Multi-loop Calculations in the Standard Model: Techniques and Applications *

We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various techniques for the evaluation of scalar diagrams are described, based on the Taylor expansion method and large mass expansion. 1. Automation of Feynman diagram evaluation Recent high precision experiments require, on the side of the theory, high-precision calculations resulting in the evaluation of higher loop diagrams in the Standart Model (SM). For specific processes thousands of multiloop Feynman diagrams do contribute, and it turns out to be impossible to perform these calculations by hand. This makes the request for automation a high-priority task. Several different packages have been developed with different areas of applicability. For example, FEYNARTS / FEYNCALC [1] are MATHEMA-TICA packages convenient for various aspects of the calculation of radiative corrections in the SM. There are several FORM packages for evaluating mul-tiloop diagrams, like MINCER [2], and a package [3] for the calculation of 3-loop bubble integrals with a mass. Other automatic packages are GRACE [4] and COMHPEP [5], which partially perform full calculations, from the process definition to the cross-section values. A somewhat different approach is persued by XLOOPS [6]. A graphical user interface makes XLOOPS an 'easy-to-handle' program package, but is mainly aimed to the evaluation of single diagrams. To deal with thousands of diagrams, it is neccessary to use special techniques like databases and special controlling programs. In [7] for evaluating more than 11000 diagrams the