Status reports from the GRACE Group

Abstract

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 $ε$-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.

6 pages, 3 figures, Proceedings for the International Workshop LCWS/ILC 2007, DESY in Hamburg, Germany, between May 30, 2007, and June 3, 2007