Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations∗

A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic computations of next-to-next-to-leading corrections to physical observables is emphasised. A classification of infrared singular configurations, based on solutions of Landau equations, is introduced. Algorithms for the numerical evaluation of the residues of the infrared poles and of the infrared finite parts of diagrams are introduced and discussed within the scheme of dimensional regularization. Integral representations of Feynman diagrams which form a generalization of Nielsen Goncharov polylogarithms are introduced and their numerical evaluation discussed. Numerical results are shown for all different families of multi-scale, two-loop, three-point infrared divergent diagrams and successful comparisons with analytical results, whenever available, are performed. Part of these results has already been included in a recent evaluation of electroweak pseudo-observables at the two-loop level.