1. 9/22/06William Horowitz 1 Surface or Volume Emission at RHIC: Is Jet Tomography Possible? William Horowitz Columbia University September 22, 2006 With many thanks to Simon Wicks, Azfar Adil, Magdalena Djordjevic, and Miklos Gyulassy.

2. 9/22/06William Horowitz 2 Outline Possibility of Tomography –Surface vs. Volume Time Permitting –LHC Pion Predictions –Azimuthal Anisotropy Puzzle –Heavy Quark R AA Puzzle –LHC Heavies Predictions

3. 9/22/06William Horowitz 3 The Big Picture Ultimate goal: Jet Tomography 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. 9/22/06William Horowitz 4 R AA (  )=R AA (1+2v 2 Cos(2  )+…) R AA : ratio of Au+Au to binary scaled p+p Modest Goal: reproduce R AA to estimate the medium density

5. 9/22/06William Horowitz 5 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

6. 9/22/06William Horowitz 6 Surface Emission: A Simple (Specious?) Picture Claim: only jets originating close to the medium edge escape –No matter the input density, a corona of jets always escape Surface Emission => Fragile Probe => No Tomography

7. 9/22/06William Horowitz 7 Baseline: Fractional energy loss: I. Vitev, Phys.Lett.B in press, hep-ph/0603010 Prediction: Natural variables Scalings: Suppression: Approximately universal behavior Simplistic Volume Emission I. Vitev, HP2006

8. 9/22/06William Horowitz 8 Reframe the Debate Disentangle Surface Bias from Surface Emission –All energy loss models must have surface bias Fragility is a poor descriptor of a theory –All energy loss models with a formation time saturate at some R min AA > 0 –The questions asked should be quantitative : Where is R data AA compared to R min AA ? How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? How sensitive are the jets?

9. 9/22/06William Horowitz 9 BDMPS-Z-SW Energy Loss Highly Biased? Insensitive Jets? 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)

10. 9/22/06William Horowitz 10 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

11. 9/22/06William Horowitz 11 A Closer Look at BDMPS –Difficult to draw conclusions on inherent surface bias in BDMPS from this plot for three reasons: No Bjorken expansion Glue and light quark contributions not disentangled Plotted against L input (complicated mapping from L input to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 :461-474 (2005)

12. 9/22/06William Horowitz 12 A Closer Look at BDMPS (cont’d) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747 :511:529 (2005) The lack of sensitivity needs to be more closely examined because of the use of unrealistic geometry (hard cylinders) and no expansion

13. 9/22/06William Horowitz 13 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

14. 9/22/06William Horowitz 14 Elastic Can’t be Neglected! M. Mustafa, Phys. Rev. C72 :014905 (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

15. 9/22/06William Horowitz 15 Length Definitions –Define a mapping from the line integral through the realistic medium to the theoretical block –where –Then

16. 9/22/06William Horowitz 16 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

17. 9/22/06William Horowitz 17 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

18. 9/22/06William Horowitz 18 Elastic Width Increases Sensitivity –The whole distribution is important:, but   el <   rad S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

19. 9/22/06William Horowitz 19 Other Models Probe the Volume Higher Twist BDMPS w/ Geom A. Majumder, HP2006 T. Renk, hep-ph/0608333

20. 9/22/06William Horowitz 20 Conclusions I In order to make nontrivial statements about fragility, one must use diffuse nuclear geometries with Bjorken expansion –Otherwise surface emission is a reflection of the inherent surface bias of the geometry –RHIC is not a Brick

21. 9/22/06William Horowitz 21 Conclusions I (cont’d) Our model emits from the volume and is falsified by data for too-large medium densities –Renk: Volume Emission –Majumder: Volume Emission and Sensitive –Vitev: Sensitive Pion R AA is a good tomographic probe of the medium

22. 9/22/06William Horowitz 22 LHC Pion Predictions

23. 9/22/06William Horowitz 23 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Elastic Remains Important

24. 9/22/06William Horowitz 24 LHC Pions Note the large rise in R AA with energy Note the dependence on medium density WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

