We extend the Standard Model gauge group by\documentclass[12pt]{minimal}
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				\begin{document}$$U(1)_{L_e-L_\mu }$$\end{document}U(1)Le-Lμand introduce two scalars, a doublet and a singlet, that are charged under this new group and have lepton flavour violating couplings. Since in this model\documentclass[12pt]{minimal}
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				\begin{document}$$\mu \rightarrow e$$\end{document}μ→eprocesses can only be mediated by\documentclass[12pt]{minimal}
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				\begin{document}$$\mu \rightarrow \tau \times \tau \rightarrow e$$\end{document}μ→τ×τ→einteractions, bounds from\documentclass[12pt]{minimal}
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				\begin{document}$$\mu \rightarrow e$$\end{document}μ→etransitions can be avoided while allowing for accessible new physics. We consider the case of a\documentclass[12pt]{minimal}
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				\begin{document}$$Z'$$\end{document}Z′boson with a mass of\documentclass[12pt]{minimal}
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				\begin{document}$$M_{Z'}\simeq 10~$$\end{document}MZ′≃10GeV and a gauge coupling\documentclass[12pt]{minimal}
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				\begin{document}$$g'\simeq 10^{-4}$$\end{document}g′≃10-4, which is in reach of Belle-II, and a long-lived\documentclass[12pt]{minimal}
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				\begin{document}$$Z'$$\end{document}Z′boson with a mass of\documentclass[12pt]{minimal}
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				\begin{document}$$\text {MeV}\lesssim M_{Z'}\lesssim m_\mu -m_e$$\end{document}MeV≲MZ′≲mμ-mewhich can be probed by searching for\documentclass[12pt]{minimal}
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				\begin{document}$$\ell \rightarrow \ell ' +\mathrm {inv.}$$\end{document}ℓ→ℓ′+inv.. Neutrino masses and mixing angles can also be accounted for if sterile neutrinos are added to the spectrum.