The heavy-quark forward-backward asymmetry to order α2s

The goal of this thesis was the computation of the forward-backward asymmetry in the e+e--production of heavy quarks to next-to-next-to-leading order in QCD (NNLO-QCD). Final states comprising up to four partons contribute to the corrections of order α2s. The two-parton contributions are known for a while. The novel part is the computation of the three- and four-parton contributions. One main task of these computation was to explicitly show the cancellation of the infrared singularities arising in many of the contributing expressions. The other task was to ensure a stable numerical evaluation of the forward-backward asymmetry. The ultraviolet-divergences of the one loop integrals in the three-parton contributions are removed using renormalized perturbation theory. The infrared-divergence in the the three-parton final state contribution to the symmetric and antisymmetric cross sections cancels when building the forward-backward asymmetry out of these cross sections. This has been shown explicitly in this thesis by performing a Laurent-expansion of the relevant differential cross sections around the singular point in phase space. The infrared-divergences in the second-order three-parton contribution to the forward-backward asymmetry arising in the loop integrals, which are regularized in d = 4 - 2ε dimensions are quantified by ε-poles of up to second order and proportional to the leading-order contribution to the observable. The symmetric and antisymmetric contributions to the four-parton final state exhibit one-parton and two-parton unresolved infrared-singularities. In this thesis a modified version of the dipole subtraction formalism has been used to show that the one-parton-unresolved singularities of the four-parton final state cancel the infrared-singularities in the loop integrals of the contributions from the three-parton final states. Identifying the points in the four-parton phase space corresponding to the two-parton-unresolved singularities and computing homogeneous trajectories of the four-parton final state contributions to the forward-backward asymmetry the cancellation of this type of singularities was shown numerically. The results of the described procedures were analytic expressions which in principle can be integrated in a numerically stable way over the respective phase spaces. Using the expressions for the three- and four-parton final states of the symmetric and antisymmetric cross sections in NNLO-QCD, calculated as described above and reproducing the remaining contributions to order α2s, the forward-backward asymmetry for massive b quarks was calculated at the Z pole using both the quark and the thrust direction. For t quarks the forward-backward asymmetry was calculated using the quark direction for center of mass energies ranging from 360 GeV to 1000 GeV.