Calculation of two-loop QCD corrections for hadronic single top-quark production in the $t$ channel

In this article we discuss the calculation of single top-quark production in the $t$ channel at two-loop order in QCD. In particular we present the decomposition of the amplitude according to its spin and color structure and present complete results for the two-loop amplitudes in terms of master integrals. For the vertex corrections compact analytic expressions are given. The box contributions are implemented in a publicly available c program.

Figure 1

Born diagram for $t$-channel production of a single top quark.

Figure 2

Sample diagrams for single top-quark production at two-loop order.

Figure 3

Diagrams whose interference with the Born amplitude vanishes.

Figure 4

Sample topologies contributing to $A_{1,LC}^{(2)}$.