Abstract
We extend the Standard Model gauge group by U(1)_{L_e-L_mu } and 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 mu rightarrow e processes can only be mediated by mu rightarrow tau times tau rightarrow e interactions, bounds from mu rightarrow e transitions can be avoided while allowing for accessible new physics. We consider the case of a Z' boson with a mass of M_{Z'}simeq 10~GeV and a gauge coupling g'simeq 10^{-4}, which is in reach of Belle-II, and a long-lived Z' boson with a mass of text {MeV}lesssim M_{Z'}lesssim m_mu -m_e which can be probed by searching for ell rightarrow ell ' +mathrm {inv.}. Neutrino masses and mixing angles can also be accounted for if sterile neutrinos are added to the spectrum.
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