Thesis defense of Rigo Bause

This thesis comprises recent studies on extensions of the standard model (SM) involving a heavy Z' boson. In the SM, flavour-changing neutral current (FCNC) quark transitions only appear at loop level and are highly suppressed. This puts forward flavourful Z' models, where the new gauge boson couples non-universally to the known quarks and leptons at tree level. The models are able address the persistent deviations of the SM seen in observables of rare B-meson decays referred to as the B-anomalies. By supplementing the particle content of the SM with new scalars and vector-like fermions, the occurrence of putative Landau poles present in general Z' scenarios can be averted. We discuss dedicated models in the context of the B-anomalies that allow for a stable and predictive theory up to the Planck scale. Moreover, flavour rotations also enable FCNC transitions in the charm sector, where the resonance pollution in branching ratios of semileptonic decays demands null test observables sensitive to physics beyond the SM. We investigate effects in such decays and present unique correlations to CP-violating observables in hadronic decays, accessible with future measurements by the LHCb and Belle II experiments. Recent studies involving dineutrino modes are discussed as well. We exploit an interplay between neutrino and charged lepton couplings within the SM effective field theory approach that connects decays of opposite flavour sectors. In doing so, we derive limits on diverse sets of dineutrino branching ratios and find novel tests of lepton universality using data from global fits of the B-anomalies.