Top and bottom quark forward-backward asymmetries at next-to-next-to-leading order QCD in (un)polarized electron positron collisions

We consider, at order αs2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\alpha}_s^2 $$\end{document} in the QCD coupling, top-quark pair production in the continuum at various center-of-mass energies and b-quark pair production at the Z resonance by (un)polarized electron and positron beams. For top quarks we compute the forward-backward asymmetry with respect to the top-quark direction of flight, the associated polar angle distribution, and we analyze the effect of beam polarization on the QCD corrections to the leading-order asymmetry. We calculate also the polarized forward-backward asymmetry. For b-quark production at the Z peak we explore different definitions of AFB. In particular, we analyze b jets defined by the Durham and the flavor-kT clustering algorithms. We compute the inclusive b-jet and two-jet asymmetry with respect to the b-jet direction. For the latter asymmetry the QCD corrections to order αs2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\alpha}_s^2 $$\end{document} are small. That predestines it to act as a precision observable.