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)