194 Appendix B: Power Law R$_{AA}$ From the definition of a fragmentation function we have that where we get to the last line by employing Eq. (B.2) twice. For in-medium momentum loss in which the final momentum is related to the initial momentum by p$_{f}$ = (1 − ϵ ) p$_{i}$ we have the probability of fractional energy loss for parton q with initial momentum p$_{i}$ is P$_{q}$ ( ϵ | p$_{i}$ ). Then, exactly as for fragmentation functions (Eq. (B.4)), where we have suppressed the q index on P , and hence (Eq. (B.5)) If we assume that the production spectrum can be approximated by a dN q final dp$_{f}$ ( p$_{f}$ ) = ∫ dϵ dN q prod dp$_{i}$ ( p$_{f}$ 1 − ϵ$^{)}$ 1 1 − ϵ P ( ϵ$^{∣}$ ∣ ∣ p$_{f}$ 1 − ϵ$^{)}$ . (B.7) dN $^{q}$( p$_{f}$ ) = dN $^{q}$( p$_{i}$ ) P ( ϵ | p$_{i}$ ) dϵ, (B.6) dN $^{h}$( p$_{h}$ ) = dN $^{q}$( p$_{q}$ ) D ( z ) dz. (B.4) ⇒ dN h dp$_{h}$ ( p$_{h}$ ) = ∫ dN q dp$_{h}$ ( p$_{q}$ ) D ( z ) dz = ∫ dN q dp$_{q}$ ( p$_{h}$ z ) 1 z D ( z ) dz, (B.5) B.2 Partonic R Q AA