25. 9/22/06William Horowitz 25 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

26. 9/22/06William Horowitz 26 Conclusions II With current predictions, the momentum dependence of R AA at LHC could distinguish between BDMPS and GLV type loss models

27. 9/22/06William Horowitz 27 Azimuthal Anisotropy

28. 9/22/06William Horowitz 28 What is the Puzzle?–Data –Naïvely combine published R AA (p T ) and v 2 (p T ) data –Preliminary PHENIX  0 data –Data centrality classes: STAR charged hadron –0-5%, 10-20%, 20-30%, 30- 40%, 40-60% PHENIX charged hadron –0-20%, 20-40%, 40-60% PHENIX  0 –10-20%, 20-30%, …, 50-60% Note: error regions are only a rough estimate W. Horowitz, nucl-th/0511052

29. 9/22/06William Horowitz 29 What is the Puzzle?–Theory Nothing matches the RHIC phenomena Hydrodynamics –Not applicable at intermediate and higher p T –Boltzmann factors crush R AA to 0 Parton Cascade and Energy Loss –Don’t work: jet quenching and anisotropy are anti-correlated –Models over-suppress R AA in order to reproduce large observed v 2 or vice-versa

30. 9/22/06William Horowitz 30 Model Failures Models can’t match intended data point for any value of their free parameter (opacity of the medium) –MPC: calculated for 25-35% centrality –gGLV: 40-50% centrality W. Horowitz, nucl-th/0511052

31. 9/22/06William Horowitz 31 Success! Add a small, outward-pointing momentum punch, –Reasonable, deconfinement- like value of.5 GeV

32. 9/22/06William Horowitz 32 Cu+Cu Predictions and Improved PHENIX Data W. Horowitz, nucl-th/0511052D. Winter, QM2005

33. 9/22/06William Horowitz 33 Conclusions II The punch is an interesting toy model that suggests the larger than pQCD intermediate-p T v 2 may provide a unique signature of deconfinement Work is needed to extend the results out in p T and more closely associate the punch with a deconfinement mechanism

34. 9/22/06William Horowitz 34 Heavy Quark Puzzle

35. 9/22/06William Horowitz 35 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

36. 9/22/06William Horowitz 36 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)

37. 9/22/06William Horowitz 37 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)

38. 9/22/06William Horowitz 38 Entropy-constrained radiative- dominated loss FALSIFIED by e - R AA Problem: Qualitatively,   R AA ~ e - R AA

39. 9/22/06William Horowitz 39 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

40. 9/22/06William Horowitz 40 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

41. 9/22/06William Horowitz 41 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

42. 9/22/06William Horowitz 42 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

43. 9/22/06William Horowitz 43 Our Results Inclusion of elastic decreases the discrepancy Direct c and b measurements required to truly rule out this approach S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

44. 9/22/06William Horowitz 44 LHC Predictions for Heavies WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

45. 9/22/06William Horowitz 45 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

46. 9/22/06William Horowitz 46 This Slide Intentionally Left Blank

47. 9/22/06William Horowitz 47 Backup Slides

48. 9/22/06William Horowitz 48

49. 9/22/06William Horowitz 49 Insensitive Jets? 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)

50. 9/22/06William Horowitz 50 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

51. 9/22/06William Horowitz 51 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

52. 9/22/06William Horowitz 52 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

53. 9/22/06William Horowitz 53 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)

54. 9/22/06William Horowitz 54 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!

55. 9/22/06William Horowitz 55 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

56. 9/22/06William Horowitz 56 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

57. 9/22/06William Horowitz 57 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

58. 9/22/06William Horowitz 58 Let’s Look at the Data STAR moderate-pt charged hadrons RAA (nucl-ex/0305015) STAR moderate-pt charged hadrons v2 (nucl-ex/0206006, 0409033) PHENIX moderate-pt charged hardrons RAA (nucl-ex/0308006) PHENIX moderate-pt charged hadrons v2 (nucl-ex/0305013) PHENIX unpublished RAA 