Novel and Updated Bounds on Flavor-violating Z Interactions in the Lepton Sector

We investigate the experimental bounds on the Flavor-Violating (FV) couplings of the $Z$ boson to the charged leptons. In addition to the direct LHC searches for FV $Z$ decays to leptons, we investigate indirect bounds from flavor-conserving $Z$ decays to leptons at 1-loop, bounds from LEP searches, Electroweak Precision Observables (EWPO), $\ell_{i}\to\ell_{j}γ$ decays, $\ell_{i}\to3\ell_{j}$ decays, $\ell_{i}\to\ell_{j}+\text{inv.}$ decays, FV meson decays to leptons, FV $τ$ decays to $μ(e)$ + mesons, muon conversion in nuclei, and from muonium-antimuonium oscillations. For FV $Z$ couplings to $τμ$, we find that $τ\toμγ$ yields the strongest bounds, with a level reaching $\mathcal{O}(10^{-5})$, followed by bounds from $τ\to3μ(μee)$. For FV $Z$ couplings to $τe$, we find that the strongest bounds arise from the decay $τ\toμμe$, reaching $\mathcal{O}(10^{-7})$ as well, with bounds from $τ\to3e$ also yielding strong bounds. For FV $Z$ couplings to $μe$, we find that the strongest bounds are obtained from the decay $μ\to3e$, reaching $\mathcal{O}(10^{-11})$, with bounds from $μ\to eγ$, muon conversion, $K_{L}^{0}\rightarrowμe$ and $μ\to e+\text{inv.}$ also providing strong bounds. We also study projections from future experiments, such as the FCC-ee, Belle II and the Mu2e experiment. For the $Z$ couplings to $τμ$, we find that future experiments could improve the bound to $\mathcal{O}(10^{-6})$, whereas for the $Z$ couplings to $τe$, we find that future experiments could improve the bound to $\mathcal{O}(10^{-8})$, and for the $Z$ couplings to $μe$, they could improve the bound to $\mathcal{O}(10^{-13})$