Wave-Packet Treatment of Neutrino Oscillation Based on the Solution to Dirac Equation

TL;DR

This paper models neutrino flavor oscillation using wave packets derived from solutions to the Dirac equation, providing a rigorous framework for interpreting experimental data and assessing CP violation.

Contribution

It introduces a wave-packet approach based on Dirac equation solutions, offering a precise method to analyze neutrino oscillations and their experimental implications.

Findings

Normalizable Gaussian wave packets cannot propagate as pure parity states.

A superposition of parity states with equal weight maximizes energy-dependent velocity.

The approach enables accurate interpretation of neutrino oscillation experiments.

Abstract

Flavor oscillation of traveling neutrinos is treated by solving the one-dimensional Dirac equation for massive fermions. The solutions are given in terms of squeezed coherent state as mutual eigenfunctions of parity operator and the corresponding Hamiltonian, both represented in bosonic creation and annihilation operators. It was shown that a mono-energetic state is non-normalizable, and a normalizable Gaussian wave packet, when of pure parity, cannot propagate. A physical state for a traveling neutrino beam would be represented as a normalizable Gaussian wave packet of equally-weighted mixing of two parities, which has the largest energy-dependent velocity. Based on this wave-packet representation, flavor oscillation of traveling neutrinos can be treated in a strict sense. These results allow the accurate interpretation of experimental data for neutrino oscillation, which is critical in judging whether neutrino oscillation violates CP symmetry.