Suppression of the high $p_T$ charged hadron $R_{AA}$ at the LHC

We present a parameter free postdiction of the high-$p_T$ charged-hadron nuclear modification factor ($R_{AA}$) in two centralities, measured by the CMS collaboration in $Pb$-$Pb$ collisions at the Large Hadron Collider (LHC). The evolution of the bulk medium is modeled using viscous fluid dynamics, with parameters adjusted to describe the soft hadron yields and elliptic flow. Assuming the dominance of radiative energy loss, we compute the medium modification of the $R_{AA}$ using a perturbative QCD based formalism, the higher twist scheme. The transverse momentum diffusion coefficient $\hat{q}$ is assumed to scale with the entropy density and normalized by fitting the $R_{AA}$ in the most central $Au$-$Au$ collisions at the Relativistic Heavy-Ion Collider (RHIC). This set up is validated in non-central $Au$-$Au$ collisions at RHIC and then extrapolated to $Pb$-$Pb$ collisions at the LHC, keeping the relation between $\hat{q}$ and entropy density unchanged. We obtain a satisfactory description of the CMS $R_{AA}$ over the $p_{T}$ range from 10-100 GeV.