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

TL;DR

This paper investigates charged lepton flavor violating decays of the Z boson within the inverse seesaw model, calculating one-loop contributions from neutral leptons and assessing experimental prospects for detection.

Contribution

It provides a detailed calculation of Z decay rates in the inverse seesaw framework, linking non-unitarity effects to observable decay branching ratios and analyzing experimental sensitivities.

Findings

Decay rates proportional to non-unitarity matrix elements.

Current experiments are far from detecting these decays.

Future colliders could probe inverse seesaw contributions.

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.