Two-loop splitting functions in QCD

Abstract

We present the universal two-loop splitting functions that describe the limits of two-loop $n$-point amplitudes of massless particles when two of the momenta are collinear. To derive the splitting amplitudes, we take the collinear limits of explicit two-loop four-point helicity amplitudes computed in the 't Hooft-Veltman scheme. The $g\to gg$ splitting amplitude has recently been computed using the unitarity sewing method and we find complete agreement with the results of Ref. \cite{Bern:2lsplit}. The two-loop $q\to qg$ and $g\to q\bar{q}$ splitting functions are new results. We also provide an expression for the two-loop soft splitting function.

Comments: 28 pages, 3 encapsulated postscript figures, JHEP3 class