Bottom quark forward-backward asymmetry at the future electron-positron collider FCC-ee

The Standard Model (SM) prediction for the \PZ-boson pole $b$-quark forward-backward (FB) asymmetry is: $(A_{FB}^{0,b})_{th} = 0.1030 \pm 0.0002$. The LEP electron-positron collider measured instead $A_{FB}^{0,b} = 0.0992 \pm 0.0016$, value which presents the largest discrepancy with any of the SM predictions as of today. All the $A_{FB}^b$ measurements performed at LEP suffered however of an important statistical uncertainty and of different sources of systematic uncertainties. This study shows that the proposed high-luminosity electron-positron collider FCC-ee, collecting orders of magnitude more data at the \PZ-pole than LEP, will significantly reduce the statistical uncertainties on the measurement of $A_{FB}^{0,b}$, thus allowing us to shed further light on this tension.