On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

TL;DR

This paper introduces an enhanced numerical method using Mellin-Barnes representations for evaluating multi-loop integrals, addressing convergence issues in diagrams with masses and branch cuts, and demonstrates its effectiveness on new two-loop examples.

Contribution

The paper presents a significantly improved numerical approach for multi-loop integrals using Mellin-Barnes representations, enabling calculations of previously unknown two-loop diagrams.

Findings

Improved convergence of numerical integrals with massive propagators.

Successful calculation of new two-loop integrals.

Enhanced method for handling branch cuts in loop diagrams.

Abstract

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.