Description
The study of the properties of the top quark is one of the main goals of the LHC physics program.
At both Tevatron and the LHC, top and antitop quarks are mainly produced in pairs. The experimental precision expected at the LHC demands the calculation of the top-quark pair-production cross section
up to next-to-next-to-leading order (NNLO) corrections.
In this talk, we describe the calculation of the two-loop corrections to the top-quark pair-production
cross section. The latter are a crucial part of the NNLO corrections, and their evaluation poses
interesting technical challenges. We describe the methods employed in obtaining the results currently
available and discuss the ongoing effort aimed to complete the calculation of the virtual corrections to
the top-quark pair-production process ad hadron colliders.