Role of Dynamic Geometry in Jet Tomography

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

2. 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 Workshop

3. Significance of Nuclear Profile • Simpler densities create a surface bias Hard Cylinder Hard Sphere Woods-Saxon Heavy Flavor Productions Workshop Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909

4. 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 Heavy Flavor Productions Workshop

5. Partonic RAA Model • where Pincoherently convolves DGLV energy loss (including multigluon fluctuations) with the infinite-time elastic energy loss for fixedas Heavy Flavor Productions Workshop Momentum Jacobian as survival probability; see, e.g., Gyulassy, nucl-th/0403032

6. Volume Emission of Partons • fixed pT = 15 GeV, yT = f = 0, and as = .3 Heavy Flavor Productions Workshop

7. 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 Heavy Flavor Productions Workshop

8. Electrons Pions The Results as = .3 Heavy Flavor Productions Workshop

9. Electrons Pions The Results as = .4 Heavy Flavor Productions Workshop

10. 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 Heavy Flavor Productions Workshop

11. 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 Workshop

12. 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 Heavy Flavor Productions Workshop

13. Let’s Eat! Heavy Flavor Productions Workshop

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17. 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 Heavy Flavor Productions Workshop

18. 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 Workshop

19. Vary as • We expect a big change since • DErad ~ as3 • DEelas ~ as2 Heavy Flavor Productions Workshop

20. Heavies Lights Finding Fixed L Heavy Flavor Productions Workshop

21. Heavies alph=.4 BT and TG Heavy Flavor Productions Workshop

22. Theoretical Error from Length Uncertainty Heavy Flavor Productions Workshop

23. Volume Emission foras = .4 Heavy Flavor Productions Workshop

24. Volume Emission for as = .4 (cont’d) Heavy Flavor Productions Workshop