203 Appendix D: Formation Time and Brick Estimates Defining the fractional momentum loss ϵ as From Eq.[] we have that for a quark (or gluon) with slowly varying power law production index n$_{Q}$ ( p$_{T}$ ) + 1, where 〈· · · 〉$_{geom}$ indicates averaging over the geometry of the collision. p$_{f}$ = (1 − ϵ ) p$_{i}$ (D.18) ⇒ ϵ = 1 − e − ∫ dt $^{′}$µ ( t $^{$^{′}$)}$. (D.19) R$_{AA}$ ( p$_{T}$ ) ≃ 〈 (1 − ϵ ) $^{n}$〉$_{geom}$ , (D.20) R$_{AA}$ ( p$_{T}$ ) ≃ e − n$_{Q}$ ( p$_{T}$ ) $^{µL/v}$, (D.21) In a static, constant medium µ ( ⃗ x + ⃗ vt ) = µ . For this case R$_{AA}$ for a single, fixed path of length L is 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. D.2.1 Static, Constant Medium One may also readily find the nuclear modification factor assuming a uni-