Abstract
The $\mu^-e^-\to e^-e^-$ process in a muonic atom is one of the promising probes to study the charged lepton flavor violation (CLFV). We have investigated the angular distribution of electrons from the polarized muon of the atomic bound state. The parity violating asymmetric distribution of electrons is analyzed by using lepton wave functions under the Coulomb interaction of a finite nuclear charge distribution. It is found that the asymmetry parameters of electrons are very sensitive to the chiral structure of the CLFV interaction and the contact/photonic interaction. Therefore, together with the atomic number dependence of the decay rate studied in our previous work, the angular distribution of electrons from a polarized muon should be a very useful tool to constrain the model beyond the standard model.
Highlights
The charged lepton flavor violation (CLFV) is an excellent probe of new physics beyond the standard model (SM) [1] since it is highly suppressed in the SM
Together with the atomic number dependence of the decay rate studied in our previous work, the angular distribution of electrons from a polarized muon should be a very useful tool to constrain the model beyond the standard model
We have studied the energy-angular distributions of emitted electrons of μ−e− → e−e− decay in a muonic atom with a polarized muon
Summary
The charged lepton flavor violation (CLFV) is an excellent probe of new physics beyond the standard model (SM) [1] since it is highly suppressed in the SM. In our recent work [11, 12], careful calculations were made for the transition rate of the μ−e− → e−e−, which included the calculation of wave functions for the bound leptons in the initial state and the emitted electrons in the final state using a Dirac equation with a realistic charge distribution of nuclei. It is well known that SU(5) and SO(10) supersymmetric grand unified theory gives different chiral structures in the CLFV interaction To observe it in μ → eγ and μ → eee, to make use of the muon polarization has been discussed in Refs. We focus on the μ−e− → e−e− search with a muon polarized in a muonic atom to extract the chiral property of the CLFV interaction.
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