Numerical Approach to Calculation of Feynman Loop Integrals

TL;DR

This paper introduces a fully numerical method combining integration and extrapolation techniques to evaluate Feynman loop integrals, applicable to complex masses and multi-loop diagrams, demonstrated with scalar box integrals.

Contribution

The paper presents a novel numerical approach that avoids analytic methods, enabling the calculation of complex-mass and multi-loop Feynman integrals with high accuracy.

Findings

Successfully computed one-loop and two-loop box integrals with complex masses.

Demonstrated the method's accuracy through comparisons with existing techniques.

Provided a self-consistency check for numerical results.

Abstract

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried out in a fully numerical way, our approach is applicable to one-, two- and multi-loop diagrams. Without any analytic treatment it can compute diagrams with not only real masses but also complex masses for the internal particles. As concrete examples we present numerical results of a scalar one-loop box integral with complex masses and two-loop planar and non-planar box integrals with masses. We discuss the quality of our numerical computation by comparisons with other methods and also propose a self consistency check.