$CP$ violation due to a Majorana phase in two flavor neutrino oscillations with decays

TL;DR

This paper investigates how Majorana phases influence CP violation in two-flavor neutrino oscillations with decays, highlighting conditions where these phases affect oscillation probabilities and depend on neutrino mass ordering.

Contribution

It identifies conditions for Majorana phases to impact CP violation in neutrino oscillations with decays, including the role of decay eigenstates and mass ordering effects.

Findings

Majorana phase affects oscillation probabilities when decay eigenstates are misaligned with mass eigenstates.

Two types of CP violation are identified: from Majorana phase and decay matrix phase.

CP violation terms are sensitive to neutrino mass ordering.

Abstract

We study the conditions under which the Majorana phase of the two flavor neutrino mixing matrix appears in the oscillation probabilities and causes $CP$ violation. We find that the Majorana phase remains in the neutrino evolution equation if the neutrino decay eigenstates are not aligned with the mass eigenstates. We show that, in general, two kinds of $CP$ violation are possible: one due to the Majorana phase and the other due to the phase of the off-diagonal element of the neutrino decay matrix. We find that the $CP$ violating terms in the oscillation probabilities are also sensitive to neutrino mass ordering.