https://doi.org/10.1140/epjc/s10052-013-2321-1
Regular Article - Theoretical Physics
Direct numerical integration for multi-loop integrals
1
High Energy Physics Division, Argonne National Laboratory, Argonne, IL, 60439, USA
2
PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany
* e-mail: stefanw@thep.physik.uni-mainz.de
Received:
6
November
2012
Revised:
9
January
2013
Published online:
22
February
2013
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.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013
