Surface or Volume Emission at RHIC: Is Jet Tomography Possible?

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. Outline • Possibility of Tomography • Surface vs. Volume • Time Permitting • LHC Pion Predictions • Azimuthal Anisotropy Puzzle • Heavy Quark RAA Puzzle • LHC Heavies Predictions

3. The Big Picture • Ultimate goal: Jet Tomography Probe the unknown rQGP with energy loss Quark or Glue Jet probes: (h, pT, j - jreac, MQ) init Hadron Jet fragments: (h, pT, j – jreac ) final

4. RAA(j)=RAA(1+2v2Cos(2j)+…) • RAA: ratio of Au+Au to binary scaled p+p • Modest Goal: reproduce RAA to estimate the medium density

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

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 RminAA > 0 • The questions asked should be quantitative : • Where is RdataAA compared to RminAA? • 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. Highly Biased? Insensitive Jets? BDMPS-Z-SWEnergy Loss A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)

10. Significance of Nuclear Profile • Simpler densities create a surface bias Hard Cylinder Hard Sphere Woods-Saxon Illustrative Only! Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909

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 Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)

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

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

15. Length Definitions • Define a mapping from the line integral through the realistic medium to the theoretical block • where • Then

16. Geometry Can’t be Neglected! • P(L) is a wide distribution • Flavor independent • Flavor dependent fixed length approximations LQ’s not a priori obvious S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

17. Our Jets Probe the Volume and are Sensitive to the Medium S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

18. Elastic Width Increases Sensitivity • The whole distribution is important: , but sDE,el < sDE,rad S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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

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. 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 RAA is a good tomographic probe of the medium

22. LHC Pion Predictions

23. Elastic Remains Important WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

24. LHC Pions • Note the large rise in RAA with energy • Note the dependence on medium density WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

25. BDMPS-Based Predictions 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)

26. Conclusions II • With current predictions, the momentum dependence of RAA at LHC could distinguish between BDMPS and GLV type loss models

27. Azimuthal Anisotropy

28. What is the Puzzle?–Data • Naïvely combine published RAA(pT) and v2(pT) data • Preliminary PHENIX p0 data • Data centrality classes: • STARcharged hadron • 0-5%, 10-20%, 20-30%, 30-40%, 40-60% • PHENIX charged hadron • 0-20%, 20-40%, 40-60% • PHENIX p0 • 10-20%, 20-30%, …, 50-60% • Note: error regions are only a rough estimate W. Horowitz, nucl-th/0511052

29. What is the Puzzle?–Theory • Nothing matches the RHIC phenomena • Hydrodynamics • Not applicable at intermediate and higher pT • Boltzmann factors crush RAA to 0 • Parton Cascade and Energy Loss • Don’t work: jet quenching and anisotropy are anti-correlated • Models over-suppress RAA in order to reproduce large observed v2 or vice-versa

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. Success! • Add a small, outward-pointing momentum punch, • Reasonable, deconfinement-like value of .5 GeV

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

33. Conclusions II • The punch is an interesting toy model that suggests the larger than pQCD intermediate-pT v2 may provide a unique signature of deconfinement • Work is needed to extend the results out in pT and more closely associate the punch with a deconfinement mechanism

34. Heavy Quark Puzzle

35. Before the e- RAA, the picture looked pretty good: • Null Control: RAA(g)~1 Y. Akiba for the PHENIX collaboration, hep-ex/0510008 • Consistency: RAA(h)~RAA(p) • GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy

36. Theory v2 too small Fragile Probe? But with Hints of Trouble: 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. 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. Entropy-constrained radiative-dominated loss FALSIFIED by e- RAA Problem: Qualitatively, p0 RAA~ e- RAA

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

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. What Does Mean? We believe it’s nonperturbative: • a = .5 => dNg/dy ~ 13,000 “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” R. Baier, Nucl. Phys. A715:209-218 (2003) U. A. Wiedemann, SQM 2006

42. Is this Plausible? Maybe • Flow nonperturbative at low-pT • v2 possibly nonperturbative at mid-pT • Asymptotic Freedom MUST occur • But at what momentum? WH, nucl-th/0511052 D. Winter, QM2005

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. LHC Predictions for Heavies WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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 a must be allowed to run; the size of the irreducible error due to integration over low, nonperturbative momenta, where a > .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

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47. Backup Slides

49. Insensitive Jets? 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) 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)

50. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation