Heavy Quark Energy Loss
William Horowitz
Columbia University
June 6, 2006
Simon Wicks
6/6/06
With many thanks to Simon Wicks, Azfar Adil,
Miklos Gyulassy, Magdalena Djordjevic, and
Brian Cole
RHIC & AGS Annual Users’ Meeting ‘06
Azfar Adil
William Horowitz
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RAA(j)=RAA(1+2v2Cos(2j)+…)
• Glue and Lights
• Charm and Bottom
•Correlations of back-to-back jets, etc.
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Jets as a Tomographic Probe
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
• Tomography requires precision
measurements AND precision, pQCD
theory
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Jets as a Tomographic Probe (cont’d)
• If pQCD makes the correct predictions,
we can use
to understand the medium
•Otherwise, jet suppression is just
another non-perturbative anomaly of
A+A collisions (like J/Y suppression)
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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
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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))
6/6/06
• Fragile Probe?
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
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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)
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Entropy-constrained radiativedominated loss FALSIFIED by e- RAA
Problem: Qualitatively, p0 RAA~ e- RAA
6/6/06
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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
6/6/06
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
RHIC & AGS Annual Users’ Meeting ‘06
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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
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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
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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?
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But what if we Neglected an
Important Effect?
M. Mustafa, Phys. Rev. C72:014905 (2005)
6/6/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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Elastic History
People have thought about Elastic Loss for a long time, and in
different ways—all assume parton starts in asymptotic past
(a)
(b)
(c)
(d)
J. D. Bjorken, FERMILAB-PUB-82-059-THY (Quantal)
M. H. Thoma and M. Gyulassy, Nucl. Phys. B351:491-506 (1991) (Classical)
E. Braaten and M. H. Thoma, Phys. Rev. D24:2625-2630 (1991) (Quantal)
P. Romatschke and M. Strickland, Phys. Rev. D71:125008 (2005) (Quantal)
Bottom
Charm
Most correct (infinite time) elastic loss calculation
approximately bounded by BT and TG curves
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Include Path Length Fluctuations
with Realistic Geometry
– For fixed L~5 fm, Collisional+Radiative leads to
pion overquenching
– Use Woods-Saxon density
• hard production ~ TAA
• medium ~ rparticipant
– This allows a selfconsistent pion prediction
without “fixed L”approx
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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Our Extended Theory
• Convolve Elastic with Inelastic energy
loss fluctuations
• Include path length fluctuations in
diffuse nuclear geometry
• Separate calculations with BT and TG
collisional formulae provide a measure
of the elastic theoretical uncertainty
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Conservative Results
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
6/6/06
•Elastic loss
improves quench
•keeping
dNg/dy = 1000
as = .3
• and No change in c
or b production cross
sections
•Extended Theory is
consistent with data
for pT > 7 GeV
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Consistency Test with Pions
Not flat, which
requires a balance of
many competing
effects (Cronin,
EMC, etc.) but not at
odds with data
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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El+Rad+Geom NOT a Fragile Probe
WH, S. Wicks, M. Gyulassy, M.
Djordjevic, in preparation
• Why? First, experimental error bars have shrunk considerably
since 2004. Second, sDE,el < sDE,rad
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Why Widths are Vital
– The whole distribution is important:
, but sDE,el < sDE,rad
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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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?
6/6/06
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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
6/6/06
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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
6/6/06
RHIC & AGS Annual Users’ Meeting ‘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
6/6/06
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Heavy Quark Tomography of the
LHC
• Additional systematic
tests of the energy loss
theory
– 2-3 times RHIC medium
densities
– Enormous pT range
• At very high momenta,
GLV and BDMPS-Z-WS
results converge, but
elastic effects persist!
6/6/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06
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LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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Conclusions
– Fantastic new RHIC data challenging, surprising
• Better understanding of heavy quark loss mechanisms,
production critical for interpreting experimental results
– 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
• FONNLL would provide better information on theoretical
production error
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Conclusions (cont’d)
– BDMPS-Z-WS:
• IF extreme is assumed
• IF elastic loss is assumed to vanish
• IF they assume fragility
• Then not inconsistent with data
• No hope for tomography
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Conclusions (cont’d)
– DGLV:
• Include elastic, inelastic, and path length
fluctuations
• Consistent results for high-pT e- RAA
• Pion RAA predictions agree well with data
over large momentum range, are sensitive
to changes in medium density, consistent
with multiplicity constraints
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Conclusions (cont’d)
– Far from finished:
• 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
• Where will e- RAA data and theoretical calculations settle
down as research progresses and error bars are reduced
over time?
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Conclusions (cont’d)
– AMY: a third approach?
P. Arnold, G.D. Moore, and L. Yaffe, JHEP 011:057 (2001)
S. Turbide, C. Gale, S. Jeon, G. D. Moore, Phys. Rev. C72:014906 (2005)
• Produced a pion RAA; no calculation of e- RAA, a crucial
consistency check
– The LHC will provide an excellent new testing
ground for systematic study (falsification?) of energy
loss theory
– Jet tomography is an elusive, but achievable goal
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Backup Slides
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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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)
RHIC & AGS Annual Users’ Meeting ‘06
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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)
RHIC & AGS Annual Users’ Meeting ‘06
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A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
6/6/06
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S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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