Resolution of singularities for multi-loop integrals

TL;DR

This paper presents an improved, guaranteed-termination algorithm for numerically evaluating divergent multi-loop integrals using sector decomposition, enabling efficient Laurent expansion in dimensional regularisation.

Contribution

An enhanced algorithm for sector decomposition that guarantees termination and combines symbolic and numerical steps for multi-loop integral evaluation.

Findings

Algorithm guarantees termination for multi-loop integrals.

Program successfully computes Laurent expansions.

Combines symbolic and numerical computations seamlessly.

Abstract

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.