Charged lepton flavor violating decays $Z\to \ell_\alpha\ell_\beta$ in the inverse seesaw

Abstract

After confirmation of massiveness and mixing of neutrinos, by neutrino oscillation data, the origin of neutrino mass and the occurrence of charged-lepton-flavor non-conservation in nature have become two main objectives for the physics of elementary particles. Taking inspiration from both matters, we address the decays $Z\to\ell_\alpha\ell_\beta$, with $\ell_\alpha\ne\ell_\beta$, thus violating charged-lepton flavor. We calculate the set of contributing one-loop diagrams characterized by virtual neutral leptons, both light and heavy, emerged from the inverse seesaw mechanism for the generation of neutrino mass. By neglecting charged-lepton and light-neutrino masses, and then assuming that the mass spectrum of the heavy neutral leptons is degenerate, we find that a relation $\textrm{Br}\big( Z\to\ell_\alpha\ell_\beta \big)\propto\big| \eta_{\beta\alpha} \big|^2$, with $\eta$ the matrix describing non-unitarity effects in light-lepton mixing, is fulfilled. Our quantitative analysis, which considers both scenarios of degenerate and non-degenerate masses of heavy neutral leptons, takes into account upper bounds on $\eta_{\mu e}$, imposed by current constraints on the decay $\mu\to e\gamma$ from the MEG II experiment, while projected future sensitivity of this experiment is considered as well. We find that, even though current constraints on $Z\to\ell_\alpha\ell_\beta$, by the ATLAS Collaboration, remain far from inverse-seesaw contributions, improved sensitivity from in-plans machines, such as the Future Circular Collider and the Circular Electron Positron Collider, shall be able to probe this mass-generating mechanism through these decays.