# Direct numerical integration for multi-loop integrals

Regular Article - Theoretical Physics

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## Abstract

We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be performed directly in loop momentum space without the introduction of Feynman or Schwinger parameters. The method can be applied to finite multi-loop integrals and to divergent multi-loop integrals with suitable subtraction terms. The algorithm extends techniques from the one-loop case to the multi-loop case. Examples at two and three loops are discussed explicitly.

## Keywords

External Momentum Subtraction Term Feynman Graph Loop Momentum Ladder Diagram
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© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013