Shower Development of High Energy Gluons in the Quark Gluon Plasma

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 that characterizes properties of the medium. In ref [ 50 , 56 ], we investigated a measure of overlap effects that cannot be absorbed into an effective value of the jet-quenching parameter in the simplest theoretical situation, which includes imagining a very large, static, homogeneous medium and taking the large N_c limit. The latter assumption is challenged in ref [ 49 ], where we calculated the 1/ N_c² correction to the previous N_c = ∞ results for overlap g → gg → ggg of two consecutive gluon splittings g → gg . We found that, at order 1/ N_c² , there is interesting and non-trivial color dynamics that must be accounted for during the overlap of formation time.