Regularization and Extrapolation Methods for Infrared Divergent Loop Integrals

Abstract

Loop integrals occur in higher order perturbation calculations for the cross section of particle interactions in high energy physics. In previous work we introduced a numerical extrapolation method to handle a class of Feynman loop diagrams where the integrand shows a singular behavior on a hypersurface which may intersect the domain of integration. The integral is considered in the limit as a parameter in the integrand tends to zero. Under certain conditions, the extrapolation process achieves convergence acceleration to the limit. In order to handle massless cases, we apply a dimensional regularization technique to extract infrared divergences from the integral. We illustrate the combined technique using a scalar one-loop sample integral.

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