Factorizing one-loop contributions to two-loop Bhabha scattering and automatization of Feynman diagram calculations

Abstract

In higher order calculations a number of new technical problems arise: one needs diagrams in arbitrary dimension in order to obtain their needed $\epsilon$-expansion, zero Gram determinants appear, renormalization produces diagrams with `dots' on the lines, i.e. higher order powers of scalar propagators. All these problems cannot be accessed by the `standard' Passarino-Veltman approach: there is not available what is needed for higher loops. We demonstrate our method of how to solve these problems.