William Horowitz Columbia University June 14, 2006 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

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

Reframing the Debate Experimental measurements and theoretical calculations are hard We must be careful not to oversimplify the issues involved Hard Probes 2006

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

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

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

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

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

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

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

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

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

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

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

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

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

Backup Hard Probes 2006

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

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

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

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

K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl 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

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

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

N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A 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

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