26 Chapter 2: Motivation of energy loss P ( ϵ ), where p f T = (1 − ϵ ) p i $_{T}$. Although it is called a probability of energy loss there are processes—e.g. 3 → 2 detailed balance and rare elastic events—in which momentum is gained and ϵ < 0 ( ϵ is certainly restricted from above by 1; more on this later). Given this Eq. (2.2) becomes where P ( ϵ ) in general depends on the position of hard parton production ⃗ x$_{0}$ , its direction of propagation φ , and the properties { p }$_{i}$ of the medium; we will often refer to P ( ϵ ; ⃗ x$_{0}$, φ, { p }$_{i}$ ) in shorthand as P ( ϵ ). See Fig. 2.5 for a schematic picture of Eq. (2.4). A common means of reexpressing the spectrum of hadrons produced in a nu- clear collision A + B → h + X is to divide out by the trivially binary scaled proton-proton spectrum: For symmetric collisions (such as Au + Au or P b + P b ) we will denote the above quantity as R$_{AA}$ . Often R$_{AA}$ is given as a function of transverse momenta p$_{T}$ R h $_{AB}$( { x }$_{i}$ ) ≡ dσ h $_{AB}$( { x }$_{i}$ ) N$_{coll}$ ( { x }$_{i}$ ) dσ h $_{pp}$( { x }$_{i}$ ) . (2.5) dσ $^{h}$( b ) = ∑ a,b,c ∫ dx$_{a}$dx$_{b}$dz$_{c}$f$_{a/A}$ ( x$_{a}$, µ$_{F}$ ) f$_{b/B}$ ( x$_{b}$, µ$_{F}$ ) D h $_{c}$( z$_{c}$, µ $^{′}$$_{F}$) ×$^{∫}$ d⃗ x$_{0}$T$_{AB}$ ( ⃗ x$_{0}$ ; b )$^{∫}$ dφ 2 π dϵP ( ϵ ; ⃗ x$_{0}$, φ, { p }$_{i}$ ) × d ˆ σ c $_{ab}$( x$_{a}$P$_{A}$, x$_{b}$P$_{B}$, P$_{h}$/ (1 − ϵ ) z$_{c}$, µ$_{R}$, µ$_{F}$ , µ $^{′}$$_{F}$) , (2.4) 2.2.2 R$_{AA}$ and Final State Suppression