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

TL;DR

This paper revises the QCD uncertainties in the measurement of the Z boson decay asymmetry to b quarks at LEP, reducing systematic errors and slightly decreasing the discrepancy with the Standard Model prediction.

Contribution

It provides a modern reassessment of QCD effects on $A_{FB}^{0,b}$ using updated simulations and calculations, refining the systematic uncertainties and the measured asymmetry value.

Findings

QCD uncertainties are about half of previous estimates.

Updated analysis slightly reduces the tension with the Standard Model.

Revised asymmetry value is $0.0995 \\pm 0.0016$.

Abstract

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.