Natural Understanding of Sterile Neutrino by Relativistic Equation

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.