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

qq

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