Coherence of neutrino oscillations in the wave packet approach

The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation process is lost. PACS number: 14.60.Pq Typeset using REVTEX 1 A complete understanding of neutrino oscillations must take into account the localization of microscopic processes by which a neutrino is produced and detected. This localization is appropriately described by a wave packet treatment of neutrino oscillations [1–9] (different treatments are discussed in [10,11]). As the authors of [9] noticed, in the quantum mechanical wave packet approach presented in [4] the dependence of the oscillation probability on the temporal and spatial coherence widths of the detection process was neglected. In this brief report, we wish to incorporate, in a simple and straightforward way, the temporal and spatial coherence widths of the detection process in the quantum mechanical wave packet description of neutrino oscillations and show that, as an immediate consequence of this, performing an accurate measurement of the energies of the particles involved in the detection process leads to an increase of the coherence length for neutrino oscillations, as was noticed for the first time in [6]. Let us consider a neutrino of flavor α produced by a weak interaction process at the origin of the space-time coordinates and detected at a distance L after a time T 1 by a weak interaction process capable of detecting a neutrino of flavor β. As in [4], we describe the neutrino propagating between the production and detection processes with the timedependent state in the Schrödinger picture |να(t)〉 = ∑