Angular Distributions of Higher Order Splitting Functions

We study the angular distributions of the splitting functions for processes for which a parton splits into three partons. Unlike the case of coherent branching, we find that both in vacuum and in the presence of the dense QCD matter, such collinear splitting functions are neither ordered, nor anti-ordered. In the medium-induced splitting functions the angular distributions are broader compared to the similar vacuum distribution, a feature previously noticed from the lowest order medium-induced splitting functions.