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 configurati
ons. 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.
We discuss a new approach for the numerical evaluation of loop integrals. The fully numerical calculations of an infrared one-loop vertex and a box diagram are demonstrated. To perform these calculations, we apply an extrapolation method based on the
$epsilon$-algorithm. In our approach, the super high precision control in the numerical manipulation is essential to handle the infrared singularity. We adopt a multi-precision library named {tt HMLib} for the precision control in the calculations.
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numer
ical integration routine with an extrapolation method, together with a multi-precision library, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as $10^{-150}$ GeV in the infrared vertex diagram.
