Numerical evaluation of multi-loop integrals using subtraction terms

Abstract

A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is performed in the Feynman parameter space, using a complex contour deformation to ensure robust convergence even in the presence of physical thresholds. The application of the proposed procedure is demonstrated with several one- and two-loop examples. An implementation in the program NICODEMOS is publicly available, which currently incorporates only one-loop functionality, but an extension to two-loop cases is planned for future versions.

14 pages; public code NICODEMOS is available at http://www.pitt.edu/~afreitas/; v2: minor typos corrected, evaluation timing information added, published version; v3: numerical errors in Tab.2+3 corrected

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