Quantum flavor oscillations extended to the Dirac theory

TL;DR

This paper extends the quantum theory of flavor oscillations to fermionic particles using the Dirac equation, revealing effects like chiral oscillations and initial flavor violation, with implications for neutrino physics.

Contribution

It introduces a Dirac-based framework for flavor oscillations, incorporating chiral effects and initial flavor violation, advancing the understanding beyond scalar approximations.

Findings

Chiral oscillations naturally emerge in Dirac theory.

Initial flavor violation is inevitable and larger than loop effects.

Rapid oscillations or initial flavor violation are predicted in relativistic models.

Abstract

This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first and second quantization theories. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass-eigenstates since in the standard treatment of oscillations the mass-eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac-type particle. The left-handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. The conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations.