1. 11/1/06William Horowitz 1 Jet Quenching at RHIC and the LHC William Horowitz Columbia University November 1, 2006 With many thanks to Simon Wicks, Azfar Adil, Magdalena Djordjevic, and Miklos Gyulassy.

2. 11/1/06William Horowitz 2 Outline What a difference the LHC makes! –HUGE disagreement over LHC predictions –Why there’s a difference –Why we’re right (hopefully robustly) P 0, P 0, P 0 …

3. 11/1/06William Horowitz 3 LHC Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

4. 11/1/06William Horowitz 4 K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005) BDMPS-Based Predictions

5. 11/1/06William Horowitz 5 Suppression of BDMPS –LHC predictions require an extrapolation from RHIC Their pQCD-based controlling parameter qhat must be nonperturbatively large to fit RHIC data -pQCD gives qhat = c  3/4, where c ~ 2; they require c ~ 8-20 for RHIC -Needed because radiative only energy loss (and P g 0 > 1?); R = (1/2) qhat L 3 K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005)

6. 11/1/06William Horowitz 6 BDMPS Extrapolation to the LHC Importance of medium density –qhat ~  scatterers –EKRT used =>  LHC ~ 7  RHIC –qhat goes from 14 at RHIC to 100 at the LHC! –Almost all the energy loss is in  (  -1) part of P(  )

7. 11/1/06William Horowitz 7 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Asymptopia at the LHC Asymptotic pocket formulae:  E rad /E   3 Log(E/  2 L)/E  E el /E   2 Log((E T) 1/2 /m g )/E

8. 11/1/06William Horowitz 8 LHC Production Spectra Much flatter power law and asymptotic jet energies allows for easy interpretation of LHC predictions

9. 11/1/06William Horowitz 9 LHC Conclusions LHC appears to reach jet asymptopia where pocket formulae hold Lack of fragility means pions will make a good, independent probe of the density With current predictions, the momentum dependence of R AA at LHC should distinguish between BDMPS and GLV type loss models

10. 11/1/06William Horowitz 10 A Quick Update on Fragility

11. 11/1/06William Horowitz 11 Jets as a Tomographic Probe Requires: –Theoretical understanding of underlying physics (esp. quenching mechanisms) –Mapping from the controlling parameter of the theory to the medium density –Sensitivity in the model + data for the measurement used (FRAGILITY???)

12. 11/1/06William Horowitz 12 Recall the BDMPS-based Plots K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005) The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a)(b)

13. 11/1/06William Horowitz 13 Our Jets Probe the Volume and are Sensitive to the Medium WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

14. 11/1/06William Horowitz 14 BDMPS with Realistic Geometry is Not Fragile! T. Renk and K. J. Eskola, hep-ph/0610059

15. 11/1/06William Horowitz 15 Heavy Quark Puzzle

16. 11/1/06William Horowitz 16 Before the e - R AA, the picture looked pretty good: –Null Control: RAA(  )~1 –Consistency: R AA (  )~R AA (  ) –GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g /dy~dN  /dy Y. Akiba for the PHENIX collaboration, hep-ex/0510008

17. 11/1/06William Horowitz 17 But with Hints of Trouble: Theory v 2 too small Fragile Probe? A. Drees, H. Feng, and J. Jia, Phys. Rev. C71 :034909 (2005) (first by E. Shuryak, Phys. Rev. C66 :027902 (2002)) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005)

18. 11/1/06William Horowitz 18 What Can Heavies Teach Us? Provide a unique test of our understanding of energy loss –Mass => Dead Cone => Reduction in E loss Bottom Quark = (Gratuitous Pop Culture Reference)

19. 11/1/06William Horowitz 19 Entropy-constrained radiative- dominated loss FALSIFIED by e - R AA Problem: Qualitatively,   R AA ~ e - R AA

20. 11/1/06William Horowitz 20 Inherent Uncertainties in Production Spectra M. Djordjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632 :81-86 (2006) How large is bottom’s role? –Vertex detectors could de- convolute the e - contributions N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph-0511257

21. 11/1/06William Horowitz 21 The BDMPS-Z-WS Approach Increase to 14 to push curve down Fragility in the model allows for consistency with pions N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph-0511257

22. 11/1/06William Horowitz 22 What Does Mean? We believe it’s nonperturbative: –  =.5 => dN g /dy ~ 13,000 R. Baier, Nucl. Phys. A715 :209-218 (2003) “Proportionality constant ~ 4-5 times larger than perturbative estimate” K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) “Large numerical value of not yet understood” U. A. Wiedemann, SQM 2006

23. 11/1/06William Horowitz 23 Is this Plausible? Renk says No T. Renk and K. J. Eskola, hep-ph/0610059

24. 11/1/06William Horowitz 24 Our Results Inclusion of elastic decreases the discrepancy Direct c and b measurements required to truly rule out approaches S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

25. 11/1/06William Horowitz 25 LHC Predictions for Heavies WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

26. 11/1/06William Horowitz 26 Conclusions III –Elastic loss cannot be neglected when considering pQCD jet quenching Coherence and correlation effects between elastic and inelastic processes that occur in a finite time over multiple collisions must be sorted out Fixed  must be allowed to run; the size of the irreducible error due to integration over low, nonperturbative momenta, where  >.5, needs to be determined –Large uncertainties in ratio of charm to bottom contribution to non-photonic electrons Direct measurement of D spectra would help separate the different charm and bottom jet dynamics

27. 11/1/06William Horowitz 27 Backup Slides

28. 11/1/06William Horowitz 28 Our Extended Theory Convolve Elastic with Inelastic energy loss fluctuations Include path length fluctuations in diffuse nuclear geometry with 1+1D Bjorken expansion

29. 11/1/06William Horowitz 29 Significance of Nuclear Profile Simpler densities create a surface bias Hard CylinderHard SphereWoods-Saxon Illustrative Only! Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909

30. 11/1/06William Horowitz 30 –Null Control: RAA(  )~1 –Consistency: R AA (  )~R AA (  ) Y. Akiba for the PHENIX collaboration, hep-ex/0510008

31. 11/1/06William Horowitz 31 Elastic Can’t be Neglected! M. Mustafa, Phys. Rev. C72 :014905 (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

32. 11/1/06William Horowitz 32 Length Definitions –Define a mapping from the line integral through the realistic medium to the theoretical block –where –Then

33. 11/1/06William Horowitz 33 Geometry Can’t be Neglected! P(L) is a wide distribution –Flavor independent Flavor dependent fixed length approximations L Q ’s not a priori obvious S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

34. 11/1/06William Horowitz Comparison to Vitev

35. 11/1/06William Horowitz 35 Increasing dNg/dy

36. 11/1/06William Horowitz 36 Our Extended Theory Convolve Elastic with Inelastic energy loss fluctuations Include path length fluctuations in diffuse nuclear geometry with 1+1D Bjorken expansion Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty

37. 11/1/06William Horowitz 37 Qhat = c eps^3/4 \propto rho (density of scattering centers) pQCD=> c~=2 To fit RHIC, c ~ 8-20 Extend to LHC, everything crushed to nothing

38. 11/1/06William Horowitz 38 BDMPS RHIC  ’s K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005) Huge qhat needed! (a)(b) Note: fragility due to lack of Bjorken expansion