Algorithmic Calculation of Two-loop Feynman Diagrams *

In a recent paper [1] a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of Padé approximants it is possible to obtain high precision numerical values of the Feynman integrals in the whole cut plane. The real problem in this approach is the calculation of the Taylor coefficients for the arbitrary mass case. Since their analytic evaluation by means of CA packages uses enormous CPU and yields very lengthy expressions, we develop an algorithm with the aim to set up a FORTRAN package for their numerical evaluation. This development is guided by the possibilities offered by the formulae manipulating language FORM [2]. 1. Introduction Standard-model radiative corrections of high accuracy have obtained growing attention lately in order to cope with the increasing precision of LEP experiments [3]. In particular two-loop calculations with nonzero masses became relevant [4]. While in the one-loop approach there exists a systematic way of performing these calculations [5], in the two-loop case there does not exist such a developed technology and only a series of partial results were obtained [6], [7] but no systematic approach was formulated. Our approach consists essentially in performing a Taylor series expansion in terms of external momenta squared and analytic continuation into the whole region of kinemati-cal interest. Simple as this may sound, there are some unexpected methodical advantages compared to other procedures. Considering a Taylor series expansion in terms of one external momentum squared, q 2 say, the differential operator by the repeated application of which the Taylor coefficients are obtained, subsequently setting q = 0, is