Charged lepton flavor violating decays $Z\to \ell_α\ell_β$ in the inverse seesaw

TL;DR

This work analyzes charged-lepton-flavor violation in $Z$ boson decays within the inverse seesaw framework, computing one-loop contributions from both light and heavy neutral leptons. It derives the on-shell $Z\to \ell_\alpha\ell_\beta$ amplitude $\Gamma_\mu^{\beta\alpha}$ using a Feynman-gauge calculation with Majorana neutrinos, showing ultraviolet finiteness through a GIM-like mechanism and expressing the branching ratio in terms of a non-unitarity matrix $\eta$. In the degenerate-HNL mass limit, they obtain a simplified relation $\mathrm{Br}(Z\to\ell_\alpha\ell_\beta) \propto |\eta_{\beta\alpha}|^2$, enabling direct connection to light-lepton non-unitarity and existing $\mu\to e\gamma$ bounds. Numerically, current ATLAS limits are well above ISSM predictions, but projected FCC-ee/CEPC sensitivities could probe ISSM-induced $Z$ decays, notably $Z\to \mu e$, while non-degenerate-HNL analyses explore broader parameter space under $\mu\to e\gamma$ constraints.

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 $Z\to\ell_α\ell_β$, with $\ell_α\ne\ell_β$, 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 $\textrm{Br}\big( Z\to\ell_α\ell_β\big)\propto\big| η_{βα} \big|^2$, with $η$ 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 $η_{μe}$, imposed by current constraints on the decay $μ\to eγ$ from the MEG II experiment, while projected future sensitivity of this experiment is considered as well. We find that, even though current constraints on $Z\to\ell_α\ell_β$, 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.

Figures (5)

• Figure 1: Conventions for the $Z\to\ell_\alpha\ell_\beta$ amplitude.
• Figure 2: Branching ratios of cLFV decays $Z\to\mu e$ (upper panel), $Z\to\tau e$ (middle panel), and $Z\to\tau\mu$ (lower panel). The branching ratios have been plotted in base-10 logarithmic scale, and values $0\,\textrm{MeV}\leqslant v_\sigma\leqslant10\,\textrm{MeV}$ have been considered. Regions above solid horizontal lines represent values discarded by current experimental sensitivity ATLASZtotaualgoATLASZtoemu, whereas dashed horizontal lines correspond to expected sensitivity of the FCC-ee FCCeebounds and the CEPC CEPCbounds. The plots also fulfill current and projected bounds on the cLFV decay $\mu\to e\gamma$, by MEG II MEG2MEG2future.
• Figure 3: Comparison of $\textrm{Br}( Z\to\ell_\alpha\ell_\beta )$ in the scenario of degenerate HNL masses, Eq. \ref{['Brdegeneratecase']}, VS current constraints by the ATLAS Collaboration ATLASZtotaualgoATLASZtoemu. Plots have been carried out in base-10 logarithmic scale, in the $( | \eta_{\beta\alpha} |,m_N )$ plane, with $1\,\textrm{TeV}\leqslant m_N\leqslant8\,\textrm{TeV}$, and either $0\leqslant| \eta_{\beta\alpha}| \leqslant10^{-2}$ (upper panel) or $0\leqslant| \eta_{\beta\alpha} |\leqslant10^{-3}$ (lower panel). Current experimental sensitivities are represented by green ($Z\to\mu e$), purple ($Z\to\tau e$), and red ($Z\to\tau\mu$) curves.
• Figure 4: Comparison of $\textrm{Br}( Z\to\mu e )$ in the scenario of degenerate HNL masses, Eq. \ref{['Brdegeneratecase']}, VS projections of future sensitivity of either the FCC-ee FCCeebounds or the CEPC CEPCbounds. The plots has been carried out in base-10 logarithmic scale, in the $( | \eta_{\mu e} |,m_N )$ plane, with $1\,\textrm{TeV}\leqslant m_N\leqslant8\,\textrm{TeV}$, and $0\leqslant| \eta_{\mu e}| \leqslant10^{-5}$. Projected sensitivity has been represented by the orange curve.
• Figure 5: Comparison of $\textrm{Br}( Z\to\tau\ell_\alpha )$ in the scenario of degenerate HNL masses, Eq. \ref{['Brdegeneratecase']}, VS projections of future sensitivity of either the FCC-ee FCCeebounds or the CEPC CEPCbounds. The plots has been carried out in base-10 logarithmic scale, in the $( | \eta_{\tau\alpha} |,m_N )$ plane, with $1\,\textrm{TeV}\leqslant m_N\leqslant8\,\textrm{TeV}$, and $0\leqslant| \eta_{\tau\alpha}| \leqslant10^{-4}$. Projected sensitivity has been represented by the orange curve.