1. 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

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
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3. Reframing the Debate
Experimental measurements and theoretical calculations are hard
We must be careful not to oversimplify the issues involved
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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
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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
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6. Length Definitions
Define a mapping from the line integral through the realistic medium to the theoretical block
where
Then
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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/
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/
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”
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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
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11. 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

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: (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/
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: (2005)
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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
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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
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17. Backup
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18. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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19. S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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20. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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21. LHC Predictions Hard Probes 2006
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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22. 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: (2005)
Hard Probes 2006

23. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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24. WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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25. 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
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (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/
Hard Probes 2006