Improved analysis of the CLFV decay of muonic atoms $\mu^-e^-\rightarrow e^-e^-$

TL;DR

This paper presents an improved theoretical analysis of the CLFV decay of muonic atoms, accounting for electron distortion and relativistic effects, leading to a significant increase in predicted transition rates and enhanced experimental sensitivity.

Contribution

The study introduces a more accurate relativistic and Coulomb distortion treatment of the CLFV decay process, significantly increasing the predicted transition rate for heavy nuclei.

Findings

Transition rate for $^{208}$Pb increased by about 7 times.

Enhanced sensitivity for detecting CLFV interactions.

Detailed energy spectrum of outgoing electrons provided.

Abstract

Koike et al. proposed the charged lepton flavor violation (CLFV) decay of the muonic atom $\mu^-e^-\rightarrow e^-e^-$ as one of the promising processes to search for new physics beyond the standard model. It was found that the attractive interaction of leptons with the nucleus enhances the transition rate of the $\mu^-e^-\rightarrow e^-e^-$ process. We report on our improved analysis of this process by taking into account the distortion of the out-going electrons in the nuclear Coulomb potential and the relativistic treatment of the muon and the electrons. As results, we found significant enhancement of the transition rate. The transition rate for $^{208}$Pb becomes about 7 times larger than the previous estimation, which enhances the sensitivity of this process to discover the CLFV interaction. We also report on the energy spectrum of the out-going electron.