1. Simon Wicks Columbia University Work done with William Horowitz, Magdalena Djordjevic and Miklos Gyulassy with input from Azfar Adil BNL Heavy Flavor Workshop, 12th December 2005 Influence of Elastic Energy Loss on Heavy Flavor Quenching

2. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)2 Radiative energy loss ● Radiative energy loss insufficient to explain electron data. DGLV predictions: Djordjevic, Gyulassy, Vogt, Wicks Phys Lett B (in press) Radiative energy loss

3. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)3 The Bottom Line: STAR Dong QM05Djordjevic et al PLB Even a factor 4 violation of Bulk entropy constraint fails to account for data Radiative energy loss

4. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)4 Radiative energy loss ● Radiative energy loss insufficient to explain electron data. ● Constraint on dN g /dy: bulk entropy density from total pion rapidity density. ➔ Cannot just 'dial in' dN g /dy = ~3500 ● Non-perturbative effects? ➔ Stay with pQCD, where falsifiable predictions are possible ➔ Include collisional energy loss in addition to radiative. (as suggested in M. Djordjevic thesis) DGLV predictions: Djordjevic, Gyulassy, Vogt, Wicks Phys Lett B (in press) Radiative energy loss

5. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)5 Radiative energy loss ● Radiative energy loss insufficient to explain electron data. ● Constraint on dN g /dy: bulk entropy density from total pion rapidity density. ➔ Cannot just 'dial in' dN g /dy = ~3500 ● Non-perturbative effects? ➔ Stay with pQCD, where falsifiable predictions are possible ➔ Include collisional energy loss in addition to radiative. (as suggested in M. Djordjevic thesis) DGLV predictions: Djordjevic, Gyulassy, Vogt, Wicks Phys Lett B (in press) AIM: To establish experimental limits on the kinematic range in (p T,y) where perturbative QCD can be accurately used to predict jet dynamics in dense QCD media. Radiative energy loss

6. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)6 Models of elastic energy loss ● Collisional energy loss is of the same magnitude as radiative in the kinematic region of interest (see M. G. Mustafa, Phys.Rev.C72:014905,2005) ● First estimate: Bjorken kinematic estimate of magnitude (FERMILAB-PUB-82-059-THY, unpublished), then over time, improved treatment of IR and UV. ● Further possible improvement: input from evolving medium simulations by Molnar and Hirano. BT: E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). TG: M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991).

7. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)7 Models of elastic energy loss ● Collisional energy loss is of the same magnitude as radiative in the kinematic region of interest (see M. G. Mustafa, Phys.Rev.C72:014905,2005) ● First estimate: Bjorken kinematic estimate of magnitude (FERMILAB-PUB-82-059-THY, unpublished), then over time, improved treatment of IR and UV. ● Further possible improvement: input from evolving medium simulations by Molnar and Hirano. BT: E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). TG: M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991). BT: unphysical energy gain for bottom due to a failure of the extrapolation from the weak-coupling limit (Romatschke, Strickland).

8. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)8 Models of elastic energy loss (II) P. Romatschke, M. Strickland (Phys. Rev. D 69, 065005 (2004) ● For a parton p=10GeV: ➔ Bottom elastic energy loss ~ TG >> BT ➔ Charm elastic energy loss ~ BT > TG

9. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)9 Open problem: Retardation effects? ● Naive expectation: Formation effects only non-negligible for time on order of the Debye length ➔ ie small effect Particle(s) created at finite time in the plasma, rather than at t=-∞

10. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)10 Open problem: Retardation effects? Peigné, Gossiaux, Gousset (hep-ph/0509185) Peigné et al claim: strong suppression of elastic due to transient field and retardation effects (unexpected positive energy gain due to transverse response function) ➔ Challenge to all applications of elastic energy loss (Bjorken, TG, BT, RS and parton cascade)

11. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)11 Open problem: Retardation effects? Peigné, Gossiaux, Gousset (hep-ph/0509185) Peigné et al claim: strong suppression of elastic due to transient field and retardation effects (unexpected positive energy gain due to transverse response function) ➔ Challenge to all applications of elastic energy loss (Bjorken, TG, BT, RS and parton cascade) BUT: formalism used mixes radiative (zerorth order) and elastic mechanisms Part of medium induced energy gain is due to Ter-Mekilian (see M. Djordjevic) that is cancelled by Transition Radiation (not included by Peigne).

12. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)12 Remaining theoretical uncertainties ● Interference between radiative and collisional energy loss? ● (X.N. Wang found small interference) ➔ Used here: incoherent addition of the two effects. ●  s (q) - running coupling constant. – Effect of full running with  q   max ~ 0.5? ➔ Used here: fixed  s=0.3 ● Length scale ➔ Used in this talk : fixed L=5fm as “typical” length ➔ See next talk (W. Horowitz) dynamical geometry

13. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)13 Results - Partonic Raa (fixed L=5fm) Charm Bottom ➔ Radiative + collisional ~2x suppression of radiative alone ➔ Large difference between BT and TG for bottom quark quenching Fixed L=5fm;  =0.3; dN g /dy=1000

14. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)14 Results - Electron Raa (fixed L=5fm) Fixed L=5fm;  =0.3; dN g /dy=1000

15. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)15 Results - Pion Raa (fixed L=5fm) Fixed L=5fm;  =0.3; dN g /dy=1000 Pions overquenched at low p T (for fixed L=5fm)

16. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)16 Conclusion ● Collisional energy loss must be included to account for all perturbative physical effects ● Important theoretical issues remain to be resolved – Retardation effects – Collisional - radiative interference – Running coupling ● Fixed L predictions get closer to single electron R AA data ● Fixed L predictions move away from the π 0 R AA data

17. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)17

18. Simon Wicks, Columbia University (Heavy Flavor Workshop, 12th Dec 2005)18 Key new physics insight: A: Elastic has greater quenching effect than Inelastic because  E el /E Fluctuates Less than  E rad /E!! BUT GLV,WW So what if elastic ~ inelastic? Q: Can’t this be just absorbed into the effective dN eff /dy or ? Elastic and inelastic: Fluctuations