Numerical Evaluation of Feynman Integrals by a Direct Computation Method

TL;DR

This paper introduces a numerical method for evaluating Feynman integrals that combines efficient numerical integration, extrapolation, high-precision arithmetic, and parallelization, demonstrated on complex loop integrals.

Contribution

The paper presents a novel direct computation method for Feynman integrals, enhancing accuracy and efficiency through numerical techniques and parallel computing.

Findings

Successfully evaluated one-loop 5-point integrals

Achieved results for two-loop 3-point integrals

Demonstrated method's potential for complex Feynman integrals

Abstract

A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision arithmetic and parallelization technique can be used in this method if required. We present the recent progress in development of this method and show results such as one-loop 5-point and two-loop 3-point integrals.