expansion (THE)(XNW, Guo,

Majumder, Osborne, Owens, E. Wang, B. Zhang, H. Zhang,…)

Comparative study of jet quenching schemes; A. Majumder QM06 (nucl-th/0702066 )

Jet Quenching in High-Twist Expansion

2 1 22

40 0

1 (1 ) ( , )

( )

Q

s

Aqg L

s Aq

TT

E zd dz

E

T x x

f x

_2 1

( )1 2 1 2

( )2 1

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

1 ( ) ( )1

B L

L L

i x x p y

ix p y ix p y

Aqg L

y

dyT x x dy dy A y F y F y A

y

e

e e y y

2 122

40

( , ) ( , ) ( )2

H

Q

S hq h h L q h

z

zd dzD z Q z x D g h

z z

2 ( , ) 21( , ) (virtual)

(1 ) ( )

Aqg L A S

L Aq c

T x x Czz x

z f x N

Gluon distribution of the medium

(0) 1 )[1 cos( )]( , )

) (( )

(T LixAqg L ix p

Lq

pA

F Fe eT x x

dy x p ydf x

[1[ ( ) cos( , )

( )( ) ( ( )]( ) )]

Aqg L

s s T T L T T LLAq

x G xT x x

d y x p yx xx

G xy xf

21( , ) (0) ( , )

2T Tixp i i

T T i T

dx q d e p F F p

p

q ξξ ξ

2

2( ) ( , )

(2 )T

T

d qxG x x q

2 / 2ˆ ˆ( , ) , |( )

T TT x q Ep

q E y q x y

pT broadening and gluon distribution

2 2 2

2 2 ( ) ( , )

1 (2 )R T T

Tc

g C d q qdx x x q

N s

2 22

ˆ qdq dq q

dq

22

2ˆ 4 ( ) ( )

21s A

T Tc

T

qx

Cq x G x

pN E

4 22 4

4 2

12 (( ) ) (0) ( )

2 (2 ) 1iqR

c

d q g Ck q d e p A A p

s N

k=E

pq

Elastic Energy Loss

2 12 22

40 0

1 (1 )( )( c )) 1 os(

Q

A sT L L

c Tg L

C zd dz x G xz x p yd y

Ny

0( ) ( ) 1

( , )( )

( )L

Aq ix p y

Ag

LA x

LL

q

dy y xGT

x ex x

x G xf x

+ + +….

2 22

4

1 (1 )2 ( )

2A

q a q g s L a Lc

C d zdz x G x

N z

0

20 0

/2( ) ( ) ( 1)

2 1g L g Lp T

dp py G x d x

e

Elastic vs. Radiative Energy Loss

2

22

21 cos( )

1 cos( )12 (3)

( )2

ˆ( )

gel

Tg T

L

TLE x p ydy

dy

dy d

d

q y x p yT

21

2 12 (3)T

2 22

4

1 (1ˆ

)[1 cos( ) ( )]

2 (1 )Rad c s T

TT

qE N z y

dy d dzE Ez z

y

2

9 (3)ln 10

2 11rad c

sel

E N ELLT

E

For E=10 GeV, T=0.2 GeV, L=6 fm, s=0.3

Quark-quark Scattering

2 1 22 2

20 0

( )1 (1 )

1 cos(2

) ( )Q

Fs T Lq L

c T

C dz zdy yz d x p y

Nx

qf

z p

arXiv:0704.0106 [hep-ph]

Schafer, XNW and B.Zhang,

Gluon –parton scattering

Coupled equation for modified fragmentation functions forQuarks and gluons

NLO pQCD Calculation

0

0

0

1 0 0

( , , )L

q gd

dEE d b r n

dL

1-D expanding

0 0g

10

.20 0

1

( / 1.6) /(7.5 / )d

dEE E

dL

Energy loss parameter

0 0 0ˆ1.6 A sCq

Transport coefficient

Geometry: Hard Sphere: Good approximation to Wood-Saxon

Single and Dihadron hadron suppression at RHIC

00

zT=pTass/pT

trig

Sensitivity to initial density

2

20 0ˆ 1 2 GeVAq

2

Surface emission?

Surface vs. Volume

Multiplicity at LHC

2dN/dpart

Parton Shadowing at LHC

Single hadron suppression at LHC

Dihadron suppression at LHC

Dihadron suppression at LHC

A roadmap for jet study at LHC

Re-constructed jets open up a whole new world for jet quenching study

(I always believe what my experimental colleagues tell me)

Reconstructed jets:

(1) Single inclusive jets

(2) Di-jets

(3) Gamma-jets

(1) Measurements of jet shape

• RAA(ET) for jets: 1

Jet cone size R

RAA

For single hadrons

(2) Direct measurement of qhat

2 ˆ( , )T q Edy yq

J. Casalderrey-Solana and XNW, arXiv:0705.1352 [hep-ph].

33ˆ2 ( )

T

s q T

Majumder, Muller and XNW, arXiv:hep-ph/0703082

q-hat in a nucleus

2ˆ 0.01 GeV /Fq fm

20ˆ 1.0 GeV / ( =1 fm)Fq fm

e-

E. Wang & XNW PRL 89, 162301(2002)

(3) Modified fragmentation functions

XNW, Huang and Sarcevic, Phys.Rev. Lett. 77, 231 (1996)

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