We review some results obtained in the context of the Collaborative Research Center/Transregio~9. In particular we discuss three-loop corrections to the Higgs boson mass in the Minimal Supersymmetric Standard Model, higher order corrections to Higgs
boson production, and the calculations of renormalization group functions and decoupling constants.
We consider the interaction between two static sources in the colour octet configuration and compute the potential to three loops. Special emphasis is put on the treatment of pinch contributions and two methods are applied to reduce their evaluation to diagrams without pinches.
In this paper we compute the three-loop corrections to the beta functions of the three gauge couplings in the Standard Model of particle physics using the minimal subtraction scheme and taking into account Yukawa and Higgs self couplings.
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons to three-loop order within massless perturbative Quantum Chromodynamics. These results provide building blocks for many third-o
rder cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
