jet quenching: what it really measures?
DESCRIPTION
Jet Quenching: What it really measures?. Xin-Nian Wang Lawrence Berkeley National Laboratory. High-pT physics at LHC, Jyvaskyla, March 21-27,2007. Jet Quenching in A+A Collisions. leading particle. hadrons. q. q. hadrons. leading particle. Leading particle suppressed. hadrons. q. q. - PowerPoint PPT PresentationTRANSCRIPT
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Jet Quenching: What it really measures?
Xin-Nian WangLawrence Berkeley National Laboratory
High-pT physics at LHC, Jyvaskyla, March 21-27,2007
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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Interference effect in elastic energy loss
XNW
nucl-th/0604040
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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
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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
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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
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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
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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?
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NLO pQCD Calculation
Jet quenching in 2→3 processes
NLO (Next to Leading Order ):
Zhang, Owens, Enke Wang and XNW (nucl-th/0701045 )
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Single hadron spectra
0
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Modification Factor RAA
0
NLOAA
LOAAR R
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Surface emission?
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Fragility of single hadron suppression
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Centrality dependence of RAA
)( partAA NR
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Surface vs. Volume
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Dihadron sensitivity
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Centrality Dependence
trigpp
hhpp
trigAA
hhAA
trigpp
hhpp
trigAA
hhAA
yieldpp
partyieldAA
partAA
bb
NN
bNbN
D
NDNI
/
)(/)(
/
)(/)()()(
PRL95(2005)152301
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Centrality Dependence
PRL95(2005)152301
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Dihadron suppression
1( ) , /
hhAA
AA T T Tasso TtrigtrigAA T
dND z z p p
N dz
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Sensitivity to initial density
2
20 0ˆ 2.6 3.1 GeVq
2
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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)
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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
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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
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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