Title: Lepton Number Violation in a Unified Framework

Speaker: Prof. Takuya Morozumi, Department of Physics, Hiroshima University

Abstract: We study the time evolution of lepton family number for neutrino which forms SU(2) doublet with charged lepton. The Lepton family number of the neutrino is defined in a weak basis of SU(2) doublet in which charged lepton mass matrix is real diagonal. The lepton family number carried by the neutrino is defined through a left-handed current of the neutrino family. The time evolution of the lepton family number operator is studied for two types of mass term of neutrinos, namely Majorana mass and Dirac mass. To be definite, we introduce the mass term at the initial time and study the time evolution of the lepton family number for later time. We relate the creation and annihilation operator for flavor eigenstates to those of mass eigenstates by demanding the continuity condition at the initial time. For the Dirac neutrino case, the total lepton number is not conserved since left-handed neutrino transits to right-handed neutrinos, while the total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of neutrino as an initial state, we compute the time evolution of all family numbers. For the Majorana neutrinos, the time dependent lepton family number is sensitive to both Majorana and Dirac phases.