Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions

TL;DR

This paper introduces advanced numerical methods and software tools for high-precision evaluation of complex Mellin-Barnes integrals in Minkowskian regions, crucial for particle physics calculations involving massive particles.

Contribution

It presents new versions of AMBRE packages for constructing MB representations and introduces MBnumerics.m for accurate numerical integration in Minkowskian regions.

Findings

High-precision results for massive vertex integrals

Effective handling of threshold effects and multiple scales

Enhanced computational tools for particle physics integrals

Abstract

Mellin-Barnes (MB) techniques applied to integrals emerging in particle physics perturbative calculations are summarized. New versions of AMBRE packages which construct planar and nonplanar MB representations are shortly discussed. The numerical package MBnumerics.m is presented for the first time which is able to calculate with a high precision multidimensional MB integrals in Minkowskian regions. Examples are given for massive vertex integrals which include threshold effects and several scale parameters.