Techniques for Calculating two-loop Diagrams

Abstract

Methods developed by the Bielefeld-DESY-Dubna collaboration in recent years are: DIANA (DIagram ANAlyser), a program to produce ``FORM input'' for Feynman diagrams, starting from the Feynman rules; methods to calculate scalar diagrams: Taylor expansion in small momenta squared in connection with a mapping and the Pad\'{e} method to sum the series. Recently program packages for the large mass expansion were written and applied to the $Z \to b\bar{b}$ decay. Reviews of these activities were presented in the proceedings of the Ustro\'{n} '97 and Rheinsberg '98 conferences. Here we concentrate on recent developements in the large mass expansion, applied to the two-loop contribution of the $Z \to b\bar{b}$ decay in the $m_b=0$ approximation, taking into account higher order terms of the expansion in $M_W^2/m_t^2$.