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The talk is on a computational set-up for calculating the production of amassive quark-antiquark pair in electron positron collisions to order$\alpha_s^2$ in the coupling of quantum chromodynamics (QCD) at thedifferential level using the antenna subtraction method. Theoreticalpredictions on the production of top quark pairs in the continuum, and thebottom quark pairs at the $Z$ resonance, will be discussed. In particular, wewould be focusing on the order $\alpha_s^2$ QCD corrections to the heavy quarkforward-backward asymmetry (AFB) in electron positron collisions. In the caseof the AFB of bottom quarks at the $Z$ resonance, the QCD corrections aredetermined with respect to both the bottom quark axis and the thrust axis. Wewill also briefly discuss improvements on these QCD corrections brought byapplying the optimization procedure based on the Principle of MaximumConformality.

Forward-backward asymmetries of the heavy quark pair production in $e^+e^-$ collisions at $\mathcal{O}(\alpha_s^2)$