$Z$ mediated Flavour Changing Neutral Currents with a Fourth Vector-Like Family

We discuss $Z$ mediated flavour changing neutral currents within a model where the hierarchical quark and lepton masses are explained via a fourth vector-like family, together with a scalar sector consisting of two Higgs doublets augmented by a gauge singlet scalar field that spontaneously breaks an extra global $U(1)^{\prime}$ symmetry. The $Z$ mediated flavor violating interactions arise from the mixings between the SM fermions and the vector-like fermions, where the mixing is discussed in an analytic approximation and also exactly numerically. We first discuss charged lepton flavor violating (CLFV) $\tau \rightarrow \mu \gamma, \tau \rightarrow 3\mu$ and $Z \rightarrow \mu \tau$ decays and find that they cannot significantly constrain the masses of charged vector-like leptons. However, the $790 \text{GeV}$ mass bound arising from collider searches on vector-like lepton doublets can set further constraints on the model parameter space. We also consider rare $t \rightarrow c Z$ decays as well as unitarity violation in the CKM mixing in order to constrain the quark sector of the model under consideration.