Jet Quenching at RHIC and the LHC
William Horowitz
Columbia University
November 1, 2006
With many thanks to Simon Wicks, Azfar Adil,
Magdalena Djordjevic, and Miklos Gyulassy.
11/1/06
William Horowitz
1
Outline
• What a difference the LHC makes!
– HUGE disagreement over LHC predictions
– Why there’s a difference
– Why we’re right (hopefully robustly)
• P0, P0, P0…
11/1/06
William Horowitz
2
LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
11/1/06
William Horowitz
3
BDMPS-Based Predictions
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
11/1/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
William Horowitz
4
Suppression of BDMPS
– LHC predictions require an extrapolation from RHIC
• Their pQCD-based controlling parameter qhat must be
nonperturbatively large to fit RHIC data
-pQCD gives qhat = c e3/4, where c ~ 2; they require c ~ 8-20 for RHIC
-Needed because radiative only energy loss (and Pg0 > 1?); R = (1/2) qhat L3
11/1/06
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
William Horowitz
5
BDMPS Extrapolation to the LHC
• Importance of medium density
– qhat ~ rscatterers
– EKRT used => rLHC ~ 7 rRHIC
– qhat goes from 14 at RHIC to 100 at the
LHC!
– Almost all the energy loss is in d(e-1) part
of P(e)
11/1/06
William Horowitz
6
Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
11/1/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
William Horowitz
7
LHC Production Spectra
• Much flatter power
law and asymptotic
jet energies allows
for easy
interpretation of
LHC predictions
11/1/06
William Horowitz
8
LHC Conclusions
• LHC appears to reach jet asymptopia
where pocket formulae hold
• Lack of fragility means pions will make
a good, independent probe of the
density
• With current predictions, the
momentum dependence of RAA at LHC
should distinguish between BDMPS
and GLV type loss models
11/1/06
William Horowitz
9
A Quick Update on Fragility
11/1/06
William Horowitz
10
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 (FRAGILITY???)
11/1/06
William Horowitz
11
Recall the BDMPS-based Plots
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)
11/1/06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
William Horowitz
12
Our Jets Probe the Volume and are
Sensitive to the Medium
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
11/1/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
William Horowitz
13
BDMPS with Realistic Geometry
is Not Fragile!
T. Renk and K. J. Eskola, hep-ph/0610059
11/1/06
William Horowitz
14
Heavy Quark Puzzle
11/1/06
William Horowitz
15
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
11/1/06
William Horowitz
16
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))
11/1/06
• Fragile Probe?
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
William Horowitz
17
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)
11/1/06
William Horowitz
18
Entropy-constrained radiativedominated loss FALSIFIED by e- RAA
Problem: Qualitatively, p0 RAA~ e- RAA
11/1/06
William Horowitz
19
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
11/1/06
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado,
U. A. Wiedemann, hep-ph-0511257
William Horowitz
20
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
11/1/06
William Horowitz
21
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
11/1/06
William Horowitz
22
Is this Plausible?
Renk says No
T. Renk and K. J. Eskola, hep-ph/0610059
11/1/06
William Horowitz
23
Our Results
• Inclusion of elastic
decreases the
discrepancy
• Direct c and b
measurements
required to truly
rule out approaches
11/1/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
William Horowitz
24
LHC Predictions for Heavies
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
11/1/06
William Horowitz
25
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
11/1/06
William Horowitz
26
Backup Slides
11/1/06
William Horowitz
27
Our Extended Theory
• Convolve Elastic with Inelastic energy
loss fluctuations
• Include path length fluctuations in
diffuse nuclear geometry with 1+1D
Bjorken expansion
11/1/06
William Horowitz
28
Significance of Nuclear Profile
• Simpler densities create a surface bias
Hard Cylinder
11/1/06
Hard Sphere
Woods-Saxon
William Horowitz
29
Illustrative Only! Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– Null Control:
RAA(g)~1
– Consistency:
RAA(h)~RAA(p)
11/1/06
William Horowitz
30
Elastic Can’t be Neglected!
M. Mustafa, Phys. Rev. C72:014905 (2005)
11/1/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
William Horowitz
31
Length Definitions
– Define a mapping from the line integral through the
realistic medium to the theoretical block
– where
– Then
11/1/06
William Horowitz
32
Geometry Can’t be Neglected!
• P(L) is a wide
distribution
– Flavor
independent
• Flavor dependent
fixed length
approximations
LQ’s not a priori
obvious
11/1/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
William Horowitz
33
Comparison to Vitev
11/1/06
William Horowitz
Increasing dNg/dy
11/1/06
William Horowitz
35
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
11/1/06
William Horowitz
36
• Qhat = c eps^3/4 \propto rho (density
of scattering centers)
• pQCD=> c~=2
• To fit RHIC, c ~ 8-20
• Extend to LHC, everything crushed to
nothing
11/1/06
William Horowitz
37
BDMPS RHIC p’s
Huge qhat needed!
(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. C38:461-474 (2005)
Note: fragility due to lack of Bjorken expansion
11/1/06
William Horowitz
38