Framework for a novel mixed analytical/numerical approach for the computation of two-loop $N$-point Feynman diagrams

Abstract

A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations over these two variables are to be performed numerically, whereas the ingredients involved in the integrands, in particular the "generalised one-loop type" functions, are computed analytically. The idea is illustrated on a few examples of scalar three- and four-point functions.

24 pages, 8 figures, changes in the title, addition of a new section on the decomposition of polytopes into simplexes, the appendix A has been completed

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Cited by in corpus (2)

• Direct numerical evaluation of multi-loop integrals without contour deformation
• Two-loop scalar functions with $I$ internal lines, $I\le 5$