Jet modification in three dimensional fluid dynamics at next-to-leading twist

The modification of the single inclusive spectrum of high transverse momentum ($p_T $) pions emanating from an ultra-relativistic heavy-ion collision is investigated. The deconfined sector is modelled using a full three dimensional (3-D) ideal fluid dynamics simulation. Energy loss of high $p_T$ partons and the ensuing modification of their fragmentation is calculated within perturbative QCD at next-to-leading twist, where the magnitude of the higher twist contribution is modulated by the entropy density extracted from the 3-D fluid dynamics simulation. The nuclear modification factor ($R_{AA}$) for pions with a $p_T \geq 8$ GeV as a function of centrality as well as with respect to the reaction plane is calculated. The magnitude of contributions to the differential $R_{AA}$ within small angular ranges, from various depths in the dense matter is extracted from the calculation and demonstrate the correlation of the length integrated density and the $R_{AA}$ from a given depth. The significance of the mixed and hadronic phase to the overall magnitude of energy loss are explored.