A novel approach to the computation of one-loop three- and four-point functions. III. The infrared divergent case

This article is the third and last of a series presenting an alternative method for computing the one-loop scalar integrals. It extends the results of the first two articles to the infrared divergent case. This novel method enjoys a couple of interesting features as compared with the methods found in the literature. It directly proceeds in terms of the quantities driving algebraic reduction methods. It yields a simple decision tree based on the vanishing of internal masses and one-pinched kinematic matrices, which avoids a profusion of cases. Lastly, it extends to kinematics more general than the physical, e.g. collider processes, relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.