Overcoming Fragility

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. 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 Hard Probes 2006

3. Reframing the Debate • Experimental measurements and theoretical calculations are hard • We must be careful not to oversimplify the issues involved 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 Lfixed will reproduce the full calculation • RHIC is not a brick 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 ~ TAA; Medium ~ rpart • 1+1D Bjorken expansion • Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty Hard Probes 2006

6. Length Definitions • Define a mapping from the line integral through the realistic medium to the theoretical block • where • Then Hard Probes 2006

7. Effective Length, Leff • Leff 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 Hard Probes 2006

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

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

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

11. Different Models have Different Sensitivities to the Pion RAA • GLV: s < 2 • Higher Twist: s < 2 • DGLV+El+Geom: s < 2 • AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Hard Probes 2006

12. A Closer Look at AWS 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) Hard Probes 2006

13. Surface Bias vs. Surface Emission • 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 A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 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 Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) Hard Probes 2006

15. Conclusions • RHIC is hard • Lengths are difficult • Currently a theoretical systematic error from mapping medium to brick • Leff must only be used a posteriori 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 RAA cannot be immediately dismissed as a useful tomographic tool Hard Probes 2006

17. Backup Hard Probes 2006

18. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Hard Probes 2006

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

20. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Hard Probes 2006

21. LHC Predictions WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation 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) Hard Probes 2006

23. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation Hard Probes 2006

24. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation 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) Hard Probes 2006

26. DGLV+El+Geom: Widths • The whole distribution is important: , but sDE,el < sDE,rad S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 Hard Probes 2006