Loop integration results using numerical extrapolation for a non-scalar integral

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards.Comment: 4 pages, 3 figures, revised, contribution to ACAT03 (Dec. 2003

Numerical Computation of Two-loop Box Diagrams with Masses

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.Comment: 16 pages, 8 figure

A numerical evaluation of the scalar hexagon integral in the physical region

We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative corrections to multi-particle cross sections. The hexagon integral is represented in terms of n-dimensional triangle functions and (n+2)-dimensional box functions. If infrared poles are present this representation naturally splits into a finite and a pole part. For a fast numerical integration of the finite part we propose simple one- and two-dimensional integral representations. We set up an iterative numerical integration method to calculate these integrals directly in an efficient way. The method is illustrated by explicit results for pentagon and hexagon functions with some generic physical kinematics