Time Evolution of Lepton Number Carried by Majorana Neutrinos

TL;DR

This paper investigates how lepton family numbers evolve over time for neutrinos with Majorana mass, highlighting their sensitivity to neutrino properties like phases, mass, and hierarchy, especially in the nonrelativistic regime relevant to cosmic background neutrinos.

Contribution

It provides a detailed analysis of lepton number evolution for Majorana neutrinos, including relativistic and nonrelativistic cases, and explores implications for cosmic neutrino background.

Findings

Lepton family numbers evolve distinctly for relativistic and nonrelativistic neutrinos.

Nonrelativistic lepton numbers are sensitive to Majorana and Dirac phases.

Results have implications for understanding cosmic neutrino background properties.

Abstract

We revisit the time evolution of the lepton family number for a SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number is evolved. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and nonrelativistic neutrinos. The nonrelativistic region is of particular interest for the Cosmic Neutrino Background predicted from big bang models. In that region we find the lepton family numbers are sensitive to Majorana and Dirac phases, the absolute mass, and mass hierarchy of neutrinos.