Jet Quenching: What it really measures?

Xin-Nian WangLawrence Berkeley National Laboratory

High-pT physics at LHC, Jyvaskyla, March 21-27,2007

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

Comparative study of jet quenching schemes; A. Majumder QM06

Gyulassy-Levai-Vitev (GLV)

g

Ln

2

ˆiT

i

qq

L

•Operator formalism that sums order by order in opacity

M. Gyulassy, P. Levai, I. Vitev, Nucl.Phys.B571:197,2000; Phys.Rev.Lett.85:5535,2000; Nucl.Phys.B594:371,2001; Phys. Lett.B538:282-288,2002.

1 2.5ˆ /Geq V fm

Twist Expansion

22

ˆsqg T

g

LT q Lq

Q

•Expansion in higher-twist operator of multiple parton scattering

1 2.5ˆ /Geq V fm

X. Guo, X. N. Wang, Phys. Rev. Lett. 85:3591 (2000); X. N. Wang, X. Guo, Nucl. Phys. A. A696:788, (2001); E. Wang, X. N. Wang, Phys. Rev. Lett.87, 142301,(2001); ibid 89 162301 (2002); B. Zhang, X.N.Wang, Nucl.Phys. A720:429-

451,2003.

Armesto-Salgado-Wiedeman (ASW)

U. Wiedemann, Nucl. Phys. B.582, 409 (2000); ibid. 588, 303 (2000), Nucl. Phys. A.690 (2001); C. Salgado, U. Wiedemann, Phys.Rev. D. 68 014008 (2003); K. Eskola, H. Honkanen, C. Salgado, U. Wiedemann, Nucl. Phys. A.747, 511(2005); N. Armesto, C. Salgado, U. Wiedemann, Phys.Rev.D.72,064910 (2005).

25 15 ˆ /GeV mq f

•Path integral in opacity with summation of many soft scatterings, dipole model of the parton interaction with medium

Arnold-Moore-Yaffe (AMY)

P. Arnold, G. Moore, L. Yaffe, JHEP 0111:057,2001; ibid 0112:009,2001 ; ibid. 0206:030, 2002; S. Jeon, G. Moore Phys. Rev. C71:034901,2005; S.Turbide, C.Gale, S. Jeon, G. Moore, Phys. Rev. C72:014906,2005.

•Finite temperature field theory approach, transport equation for leading parton with HTL resumed interaction

22 2 3ˆ Dc s

g

q N T

/

(

ˆ 2

370 MeV)

GeV fm

T

q

Energy Loss in 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

( ) ( ) ( )(

1( , )

)Lix p y

s T T

Aqg L

s Aq

L T L Tx G x x x GT x

fx x

x

xe

2 ~ 0xB Lx x

[ , , ]Tzq

2

2 (1 )T

Lxp q z z

Bx

22 1 2( ) ( )(1 ) (1 )L LL LB Bi x x p y ix pix p ix p y yy ix py yee ee

Gluon distribution of the medium

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

) (( )

(T LixA

qg L ix pL

q

pA

F Fe eT x x

dy x p ydf x

3

3( )

(2 ) 2

d pO f p p O p

p

[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

+ + +….

22

2( )

11 cos( )

2Tg T L

Tdd

dz

zdy y dyx p y

E

2 22

4

1 (1 )2 ( )

2A

q a q g X s L a Lc

C d zdz x G x

N z

Elastic Energy Loss

0

20 0

/2( ) ( ) ( 1)

2 1g L g Lp T

dp py G x d x

e

3 11 cth( )ele

L

lETL

L TL

E

TLL

2

02 (1 )LxEp z z

22

22

4 3 6lnˆ

12 ( ) 3 23el

Ls

Eq T

T

E

L

T

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

2

0

1

2 12 (3)p T

Interference effect in elastic energy loss

XNW

nucl-th/0604040

Radiative energy loss

2 22

4

1 (1 )[1 cos( )

)ˆ ) ]

2 (1(c s T

TT

NE z ydy d dz

E Ez zq y

( ) (( , )

( )(

) 1)

Lix p yA

Aqg L

T TA L Lq

T x xxdy G x

fy x e

xG x

+ + +….

3ln

8 1ˆ

1rad c sE N L

qE

LL

2

/ 22 2

2ˆ

Eg

g

dq dq q

dq

Radiative vs elastic energy loss

2 3 11 cth( )

12 (3)ˆelE

TLL TL

qT TL

3 ln

8ˆ

11 rad c sE N

qEL

LL

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

0

20 0

/2( ) ( ) ( 1)

2 1q q L q Lp T

dp py f x d x

e

2

02 (1 )LxEp z z

2 22

6 11 -cos

3ln ec( )

6f

F sel TL

T

n TEC

LT

TL

E

L

q-hat and shear viscosity

trC sT

2 22 2 2

ˆ1 4 2

9tr T Ttr cm T

d qdq q

E dq T

39ˆ2

TC

s q

Majumder, Muller and XNW (hep-ph/0703082)

Shear viscosity

1/ 3C

Tested against different transport calculations of h and q-hat, Either through collisions or color field fluctuations

Jet quenching ˆ( ) q T ˆ( )q E

1

4s

Fragility of single hadron suppression

Eskola et al., hep-ph/0406319

q 5GeV

2

fm

fmGeVq 20ˆ

fmGeVq 21ˆ

fmGeVq 2155ˆ

Robustness of jet quenching as probes?

NLO pQCD Calculation

Jet quenching in 2→3 processes

NLO (Next to Leading Order ):

Zhang, Owens, Enke Wang and XNW (nucl-th/0701045 )

Single hadron spectra

0

Modification Factor RAA

0

NLOAA

LOAAR R

Surface emission?

Fragility of single hadron suppression

Centrality dependence of RAA

)( partAA NR

Surface vs. Volume

Dihadron sensitivity

Centrality Dependence

trigpp

hhpp

trigAA

hhAA

trigpp

hhpp

trigAA

hhAA

yieldpp

partyieldAA

partAA

bb

NN

bNbN

D

NDNI

/

)(/)(

/

)(/)()()(

PRL95(2005)152301

Centrality Dependence

PRL95(2005)152301

Dihadron suppression

1( ) , /

hhAA

AA T T Tasso TtrigtrigAA T

dND z z p p

N dz

Sensitivity to initial density

2

20 0ˆ 2.6 3.1 GeVq

2

q-hat in a nucleus

2ˆ 0.01 GeV /Fq fm

e-

20ˆ 1.3 GeV / ( =1 fm)Fq fm

Enke Wang & XNW PRL 89, 162301(2002)

Conclusions

• Jet quenching measures q-hat- gluon distribution of the medium

• Elastic energy loss negligible • qhat viscosity • NLO pQCD analysis of jet quenching

– both single and dihadrons– RAA

NLO < RAALO

• Sensitivity of single and dihadron suppression to the initial gluon density– Centrality dependence of single and dihadron suppression

• Single hadron suppression become fragile while dihadron suppression is more robust probe at LHC

Modified Fragmentation Functions

'/ /0 ' 0

/ / /( , ) (1 ) ( ) ( )L Lch c c c h c c h c c

c

zD z E e D z e D z

z

' /( )c T Tc cz p p E

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

LO pQCD of high pT hadron spectra

)(),,(|)|,,(),,(

2

1|)(|)(

2

1

2/

2/

2/

22

)(

cdabEQzDbrQxfrQxf

sxxbrtrtdzdxrdxbdddK

d

d

ccchbAbaAa

baBAcba

eabcd

hAA

Jet quenching in 2→2 processes2→2 processes

A factor K=1.5-2 account for higher order corrections