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

TL;DR

This paper extends the analysis of the lepton flavor violating process $^-e^- o e^-e^-$ in muonic atoms by including photonic interactions, revealing suppression effects and potential for distinguishing interaction types based on atomic number dependence.

Contribution

It introduces a detailed wave function calculation with Coulomb interaction for both muons and electrons, highlighting differences between photonic and four Fermi interactions.

Findings

Photonic interaction causes suppression of the process rate.

Relativistic wave functions and Coulomb effects are crucial.

Atomic number dependence can differentiate interaction types.

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.