Status reports from the GRACE Group

TL;DR

This paper presents a novel numerical method for evaluating infrared one-loop integrals using an extrapolation technique and high-precision arithmetic, demonstrated on vertex and box diagrams.

Contribution

It introduces a fully numerical approach with an extrapolation method and high-precision control for infrared loop integrals, improving accuracy and stability.

Findings

Successful numerical evaluation of infrared one-loop vertex and box diagrams

Effective use of the $psilon$-algorithm for extrapolation

High-precision calculations enabled by HMLib

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 $\epsilon$-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.