Reconstructed exclusive $b$-hadron decays as hemisphere jet charge tagger and its application for the measurement of $R_b$ and $A_{\text{FB}}^b$

This note presents a novel approach using exclusively reconstructed $b$-hadron decays as a hemisphere tagger and its application for the measurement of $R_b$, the ratio of the $Z$-boson coupling to $b$-quarks to its coupling to all quarks, as well as the $b$-quark forward-backward asymmetry ($A_{\text{FB}}^b$). By focusing on the identification and reconstruction of $b$-hadrons exclusively within one hemisphere of an event, the technique aims to enhance the purity of the $b$-quark sample and improve the precision of these measurements as important tests of the Standard Model's parameters. We present the implementation and validation of the hemisphere tagger technique, including the selection criteria, event reconstruction algorithms and the discussion of uncertainties in the experimental environment of the Tera-$Z$ programme at the FCC-ee.

This analysis note is intended to provide input for the "Mid-term Review Report on Detector Requirements". It is important to emphasise that the analysis pertaining to the hemisphere-hemisphere efficiency correlation is currently in a state of ongoing development.