Automatic numerical integration methods for Feynman integrals through 3-loop

Automatic numerical integration methods for Feynman integrals through 3-loop

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QUADPACK accommodates boundary singularities of fairly gener...

Numerical contour integration for loop integrals

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculation...

Feynman loop integrals and their automatic computer aided evaluation

Computation of Feynman loop integrals

We address multivariate integration and extrapolation techniques for the computation of Feynman loop integrals. Loop integrals are required for perturbation calculations in high energy physics, as they contribute corrections to the scattering amplitude and the cross section for the collision of elementary particles. We use iterated integration to calculate the multivariate integrals. The combin...

Parallel computation of Feynman loop integrals

The need for large numbers of compute-intensive integrals, arising in quantum field theory perturbation calculations, justifies the parallelization of loop integrals. In earlier work, we devised effective multivariate methods by iterated (repeated) adaptive numerical integration and extrapolation, applicable for some problem classes where standard multivariate integration techniques fail throug...