Reduction of general two-loop self-energies to standard scalar integrals

Abstract

A method is presented for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model (SM). We develop a technique for treating the tensor structure of two-loop integrals appearing in self-energy calculations. It is used together with the symmetry properties of the integrals to obtain a result in terms of a small number of standard scalar integrals. 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 ζ i ( i = γ Z, W). The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows us 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 of our algorithm 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.