There are steady advances in the calculation of electroweak corrections to massive scattering problems at colliders, from the very beginning in the nineteen seventies until contemporary developments. Recent years brought a remarkable progress due to
new calculational technologies. This was motivated by demands from phenomenological applications at particle accelerators: higher multiplicities of the final states, extreme kinematics, need of higher precision and thus of higher orders in perturbation theory. We describe selected contributions from the project Massive particle production of Sonderforschungsbereich/Transregio 9 of Deutsche Forschungsgemeinschaft.
We present a new algorithm for the reduction of one-loop emph{tensor} Feynman integrals with $nleq 4$ external legs to emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l geq 0$ and generic dimen
sion $d=4-2epsilon$, thus avoiding the appearance of inverse Gram determinants $()_4$. As long as $()_4 eq 0$, the integrals $I_{3,4}^D$ with $D>d$ may be further expressed by the usual dimensionally regularized scalar functions $I_{2,3,4}^d$. The integrals $I_{4}^D$ are known at $()_4 equiv 0$, so that we may extend the numerics to small, non-vanishing $()_4$ by applying a dimensional recurrence relation. A numerical example is worked out. Together with a recursive reduction of 6- and 5-point functions, derived earlier, the calculational scheme allows a stabilized reduction of $n$-point functions with $nleq 6$ at arbitrary phase space points. The algorithm is worked out explicitely for tensors of rank $Rleq n$.
Virtual hadronic contributions to the Bhabha process at the NNLO level are discussed. They are substantial for predictions with per mil accuracy. The studies of heavy fermion and hadron corrections complete the calculation of Bhabha virtual effects at the NNLO level.
We discuss the determination of the infrared singularities of massive one-loop 5-point functions with Mellin-Barnes (MB) representations. Massless internal lines may lead to poles in the $eps$ expansion of the Feynman diagram, while unresolved massle
ss final state particles give endpoint singularities of the phase space integrals. MB integrals are an elegant tool for their common treatment. An evaluation by taking residues leads to inverse binomial sums.
