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Luan Cheng (Institute of Particle Physics, Huazhong Normal University)
I. IntroductionII. Potential Model with Flow III. Flow Effects on Parton Energy Loss with
Detailed BalanceIV. Summary and Discussion
Collaborator: Enke Wang
ArXiv:0902.1896 [nucl-th]
Flow Effects on Jet Quenching with Detailed Balance
I. IntroductionJet (hard probe) created by parton scattering before QGP is formed
– high transverse momentum---”tomographically” hottest and densest phases of the reaction
– calculable in pQCD
hadrons
q
q
hadrons
leadingparticle
leading particle
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
p-p collision A-A collision
Suppression of high Pt hadron spectra
G-W (M. Gyulassy, X. –N. Wang) Model
Nucl. Phys. B420 (1994) 583; Phys. Rev. D51 (1995) 3436
Static Color-Screened Yukawa Potential
Radiated Energy Loss vs. Opacity
First order in opacity contribution is dominant!
Induced radiative energy loss:
Detailed Balance Formulism (WW)
E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001) 142301
k
x0 p
k
x0 p
Stimulated Emission Thermal Absorption
B-E Enhancement Factor
1+N(k)
Thermal Distribution Func.
N(k)
Numerical Result for Energy Loss
3.0S
)1()1()0(
radabsabsEEEE
• Intemediate large E, absorption is important
•Energy dependence becomes strong
•Very high energy E, net energy gain can be neglected
Light Quark Energy Loss
PHENIX,
Nucl. Phys. A757 (2005) 184
Theoretical results from the light quark energy loss is consistent with the experimental data
Motivation
QGP system is not static, it is a expanding system
Reactionplane
Y
XFlow
Flo
w
QCD:Static Target: static color-electric field Moving Target: color-electric and
color-magnetic field
B
Static Charge: Coulomb electric field
Movement
Moving Charge: electric and magnetic field
QED
II. Interaction Potential with Flow
system fixed at target parton:
Static potential
'
system for observer:
Lorentz boost from system
'
vqvqvv
qvqq
nnnn
nnn
02
00
)(1
'
)('
vVvAvv
AA
AvVV
nnnn
nnn
')'(1
'
)''(
2
21
1
v
)()()'()'(2' 0 nTRTqvqVnn aannn
0' nA
22'
4)'(
n
sn qqv
New Model Potential with Flow
)()()(~)(2),(
)()()(~)(2),(
0
0
nTRTveqvqvqxqA
nTRTeqvqvqxqV
nn
nn
nn
nn
aaxqi
nnnnnn
aaxqi
nnnnnn
222 )(
4)(~
nn
sn qvqqv
The features of the new potential:
1) Collective flow produces a color-magnetic field
2) non-zero energy transfor:
Four-vector potential : )),(),,(( nnnnnnflow xqAxqVA
vxqA nnn
),(
nn qvq
0
III. Flow Effects on Parton Energy Loss with Detailed Balance
k
z0 z1 p
Double Born Scattering
Elastic Scattering:
Inelastic Scattering:
Final-state Radiation
k
x0 p
k
x0 p
Energy loss induced by thermal medium:
0
)0()0(
)0(
T
abs d
dp
d
dpdE
22
2 )2('62
4ln
3
E
FsET
E
TC=
Net contribution: Energy gain
Stimulated emission increase E loss Thermal absorption decrease E loss
Feynman Diagram to the First Order in opacity
Radiation Amplitude for Single Scattering
Single scattering amplitude depends on the flow velocity along the jet direction
Radiation Amplitude for Double Born Scattering
Double Born scattering amplitude is related also with the flow velocity along the jet direction
Radiation Probability to First Order in opacity
Non-Abelian LPM Effect-Destructive Interference
Stimulated Emission
Thermal Absorption
Flow Effect
Mean-free-path:
Gluon Formation Factor and Mean-free-path
Gluon Formation Factor (LPM):
Flow Effect
Gluon Radiation Formation Time:
In the presence of the collective flow in the positive (negative) jet direction, the formation time of gluon radiation becomes shorter (longer), the LPM effect is reduced (enhanced).
Gluon Formation Factor and Mean-free-path
Gluon Formation Factor (LPM):
Mean-free-path: Flow Effect
Energy Loss in First Order of Opacity
Energy loss induced by rescattering in thermal medium: )1()1()1(
absradEEE
Take limit:
,1EL ,E LT 2Zero Temperature Part:
0
)0(
)1(
T
rad d
dpdE
048.0
2ln
4 2
2
L
EC
g
Rs
GLV ResultTemperature-dependent Part:
0
)1()1()1(
T
abs d
dp
d
dpdE
2
22 )2('61ln
3
Eg
Rs
T
L
E
LTC
Energy gain
2)1( LE LE )1(
QCD:
QED:
)1( zv 2L )|(| 2v
)1( zv )|(| 2v
Flow Effect )3.01.0|(| v
Numerical Result for Energy Gain via Gluon Absorption
• At large E region,
• Energy gain decrese with increasing flow velocity in the positive jet direction
• Very high energy E, energy gain can be neglected
)0()1(abs
flowabs EE
IV. Summary and Discussion
Summary:
1) New potential for the interaction of a hard jet with the parton target has been derived, which can be used to study the jet quenching phenomena in the presence of collective flow of the QGP medium.
2) Collective flow along jet direction reduce the opacity, short the formation time of gluon radiation, increase gluon formation factor.
3) Collective flow has observable influence on the parton energy loss. For the flow velocity in the positive jet direction, jet energy loss decrease by 10-30%.
3.01.0|| v
Discussion
1) Collective flow effects affect the suppression of high Pt spectrum in high-energy heavy ion collision.
2) Collective flow effects affect anisotropy parameter v2 in high-energy heavy ion collision.
3) Our new potential can be used for heavy quark energy loss calculation and will alter the dead cone effect of heavy quark jet.
Thank YouThank You
Assumption
• The targets are distributed with the density:
Opacity: Mean number of the collision in the medium
For a scattering center i:
),,,(),,,( 2121 NN zzzA
Nxxx
)(/
121 )(
)(),,,( NLz
e
jN
jN
ejeNL
zzzz
jjj zzz 1
1)(
N
LNLe
A
NLn el
el 1