An automatized algorithm to compute infrared divergent multi-loop integrals

Details An automatized algorithm to compute infrared divergent multi-loop integrals An automatized algorithm to compute infrared divergent multi-loop integrals

2000-04-03

arxiv.org/abs/hep-ph/0004013v2

Nucl.Phys. B585 (2000) 741-759

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, 5 eps figures. Replaced by slightly extended, published version, typos corrected

Scientific paper

10.1016/S0550-3213(00)00429-6

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon, 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.

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