Muon decays revisited: Effects of massive neutrinos, their mixings, and grand unification

We have calculated the effects of massive Dirac and Majorana neutrinos and their mixings in the $e^{+}$ spectrum in ${\mu }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\mu }\left({\nu }_{\mu }^c\right)$ decays. Particular attention was paid to the three-neutrinos world with the mass of ${\nu }_{\tau }$ in the ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^2$ range. We also obtained electron-neutrinos correlations and indicated their use as a signature of Majorana neutrinos.