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Direct numerical integration for multi-loop integrals

  • Sebastian Becker
  • Stefan Weinzierl
Regular Article - Theoretical Physics

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.High Energy Physics DivisionArgonne National LaboratoryArgonneUSA
  2. 2.PRISMA Cluster of Excellence, Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany

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