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 μ ⁺ → 3e ⁺ 2e ⁻ 2ν (B = 4.0 × 10 ⁻¹⁰) and find that the Mu3e experiment should have tens to hundreds of signal events per 10¹⁵ μ ⁺ decays, depending on the signal selection strategy. We then turn to a neutrinoless μ ⁺ → 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 μ ⁺ → e ⁺ h_d decays, the dark Higgs can undergo a decay cascade to two e ⁺ e ⁻ pairs through two dark photons, h_d → γ_d γ_d → 2(e ⁺ e ⁻). We show that a μ ⁺ → 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 Λ ∼ 10¹⁵ GeV.