Rare Muon Decay $\mu^+ \to e^+e^-e^+\nu_e\bar{\nu_\mu}$

TL;DR

This paper derives an analytical expression for the decay amplitude of a rare muon decay process, enabling detailed simulation and analysis of charged lepton distributions and the impact of experimental energy resolution.

Contribution

It provides the first analytical formula for the spin-averaged amplitude squared of this rare decay, facilitating precise Monte Carlo simulations and energy spectrum analysis.

Findings

Analytical expression for decay amplitude derived.

Monte Carlo simulations of charged lepton distributions performed.

Branching ratio sensitivity to energy resolution demonstrated.

Abstract

An analytical expression for the spin-averaged amplitude squared of the rare muon decay $\mu^+ \to e^+e^-e^+\nu_e\bar{\nu_\mu}$ is calculated. Monte Carlo phase space simulation using the analytical expression for the amplitude has been used to get various differential distributions of charged leptons. The approximate analytical expression for the total energy spectrum of charged leptons near the end point is presented. The dependence of branching ratio on cuts in total energy of charged leptons is studied taking into account an experimental energy resolution. It is shown that the measured branching ratio is very sensitive to the energy resolution.