1. 6/6/06William Horowitz Hard Probes 2006 1 Overcoming Fragility William Horowitz Columbia University June 14, 2006 With many thanks to Simon Wicks, Azfar Adil, Magdalena Djordjevic, and Miklos Gyulassy. Also thanks to all of you with whom I had many enlightening discussions.

2. 6/6/06William Horowitz Hard Probes 2006 2 The Big Picture Our ultimate goal: jet tomography 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

3. 6/6/06William Horowitz Hard Probes 2006 3 Reframing the Debate Experimental measurements and theoretical calculations are hard We must be careful not to oversimplify the issues involved

4. 6/6/06William Horowitz Hard Probes 2006 4 Theory Perspective: The Devil’s in the Details Pocket asymptotic formulas don’t work for RHIC – One cannot be assured that “reasonable,” but unjustified L fixed will reproduce the full calculation –RHIC is not a brick

5. 6/6/06William Horowitz Hard Probes 2006 5 Correct Geometry is Difficult: DGLV+El+Geom –Convolve Elastic with Inelastic energy loss fluctuations –Include path length fluctuations in diffuse nuclear geometry Woods-Saxon base nuclear density Production ~ T AA ; Medium ~  part 1+1D Bjorken expansion –Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty

6. 6/6/06William Horowitz Hard Probes 2006 6 Length Definitions –Define a mapping from the line integral through the realistic medium to the theoretical block –where –Then

7. 6/6/06William Horowitz Hard Probes 2006 7 Effective Length, L eff – L eff given by the one fixed length that best reproduces the full fluctuating geometry calculation (if it exists) –Only found AFTER full computation S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

8. 6/6/06William Horowitz Hard Probes 2006 8 Effective Length, L eff (cont’d) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Comparison of the full distribution of fluctuating lengths and the flavor- dependent L eff

9. 6/6/06William Horowitz Hard Probes 2006 9 Pion R AA Is it a good measurement for tomography? –Yes: small experimental error Claim: we should not be so immediately dis- missive of the pion R AA as a tomographic tool –Maybe not: some models appear “fragile”

10. 6/6/06William Horowitz Hard Probes 2006 10 Fragility: A Poor Descriptor 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? –Define sensitivity, s = min. param/max. param that predicts the data within error

11. 6/6/06William Horowitz Hard Probes 2006 11 Different Models have Different Sensitivities to the Pion R AA GLV: s < 2 Higher Twist: s < 2 DGLV+El+Geom: s < 2 AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

12. 6/6/06William Horowitz Hard Probes 2006 12 A Closer Look at AWS 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. 6/6/06William Horowitz Hard Probes 2006 13 –Surface Emission: one phrase explanation of fragility All models become surface emitting with infinite E loss –Surface Bias occurs in all energy loss models Expansion + Realistic geometry => model probes a large portion of medium Surface Bias vs. Surface Emission A. Majumder, HP2006S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

14. 6/6/06William Horowitz Hard Probes 2006 14 A Closer Look at AWS –Difficult to draw conclusions on inherent surface bias in AWS from this 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)

15. 6/6/06William Horowitz Hard Probes 2006 15 Conclusions RHIC is hard Lengths are difficult –Currently a theoretical systematic error from mapping medium to brick – L eff must only be used a posteriori

16. 6/6/06William Horowitz Hard Probes 2006 16 Conclusions (cont’d) Fragility is not a useful descriptor for a theoretical model + data –The important quantifier is the sensitivity of the model to changes in its controlling parameter around the data: is jet tomography possible? Pion R AA cannot be immediately dismissed as a useful tomographic tool

17. 6/6/06William Horowitz Hard Probes 2006 17 Backup

18. 6/6/06William Horowitz Hard Probes 2006 18 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

19. 6/6/06William Horowitz Hard Probes 2006 19 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

20. 6/6/06William Horowitz Hard Probes 2006 20 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

21. 6/6/06William Horowitz Hard Probes 2006 21 LHC Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

22. 6/6/06William Horowitz Hard Probes 2006 22 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)

23. 6/6/06William Horowitz Hard Probes 2006 23 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

24. 6/6/06William Horowitz Hard Probes 2006 24 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

25. 6/6/06William Horowitz Hard Probes 2006 25 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)

26. 6/6/06William Horowitz Hard Probes 2006 26 DGLV+El+Geom: Widths –The whole distribution is important:, but   el <   rad S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076