Numerical contour integration for loop integrals

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...

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...

Evaluatiom of Integrals Using Contour Integration

In our lectures on integral solutions to differential equations using Laplace kernels ,we encountered integrals of the type-∫ = + C n t xt t f x y 1) exp() () (where t=γ+iτ and C is a closed contour within the complex plane. To evaluate this type of integrals under conditions where the curve partially lies at infinity, one makes use of complex variable methods and in particular the Cauchy Integ...

Numerical calculation of massive multi-loop integrals

The program package SECDEC is presented, allowing the numerical evaluation of multi-loop integrals. The restriction to Euclidean kinematics of version 1.0 has been lifted: thresholds can be handled by an automated deformation of the integration contour into the complex plane. Other new features of the program, which go beyond the standard decomposition of loop integrals, are also described. The...

Computation of contour integrals