Abstract
Abstract We revisit the time evolution of the lepton family number for an 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 that the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number evolves. 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 non-relativistic neutrinos. The non-relativistic region is of particular interest for the cosmic neutrino background predicted from Big Bang models. In that region we find that the lepton family numbers are sensitive to the Majorana and Dirac phases, the absolute mass, and the mass hierarchy of neutrinos.
Highlights
Studies of lepton number violation in the neutrino sector are classified into two categories
We study the expressions for time evolutions of its expectation values
In our numerical calculations we show the time evolution of electron number, muon number, and tauon number for an electron neutrino with lepton number equal to one as the initial state
Summary
Studies of lepton number violation in the neutrino sector are classified into two categories. Neutrinoless double β decay studies are focused on neutrino-antineutrino oscillation of Majorana neutrinos [3, 4, 5, 6, 7]. In this paper we revisit the development of a single framework in which both phenomena, i.e. flavor oscillation and neutrino-antineutrino oscillation, are formulated together This was developed; the calculation results were found to be incorrect [8]. We study the time evolution of the lepton family number operator for Majorana neutrino. We introduce the mass term at t = 0 and study the time evolution of the lepton family number for the later time.
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