High Performance and Increased Precision Techniques for Feynman Loop Integrals

For the investigation of physics within and beyond the Standard Model, a precise evaluation of higher order corrections in perturbative quantum field theory is required. We have worked on the development of a computational method for Feynman loop integrals with a fully numerical approach. It is based on numerical integration and extrapolation techniques. In this paper, we describe the status and new developments in our techniques for the numerical computation of Feynman loop integrals. Separation of ultra-violet divergences is important for the renormalization procedure. In our analyses, the separation can be done numerically. For 2-loop integrals we have performed the calculations for up to 4-point functions, and for 2-point functions we can handle up to 4- loop integrals. We report the status and accuracy of the computations with detailed numerical comparisons to results in the literature, in order to demonstrate that our method will evolve into an important component of automated systems for the study of higher-order radiative corrections.