Neutrino Oscillations in Intermediate States.II -- Wave Packets

Abstract

We analyze oscillations of intermediate neutrinos in terms of the scattering of particles described by Gaussian wave packets. We study a scalar model as in a previous paper (I) but in realistic situations, where the two particles of the initial state and final state are wave packets and neutrinos are in the intermediate state. The oscillation of the intermediate neutrino is found from the time evolution of the total transition probability between the initial state and final state. The effect of a finite lifetime and a finite relaxation time are also studied. We find that the oscillation pattern depends on the magnitude of wave packet sizes of particles in the initial state and final state and the lifetime of the initial particle. For $\Delta m^2_{21}=3\times 10^{-2}$ eV$^2$, the oscillation probability deviates from that of the standard formula if the wave packet sizes are around $10^{-13}$ m for 0.4 MeV neutrino.Comment: 29 pages, 11 figures. typos corrected, appendix adde