Remark on neutrino oscillations

TL;DR

This paper discusses a quantum field theory perspective on neutrino oscillations, emphasizing the role of phase modulation by small neutrino masses and the conservation of momentum in detection, with considerations for Majorana neutrinos.

Contribution

It provides a novel first quantization and field theory framework for understanding neutrino oscillations, highlighting the importance of phase modulation and the conservation laws.

Findings

Neutrino oscillations arise from phase modulation due to small mass terms.

Conventional detectors are insensitive to neutrino masses, conserving energy-momentum assumptions.

The framework addresses conceptual issues for Majorana neutrinos in four dimensions.

Abstract

The oscillations of ultra-relativistic neutrinos are realized by the propagation of assumed zero-mass on-shell neutrinos with the speed of light in vacuum combined with the phase modulation by the small mass term $\exp[-i(m^{2}_{\nu_{k}}/2|\vec{p}|)\tau]$ with a time parameter $\tau$. This picture is realized in the first quantization by the mass expansion and in field theory by the use of $\delta(x^{0}-y^{0}-\tau) \langle 0|T^{\star}\nu_{L k}(x)\overline{\nu_{L k}(y)}|0\rangle$ with the neutrino mass eigenstates $\nu_{L k}$ and a finite positive $\tau$ after the contour integral of the propagating neutrino energies. By noting that the conventional detectors are insensitive to neutrino masses, the measured energy-momenta of the initial and final states with assumed zero-mass neutrinos are conserved. The propagating neutrinos preserve the three-momentum in this sense but the energies of the massive neutrinos are conserved up to uncertainty relations and thus leading to oscillations. Conceptual complications in the case of Majorana neutrinos due to the charge conjugation in $d=4$ are also discussed.