Recursion relations for the general tree-level amplitudes in QCD with massive dirac fields

Abstract

QCD amplitudes with many external fields have been studied for a long time. At tree-level, the amplitudes can be obtained effectively by the BCFW recursion relations. In this article, we extend the Britto-Cachazo-Feng-Witten (BCFW) relations to the QCD amplitude of which the external fields are all massive or include only one massless line. We find such amplitude can be split into two parts and each part of the amplitude is of some correlated spin configuration between the two shifted lines. After choosing proper momentum shift scheme, we can show that each part is constructible directly. Hence, we can obtain a general procedure for the amplitudes in QCD by the BCFW recursion relations. We apply the procedure to several amplitudes as examples. We find such methods are very efficient when there are many massive external fields in the amplitudes.