Revised QCD effects on the Z \(\rightarrow \,b\overline{b}\) 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, \(A_{_{\textsc {fb}}}^{0,b}= 0.0992\pm 0.0016\), remains today one of the electroweak precision observables with the largest disagreement (2.4\(\sigma \)) with respect to the Standard Model prediction, \((A_{_{\textsc {fb}}}^{0,b})_{_\textrm{th}} = 0.1030 \pm 0.0002\). Beyond the dominant statistical uncertainties, QCD effects, such as b-quark showering and hadronization, are the leading sources of \(A_{_{\textsc {fb}}}^{0,b}\) systematic uncertainty, and have not been revised in the last twenty years. We reassess the QCD uncertainties of the eight original \(A_{_{\textsc {fb}}}^{0,b}\) 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 \(A_{_{\textsc {fb}}}^{0,b}= 0.0995\pm 0.0016\) 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 \(A_{_{\textsc {fb}}}^{0,b}\) statistical uncertainties, and to improve our understanding of b-quark showering and hadronization.