Coherence and Wave Packets in Neutrino Oscillations

Abstract

General arguments in favor of the necessity of a wave packet description of neutrino oscillations are presented, drawing from analogies with other wave phenomena. We present a wave packet description of neutrino oscillations in stationary beams using the density matrix formalism. Recent claims of the necessity of an equal energy of different massive neutrinos are refuted.

Quantum Mechanics of ‘Two Path’ Experiments: Comparison of Neutrino Oscillations and the Young Double Slit

“…Giunti has claimed [24] that the argument just presented is flawed and that coherent 'flavour eigenstates' of massive neutrinos are indeed produced in weak decay processes. To substantiate this claim it is suggested to define a 'lepton flavour eigenstate', not according to Eq.…”

Theory of Neutrino Oscillations

“…In order to justify the assumption (A3) it is necessary to treat massive neutrinos as wave packets [7], which are localized on the production process at the production time and propagate between the production and detection processes at a velocity close to the velocity of light. Such wave packet treatment [7,8,4,9] yields the standard formula for the oscillation length. In addition, the different group velocities of different massive neutrinos imply the existence of a coherence length for the oscillations, beyond which the wave packets of different massive neutrinos do not jointly overlap with the detection process [10,11].…”

“…The wave packet treatment of neutrino oscillations is also necessary for a correct description of the momentum and energy uncertainties necessary for the coherent production and detection of different massive neutrinos [12,13,9], whose interference generates the oscillations.…”

“…[14,9] on the basis of simple relativistic arguments. Indeed, the relativistic transformation of energy and momentum implies that the equal momentum assumption cannot hold concurrently in different inertial systems.…”

“…Therefore, the probability of neutrino oscillations is Lorentz invariant [15,16] and must be derived in a covariant way. In fact, the oscillation probability has been derived without special assumptions about the energies and momenta of the different massive neutrino components both in the plane wave approach [17,15,6] and in the wave packet treatment [7,8,14,9].…”