Surface or Volume Emission at RHIC:
Is Jet Tomography Possible?
William Horowitz
Columbia University
September 22, 2006
With many thanks to Simon Wicks, Azfar Adil,
Magdalena Djordjevic, and Miklos Gyulassy.
9/22/06
William Horowitz
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Outline
• Possibility of Tomography
– Surface vs. Volume
• Time Permitting
–
–
–
–
LHC Pion Predictions
Azimuthal Anisotropy Puzzle
Heavy Quark RAA Puzzle
LHC Heavies Predictions
9/22/06
William Horowitz
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The Big Picture
• Ultimate goal: Jet Tomography
Probe the unknown rQGP
with energy loss
Quark or Glue Jet probes:
(h, pT, j - jreac, MQ) init
Hadron Jet fragments:
(h, pT, j – jreac ) final
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RAA(j)=RAA(1+2v2Cos(2j)+…)
•RAA: ratio of Au+Au to
binary scaled p+p
•Modest Goal:
reproduce RAA to
estimate the medium
density
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Jets as a Tomographic Probe
• 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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Surface Emission:
A Simple (Specious?) Picture
• Claim: only jets originating
close to the medium edge
escape
– No matter the input density, a
corona of jets always escape
• Surface Emission =>
• Fragile Probe =>
• No Tomography
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Simplistic Volume Emission
d
a
a


dyd 2 pT ( p0  pT ) n pT n
Baseline:
Approximately universal behavior
2/ 3
Prediction: ln RAA   N part
Scalings:
L A
1/ 3
N
1/ 3
part
L dN g
2/3
,
 A2 / 3  N part
A dy
Natural variables
dN g
 A  N part
dy
Fractional energy loss:
E
L dN g
2/3


