Angular distributions of higher order splitting functions in the vacuum and in dense QCD matter

Abstract

We study the collinear splitting functions needed for next-to-next-to-leading order calculations of jet production in the vacuum and in dense QCD matter. These splitting functions describe the probability of a parton to evolve into three-parton final state and are generalizations of the traditional DGLAP splitting kernels to a higher perturbative order. Of particular interest are the angular distributions of such splitting functions, which can elucidate the significance of multiple parton branching for jet observables and guide the construction of parton shower Monte Carlo generators. We find that to ${\cal O}(\alpha_s^2)$ both the vacuum and the in-medium collinear splitting functions are neither angular ordered nor anti-angular ordered. Specifically, in dense QCD matter they retain the characteristic broad angular distribution already found in the ${\cal O}(\alpha_s)$ result.