Quadpack computation of Feynman loop integrals

The paper addresses a numerical computation of Feynman loop integrals, which are computed by an extrapolation to the limit as a parameter in the integrand tends to zero. An important objective is to achieve an automatic computation which is effective for a wide range of instances. Singular or near singular integrand behavior is handled via an adaptive partitioning of the domain, implemented in an iterated/repeated multivariate integration method. Integrand singularities possibly introduced via infrared (IR) divergence at the boundaries of the integration domain are addressed using a version of the Dqags algorithm from the integration package Quadpack, which uses an adaptive strategy combined with extrapolation. The latter is justified for a large class of problems by the underlying asymptotic expansions of the integration error. For IR divergent problems, an extrapolation scheme is presented based on dimensional regularization.

► Feynman loop integrals computed by numerical integration and extrapolation. ► One-loop vertex, box, pentagon and two-loop ladder Feynman diagrams. ► Iterated multivariate integration using adaptive Quadpack algorithms Dqag and Dqags. ► Asymptotic expansions via dimensional regularization for infrared divergence. ► Extrapolation approach for hypergeometric functions.