Abstract
Abstract We study the time evolution of lepton family number for a neutrino that forms an SU(2) doublet with a charged lepton. The lepton family number is defined through a weak basis of the SU(2) doublet in which the charged lepton mass matrix is a real and diagonal one. The lepton family number carried by the neutrino is defined with a left-handed current of the neutrino family. We study the time evolution of the lepton family number operator for the Majorana neutrino. To be definite, we introduce the mass term at $t=0$ and study the time evolution of the lepton family number for the later time. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the flavor eigenstates are related to those of the mass eigenstates. The total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of the neutrino as an initial state, we compute the time evolution of all lepton family numbers. They are sensitive to Majorana and Dirac phases and are also sensitive to the absolute mass and mass hierarchy of neutrinos.
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