Improved analysis for 𝜇−⁢𝑒−→𝑒−⁢𝑒− in muonic atoms by photonic interaction

Authors

Yuichi Uesaka¹, Yoshitaka Kuno¹, Joe Sato², Toru Sato^1,3, and Masato Yamanaka⁴

Affiliations

¹Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
²Physics Department, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, Saitama 338-8570, Japan
³J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, Tokai, Ibaraki 319-1106, Japan
⁴Maskawa Institute, Kyoto Sangyo University, Kyoto 603-8555, Japan

Journal

Published Date

1/30/18

DOI

Abstract

Studies of the charged lepton flavor violating process of 𝜇−⁢𝑒−→𝑒−⁢𝑒− in muonic atoms by the four Fermi interaction [Y. Uesaka et al., Phys. Rev. D 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 𝜇−⁢𝑒− →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 𝜇−⁢𝑒− →𝑒−⁢𝑒− rate could be used to distinguish between the photonic and the four Fermi interactions.