content_image/303569.jpg
initial Q distributions as in Eq. (4.4). In this case 

<img src='content_image/303569.jpg'>

The branching implementation is seen via the product of two distinct factors in contrast to the one quenching factor in Eq. (4.4). For small 〈 ϵ r,e Q 〉 both approaches obviously give rise to the same R$_{Q}$ = 1 − n 〈 ϵ$_{Q}$ 〉 . 

In both approaches, fluctuations of the radiative energy loss due to gluon number fluctuations are computed as discussed in detail in Ref. [374, 387]. This involves using the DGLV generalization [278] of the GLV opacity ex- pansion [274] to heavy quarks. Bjorken longitudinal expansion is taken into account by evaluating the bulk density at an average time τ = L/ 2 [374, 387]. For elastic energy loss fluctuations, the full Fokker-Planck solution applica- ble for small fractional energy loss is approximated by a Gaussian centered at the average loss with variance σ 2 el = 2 T 〈 Δ E $^{el}$( p$_{T}$ , L ) 〉 [249]. In approach I the correct, numerically intensive integration through the Bjorken expanding medium provides Δ E $^{el}$( p$_{T}$ , L ). In approach II the τ = L/ 2 approximation is again used; numerical comparisons show that for L ∼ 2 − 7 fm this reproduces the full calculation well. Finally, we note that we use the additional numerical simplification of keeping the strong coupling constant α$_{S}$ fixed at 0 . 3. 

