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An automatized algorithm to compute infrared divergent multi-loop integrals

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arxiv hep-ph/0004013 v2 pith:IQCZTA2X submitted 2000-04-03 hep-ph

An automatized algorithm to compute infrared divergent multi-loop integrals

classification hep-ph
keywords integralsalgorithmautomatizedepsiloninfraredloopmulti-loopnumerically
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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