Lepton Flavour Eigenstates Do Not Exist If Neutrinos Are Massive: 'neutrino Oscillations' Reconsidered

If neutrinos are massive, 'lepton flavour eigenstates' are absent from the amplitudes of all Standard Model processes. Measurements of Γ(π → eν)/Γ(π → µν) 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 'ν µ disappearance' of neutrinos from pion and kaon decay. In the Standard Electroweak Model, the coupling of a charged lepton, ℓ i , of generation i and a massive neutrino, ν j , of generation j to the W-boson is described by the leptonic charged current: J µ (CC) lept = i,j ψ ℓ i γ µ (1 − γ 5)U ij ψ ν j (1) where U ij is the Maki-Nakagawa-Sakata (MNS) [1] charged lepton flavour/ neutrino mass mixing matrix. Table 1 shows the elements of this matrix as estimated [2] from experimental measurements of atmospheric and solar neutrino oscillations. The non-diagonal nature of this matrix gives evidence for strong violation of generation number (or lepton flavour) by J µ (CC) lept. Conservation of generation number corresponds to a diagonal MNS matrix with ν 1 = ν e , ν 2 = ν µ and ν 3 = ν τ. This is the conventional massless neu-trino scenario. With massive neutrinos and a non-diagonal MNS matrix, 'ν e ', 'ν µ ' and 'ν τ ' do not exist as physical states. That is, they do not appear in the amplitude for any physical process. This is because the neutrino charged lepton couplings to the W are completely specified by J µ (CC) lept which contains only the wavefunctions of the neutrino mass eigenstates ν 1 , ν 2 and ν 2. Indeed, the introduction of such 'lepton flavour eigenstates' as a linear superposition of neutrino mass eigenstates leads to predictions that are excluded by experiment. To show this, the pion decays: π → eν and π → µν may be considered. The invariant 1