content_image/311554.jpg content_image/311555.jpg content_image/311556.jpg content_image/311557.jpg
Defining the fractional momentum loss ϵ as 

<img src='content_image/311554.jpg'>

<img src='content_image/311555.jpg'>

From Eq.[] we have that for a quark (or gluon) with slowly varying power law production index n$_{Q}$ ( p$_{T}$ ) + 1, 

<img src='content_image/311556.jpg'>

where 〈· · · 〉$_{geom}$ indicates averaging over the geometry of the collision. 

## D.2.1 Static, Constant Medium 

In a static, constant medium µ ( ⃗ x + ⃗ vt ) = µ . For this case R$_{AA}$ for a single, fixed path of length L is 

<img src='content_image/311557.jpg'>

where we have assumed v ≈ constant (a good approximation for ultrarela- tivistic motion with v ≃ 1). From now on we will simply take v ≃ 1 and suppress it in our derivations. One can see that Eq. (D.21), plotted in Fig. D.1, qualitatively reproduces the full numerical results of Fig. 5.2 for the a posteriori input parameter choice of L = 1 fm. 

One may also readily find the nuclear modification factor assuming a uni- 

