Thesis defense of Lars Röhrig

The heaviest third-generation fermions are expected to be most sensitive to effects from Beyond the Standard Model (BSM) physics, which will be probed with very high precision at a possible FCC-ee. In this thesis, a novel approach to measuring Electroweak PrecisionObservables in the beauty-quark sector is pioneered using exclusively reconstructed beauty-hadrons as hemisphere-flavour taggers for the partial decay-width ratio Rb and the forward-backward asymmetry Ab FB, which receive virtual contributions from the heaviest states of the Standard Model (SM): top quarks, Higgs, and W boson. This approach effectively eliminates the contamination from light- quark physics events and reduces leading systematic uncertainties; arising from background contamination, tagging-efficiency correlations, and radiated gluon 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. From Ab FB, the weak mixing angle can be determined with a relative precision of 0.002 %. Building on this innovative methodology, the thesis is extended to the top-quark sector by extracting the sensitivity of top-quark observables to SM Effective Field Theory operators, which describe the effects of BSM physics by extending the SM with higher-dimensional operators on energy scales that are currently inaccessible. In a FCC-ee environment, top-quark pairs are reconstructed, and the expected observational precision is used to derive constraints on the Wilson coefficients that are up to a factor of five and three more stringent than those derived from top-quark measurements at LHC and HL-LHC, respectively.