Heavy Quark Energy Loss due to Three-body Scattering in a Quark-Gluon Plasma

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

2. Jet quenching 1. Light jet: light quark or gluon I, vitev, hep-ph/0511237 Energy loss by radiation when passing through the hot dense medium WG model: static color scattering center, fit data at dN/dy=1000 2. Heavy quark jet S. Wicks et al, nucl-th/0512076 WG models fails by including only radiative contribution Dead cone: Possible solutions? a. Non-perturbative process (resonance) b. First order radiation (dN/dy=3500) c. Elastic plus radiation (dN/dy=1000)

3. Our approach 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: studying heavy quark momentum degradation Lowest order QCD approach: Binary elastic + radiative + three-body elastic

4. Fokker-Planck equation

5. Processes calculated exactly 1. 2-body elastic 2. Radiative

6. 3. 3-body elastic collisions true three-body process

7. Processes calculated approximately 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.

8. Collision width of heavy and light partons charm • 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. Light quark

9. Drag coefficient M. Djordjevic and M. Gyulassy, Nucl. Phys. A733 265 (2004) At high pT, radiation dominates for charm; contributions from three-body elastic collisions is 80% of those from two-body elastic collisions.

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

11. 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.

12. Heavy quark spectrum and electron spectrum R0

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

14. Strongly coupled QGP ? O. Kaczmarek, F. Karsch, and F. Zantow, Phys. Rev. D 70, 074505 (2004); O. Kaczmarek, F. Zantow,Phys. Rev. D 71, 114510 (2005) From lattice calculation Using two loop pQCD running coupling

15. Summary and discussions • 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).