Heavy Quark Energy Loss due to Three-body Scattering in a Quark- Gluon Plasma Wei Liu Texas A&M University  Introduction  Heavy quark scattering in QGP  Heavy quark drag coefficients  Heavy quark momentum spectra  Nuclear modification factor for electron  Summary and discussions Original work was done in collaboration with C. M. Ko. QM2006, shanghai, china

Energy loss by radiation when passing through the hot dense medium WG model: static color scattering center, fit data at dN/dy=1000 Possible solutions? a. Non-perturbative process (resonance) b. First order radiation (dN/dy=3500) c. Elastic plus radiation (dN/dy=1000) 1. Light jet: light quark or gluon 2. Heavy quark jet Dead cone: WG models fails by including only radiative contribution Jet quenching I, vitev, hep-ph/ S. Wicks et al, nucl-th/

Our approach Fokker-Planck equation: studying heavy quark momentum degradation Lowest order QCD approach: Binary elastic + radiative + three-body elastic Multiple partonic collisions may be important ! Three-quark and gluon elastic scattering are found to be important for quark and gluon thermalization in the initial stage X. M. Xu et al. Nucl. Phys. A 744, 347 (2004); X. M. Xu et al. Phys. Lett. B 629, 68 (2005)

Fokker-Planck equation

1. 2-body elastic2. Radiative Processes calculated exactly

3. 3-body elastic collisions true three-body process

6 extra diagrams are obtained by interchanging final two light quarks, and give same contribution as that due to direct diagrams. Interference terms are found to be two order of magnitude smaller and neglected. 5 extra diagrams are obtained by exchanging a gluon between heavy quark, and light quark, antiquark, or virtual gluon from quark and antiquark annihilation. The contribution is also two order of magnitude smaller than that due to direct diagrams. 36 diagrams are obtained by attaching an extra gluon to all parton lines and three-gluon vertex in Qq→Qqg. Only six diagrams with two gluons attached to both heavy quark and light partons are evaluated. 123 diagrams are obtained from Qg→Qgg by attaching an extra gluon. Again, only six diagrams with two gluons attached to both heavy quark and light partons are calculated. Processes calculated approximately

Collision width of heavy and light partons  Widths are mainly due to 2-body elastic scattering.  Width of gluon is about twice of that of light quark.  Width of bottom quark is two thirds of that of charm quark. charm Light quark

At high p T, radiation dominates for charm; contributions from three- body elastic collisions is 80% of those from two-body elastic collisions. M. Djordjevic and M. Gyulassy, Nucl. Phys. A (2004) Drag coefficient

This model gives a total transverse energy comparable to that measured in experiments, and the time dependence of temperature is obtained from entropy conservation. QGP fireball dynamics Initial heavy quark spectra

Charm quarks: spectrum determined from fitting simultaneously measured transverse spectrum of charm mesons from d+Au collisions and of electrons from heavy meson decays in p+p collisions. Bottom quarks: spectrum taken from the pQCD prediction.

Heavy quark spectrum and electron spectrum R0R0

Charm: Radiation dominates at high transverse momentum. Bottom: 3-body elastic scattering is comparable to 2-body and radiative scattering. Electron R AA for charm and bottom Combination of contributions from charm and bottom are still above experimental data.

Strongly coupled QGP ? O. Kaczmarek, F. Karsch, and F. Zantow, Phys. Rev. D 70, (2004); O. Kaczmarek, F. Zantow,Phys. Rev. D 71, (2005) From lattice calculation Using two loop pQCD running coupling

 We have calculated the drag coefficient for heavy quark in quark gluon plasma, and found that three- body elastic collision is important for the heavy quark momentum degradation.  More reliable calculation is needed for the most important process Qqg → Qqg (36 Feynman diagrams).  New experimental data seem to favor a strongly coupled quark gluon plasma.  Multiple partonic processes involving more than 6 partons need to be considerd (a theoretical challenge). Summary and discussions