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

Abstract We consider, at order α s 2 $$ {\alpha}_s^2 $$ 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 A FB. In particular, we analyze b jets defined by the Durham and the flavor-k T 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 α s 2 $$ {\alpha}_s^2 $$ are small. That predestines it to act as a precision observable.