Natural Understanding of Sterile Neutrino by Relativistic Equation

TL;DR

This paper derives neutrino oscillation probabilities including sterile neutrinos using the Dirac equation, suggesting their natural emergence within three generations and indicating the necessity of both Dirac and Majorana mass terms for neutrinos to be Majorana particles.

Contribution

It provides a relativistic derivation of sterile neutrino oscillations within the Dirac framework, offering a natural understanding of sterile neutrinos without adding extra generations.

Findings

Sterile neutrinos can be understood within three generations.

Oscillations into sterile neutrinos imply both Dirac and Majorana mass terms.

Neutrinos are likely Majorana particles due to these oscillation properties.

Abstract

We derive the neutrino oscillation probabilities including sterile neutrinos by using the Dirac equation. If neutrinos have both the Dirac and the Majorana mass terms, left-handed neutrino $\nu_L$ and right-handed anti-neutrino $\nu_R^c$ enter the same multiplet and can transfer each other. Sterile neutrinos have been introduced by hand as the fourth generation neutrino in many papers, however, we can understand sterile neutrinos naturally in the framework of three generations. We also point out that the oscillations into sterile neutrinos strongly suggest the existence of both the Dirac and the Majorana mass terms, and for neutrinos to be the Majorana particles.