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An analytical expression for the spin-averaged amplitude squared of the raremuon decay $\mu^+ \to e^+e^-e^+\nu_e\bar{\nu_\mu}$ is calculated. Monte Carlophase space simulation using the analytical expression for the amplitude hasbeen used to get various differential distributions of charged leptons. Theapproximate analytical expression for the total energy spectrum of chargedleptons near the end point is presented. The dependence of branching ratio oncuts in total energy of charged leptons is studied taking into account anexperimental energy resolution. It is shown that the measured branching ratiois very sensitive to the energy resolution.

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