Lepton flavor violating decays of vector quarkonia and of the $Z$ boson

We address the impact of sterile fermions on the lepton flavor violating decays of quarkonia as well as of the $Z$ boson. We compute the relevant Wilson coefficients and show that the ${\rm B}(V\to\ell_\alpha\ell_\beta)$, where $V=\phi,\psi^{(n)}$, $\Upsilon^{(n)},Z$ can be significantly enhanced in the case of large sterile fermion masses and a non-negligible active-sterile mixing. We illustrate that feature in a specific minimal realization of the inverse seesaw mechanism, known as $(2,3)$-ISS, and in an effective model in which the presence of non-standard sterile fermions is parameterized by means of one heavy sterile (Majorana) neutrino.