Lepton Flavour Eigenstates do not Exist if Neutrinos are Massive: `Neutrino Oscillations' Reconsidered

Abstract

If neutrinos are massive, `lepton flavour eigenstates' are absent from the amplitudes of all Standard Model processes. Measurements of $\Gamma(\pi \to e \nu)/\Gamma(\pi \to \mu \nu)$ and of the MNS matrix are shown to exclude the existence of such states. Incoherent production of neutrinos of different flavour modifies the usual oscillation phase derived assuming production of a lepton flavour eigenstate. The new prediction can be tested in long line-base experiments by comparison of `$\nu_{\mu}$ disappearance' of neutrinos from pion and kaon decay.