o Overview Selected results from RHIC “light quark” jet quenching
Jet Quenching: What it really measures?
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Transcript of Jet Quenching: What it really measures?
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
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