Are gluon showers inside a QGP strongly or weakly coupled ? a theorist's test*

Jets produced from colliding two heavy nuclei play an important role in understanding properties of the Quark Gluon Plasma. During their travel through the medium, high energy partons lose energy through splitting processes like bremsstrahlung and pair production, induced by elastic scatterings with the medium. In the high energy limit, these splitting processes are coherent over large distances and the underlying elastic scatterings can no longer be treated as quantum mechanically independent, leading to a suppression of the splitting rate known as the Landau-Pomeranchuk-Migdal effect. An important question is whether consecutive splittings are themselves quantum mechanically independent or instead overlap significantly. Previously, the overlap of splitting rates has been calculated in the soft bremsstrahlung limit and it was found that such corrections are large but can be absorbed into an effective value of the jet-quenching parameter q^{^} that characterises properties of the medium. We investigate a measure of overlap effects that cannot be absorbed into an effective value of q^{^} in the simplest theoretical situation, which includes imagining a very large, static, homogeneous medium and taking the large N_color limit.