Production of lepton-flavor-violating scalars through resonant positive-muon annihilation on atomic electrons

We investigate an invisible lepton-flavor-violating scalar $\phi$ with exclusive $e-\mu$ couplings and study its resonant production via ${\mu }^{+}{e}^{-}\to \phi$ in fixed-target experiments. Since the effective center-of-mass energy is determined by the momentum of the initial-state bound electrons, atomic effects can significantly affect the resonance behavior. We therefore employ relativistic bound-state electron wave functions to calculate the production cross section and reveal a material-dependent broadening of the resonance lineshape. For the proposed HIAF experiment, fewer than one day of data taking ($6\times {10}^{10}$ MOT) can probe couplings at the ${10}^{-5}$ level at 90% confidence level near resonance, demonstrating that high-intensity muon fixed-target experiments provide a powerful complementary probe of lepton-flavor violation.