QCD corrections for the production of single top quarks in association with two jets

The top quark is the heaviest known elementary particle. In the standard model (SM) of elementary particle physics it is produced predominantly in pairs by the strong interaction. The weak interaction enables the production of single top-quarks as well. The corresponding cross section is about one third of the cross section of pair production. The distinction from background is more difficult in the case of single top-quark production. Thus the discovery of top quarks in 1995 at the Tevatron collider at Fermilab used pair production. Despite its difficult experimental signature, the production of single top-quarks is interesting as it is complementary to the production of pairs. For instance single top-quarks are highly polarized. As top quarks decay before they hadronize, the polarization affects the decay products of the top quark in an experimentally accessible way. Furthermore, the participation of bottom-quarks in the initial state allows a study of the corresponding parton distribution functions. A direct determination of the Cabibbo-Koboyashi-Maskawa matrix element V_tb is possible too. The production of single top-quarks was discovered in 2009 at the Tevatron. This thesis makes phenomenological predictions for the SM by calculating cross sections for the production of single top-quarks in association with two jets. Next-to-leading order corrections in quantum chromodynamics (QCD) are taken into account. These corrections are the most important contribution for precise predictions beyond the leading order calculation. Precise theoretical predictions for cross sections are mandatory for the search for new physics at the Large Hadron Collider at CERN. In contrast to the QCD corrections for the production of single top-quarks published in 2002 an additional particle in the final state was taken into account. As a consequence, new partonic initial states and contributions with exchange of color charge between the quark lines occur. As top quarks decay rapidly into a W boson and a bottom quark, a consistent separation from the production of top quark pairs and from the production of single top-quarks in association with a W boson must be ensured. For the leading order analytical results for the square of the absolute value of the amplitudes are presented. The corrections in next-to-leading order QCD are calculated using established methods. The tensor integrals in the virtual corrections are reduced numerically to scalar integrals using existing numerical libraries. The real corrections are calculated using a self-written implementation of the Catani-Seymour formalism. The results were validated using internal tests. The numerical cancellation of the divergences is an especially important test for internal consistency. Furthermore, an external comparison with an independent implementation was made. The presentation of results starts with inclusive cross sections. The atypical scale dependence is discussed afterwards. In addition, differential cross sections using fixed scales are shown for transverse momenta, rapidities and further observables. For high transverse momenta a dynamical choice of scales becomes advantageous. Results using a dynamical choice of scales are presented as well.