Accelerating Feynman Integral Evaluation by Avoiding Contour Deformation

TL;DR

This paper introduces a new method for evaluating Feynman integrals that avoids contour deformation, significantly improving computational efficiency and broadening applicability to various integrals.

Contribution

The authors present a novel approach to rewrite Feynman integrals as sums of real positive integrands with complex factors, eliminating the need for contour deformation.

Findings

Performance gains of up to several orders of magnitude compared to traditional methods.

Method successfully applied to multiple examples demonstrating its effectiveness.

Enhanced resolution procedure using Cylindrical Algebraic Decomposition for general integrals.

Abstract

We describe our method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for a contour deformation, which is one of the main computational bottlenecks in numerical integration. We demonstrate clearly how the method works on two examples, and benchmark the performance against contour deformation as implemented in pySecDec, where we observe performance gains of up to several orders of magnitude. We describe an improvement in the resolution procedure using the Generic Cylindrical Algebraic Decomposition algorithm, which generalises our method to any Feynman integral, including those with massive propagators.