1. 12/12/05William Horowitz Heavy Flavor Productions Workshop Role of Dynamic Geometry in Jet Tomography William Horowitz Columbia University December 12, 2005 In conjunction with Simon Wicks, Magdalenda Djordjevic, and Miklos Gyulassy

2. 12/12/05William Horowitz Heavy Flavor Productions Workshop 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

3. 12/12/05William Horowitz Heavy Flavor Productions Workshop Significance of Nuclear Profile Simpler densities create a surface bias Hard CylinderHard SphereWoods-Saxon Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909

4. 12/12/05William Horowitz Heavy Flavor Productions Workshop Edgy Geometry We use the Woods-Saxon nuclear geometry, which has a fuzzy “edge” There is no unique, natural L WS definition –Two examples (of many possibilities): We will use the latter formula

5. 12/12/05William Horowitz Heavy Flavor Productions Workshop Partonic R AA Model –where P incoherently convolves DGLV energy loss (including multigluon fluctuations) with the infinite-time elastic energy loss for fixed  s Momentum Jacobian as survival probability; see, e.g., Gyulassy, nucl-th/0403032

6. 12/12/05William Horowitz Heavy Flavor Productions Workshop Volume Emission of Partons fixed p T = 15 GeV, y =  = 0, and  s =.3

7. 12/12/05William Horowitz Heavy Flavor Productions Workshop Average Lengths of Emission Dynamic volume depends on partonic species and p T –For p T = 5, 10, 15, 20 GeV,  s =.3 – = 1.74, 1.93, 2.16, 2.41 fm – = 3.83, 4.21, 4.47, 4.62 fm – = 4.65, 4.43, 4.48, 4.50 fm – = 6.17, 5.69, 5.43, 5.29 fm

8. 12/12/05William Horowitz Heavy Flavor Productions Workshop The Results ElectronsPions  s =.3

9. 12/12/05William Horowitz Heavy Flavor Productions Workshop The Results ElectronsPions  s =.4

10. 12/12/05William Horowitz Heavy Flavor Productions Workshop 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

11. 12/12/05William Horowitz Heavy Flavor Productions Workshop 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. 12/12/05William Horowitz Heavy Flavor Productions Workshop 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

13. 12/12/05William Horowitz Heavy Flavor Productions Workshop Let’s Eat!

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17. 12/12/05William Horowitz Heavy Flavor Productions Workshop Partonic R AA Model Exploit the power law production rate to use the momentum Jacobian to define the probability of escape, (1-  ) n –p T, final =  p T, initial –n is simply related to the exponent of the power law –Assumes a slowly changing power law

18. 12/12/05William Horowitz Heavy Flavor Productions Workshop Combining Models Find a fixed L that reproduces the dynamical length-generated partonic R AA using proper initial spectra followed by fragmentation into pions and electrons

19. 12/12/05William Horowitz Heavy Flavor Productions Workshop Vary  s We expect a big change since  E rad ~  s 3  E elas ~  s 2

20. 12/12/05William Horowitz Heavy Flavor Productions Workshop Finding Fixed L HeaviesLights

21. 12/12/05William Horowitz Heavy Flavor Productions Workshop Heavies alph=.4 BT and TG

22. 12/12/05William Horowitz Heavy Flavor Productions Workshop Theoretical Error from Length Uncertainty

23. 12/12/05William Horowitz Heavy Flavor Productions Workshop Volume Emission for  s =.4

24. 12/12/05William Horowitz Heavy Flavor Productions Workshop Volume Emission for  s =.4 (cont’d)