Revised QCD effects on the $Z\to b\bar{b}$ forward-backward asymmetry in $e^+e^-$ collisions

The forward-backward (FB) asymmetry of $b$ quarks in $e^+e^-$ collisions at the Z pole measured at LEP, $A_\text{FB}^{0,b} = 0.0992\pm0.0016$, remains today one of the electroweak precision observables with the largest disagreement (2.4$\sigma$) with respect to the Standard Model prediction, $(A_\text{FB}^{0,b})_{_\text{th}} = 0.1030 \pm 0.0002$. Beyond the dominant statistical uncertainties, QCD effects, such as $b$-quark showering and hadronization, are the leading sources of $A_\text{FB}^{0,b}$ systematic uncertainty, and have not been revised in the last twenty years. We reassess the QCD uncertainties of the eight original $A_\text{FB}^{0,b}$ LEP measurements, using modern parton shower PYTHIA 8 and VINCIA simulations with nine different implementations of soft and collinear radiation as well as of parton fragmentation. Our analysis, combined with NNLO massive $b$-quark corrections independently computed, indicates total propagated QCD uncertainties of $\sim$0.7\% and $\sim$0.3\% for the lepton- and jet-charge analyses, respectively, that are about a factor of two smaller than those of the original LEP results. Accounting for such updated QCD effects leads to a new $A_\text{FB}^{0,b} = 0.0995\pm0.0016$ average, with a data-theory tension slightly reduced from 2.4$\sigma$ to 2.2$\sigma$. Confirmation or resolution of this long-term discrepancy requires a new high-luminosity $e^+e^-$ collider collecting orders-of-magnitude more data at the Z pole to significantly reduce the dominant $A_\text{FB}^{0,b}$ statistical uncertainties, and to improve our understanding of $b$-quark showering and hadronization.