The Rational Part of QCD Amplitude I: the General Formalism

A general formalism for computing only the rational part of the one-loop QCD amplitude is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the rational part directly. Explicit formulas for the rational part are given for all bubble and triangle integrals. Formulas are also given for box integrals up to two mass hard boxes which are the needed ingredients to compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly the rational part of the 5- and 6-gluon QCD amplitudes in two accompanying papers.