Eur. Phys. J. A (2025) 61: 188
https://doi.org/10.1140/epja/s10050-025-01656-9

Regular Article - Theoretical Physics

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

¹ CERN, EP Department, 1211, Geneva 23, Switzerland
² Stanford Institute for Theoretical Physics, Stanford University, 94305, Stanford, CA, USA

^a david.d'enterria@cern.ch

Received: 20 April 2025
Accepted: 30 July 2025
Published online: 14 August 2025

Abstract

The forward–backward (FB) asymmetry of b quarks in $e^{+}{e}^{-}$ collisions at the Z pole measured at LEP, $A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b}=0.0992\pm 0.0016$, remains today one of the electroweak precision observables with the largest disagreement (2.4$\sigma$) with respect to the Standard Model prediction, $(A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b})_{_{\text{th}}^{}}^{}=0.1030\pm 0.0002$. Beyond the dominant statistical uncertainties, QCD effects, such as b-quark showering and hadronization, are the leading sources of $A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b}$ systematic uncertainty, and have not been revised in the last twenty years. We reassess the QCD uncertainties of the eight original $A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b}$ 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 $A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b}=0.0995\pm 0.0016$ 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 $A_{_{\mathrm{F}\mathrm{B}}^{}}^{0,b}$ statistical uncertainties, and to improve our understanding of b-quark showering and hadronization.