Two-loop splitting functions in QCD

We present the universal two-loop splitting functions that describe thelimits of two-loop $n$-point amplitudes of massless particles when two of themomenta are collinear. To derive the splitting amplitudes, we take thecollinear limits of explicit two-loop four-point helicity amplitudes computedin the 't Hooft-Veltman scheme. The $g \to gg$ splitting amplitude has recentlybeen computed using the unitarity sewing method and we find complete agreementwith 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 expressionfor the two-loop soft splitting function.Comment: 28 pages, 3 encapsulated postscript figures, JHEP3 clas