New $b$-tagging using exclusive $b$-hadron decays at FCC-ee

The Future Circular Collider as electron-positron collider (FCC-ee) is planned to produce $\mathcal{O}(10^{12})$ $Z\to b\bar{b}$ decays. This means most measurements at the $Z$-pole will be limited by the systematic uncertainty. This proceedings motivates the use and describes the application of a novel $b$-quark hemisphere tagger for electroweak precision observables at FCC-ee to reduce systematic uncertainties to the scale of the statistical ones. The tagger uses exclusive $b$-hadron decays with a potential purity of $100\,\%$, thus being free of $c$- and light-physics background, which are the main source of systematic uncertainty. Representative $b$-hadron decay modes are presented and the application of the tagger on the measurement of $R_b$ is highlighted by using simulated samples in an FCC-ee environment.