Colour: a computer program for QCD colour factor calculations

Abstract

Abstract:A computer program for evaluating colour factors of QCD Feynman diagrams is presented, and illustrative examples on how to use the program to calculate non trivial colour factors are given. The program and the discussion in this paper is based on a diagrammatic approach to colour factors. Method of solution: QCD Feynman diagrams, with no four-gluon vertices, factorize into a colour (group) factor and a kinematical factor. The colour part of any closed QCD Feynman diagram can be transformed into a sum of diagrams including only closed quark (colour) lines. In each such term, the number of quark (colour) loops is counted, giving factors of 3 (or N c ). The sum of these terms is then the desired colour factor. To perform the translation, we need to have rules to interpret gluons and vertices into quark lines. There is in principle only need for three equalities to be able to calculate any closed QCD diagram (not containing four gluon vertices). To achieve good computing performance further equalities have been introduced. The most essential ones are listed in Appendix A.Restriction of complexity of the problem: Four gluon vertices cannot be included directly in diagrams to be calculated. The number of gluons in diagrams to be calculated are limited to 200, but can easily be changed prior to compiling. Typical running time:For typical diagrams, fractions of a second. Complicated diagramsa few seconds to hours.

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