Numerical Scattering Amplitudes with pySecDec

TL;DR

The paper introduces an updated version of pySecDec that significantly improves the evaluation of multi-loop Feynman integrals and amplitudes, incorporating new algorithms, GPU support, and performance enhancements.

Contribution

The update includes a new integration method using median Quasi-Monte Carlo rules, support for integrals with numerators, and automatic regulator determination, enhancing speed and flexibility.

Findings

Up to 10x faster performance

Median lattice rules outperform previous methods by a factor of 5

Extended capabilities for integrals with numerators

Abstract

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples.