Improved analyses for $\mu^-e^-\rightarrow e^-e^-$ in muonic atoms by contact interactions

TL;DR

This paper improves the analysis of muon-electron to electron-electron decay in muonic atoms by accurately modeling wave functions, revealing a stronger dependence on atomic number and higher decay rates, especially in heavier atoms.

Contribution

It introduces a refined method for calculating decay rates using Dirac equations with Coulomb interactions, showing enhanced decay rates for heavier atoms compared to previous estimates.

Findings

Decay rates increase more rapidly than Z^3 with atomic number.

Heavier atoms like lead show decay rates about ten times larger than previous estimates.

The process is promising for detecting charged lepton flavor violation.

Abstract

The charged lepton flavor violating (CLFV) processes of $\mu^-e^-\rightarrow e^-e^-$ decay by four Fermi contact interactions in a muonic atom for various atoms are investigated. The wave functions of bound and scattering state leptons are properly treated by solving Dirac equations with Coulomb interaction of the finite nuclear charge distributions. This new effect contributes significantly in particular for heavier atoms, where the obtained decay rate is about one order of magnitude larger than the previous estimation for $^{208}$Pb. We find that, as the atomic number $Z$ increases, the $\mu^-e^-\rightarrow e^-e^-$ decay rates increase more rapidly than the result of the previous work of $Z^3$, suggesting this decay as one of the promising processes to search for CLFV interaction.