Navigating Around the Algebraic Jungle of QCD: Efficient Evaluation of Loop Helicity Amplitudes

Abstract

A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear. Background Feynman gauge also helps to simplify the calculations. This method is applicable to any Feynman diagram with any number of loops as long as the external masses can be ignored, and it is at least as efficient as the string technique in the special circumstances when the latter can be used. In order to minimize the very considerable algebra encountered in non-abelian gauge theories, graphical methods are developed for most of the calculations. This enables the large number of terms encountered to be organized visually in the Feynman diagram without the necessity of having to write down any of them algebraically. A one-loop four-gluon amplitude in a particular helicity configuration is computed explicity to illustrate the method.