Transformation, Reduction and Extrapolation Techniques for Feynman Loop Integrals

We address the computation of Feynman loop integrals, which are required for perturbation calculations in high energy physics, as they contribute corrections to the scattering amplitude for the collision of elementary particles. Results in this field can be used in the verification of theoretical models, compared with data measured at colliders. We made a numerical computation feasible for various types of one and two-loop Feynman integrals, by parametrizing the integral to be computed and extrapolating to the limit as the parameter introduced in the denominator of the integrand tends to zero. In order to handle additional singularities at the boundaries of the integration domain, the extrapolation can be preceded by a transformation and/or by a sector decomposition. With the goal of demonstrating the applicability of the combined integration and extrapolation methods to a wide range of problems, we give a survey of earlier work and present additional applications with new results. We aim for an automatic or semi-automatic approach, in order to greatly reduce the amount of analytic manipulation required before the numeric approximation.