1. #: 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. #: 2 Why does it matter? If we put the pedal to the metal, how fast will it go?

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

4. #: 4 An excess of theoretical models 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... STAR Phys. Rev. Lett. 98 (2007) 192301

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

6. #: 6 Why look at collisional processes? 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.

7. #: 7 A very selective history 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.

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

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

10. #: 10 The Matrix Element

11. #: 11 The Matrix Element (cont.) After

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

13. #: 13 Average energy loss

14. #: 14 Multiple collisions 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...)

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

16. #: 16 Multiple Collisions NOT continuum limit diffusion process

17. #: 17 Geometry integrals So far, shown fixed length plots. For R AA : all results shown have been averaged over all production points and jet trajectories. ρ part bulk, ρ binary jets, Bjorken expansion.

18. #: 18 Results – RHIC - Pions WHDG α = 0.3

19. #: 19 Results – RHIC - Pions WHDG α = 0.3

20. #: 20 Results – RHIC - Electrons WHDG α = 0.3

21. #: 21 Results – RHIC - Electrons WHDG α = 0.3

22. #: 22 Predicting LHC RHIC

23. #: 23 Predicting LHC RHICLHC

24. #: 24 Predicting LHC RHICLHC

25. #: 25 Predicting - LHC

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

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

28. #: 28 Why? 1) HTL breaks down g is not << 1 2) High momentum jet eg 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. #: 29 ω << T, μ assumption / approximation is NOT ok to calculate av en loss Must take into account medium recoil.

30. #: 30 How can we quantify this uncertainty? 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)

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

32. #: 32 HTL extrapolation HTL-AMY extrapolation

33. #: 33 Result

34. #: 34 Equivalent at leading order 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

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

36. #: 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

37. #: 37

38. #: 38 What about q perp distributions? p = 10 GeV p=10GeV: ≈ 0.25 GeV 2 /fm for T = 0.24GeV

39. #: 39 The rare, hard collisions contribute most to What about q perp distributions?

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

41. #: 41 Conclusions  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?