A Calculational Formalism for One-Loop Integrals

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences analytically from the finite one-loop contributions, which can then be evaluated numerically using recursion relations. Using the formalism outlined in this paper, we are in position to construct the next-to-leading order corrections to a variety of multi-leg QCD processes such as multi-jet production and vector-boson(s) plus multi-jet production at hadron colliders. The final limiting factor on the number of particles will be the available computer power.