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 Padé 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 Ustroń '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 $M_W^2/m_t^2$.