Extrapolation Algorithms for Infrared Divergent Integrals

TL;DR

This paper develops extrapolation algorithms to accurately compute infrared divergent integrals, addressing singularities both at boundaries and interior points, with high-precision results demonstrated for massless vertex integrals.

Contribution

It introduces a double extrapolation method for massless vertex integrals and applies adaptive integration techniques for high-accuracy computation of IR divergent integrals.

Findings

High-precision quadruple results achieved

Effective handling of interior and boundary singularities

Validated methods with adaptive integration tools

Abstract

This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional regularization. While this treats typical IR singularities at the boundaries of the integration domain, special care needs to be taken in cases where the integrand is singular in the interior of the domain as well as on the boundaries. A double extrapolation is devised for a class of massless vertex integrals. Quadruple precision results are presented, demonstrating high accuracy. The computations are supported by the use of general adaptive integration programs from the QUADPACK package, in iterated integrations with highly singular integrand functions.