Improved analysis for ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ in muonic atoms by photonic interaction

Abstract

Studies of the charged lepton flavor violating process of ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ in muonic atoms by the four Fermi interaction [Y. Uesaka \textit{et al}., Phys. Rev. D {\bf 93}, 076006 (2016)] are extended to include the photonic interaction. The wave functions of a muon and electrons are obtained by solving the Dirac equation with the Coulomb interaction of a finite nuclear charge distribution. We find suppression of the ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ rate over the initial estimation for the photonic interaction, in contrast to enhancement for the four Fermi interaction. It is due to the Coulomb interaction of scattering states and relativistic lepton wave functions. This finding suggests that the atomic number dependence of the ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ rate could be used to distinguish between the photonic and the four Fermi interactions.

10 pages, 8 figures

References in corpus (5)

• COMET Phase-I Technical Design Report
• Impact of sterile neutrinos on nuclear-assisted cLFV processes
• High-energy electrons from the muon decay in orbit: radiative corrections
• Michel decay spectrum for a muon bound to a nucleus
• Improved analyses for ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ in muonic atoms by contact interactions

Cited by in corpus (10)

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• Heavy neutral leptons and high-intensity observables
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• Search for muon-to-electron conversion with the COMET experiment
• Measurements of $\mu \to 3e$ Decay with Polarised Muons as a Probe of New Physics
• A two-loop induced neutrino mass model, dark matter, and LFV processes ${\ell }_i\to {\ell }_j\gamma$, and $\mu e\to ee$ in a hidden local $U(1)$ symmetry
• Model identification in ${\mu }^{-}\to e^{-}$ conversion with invisible boson emission using muonic atoms
• A radiatively induced neutrino mass model with hidden local $U(1)$ and LFV processes ${\ell }_i\to {\ell }_j\gamma$, $\mu \to e{Z}^{\prime }$ and $\mu e\to ee$
• Momentum distribution of the electron pair from the charged lepton flavor violating process ${\mu }^{-}{e}^{-}\to e^{-}{e}^{-}$ in muonic atoms with a polarized muon