6/6/06William Horowitz Hard Probes 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.

6/6/06William Horowitz Hard Probes 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

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

6/6/06William Horowitz Hard Probes 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

6/6/06William Horowitz Hard Probes 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

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

6/6/06William Horowitz Hard Probes 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/

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

6/6/06William Horowitz Hard Probes 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”

6/6/06William Horowitz Hard Probes 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

6/6/06William Horowitz Hard Probes 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

6/6/06William Horowitz Hard Probes 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 : (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)

6/6/06William Horowitz Hard Probes –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/

6/6/06William Horowitz Hard Probes 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 : (2005)

6/6/06William Horowitz Hard Probes 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

6/6/06William Horowitz Hard Probes 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

6/6/06William Horowitz Hard Probes Backup

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

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

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

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

6/6/06William Horowitz Hard Probes 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 : (2005)

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

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

6/6/06William Horowitz Hard Probes N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38 : (2005)

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