$Z$ 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.