content_image/310302.jpg content_image/310303.jpg
now take into account geometric path length fluctuations as follows: 

<img src='content_image/310302.jpg'>

<img src='content_image/310303.jpg'>

where L is the locally determined effective path length of the jet given its initial production point ⃗ x$_{⊥}$ and its initial azimuthal direction φ relative to the impact parameter plane ( x, y ). The geometric path averaging used here is similar to that used in [359] and by Eskola et al. [306]. However, the inclusion of elastic losses together with path fluctuations in more realistic geometries was not considered before. 

We consider a diffuse Woods-Saxon nuclear density profile [394], which creates a participant transverse density, ρ$_{p}$ ( ⃗ x$_{⊥}$ ), computed using the Glauber profiles, T$_{A}$ ( ⃗ x ), with inelastic cross section σ$_{NN}$ = 42 mb. The bulk sQGP transverse density is assumed to be proportional to this participant density, and its form is shown (for the y = 0 slice) in Fig. 4.4 by the curve labeled ρ$_{QGP}$ . The distribution of initial hard jet production points, ⃗ x$_{⊥}$ , is assumed on the other hand to be proportional to the binary collision density, T$_{AA}$ = T$_{A}$ ( ⃗ x + ⃗ b/ 2) T$_{A}$ ( ⃗ x − ⃗ b/ 2). This is illustrated in Fig. 4.4 by the narrower curve labeled ρ$_{Jet}$ . 

The combination of fluctuating DGLV radiative [278] with the new elas- tic energy losses and fluctuating path lengths (via the extra d $^{2}$⃗ x$_{⊥}$dφ integra- 

