Accelerating Feynman Integral Evaluation by Avoiding Contour Deformation

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.