Lepton flavor changing charged current and interaction

TL;DR

This paper explores lepton flavor changing charged currents, neutrino mixing, and their implications for neutrino oscillation, elastic scattering, and muon decay, providing theoretical formulations and specific decay rate calculations.

Contribution

It presents a detailed formulation of lepton flavor changing interactions and neutrino mixing effects within the Standard Model framework.

Findings

Derived the flavor changing Lagrangian for lepton-W boson interactions.

Obtained the neutrino mixing angle dependence in interaction vertices.

Calculated the muon decay branching ratio involving flavor change.

Abstract

We write the neutrino mass eigenstate into the weak doublet of the group $SU(2)_L$ . The massive neutrino is written as the mixture of the flavor neutrino. The flavor changing Lagrangian of lepton-W boson coupling were obtained. The neutrino mixing angle appear in the vertex factor of the interaction of flavor neutrino with charged lepton. The results lead to the Feynman diagram of neutrino oscillation in matter and play an important role in $(\nu_e -e)$ elastic scattering . The anomalous muon decay $\mu^-\rightarrow e^-+\overline{\nu}_\mu+\nu_e$ take part in giving the muon decay lifetime of $2.197019 \mu s$ . The branching ratio $B(\mu^-\rightarrow e^-+\overline{\nu}_\mu+\nu_e)$ is obtained.