It is known that the LHC has a considerable discovery potential because of its large
centre-of-mass energy (vs =14 TeV) and the high design luminosity. In addition the two
experiments ATLAS and CMS perform precision measurements for numerous models in physics. The
increasing experimental precision demands an even higher level of accuracy on the theoretical
side. For a more precise prediction of outcomes one has to consider the corrections obtained
typically from Quantum Chromodynamics (QCD). The calculation of these corrections in the high
energy regime is described by perturbation theory. In the present study multi-loop
calculations in QCD including in particular two-loop corrections for single top quark
production are considered. There are several phenomenological motivations to study single top
quark production: Firstly the process is sensitive to the electroweak Wtb-vertex moreover
non-standard couplings can hint at physics beyond the Standard Model. Secondly the t-channel
cross section measurement provides information on the b-quark Parton Distribution Functions
(PDF). Finally single top quark production enables us to directly measure the
Cabibbo-Kobayashi-Maskawa(CKM) matrix element Vtb. The next-to-next-to-leading-order (NNLO)
calculation of the single top quark production has many building blocks. In this study two
blocks will be presented: one-loop corrections squared and two-loop corrections interfered with
Born. Initially the one-loop squared contribution at NNLO for single top quark production will
be calculated. Before we begin with the calculation of the two-loop corrections to single top
quark production we calculate the QCD form factors of heavy quarks at NNLO along with the
axial vector coupling as a first independent check. A comparison with the relevant literature
suggests that this approach is in line with generally accepted procedure. This consistency
check provides a proof of the validity of our setup. In the next step the two-loop corrections
to single top quark production will be calculated. After reducing all occurring tensor
integrals to scalar integrals we apply the integration by parts method (IBP) to find the
master integrals. This step is a major challenge compared to all similar calculations because
of the number of variables in the problem (two Mandelstam variables s and t the dimension d
and the mass of the top quark mt as well as the mass of the W boson mw). Finally the
calculation of the three kinds of topologies vertex corrections double boxes and non-planar
double boxes in the two-loop contribution at NNLO calculation will be presented.
