When do neutrinos really oscillate? Quantum mechanics of neutrino oscillations

Abstract

The quantum mechanics of neutrino oscillations is reexamined by studying the propagation of a flavor neutrino described by a superposition of mass-eigenstate wave packets, without making the usual relativistic assumption. The space-dependent oscillation probability is derived by averaging over the propagation time. The time average leads to interesting factors in the oscillation probability, from which the coherence length and the bound for the size of the wave packets are derived. The coherence length is the distance beyond which neutrinos cease to oscillate, although a flavor change may still take place. It is also shown that if one of the mass eigenstates is nonrelativistic, it may dominate the constant flavor-changing probability.