 A2 / 3  k ' N part
E
A dy
Suppression:
RAA
d ( pT (1   ) / dyd 2 pT

 (1   ) 2
2
d ( pT ) / dyd pT

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1
1   ' N 
2/3
part
n2
I. Vitev, Phys.Lett.B in press, hep-ph/0603010
I. Vitev, HP2006
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Reframe the Debate
• Disentangle Surface Bias from Surface Emission
– All energy loss models must have surface bias
• Fragility is a poor descriptor of a theory
– 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? How sensitive are the jets?
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BDMPS-Z-SW
Energy Loss
• Highly Biased?
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461474 (2005)
9/22/06
• Insensitive Jets?
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
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Significance of Nuclear Profile
• Simpler densities create a surface bias
Hard Cylinder
9/22/06
Hard Sphere
Woods-Saxon
William Horowitz
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Illustrative Only! Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909
A Closer Look at BDMPS
– Difficult to draw conclusions on
inherent surface bias in BDMPS
from this plot 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)
9/22/06
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A Closer Look at BDMPS (cont’d)
The lack of sensitivity needs
to be more closely examined
because of the use of
unrealistic geometry (hard
cylinders) and no expansion
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
9/22/06
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Our Extended Theory
• Convolve Elastic with Inelastic energy
loss fluctuations
• Include path length fluctuations in
diffuse nuclear geometry with 1+1D
Bjorken expansion
• Separate calculations with BT and TG
collisional formulae provide a measure
of the elastic theoretical uncertainty
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Elastic Can’t be Neglected!
M. Mustafa, Phys. Rev. C72:014905 (2005)
9/22/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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Length Definitions
– Define a mapping from the line integral through the
realistic medium to the theoretical block
– where
– Then
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Geometry Can’t be Neglected!
• P(L) is a wide
distribution
– Flavor
independent
• Flavor dependent
fixed length
approximations
LQ’s not a priori
obvious
9/22/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
William Horowitz
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Our Jets Probe the Volume and are
Sensitive to the Medium
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
9/22/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
William Horowitz
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Elastic Width Increases Sensitivity
– The whole distribution is important:
, but E,el < E,rad
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
9/22/06
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Other Models Probe the Volume
• Higher Twist
A. Majumder, HP2006
9/22/06
• BDMPS w/ Geom
T. Renk, hep-ph/0608333
William Horowitz
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Conclusions I
• In order to make nontrivial statements
about fragility, one must use diffuse
nuclear geometries with Bjorken
expansion
– Otherwise surface emission is a reflection
of the inherent surface bias of the geometry
– RHIC is not a Brick
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Conclusions I (cont’d)
• Our model emits from the volume and
is falsified by data for too-large medium
densities
– Renk: Volume Emission
– Majumder: Volume Emission and Sensitive
– Vitev: Sensitive
• Pion RAA is a good tomographic probe
of the medium
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LHC Pion Predictions
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Elastic Remains Important
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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LHC Pions
• Note the large rise
in RAA with energy
• Note the
dependence on
medium density
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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BDMPS-Based Predictions
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
9/22/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
William Horowitz
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Conclusions II
• With current predictions, the
momentum dependence of RAA at LHC
could distinguish between BDMPS and
GLV type loss models
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Azimuthal Anisotropy
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What is the Puzzle?–Data
– Naïvely combine
published RAA(pT) and
v2(pT) data
– Preliminary PHENIX p0
data
– Data centrality classes:
• STAR charged hadron
– 0-5%, 10-20%, 20-30%, 3040%, 40-60%
• PHENIX charged
hadron
– 0-20%, 20-40%, 40-60%
• PHENIX p0
– 10-20%, 20-30%, …, 50-60%
9/22/06
• Note: error regions are only a rough estimate
W. Horowitz, nucl-th/0511052
William Horowitz
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What is the Puzzle?–Theory
• Nothing matches the RHIC phenomena
• Hydrodynamics
– Not applicable at intermediate and higher pT
– Boltzmann factors crush RAA to 0
• Parton Cascade and Energy Loss
– Don’t work: jet quenching and anisotropy are
anti-correlated
– Models over-suppress RAA in order to
reproduce large observed v2 or vice-versa
9/22/06
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Model Failures
• Models can’t match
intended data point
for any value of
their free parameter
(opacity of the
medium)
– MPC: calculated for
25-35% centrality
– gGLV: 40-50%
centrality
9/22/06
W. Horowitz, nucl-th/0511052
William Horowitz
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Success!
• Add a small,
outward-pointing
momentum
punch,
– Reasonable,
deconfinementlike value of .5
GeV
9/22/06
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Cu+Cu Predictions and
Improved PHENIX Data
W. Horowitz, nucl-th/0511052
9/22/06
D. Winter, QM2005
William Horowitz
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Conclusions II
• The punch is an interesting toy model
that suggests the larger than pQCD
intermediate-pT v2 may provide a
unique signature of deconfinement
• Work is needed to extend the results
out in pT and more closely associate the
punch with a deconfinement
mechanism
9/22/06
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Heavy Quark Puzzle
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e
Before the RAA, the picture looked
pretty good:
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– Null Control:
RAA(g)~1
– Consistency:
RAA(h)~RAA(p)
– GLV Prediction: Theory~Data for reasonable
fixed L~5 fm and dNg/dy~dNp/dy
9/22/06
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But with Hints of Trouble:
• Theory v2 too small
A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005)
(first by E. Shuryak, Phys. Rev. C66:027902 (2002))
9/22/06
• Fragile Probe?
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
William Horowitz
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What Can Heavies Teach Us?
• Provide a unique test of our
understanding of energy loss
– Mass => Dead Cone => Reduction in E loss
Bottom Quark
=
(Gratuitous Pop Culture Reference)
9/22/06
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Entropy-constrained radiativedominated loss FALSIFIED by e- RAA
Problem: Qualitatively, p0 RAA~ e- RAA
9/22/06
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Inherent Uncertainties in
Production Spectra
How large is bottom’s role?
M. Djordjevic, M. Gyulassy, R. Vogt, S. Wicks,
Phys. Lett. B632:81-86 (2006)
– Vertex detectors could deconvolute the e- contributions
9/22/06
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
William Horowitz
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The BDMPS-Z-WS Approach
• Increase to 14 to
push curve down
• Fragility in the model
allows for consistency
with pions
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
9/22/06
William Horowitz
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What Does
Mean?
We believe it’s nonperturbative:
– a = .5 => dNg/dy ~ 13,000
“Proportionality constant
~ 4-5 times larger than
perturbative estimate”
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
“Large numerical value of
not yet understood”
R. Baier, Nucl. Phys. A715:209-218 (2003)
U. A. Wiedemann, SQM 2006
9/22/06
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Is this Plausible? Maybe
• Flow nonperturbative at low-pT
• v2 possibly nonperturbative at mid-pT
WH, nucl-th/0511052
D. Winter, QM2005
• Asymptotic Freedom MUST occur
– But at what momentum?
9/22/06
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Our Results
• Inclusion of elastic
decreases the
discrepancy
• Direct c and b
measurements
required to truly
rule out this
approach
9/22/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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LHC Predictions for Heavies
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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Conclusions III
– Elastic loss cannot be neglected when considering
pQCD jet quenching
• Coherence and correlation effects between elastic and
inelastic processes that occur in a finite time over multiple
collisions must be sorted out
• Fixed a must be allowed to run; the size of the irreducible
error due to integration over low, nonperturbative
momenta, where a > .5, needs to be determined
– Large uncertainties in ratio of charm to bottom
contribution to non-photonic electrons
• Direct measurement of D spectra would help separate the
different charm and bottom jet dynamics
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This Slide Intentionally Left Blank
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Backup Slides
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Insensitive Jets?
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)
9/22/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
William Horowitz
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
9/22/06
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N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
9/22/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
William Horowitz
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Elastic Objections
• All derivations start parton at asymptotic past:
are there formation time effects?
– Peigne et al. (Classical):
They claim NO elastic loss
until L > 10 fm!
S. Peigne, P.-B. Gossiaux, and T. Gousset, JHEP0604:011 (2006)
– This is unintuitive: one expects effects to disappear
by L ~ 1/mD ~ .5 fm, the screening scale; but perhaps
there is a hidden g factor
• What about interference effects?
9/22/06
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Adil et al. Classical Refutation of
Peigne et al.
Two issues:
– Peigne et al. do not disentangle
known radiative effects
• small
– Peigne et al. neglect a term in
their classical current, thereby
violating current conservation
A. Adil, M. Gyulassy, WH, and S. Wicks,
nucl-th/0606010
and resulting in a spurious
subtraction of the (negative) binding energy of the
quark-antiquark pair
•HUGE
9/22/06
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Classical Finite Time Results
By L ~ 1/mD, stable field reaches ~ 90% of the asymptotic
10 GeV Charm
10 GeV Charm
A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/0606010
9/22/06
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Quantal Finite Time Results
Again, formation effects negligible beyond 1/mD
M. Djordjevic, nucl-th/0603066
X. N. Wang, nucl-th/0604040
No one as yet fully combines El+Rad with interference
9/22/06
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Let’s Look at the Data
• STAR moderate-pt charged hadrons RAA
(nucl-ex/0305015)
• STAR moderate-pt charged hadrons v2
(nucl-ex/0206006, 0409033)
• PHENIX moderate-pt charged hardrons RAA
(nucl-ex/0308006)
• PHENIX moderate-pt charged hadrons v2
(nucl-ex/0305013)
• PHENIX unpublished RAAj
9/22/06
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