Transcript Overcoming Fragility

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.
6/6/06
Hard Probes 2006
William Horowitz
1
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
6/6/06
Hard Probes 2006
William Horowitz
2
Reframing the Debate
• Experimental measurements and
theoretical calculations are hard
• We must be careful not to oversimplify
the issues involved
6/6/06
Hard Probes 2006
William Horowitz
3
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
6/6/06
Hard Probes 2006
William Horowitz
4
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
6/6/06
Hard Probes 2006
William Horowitz
5
Length Definitions
– Define a mapping from the line integral through the
realistic medium to the theoretical block
– where
– Then
6/6/06
Hard Probes 2006
William Horowitz
6
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
6/6/06
Hard Probes 2006
William Horowitz
7
Effective Length, Leff (cont’d)
• Comparison of
the full
distribution of
fluctuating
lengths and the
flavordependent Leff
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
6/6/06
Hard Probes 2006
William Horowitz
8
Pion RAA
• Is it a good measurement for tomography?
– Yes: small experimental error
– Maybe not: some models
appear “fragile”
• Claim: we should not be so immediately dismissive of the pion RAA as a tomographic tool
6/6/06
Hard Probes 2006
William Horowitz
9
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
6/6/06
Hard Probes 2006
William Horowitz
10
Different Models have Different
Sensitivities to the Pion RAA
• GLV:
s<2
• Higher Twist:
s<2
• DGLV+El+Geom:
s<2
• AWS:
s~3
6/6/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Hard Probes 2006
William Horowitz
11
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)
6/6/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Hard Probes 2006
William Horowitz
12
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
6/6/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
Hard Probes 2006
William Horowitz
13
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)
6/6/06
Hard Probes 2006
William Horowitz
14
Conclusions
• RHIC is hard
• Lengths are difficult
– Currently a theoretical systematic error
from mapping medium to brick
– Leff must only be used a posteriori
6/6/06
Hard Probes 2006
William Horowitz
15
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
6/6/06
Hard Probes 2006
William Horowitz
16
Backup
6/6/06
Hard Probes 2006
William Horowitz
17
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
6/6/06
Hard Probes 2006
William Horowitz
18
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
6/6/06
Hard Probes 2006
William Horowitz
19
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
6/6/06
Hard Probes 2006
William Horowitz
20
LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
6/6/06
Hard Probes 2006
William Horowitz
21
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
6/6/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Hard Probes 2006
William Horowitz
22
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
6/6/06
Hard Probes 2006
William Horowitz
23
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
6/6/06
Hard Probes 2006
William Horowitz
24
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
6/6/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Hard Probes 2006
William Horowitz
25
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
6/6/06
Hard Probes 2006
William Horowitz
26