English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In three generations or more, we derive the oscillation probabilities of bothDirac and Majorana neutrinos relativistically by using the Dirac equation. Wepresent various oscillation probabilities for including wrong-helicityneutrinos, right-handed neutrinos, and anti-neutrinos. We summarize therelations between these probabilities. As neutrinos have finite mass, there aretwo components for each chirality corresponding to positive and negativehelicities. We show that the probability is different for each component evenif neutrinos have the same chirality. The probabilities derived by therelativistic equation depend on not only the mass squared differences but alsothe absolute masses of neutrinos. Besides, the new CP phases appear in theprobabilities of oscillations with chirality-flip. These new CP phases areequivalent to the Majorana CP phases in the case of Majorana neutrinos. Weinvestigate the CP dependence of oscillation probabilities in vacuum. There areno direct CP violation in $\nu_{\alpha}\leftrightarrow \nu_{\beta}^c$oscillations even if the flavors, $\alpha$ and $\beta$, are different as in thesame as two generations. In other words, the difference between theCP-conjugate probabilities vanishes. However, in three generations or more, thesine terms of new CP phases appear in the probabilities in addition to thecosine terms. This is different from the result obtained in two generations.Furthermore, the zero-distance effect does not appear in our formulation.

Exact Oscillation Probabilities of Neutrinos in Three generations derived from Relativistic Equation