Antineutrinos produced from $\beta$ decays of neutrons cannot be in coherent superpositions of different mass eigenstates

The entire wavefunction of the antineutrino-proton-electron system, produced by the $\beta$ decay of a neutron is analyzed. It is proven that the antineutrino cannot be in coherent superpositions of different mass eigenstates, irrespective of the initial momentum distribution of the neutron.