Completely Automated Calculations of Multi-Loop Diagrams

Abstract

The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This makes it necessary to automate the calculations as much as possible. A program package will be described which generates automatically the Feynman diagrams, manipulates the expressions in the desired way and performs the computation. As a physical application O(\alpha\alpha_s) corrections to the decay rate of the $Z$ boson into bottom quarks are discussed.