An automatized algorithm to compute infrared divergent multi-loop integrals Original Research Article

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4−2ϵ dimensions, adequate subtractions lead to a Laurent series in ϵ , where the coefficients of the pole and finite terms are sums of regular parameter integrals which can be evaluated numerically. We fully automatized this algorithm by implementing it into algebraic manipulation programs and applied it to calculate numerically some nontrivial 2-loop 4-point and 3-loop 3-point Feynman diagrams. Finally, we discuss the applicability of our method to phenomenologically relevant multi-loop calculations such as the NNLO QCD corrections for e+e−→ 3 jets.