A numerical algorithm for efficiently obtaining a Feynman parameter representation of one-gluon loop QCD Feynman diagrams for a large number of external gluons

TL;DR

This paper introduces a numerical algorithm and program that efficiently computes one-gluon loop Feynman diagrams in QCD with many external gluons by using a master formula and parametric integrals.

Contribution

It presents a novel numerical method and software that streamline the calculation of complex one-gluon loop diagrams in QCD, handling large numbers of external gluons efficiently.

Findings

Program effectively computes diagrams with many external gluons

Reduces computational complexity by grouping similar terms

Demonstrates fast runtime for large M

Abstract

A numerical program is presented which facilitates a computation pertaining to 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 program carries out the Grassmann integration and performs the Lorentz trace on the involved functions, expressing the result as a compact sum of parametric integrals. The computation is based on tracing the structure of the final result, thus avoiding all intermediate unnecessary calculations and directly writing the output. Similar terms entering the final result are grouped together. The running time of the program demonstrates its effectiveness, especially for large M.