USE OF HELICITY METHODS IN EVALUATING LOOP INTEGRALS - A QCD EXAMPLE

We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop contribution to e+e- --> qqgBAR in massless QCD. By using covariant helicity representations for the spinor and vector wave functions we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qqBAR --> (W, Z, gamma*) + g including the real photon cases. As we treat the spin degrees of freedom in four dimensions and only continue momenta to n dimensions (dimensional reduction scheme) we explicate how our results are related to the usual dimensional regularization results.