Event-by-Event Hydrodynamics+Jet Energy Loss: A Solution to the R_{AA}⊗v_{2} Puzzle

High p_{T}>10  GeV elliptic flow, which is experimentally measured via the correlation between soft and hard hadrons, receives competing contributions from event-by-event fluctuations of the low-p_{T} elliptic flow and event-plane angle fluctuations in the soft sector. In this Letter, a proper account of these event-by-event fluctuations in the soft sector, modeled via viscous hydrodynamics, is combined with a jet-energy-loss model to reveal that the positive contribution from low-p_{T} v_{2} fluctuations overwhelms the negative contributions from event-plane fluctuations. This leads to an enhancement of high-p_{T}>10  GeV elliptic flow in comparison to previous calculations and provides a natural solution to the decade-long high-p_{T} R_{AA}⊗v_{2} puzzle. We also present the first theoretical calculation of high-p_{T} v_{3}, which is shown to be compatible with current LHC data. Furthermore, we discuss how short-wavelength jet-medium physics can be deconvoluted from the physics of soft, bulk event-by-event flow observables using event-shape engineering techniques.