Role of Dynamic Geometry in
Jet Tomography
William Horowitz
Columbia University
December 12, 2005
In conjunction with Simon Wicks, Magdalenda Djordjevic, and Miklos Gyulassy
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Motivation
• Past tomographic models simplified the
calculation by neglecting either:
– Multigluon fluctuations
– Path length fluctuations
• For fixed-length calculations,
reasonable but unjustifiable length L~5
fm used
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Significance of Nuclear Profile
• Simpler densities create a surface bias
Hard Cylinder
12/12/05
Hard Sphere
Woods-Saxon
Heavy Flavor Productions Workshop
Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909
William Horowitz
Edgy Geometry
• We use the Woods-Saxon nuclear
geometry, which has a fuzzy “edge”
• There is no unique, natural LWS
definition
– Two examples (of many possibilities):


ρ( x0  nˆl )dl
ρ( x0  nˆ l )dl



L
L
,
 ρ
ρ(0)
• We will use the latter formula
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Partonic RAA Model
RAA (φ; b, pT ) 


n
2



d
x
T
(
x
;
b
)
d
ε
1

ε
P
ε,
L
(
x
, φ; b); pT 
AA


N coll (b)
– where P incoherently convolves DGLV
energy loss (including multigluon
fluctuations) with the infinite-time elastic
energy loss for fixed as
12/12/05
Heavy Flavor Productions Workshop
Momentum Jacobian as survival probability; see, e.g., Gyulassy, nucl-th/0403032
William Horowitz
Volume Emission of Partons
• fixed pT = 15 GeV, y = f = 0, and as = .3
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Average Lengths of Emission
• Dynamic volume depends on partonic
species and pT
–
–
–
–
–
For pT = 5, 10, 15, 20 GeV, as = .3
<Lg> = 1.74, 1.93, 2.16, 2.41 fm
<Lu> = 3.83, 4.21, 4.47, 4.62 fm
<Lc> = 4.65, 4.43, 4.48, 4.50 fm
<Lb> = 6.17, 5.69, 5.43, 5.29 fm
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
The Results
• Electrons
12/12/05
as = .3
• Pions
Heavy Flavor Productions Workshop
William Horowitz
The Results
• Electrons
12/12/05
as = .4
• Pions
Heavy Flavor Productions Workshop
William Horowitz
Conclusions
• There are several large effects that must
be taken into account in any energy loss
model:
–
–
–
–
Multigluon fluctuations
Path length fluctuations
Collisional energy loss
Running as
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Future Work
• Find more accurate analytic formulae
for collisional loss
– Molnár’s parton cascade provides exact
numerical answer
• Simultaneously treat elastic and
inelastic energy loss
– Find a more natural L?
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Future Work (cont’d)
• Allow as to run
– Nonzero lower bound to theoretical error
• Use even more accurate medium
density
– Hirano’s CGC-initial condition 3+1 D
evolving hydro background
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Let’s Eat!
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Partonic RAA Model
• Exploit the power law production rate
to use the momentum Jacobian to
define the probability of escape, (1-e)n
– pT, final = e pT, initial
– n is simply related to the exponent of the
power law
– Assumes a slowly changing power law
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Combining Models
• Find a fixed L that reproduces the
dynamical length-generated partonic
RAA using proper initial spectra
followed by fragmentation into pions
and electrons
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Vary as
• We expect a big change since
• DErad ~ as3
• DEelas ~ as2
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Finding Fixed L
• Heavies
12/12/05
• Lights
Heavy Flavor Productions Workshop
William Horowitz
Heavies alph=.4 BT and TG
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Theoretical Error from Length
Uncertainty
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Volume Emission for
as = .4
12/12/05
Heavy Flavor Productions Workshop
William Horowitz
Volume Emission for
as = .4 (cont’d)
12/12/05
Heavy Flavor Productions Workshop
William Horowitz