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Luan Cheng (Institute of Particle Physics, Huazhong Normal University)
I. Introduction II. Interaction Potential with Flow III. Flow Effects on Light Quark Energy Loss with Detailed BalanceVI An Explanation for Heavy Quark Energy Loss PuzzleV. Summary
Collaborator: Enke Wang
ArXiv:0902.1896 [nucl-th] ; 0908.0918 [nucl-th]
Jet Energy Loss with Flow
I. Introduction
Suppression of high Pt hadron spectra
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
A-A collision
Jet QuenchingJet Quenching
penetrating beam (jet) absorption or scattering pattern
QGP
Hard Probes of Quark Matter:
BDMPS, 1997, Energy loss ~ Nucl. Phys. B484:265, (1997) .
G-W Model, Opacity Expansion, Phys. Rev. Lett 85, 5535, (2000)
StaticMedium!
Light hadrons supprestion observed at RHIC is consisted with predictions from jet quenching theory.
Jet Quenching in the Static Medium
2L
Puzzle for Heavy Quark Energy LossPuzzle for Heavy Quark Energy Loss
k
E
M
dP
k
dkkdCdP Fs
,
)/1()(
0
2220
022
022
22
Y. Dokshitzer & D. Kharzeev PLB 519(2001)199 B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301
Heavy quark has less dE/dx due to suppression of small angle gluon radiation
“Dead Cone” effect
J. Adams et. al, PRL 91(2003)072304
M. Djordjevic, et. al. PRL 94(2005)112301
Dead cone
STARSTAR
Non-photonic electrons from heavy quark decays
Charged hadrons fromLight quark fragmentation
No Significant Difference BetweenNo Significant Difference BetweenHeavy Quark Jet and Light Quark JetHeavy Quark Jet and Light Quark Jet
Reactionplane
Y
XFlow
Flo
w
MotivationQGP system is not static, it is a expanding system
QCDStatic Target: static color-electric field Moving Target: color-electric and
color-magnetic field
B
Static Charge: Coulomb
electric field
Movement
QEDMoving Charge: electric and
magnetic field
Coulomb Potential
Yukawa Potential
zero energy transfer
II. Interaction Potential with FlowII. Interaction Potential with FlowStatic potential
)()()'()'(2' 0 nTRTqvqVnn aannn
0' nA
22'
4)'(
n
sn q
qv
)()()(~)(2),(
)()()(~)(2),(
0
0
nTRTveqvqvqxqA
nTRTeqvqvqxqV
nn
nn
nn
nn
aaxqi
nnnnnn
aaxqi
nnnnnn
222 )(
4)(~
nn
sn qvq
qv
New Model Potential with FlowNew Model Potential with Flow
Four-vector potential :
)),(),,(( nnnnnnflow xqAxqVA
The features of the new potential:
1) Collective flow produces a color-magnetic field
2) non-zero energy transfer:
vxqA nnn
),(
nn qvq0
The features of the new potential:
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
III. Flow Effects on Light Quark III. Flow Effects on Light Quark Energy Loss with Detailed alanceEnergy Loss with Detailed alance
First Order in opacity CorrectionFirst Order in opacity Correction
Chang of the pole of light quark Chang of the pole of light quark propagatorpropagator
Static MediumMedium with flow
iqpqp
2)(
1)(
iq
iEq
z
z
2
1 2
iqkpqkp
2)(
1)(
iq
iEq
z
z
04
3 2
20
k
iq
iv
Eq
z
zz
2
1 1
2
zv1
iv
q
iv
Eq
zz
zz
1
1
2
04
3zv1
zv1
Radiation AmplitudeRadiation Amplitude
Radiation amplitude depends on the flow velocity along the jet direction
for Single Scatteringfor Single Scattering
for Double Born Scatteringfor Double Born Scattering
Radiation Probability to First Radiation Probability to First Order in opacityOrder in opacity
Non-Abelian LPM Effect-Destructive Interference
Stimulated Emission
Thermal Absorption
Flow Effect opacity
Gluon Radiation Formation Time:
In the presence of the collective flow in the positive jet direction, the formation time of gluon radiation becomes shorter, the LPM effect is reduced.
1
1
z
f
v
Gluon Formation Factor:
Energy Loss in First Order of Energy Loss in First Order of OpacityOpacity
Energy loss induced by rescattering in thermal medium: )1()1()1(
absradEEE
Take limit:,1EL ,E LT 2
Zero 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
VI.VI. An Explanation for Heavy An Explanation for Heavy Quark Energy LossQuark Energy Loss
Zero order in opacity:
k
x0 p
Distribution of soft gluon radiation:
Dead cone:
Chang of the pole of heavy quark Chang of the pole of heavy quark propagatorpropagator
Static Medium Medium with flowiMqp
qp
22)(
1)(
iq
iEq
z
z
2
1 2
iMqkpqkp
22)(
1)(
iq
iEq
mz
z
04
3 2
iv
q
iv
Eq
z
Mz
zz
1
1
2
2
1
zv1
zv1M
iv
q
iv
Eq
z
Mmz
zz
1
1
2
04
3zv1
zv1M
Dead Cone from Different ProcessesDead Cone from Different Processes
……
Dead Cone Reduce Significantly Dead Cone Reduce Significantly with Flowwith Flow
Dead Cone:
Radiation Amplitude for Heavy Radiation Amplitude for Heavy Quark JetQuark Jet
Radiation Probability in First Order OpacityRadiation Probability in First Order Opacity
Gluon Formation Time:
Energy Loss vs. Flow VelocityEnergy Loss vs. Flow Velocity
d
dPdE
)1(
Average Flow Velocity Average Flow Velocity and Effective Average Energy Lossand Effective Average Energy Loss
3D ideal Hydrodynamic simulation (T. Hirano et al, Phys. Rev. C65, 011901 (2001); Phys. Rev. C66, 054905 (2002);
Phys. Lett. B636, 299 (2006). ) for 0-10% central events of Au-Au collisions at RHIC energy:
Average Flow Velocity:
Proper time, Position
Effective Average Energy LossEffective Average Energy Loss
3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy
V. Summary1) New potential for the interaction of a hard jet with
the parton target with flow. Collective flow reduce the opacity
2) For light quarks Collective flow short the formation time of gluon radiation,
increase gluon formation factor.
3) For heavy quarks
Collective flow reduce the dead cone from mass effect.
energy loss increase obviously in the presence of folw
little difference of effective average energy loss among the charm, bottom and light quarks
2)1( zv
)1( zv
Thank YouThank You
