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