content_image/315179.jpg content_image/315186.jpg content_image/315187.jpg
the 1D expanding medium: 

<img src='content_image/315179.jpg'>

Note that I$_{2}$ has one less power of l in the integrand; this allows a unique determination of the two free parameters ( κ, k ) when fitting the model to a particular ( R$_{AA}$, v$_{2}$ ) point. 

Using the same hard sphere geometry as before, we are able to fit the 20-30% centrality Phenix π 0 R$_{AA}$ ( φ ) data point with κ = . 5 and k = . 25. Keeping κ and k fixed, Fig. 3.2 shows the results when the impact parameter is varied (long-dashed, blue curve); one can see that this matches the Rhic R$_{AA}$ and v$_{2}$ trends quite well. 

Taking Eq. (3.7) seriously, we invert the relationships and solve for dN$_{g}$/dy . Recalling that µ = gT , λ − 1 ≈ 9 πα 2 $_{s}$( ρ/ 2) 1 / $^{3}$/ 4, and the density for an expand- ing medium is ρ = dN$_{g}$ dy / $^{(}$A$_{⊥}$ ( L $_{2}$) $^{)}$, we find that, as a function of parton energy E , path length L , formation time l$_{0}$ , and α$_{s}$ , 

<img src='content_image/315186.jpg'>

<img src='content_image/315187.jpg'>

where ˜ v$_{1}$ and ˜ v$_{2}$ correspond to the bracketed terms in the energy loss and energy gain approximations, Eqs. (3.2) and (3.6), respectively. 

For our fitted values of κ and k , the choice of E = 6 GeV, L = 5 fm, 

