Luan Cheng (Institute of Particle Physics, Huazhong Normal University) I.Introduction II. Potential Model with Flow III.Flow Effects on Parton Energy Loss with Detailed Balance IV.Summary and Discussion Collaborator: Enke Wang ArXiv: [nucl-th] Flow Effects on Jet Quenching with Detailed Balance

I. Introduction Jet (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 leading particle leading particle hadrons q q Leading particle suppressed leading particle suppressed p-p collisionA-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) Stimulated EmissionThermal Absorption B-E Enhancement Factor 1+N(k) Thermal Distribution Func. N(k)

Numerical Result for Energy Loss 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 Reaction plane Y X Flow

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

New Model Potential with Flow The features of the new potential: 1)Collective flow produces a color-magnetic field 2) non-zero energy transfor: Four-vector potential :

III. Flow Effects on Parton Energy Loss with Detailed Balance k z 0 z 1 p Double Born Scattering Elastic Scattering: Inelastic Scattering:

Final-state Radiation Energy loss induced by thermal medium: = 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: Take limit: Zero Temperature Part: GLV Result Temperature-dependent Part: Energy gain QCD: QED: Flow Effect

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

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%.

Discussion 1)Collective flow effects affect the suppression of high P t spectrum in high-energy heavy ion collision. 2)Collective flow effects affect anisotropy parameter v 2 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 You Thank You

Assumption The targets are distributed with the density: Opacity: Mean number of the collision in the medium For a scattering center i: