Impact of CPV phases on flavour violating $H$ and $Z$ decays

Standard Model extensions via heavy neutral leptons lead to modifications in the lepton mixing matrix, including new Dirac and Majorana CP violating phases. Here we consider the role of the Majorana fermions and of new CP violating phases in Higgs and $Z$-boson lepton flavour violating decays, as well as in the corresponding CP-asymmetries. We confirm that these decays are sensitive to the presence of additional sterile states and show that the new CP violating phases may lead to both destructive and constructive interferences in the decay rates. Interestingly the $Z\to \mu^\pm\tau^\mp$ rates are within FCC-ee reach, with associated CP-asymmetries that can potentially reach up to 30%.