Revisiting the quantum field theory of neutrino oscillations in vacuum

We consider neutrino oscillations in vacuum in the framework of quantum field theory in which neutrino production and detection processes are part of a single Feynman diagram and the corresponding cross section is computed in the standard way, i.e. with final states represented by plane waves. We use assumptions which are realized in actual experiments and concentrate on the detection process. Moreover, we also allow for a finite time interval of length $\tau$ during which the detector records neutrino events. In this context we are motivated by accelerator-neutrino oscillation experiments where data taking is synchronized in time with the proton spill time of the accelerator. Given the final momenta and the direction of neutrino propagation, we find that in the oscillation amplitude---for all practical purposes---the neutrino energy $Q$ is fixed, apart from an interval of order $2\pi\hbar/\tau$ around a mean energy $\bar Q$; this is an expression of energy non-conservation or the time-energy uncertainty relation in the detection process due to $\tau < \infty$. We derive in excellent approximation that in the amplitude the oscillation effect originates from massive neutrinos with the same energy $\bar Q$, i.e. oscillations take place in space without any decoherece effect, while the remaining integration over $Q$ in the interval of order $2\pi\hbar/\tau$ around $\bar Q$ results in a time-correlation function expressing the time delay between neutrino production and detection.