Numerical Computation of Two-loop Box Diagrams with Masses

TL;DR

This paper introduces a fully numerical method for computing complex two-loop box diagrams with masses, applicable to various integral configurations in high-energy physics, validated through multiple comparison techniques.

Contribution

It presents a novel numerical approach for evaluating multi-loop integrals with masses, expanding computational capabilities in high-energy physics calculations.

Findings

Successfully computed two-loop box diagrams with different mass configurations.

Results agree with existing reduction methods and dispersion relation checks.

Demonstrated the method's applicability to both planar and non-planar diagrams.

Abstract

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 configurations. 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.