Lepton family numbers and non-relativistic Majorana neutrinos

TL;DR

This paper reviews recent developments in understanding how lepton family numbers evolve over time in the context of Majorana neutrinos, highlighting the sensitivity to effective mass matrix components and Majorana phases, with implications for cosmic neutrino background.

Contribution

It clarifies the derivation of lepton family number evolution and its dependence on effective Majorana mass matrix elements and phases.

Findings

Time evolution depends on $m_{ee}$ and $m_{emu}$ components.

Dependence on Majorana phases is explicitly analyzed.

Implications for cosmic neutrino background are discussed.

Abstract

In this talk, we have reviewed the recent development on the time evolution of lepton family number carried by Majorana neutrinos \cite{Adam:2021qiq}. This article focuses on the subtle points of the derivation of the lepton family numbers and their time evolution. We also show how the time evolution is sensitive to $m_{ee}$ and $m_{e\mu}$ components of the effective Majorana mass matrix by applying the formula to the two family case. The dependence on the Majorana phase is clarified and the implication on CNB (cosmic neutrino background) is also discussed.