role of dynamic geometry in jet tomography
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Heavy Flavor Productions Workshop12/12/05 William Horowitz
Role of Dynamic Geometry in Jet Tomography
William HorowitzColumbia UniversityDecember 12, 2005
In conjunction with Simon Wicks, Magdalenda Djordjevic, and Miklos Gyulassy
Heavy Flavor Productions Workshop12/12/05 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
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Significance of Nuclear Profile
• Simpler densities create a surface biasHard Cylinder Hard Sphere Woods-Saxon
Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909
Heavy Flavor Productions Workshop12/12/05 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):
• We will use the latter formula
,)0(
)ˆ( 0
ρ
dllnxρL
ρ
dllnxρL
)ˆ( 0
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Partonic RAA Model
– where P incoherently convolves DGLV energy loss (including multigluon fluctuations) with the infinite-time elastic energy loss for fixed s
)(
);;,(ε,ε1ε);(),;(
2
bN
pbφxLPdbxTxdpbφR
coll
Tn
AA
TAA
Momentum Jacobian as survival probability; see, e.g., Gyulassy, nucl-th/0403032
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Volume Emission of Partons
• fixed pT = 15 GeV, yT = = 0, and s = .3
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Average Lengths of Emission
• Dynamic volume depends on partonic species and pT
– For pT = 5, 10, 15, 20 GeV, s = .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
Heavy Flavor Productions Workshop12/12/05 William Horowitz
The Results
• Electrons • Pions
s = .3
Heavy Flavor Productions Workshop12/12/05 William Horowitz
The Results
• Electrons • Pions
s = .4
Heavy Flavor Productions Workshop12/12/05 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 s
Heavy Flavor Productions Workshop12/12/05 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?
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Future Work (cont’d)
• Allow s 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
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Let’s Eat!
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Partonic RAA Model
• Exploit the power law production rate to use the momentum Jacobian to define the probability of escape, (1-)n
– pT, final = pT, initial
– n is simply related to the exponent of the power law
– Assumes a slowly changing power law
Heavy Flavor Productions Workshop12/12/05 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
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Vary s
• We expect a big change since
• Erad ~ s3
• Eelas ~ s2
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Finding Fixed L
• Heavies • Lights
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Heavies alph=.4 BT and TG
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Theoretical Error from Length Uncertainty
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Volume Emission fors = .4
Heavy Flavor Productions Workshop12/12/05 William Horowitz
Volume Emission for s = .4 (cont’d)
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