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

In higher order calculations a number of new technical problems arise: one needs diagrams in arbitrary dimension in order to obtain their needed ε-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: what is needed for higher loops is not available there. We demonstrate our method of how to solve these problems.