We extend approximate next-to-next-to-leading order results for top-pair production to include the semi-leptonic decays of top quarks in the narrow-width approximation. The new hard-scattering kernels are implemented in a fully differential parton-le
vel Monte Carlo that allows for the study of any IR-safe observable constructed from the momenta of the decay products of the top. Our best predictions are given by approximate NNLO corrections in the production matched to a fixed order calculation with NLO corrections in both the production and decay subprocesses. Being fully differential enables us to make comparisons between approximate results derived via different (PIM and 1PI) kinematics for arbitrary distributions. These comparisons reveal that the renormalization-group framework, from which the approximate results are derived, is rather robust in the sense that applying a realistic error estimate allows us to obtain a reliable prediction with a reduced theoretical error for generic observables and analysis cuts.
We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-par
ticle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of $Gamma_X/m_X$, with $Gamma_X$ and $m_X$ the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the $q bar{q}$ partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the na ive counting $sim Gamma_t/m_t sim 1%$. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.
