overcoming fragility

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Hard Probes 2006 1 6/6/06 William Horowitz 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.

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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. The Big Picture. Our ultimate goal: jet tomography - PowerPoint PPT Presentation

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Page 1: Overcoming Fragility

Hard Probes 20061

6/6/06 William Horowitz

Overcoming Fragility

William HorowitzColumbia 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.

Page 2: Overcoming Fragility

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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

Page 3: Overcoming Fragility

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Reframing the Debate

• Experimental measurements and theoretical calculations are hard

• We must be careful not to oversimplify the issues involved

Page 4: Overcoming Fragility

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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

Page 5: Overcoming Fragility

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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 ~ part

• 1+1D Bjorken expansion

– Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty

Page 6: Overcoming Fragility

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Length Definitions– Define a mapping from the line integral

through the realistic medium to the theoretical block

– where

– Then

Page 7: Overcoming Fragility

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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

Page 8: Overcoming Fragility

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Effective Length, Leff (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 Leff

Page 9: Overcoming Fragility

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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”

Page 10: Overcoming Fragility

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Fragility: A Poor Descriptor

• All energy loss models with a formation time saturate at some Rmin

AA > 0

• The questions asked should be quantitative : – Where is Rdata

AA 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

Page 11: Overcoming Fragility

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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

Page 12: Overcoming Fragility

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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)

Page 13: Overcoming Fragility

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– 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, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

Page 14: Overcoming Fragility

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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)

Page 15: Overcoming Fragility

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Conclusions

• RHIC is hard

• Lengths are difficult– Currently a theoretical systematic

error from mapping medium to brick

– Leff must only be used a posteriori

Page 16: Overcoming Fragility

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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

Page 17: Overcoming Fragility

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Backup

Page 18: Overcoming Fragility

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

Page 19: Overcoming Fragility

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

Page 20: Overcoming Fragility

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

Page 21: Overcoming Fragility

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LHC Predictions

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

Page 22: Overcoming Fragility

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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)

Page 23: Overcoming Fragility

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

Page 24: Overcoming Fragility

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

Page 25: Overcoming Fragility

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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)

Page 26: Overcoming Fragility

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DGLV+El+Geom: Widths

– The whole distribution is important: , but el < rad

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