Measuring AFBᵇ and Rb with exclusive b-hadron decays at the FCC-ee

This paper presents a novel tagging technique to measure the beauty-quark partial decay-width ratio Rb R b and its forward–backward asymmetry AFBᵇ A FB b at the FCC-ee, using O(10¹²) O ( 10 12 ) Z -boson decays. The method is based on the exclusive reconstruction of a selected list of b -hadron decay modes in Z→ bb̄ Z → b b ¯ events at the Z pole, which can provide the flavour and possibly the charge of the hemisphere. This approach effectively eliminates the contamination from light-quark physics events and reduces the leading systematic uncertainties arising from background contamination, tagging-efficiency correlations, and gluon-radiation corrections by exploiting the geometric and kinematic properties of beauty hadrons. This results in a total relative uncertainty of the order of 0.01 % for both observables. Furthermore, this precision allows to obtain a commensurate precision on the weak mixing angle sin ²(θ Wᵉᶠᶠ) sin 2 ( θ W eff ) compared to the muon forward–backward asymmetry on the order of 0.002 %.