Efficient Numerical Evaluation of Feynman Integral

TL;DR

This paper introduces a GPU-accelerated quasi-Monte Carlo method to efficiently evaluate Feynman loop integrals, significantly reducing computation time and enabling precise higher-order quantum field theory calculations.

Contribution

It presents a novel combination of quasi-Monte Carlo and CUDA/GPU techniques to improve the speed and accuracy of numerical Feynman integral evaluations.

Findings

Feynman integrals can be computed in less than half a minute with high accuracy.

The method is effective for both Euclidean and physical kinematic regions.

Enables precise higher-order effects calculations in multi-loop processes.

Abstract

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with $\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.