What drives you?

1. ... and your jet energy loss calculation? What drives you? aka Perturbative jet energy loss mechanisms: Learning from RHIC, extrapolating to LHC Simon Wicks Miklos Gyulassy Institut für Theoretische Physik

2. If we put the pedal to the metal, how fast will it go? Why does it matter?

3. We must model the medium (and the interactions of the jet with it). No generic energy loss mechanism. Q: What is / are the dominant energy loss process(es)?

4. GLV GLV + collisional BDMPS-Z-ASW Higher Twist – Wang etc AMY van Hees / Rapp VA coll dissociation AdS/CFT – LRW AdS/CFT – TCS AdS/CFT – Kovtun et al AdS/CFT – Gubser ... An excess of theoretical models STAR Phys. Rev. Lett. 98 (2007) 192301

5. What models are available? HTL On-shell quasiparticles ie width << energy wQGP GW model (Parton cascade) Resonance models eg Rapp & Van Hees, Shuryak ... 'Dynamic quasi-particles' ie width ~ energy sQGP Peshier / Cassing model ... AdS/CFT No quasi-particles (except jets ...) ssQGP

6. 1) Know what are the energy loss mechanisms are. Different energy loss mechanisms scale differently with density and jet energy. 2) Collisions are what induces (causes the medium modification to) the radiative energy loss. Why look at collisional processes?

7. 1) Bjorken 1982 (FERMILAB-PUB-82-059-THY) Vacuum estimate, cut-off at Debye mass 2) Thoma-Gyulassy 1991 (Nucl.Phys.B351:491-506,1991) Classical EM naturally regulates the infrared (but has little to say about ultra-violet) 3) Braaten-Thoma 1991 (Phys.Rev.D44:2625-2630,1991) HTL for low momentum exchange, vacuum for high momentum exchange, cut-off between the two magically drops out under certain assumptions. All assume that momentum exchange is small compared to the momenta of the jet & medium particles. A very selective history

8. t-channel exchange Neglect difference between Q-q and Q-g (except Casimir) NOT make assumptions like ω << T, μ in coefficients. The Formalism

9. Massive jet, massless medium Phase space Similar treatment to: Moore & Teaney Phys.Rev.C71:064904,2005 Djordjevic Phys.Rev.C74:064907,2006 Arnold, Moore, Yaffe JHEP 0305:051,2003

10. The Matrix Element

11. The Matrix Element (cont.) After

12. Collisional energy loss (before multiple collision convolution) (D)GLV radiative energy loss

13. Average energy loss

14. How to approach multiple collisions? 1) Take the distribution, find average (drag) and width (diffusion), use in Fokker-Planck / Langevin diffusion process. BUT expect the number of (momentum changing) collisions to be small. (come back to this later ...) Multiple collisions

15. 2) Poisson convolution for multiple independent collisions Multiple Collisions

16. Multiple Collisions NOT continuum limit diffusion process

17. So far, shown fixed length plots. For RAA: all results shown have been averaged over all production points and jet trajectories. ρpart bulk, ρbinary jets, Bjorken expansion. Geometry integrals

18. WHDG α = 0.3 Results – RHIC - Pions

19. WHDG α = 0.3 Results – RHIC - Pions

20. WHDG α = 0.3 Results – RHIC - Electrons

21. WHDG α = 0.3 Results – RHIC - Electrons

22. RHIC Predicting LHC

23. RHIC Predicting LHC LHC

24. RHIC Predicting LHC LHC

25. Predicting - LHC

26. ... at the collisional distributions. A closer look ...

27. A different perspective ... 1) Diffusion process not applicable except for v long distances 2) Uncertainty in HTL model ...

28. Why? • 1) HTL breaks downg is not << 1 • 2) High momentum jeteg ΔE ~ log(E/gT)For log(T/gT) >> log(E/gT)-log(T/gT)=> log(1/g) >> log(E/T)E = 10 GeV, T = 0.25 GeV=> g << 0.025 • 3) Both

29. ω << T, μ assumption / approximation is NOT ok to calculate av en loss Must take into account medium recoil.

30. Look at two schemes that are equivalent 'at leading order' Both agree in limit ω,q << T, μ and in limit ω,q -> ∞ (or μ -> 0) How can we quantify this uncertainty?

31. 1) Simple extrapolation of HTL to large momentum transfer. 2) Prescription found in AMY – only modify infrared divergent part of amplitude. 'Equivalent' calculations

32. HTL extrapolation HTL-AMY extrapolation

33. Result

34. g = 2, pt = 10GeV: 1.6 or 1.3 g = 1, pt = 10GeV: 1.3 or 1.2 g = 0.1, pt = 1GeV: 1.0 or 1.0 Equivalent at leading order

35. Redistribution of longitudinal and transverse components. Longitudinal and transverse components are screened by the medium in different ways. Why are HTL and HTL-AMY so different? HTL HTL-AMY

36. Longitudinal and transverse m∞ Longitudinal and transverse modes have asymptotic masses that act differently: L: T: Equations from: Pisarski, Physica A158:246-250,1989

38. What about qperp distributions? p = 10 GeV p=10GeV: <qperp2> ≈ 0.25 GeV2/fm for T = 0.24GeV

39. What about qperp distributions? The rare, hard collisions contribute most to <qperp2>

40. If radiation is driven by <qperp2>, then we are not in the regime where: Diagram from Arnold, Moore and Yaffe: JHEP 0206:030,2002

41. Collisional energy loss is of the same order as radiative energy loss. To calculate collisional loss, cannot make assumptions (or neglect terms of order) ω << T, μ HTL gives a large uncertainty in the collisional energy loss. How to 'predict' for LHC with these large uncertainties? Conclusions