New physics in multi-electron muon decays

We study the exotic muon decays with five charged tracks in the final state. First, we investigate the Standard Model rate for $\mu^+ \to 3e^+\,2e^-\,2\nu$ ($B = 4.0\times 10^{-10})$ and find that the Mu3e experiment should have tens to hundreds of signal events per $10^{15}$ $\mu^+$ decays, depending on the signal selection strategy. We then turn to a neutrinoless $\mu^+ \to 3e^+\,2e^-$ decay that may arise in new-physics models with lepton-flavor-violating effective operators involving a dark Higgs $h_d$. Following its production in $\mu^+ \to e^+ h_d$ decays, the dark Higgs can undergo a decay cascade to two $e^+e^-$ pairs through two dark photons, $h_d \to \gamma_d \gamma_d \to 2(e^+e^-)$. We show that a $\mu^+ \to 3e^+\,2e^-$ search at the Mu3e experiment, with potential sensitivity to the branching ratio at the $O(10^{-12})$ level or below, can explore new regions of parameter space and new physics scales as high as $\Lambda \sim 10^{15}$ GeV.