Direct numerical integration for multi-loop integrals

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.

20 pages, v2: version to be published, v3: acknowledgement added

References in corpus (4)

• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Direct contour deformation with arbitrary masses in the loop
• Infrared singularities in one-loop amplitudes
• Random polarisations of the dipoles

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