A viable $L_e-L_\mu$ model with $\mu\to e$ violation

TL;DR

This paper proposes an extension of the Standard Model with a new gauge symmetry $U(1)_{L_e-L_mu}$, introducing scalars and a $Z'$ boson to enable lepton flavor violation while evading current bounds, and discusses experimental prospects.

Contribution

It introduces a novel $L_e-L_mu$ gauge symmetry extension with specific scalars and a $Z'$ boson, allowing observable lepton flavor violation without conflicting with existing constraints.

Findings

A $Z'$ boson with $M_{Z'} \u2248 10$ GeV and $g' \u2248 10^{-4}$ is within Belle-II reach.

Long-lived $Z'$ bosons with MeV masses can be probed via $ o '+$invisible decays.

Neutrino masses and mixing can be explained with sterile neutrinos.

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 $\mu \to e$ processes can only be mediated by $\mu\to \tau\times \tau\to e$ interactions, bounds from $\mu\to e$ transitions can be avoided while allowing for accessible new physics. We consider the case of a $Z'$ boson with a mass of $M_{Z'}\simeq10~$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 $\ell\to \ell'+\text{inv.}$. Neutrino masses and mixing angles can also be accounted for if sterile neutrinos are added to the spectrum.