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 Balance VI An Explanation for Heavy Quark Energy Loss Puzzle V. Summary Collaborator: Enke Wang ArXiv: [nucl-th] ; [nucl-th] Jet Energy Loss with Flow

I. Introduction Suppression of high Pt hadron spectra hadrons q q Leading particle suppressed leading particle suppressed A-A collision Jet 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) Static Medium! Light hadrons supprestion observed at RHIC is consisted with predictions from jet quenching theory. Jet Quenching in the Static Medium

Puzzle for Heavy Quark Energy Loss Y. Dokshitzer & D. Kharzeev PLB 519(2001)199 B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) Heavy quark has less dE/dx due to suppression of small angle gluon radiation “Dead Cone” effect J. Adams et. al, PRL 91(2003) M. Djordjevic, et. al. PRL 94(2005) Dead cone

STAR Non-photonic electrons from heavy quark decays Charged hadrons from Light quark fragmentation No Significant Difference Between Heavy Quark Jet and Light Quark Jet

Reaction plane Y X Flow

Motivation QGP system is not static, it is a expanding system QCD Static Target: static color-electric field Moving Target: color-electric and color-magnetic field B Static Charge: Coulomb electric field Movement QED Moving Charge: electric and magnetic field Coulomb Potential Yukawa Potential

zero energy transfer II. Interaction Potential with Flow Static potential New Model Potential with Flow

Four-vector potential : The features of the new potential: 1)Collective flow produces a color-magnetic field 2) non-zero energy transfer: The features of the new potential:

Energy loss induced by thermal medium: = Net contribution: Energy gain Stimulated emission increase E loss Thermal absorption decrease E loss III. Flow Effects on Light Quark Energy Loss with Detailed alance

First Order in opacity Correction

Chang of the pole of light quark propagator Static Medium Medium with flow

Radiation Amplitude Radiation amplitude depends on the flow velocity along the jet direction for Single Scattering for Double Born Scattering

Radiation Probability to First Order 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. Gluon Formation Factor:

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

VI.An Explanation for Heavy Quark Energy Loss VI. An Explanation for Heavy Quark Energy Loss Zero order in opacity: Distribution of soft gluon radiation: Dead cone:

Chang of the pole of heavy quark propagator Static Medium Medium with flow

Dead Cone from Different Processes ……

Dead Cone Reduce Significantly with Flow Dead Cone:

Radiation Amplitude for Heavy Quark Jet

Radiation Probability in First Order Opacity Gluon Formation Time:

Energy Loss vs. Flow Velocity

Average Flow Velocity and Effective Average Energy Loss 3D ideal Hydrodynamic simulation (T. Hirano et al, Phys. Rev. C65, (2001); Phys. Rev. C66, (2002); Phys. Lett. B636, 299 (2006). ) for 0-10% central events of Au-Au collisions at RHIC energy:T. Hirano et al, Phys. Rev. C65, (2001)Phys. Rev. C66, (2002)Phys. Lett. B636, 299 (2006) Average Flow Velocity: Proper time, Position

Effective Average Energy Loss 3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy

V. Summary 1)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

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