Incorporating Space-Time Within Medium-Modified Jet Event Generators

We outline a novel approach to develop an in-medium shower Monte-Carlo event generator based on the higher-twist formalism of jet modification. By undoing one of the light-cone integrals which sets the corresponding light-cone momentum to be equal in the amplitude and the complex conjugate, we introduce an uncertainty in the smaller light-cone momentum component. This allows for the generalization of the standard analytic formalism to a Wigner transform like formalism, where the non-conjugate large light-cone momentum and position are retained for each parton. Jets are generated event-by-event by simulating this Wigner transform kernel. Simple results for longitudinal distributions of partons and hadrons from jets propagating through a hot brick of strongly interacting matter are presented. Values of the transport coefficient $\hat{q}$ are dialed to match phenomenologically relevant cases.