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No abstract

part in four dimensions with a two-dimensional integral representation show good large momentum expansions in closed form. Numerical comparisons for the finite variables, namely Lauricella functions. These results represent previous small and ever, that they can be described by generalized hypergeometric functions of several integrals cannot be expressed in terms of polylogarithms. Here it is shown, how propagators is studied in an arbitrary number of dimensions. As it is known these In this paper the class of N loop massive scalar self·energy diagrams with N + 1 Abstract Dec. 1993 Am Hubland, D·8700 Wiirzburg, Federal Republic of Germany to the above problem. To circumvent it two approaches have been followed in the that the diagrams in which three particle cuts arise, with all particles massive, lead ould reach a precision of about 5 >< 10"5 and the forward Bhabha measurement an high and will even improve in the future. For instance, the Z mass measurementsThe precision of the experiments testing the electroweak theory is at this moment

We present a method for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model. It includes the tensor integral reduction for all two-loop integrals appearing in self-energy calculations. The results are valid for arbitrary values of the invariant momentum $p^2$, all particle masses, the space-time dimension $D$ and the gauge parameters $\xi _i \; (i = \gamma , Z, W)$. The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows to perform very stringent checks. We explicitly verify Slavnov-Taylor identities by calculating several thousand Feynman-diagrams and adding them up algebraically. As an application we calculate the light fermion contributions to the two-loop gauge boson self-energies of the electroweak SM. We study their gauge dependence and discuss the occurring standard integrals.Comment: LaTex, 32 pages, (+ 7 figures available from the authors as ps-files), to appear in Nuclear Physics

TARCER is an implementation of the recurrence algorithm of O.V. Tarasov for the reduction of two-loop propagator integrals with arbitrary masses to a small set of basis integrals. The tensor integral reduction scheme is adapted to moment integrals emerging in operator matrix element calculations.