An algorithm for the poles at dimension 4 in the dimensional regularization procedure

Abstract

One-loop Feynman diagrams, when regularized using the continuous dimension method, exhibit single poles at n = 4, and these poles can be eliminated by a counterterm Ä in the Lagrangian. In this paper a simple algorithm is derived to express Ä in terms of the components of the Lagrangian without performing integrations. It can be used in dimensional regularization, but also to derive Callan-Symanzik type equations for small distance behaviour in any renormalizable