A numerical algorithm for computing the complete set of one-gluon loop diagrams in QCD on the basis of a single master expression

Abstract

A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task rests on a suitably defined master formula, which is expressed in terms of a set of Grassmann and a set of Feynman parameters, the number of which increases with M. An important component of the numerical program is an algorithm for computing multi-Grassmann variable integrals. The cases M=2, 3, 4, which are the only ones having divergent terms, are fully worked out. A complete agreement with known, analytic results pertaining to the divergent terms is attained.