Forward-backward $b$-quark asymmetry at the Z pole: QCD uncertainties redux

The forward-backward asymmetry of $b$-quarks measured at LEP in $e^+e^-$ collisions at the Z pole, $A_{FB}^{0,b}|^{\rm exp} = 0.0992\pm0.0016$, remains today the electroweak precision observable with the largest disagreement (2.8$\sigma$) with the Standard Model theoretical prediction, $A_{FB}^{0,b}|^{\rm th} = 0.1037\pm0.0008$. The dominant systematic uncertainties are due to QCD effects --- $b,c$-quark showering and fragmentation, and $B,D$ meson decay models --- which have not been revisited in the last 20 years. We reassess the QCD uncertainties of the eight original LEP measurements of $A_{FB}^{0,b}$, using modern parton shower simulations based on PYTHIA-8 and PYTHIA-8 plus VINCIA with different tunes of soft and collinear radiation as well as of hadronization. Our analysis indicates QCD uncertainties, of order $\pm$0.4\% and $\pm$1\% for the jet-charge and lepton-charge based analyses, that are overall slightly smaller but still consistent with the original ones. Using the updated QCD systematic uncertainties, we obtain $A_{FB}^{0,b} = 0.0996\pm0.0016$.