Evaluation of Feynman integrals via numerical integration of differential equations

TL;DR

This paper presents a novel numerical method for evaluating Feynman integrals by integrating differential equations, enabling faster computations and practical applications in high-energy physics simulations.

Contribution

The authors introduce a new integrator with improved branch cut handling, significantly reducing evaluation times for complex Feynman integrals.

Findings

Evaluation times of milliseconds for one-loop integrals

Evaluation times of hundreds of milliseconds for two-loop integrals

Potential for on-the-fly evaluation in Monte Carlo generators

Abstract

We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and quadruple precision, with significantly smaller run times than other tools. This opens the door to evaluating higher complexity Feynman integrals on the fly in Monte Carlo generators, and enables a cheaper and easy to parallelise generation of grids for the topologies with prohibitive computational times. To show its performance, we test one- and two-loop integral families, achieving evaluation times in double precision of milliseconds and hundreds of milliseconds, respectively. We comment on the results and suggest room for improvement.