1. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 1 Heavy Quark Energy Loss William Horowitz Columbia University June 6, 2006 With many thanks to Simon Wicks, Azfar Adil, Miklos Gyulassy, Magdalena Djordjevic, and Brian Cole Simon Wicks Azfar Adil

2. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 2 R AA (  )=R AA (1+2v 2 Cos(2  )+…) Glue and Lights Charm and Bottom Correlations of back-to-back jets, etc.

3. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 3 Jets as a Tomographic Probe Tomography requires precision measurements AND precision, pQCD theory Probe the unknown  QGP with energy loss Quark or Glue Jet probes: ( , p T,  -  reac, M Q ) init Hadron jet fragments: ( , p T,  –  reac ) final

4. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 4 to understand the medium If pQCD makes the correct predictions, we can use Jets as a Tomographic Probe (cont’d) Otherwise, jet suppression is just another non-perturbative anomaly of A+A collisions (like J/  suppression)

5. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 5 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

6. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 6 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)

7. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 7 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)

8. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 8 Entropy-constrained radiative- dominated loss FALSIFIED by e - R AA Problem: Qualitatively,   R AA ~ e - R AA

9. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 9 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

10. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 10 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

11. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 11 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

12. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 12 Is this Plausible? Maybe Flow nonperturbative at low-p T v 2 possibly nonperturbative at mid-p T Asymptotic Freedom MUST occur –But at what momentum? WH, nucl-th/0511052D. Winter, QM2005

13. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 13 But what if we Neglected an Important Effect? M. Mustafa, Phys. Rev. C72 :014905 (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

14. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 14 Elastic History (a)J. D. Bjorken, FERMILAB-PUB-82-059-THY (Quantal) (b)M. H. Thoma and M. Gyulassy, Nucl. Phys. B351 :491-506 (1991) (Classical) (c)E. Braaten and M. H. Thoma, Phys. Rev. D24 :2625-2630 (1991) (Quantal) (d)P. Romatschke and M. Strickland, Phys. Rev. D71 :125008 (2005) (Quantal) People have thought about Elastic Loss for a long time, and in different ways—all assume parton starts in asymptotic past Bottom Charm Most correct (infinite time) elastic loss calculation approximately bounded by BT and TG curves

15. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 15 Include Path Length Fluctuations with Realistic Geometry –For fixed L ~5 fm, Collisional+Radiative leads to pion overquenching –Use Woods-Saxon density hard production ~ T AA medium ~  participant –This allows a self- consistent pion prediction without “fixed L ”approx S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

16. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 16 Our Extended Theory Convolve Elastic with Inelastic energy loss fluctuations Include path length fluctuations in diffuse nuclear geometry Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty

17. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 17 Conservative Results S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Elastic loss improves quench keeping dN g /dy= 1000  s =.3 and No change in c or b production cross sections Extended Theory is consistent with data for p T > 7 GeV

18. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 18 Consistency Test with Pions Not flat, which requires a balance of many competing effects (Cronin, EMC, etc.) but not at odds with data S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

19. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 19 El+Rad+Geom NOT a Fragile Probe Why? First, experimental error bars have shrunk considerably since 2004. Second,   el <   rad WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

20. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 20 Why Widths are Vital –The whole distribution is important:, but   el <   rad S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

21. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 21 Elastic Objections All derivations start parton at asymptotic past: are there formation time effects? –Peigne et al. (Classical): –This is unintuitive: one expects effects to disappear by L ~ 1/  D ~.5 fm, the screening scale; but perhaps there is a hidden  factor What about interference effects? S. Peigne, P.-B. Gossiaux, and T. Gousset, JHEP0604:011 (2006) They claim NO elastic loss until L > 10 fm!

22. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 22 Adil et al. Classical Refutation of Peigne et al. Two issues: –Peigne et al. do not disentangle known radiative effects small – Peigne et al. neglect a term in their classical current, thereby violating current conservation and resulting in a spurious A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/0606010 subtraction of the (negative) binding energy of the quark-antiquark pair HUGE

23. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 23 Classical Finite Time Results A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/0606010 By L ~ 1/  D, stable field reaches ~ 90% of the asymptotic 10 GeV Charm

24. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 24 Quantal Finite Time Results Again, formation effects negligible beyond 1/  D X. N. Wang, nucl-th/0604040M. Djordjevic, nucl-th/0603066 No one as yet fully combines El+Rad with interference

25. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 25 Heavy Quark Tomography of the LHC Additional systematic tests of the energy loss theory –2-3 times RHIC medium densities –Enormous p T range At very high momenta, GLV and BDMPS-Z-WS results converge, but elastic effects persist! WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

26. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 26 LHC Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

27. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 27 Conclusions –Fantastic new RHIC data challenging, surprising Better understanding of heavy quark loss mechanisms, production critical for interpreting experimental results –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 FONNLL would provide better information on theoretical production error

28. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 28 Conclusions (cont’d) –BDMPS-Z-WS: IF extreme is assumed IF elastic loss is assumed to vanish IF they assume fragility Then not inconsistent with data No hope for tomography

29. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 29 Conclusions (cont’d) –DGLV: Include elastic, inelastic, and path length fluctuations Consistent results for high-p T e - R AA Pion R AA predictions agree well with data over large momentum range, are sensitive to changes in medium density, consistent with multiplicity constraints

30. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 30 Conclusions (cont’d) –Far from finished: 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 Where will e - R AA data and theoretical calculations settle down as research progresses and error bars are reduced over time?

31. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 31 Conclusions (cont’d) –AMY: a third approach? Produced a pion R AA ; no calculation of e - R AA, a crucial consistency check –The LHC will provide an excellent new testing ground for systematic study (falsification?) of energy loss theory –Jet tomography is an elusive, but achievable goal P. Arnold, G.D. Moore, and L. Yaffe, JHEP 011 :057 (2001) S. Turbide, C. Gale, S. Jeon, G. D. Moore, Phys. Rev. C72 :014906 (2005)

32. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 32

33. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 33 Backup Slides

34. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 34 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

35. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 35 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

36. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 36 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

37. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 37 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

38. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 38 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

39. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 39 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)

40. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 40 N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph-0511257 A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005)

41. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 41 A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005)

42. 6/6/06William Horowitz RHIC & AGS Annual Users’ Meeting ‘06 42 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076