The Probability for Chiral Oscillation of Majorana Neutrino in Quantum Field Theory

Abstract We derive the probability for chiral oscillation of Majorana neutrinos based on quantum field theory. Since the Hamiltonian under the Majorana mass term does not conserve the lepton number, the eigenstates of the lepton number change continuously over time. Therefore, the transition amplitude is described by the inner product of the eigenstates of the lepton number at the time of the neutrino production and the detection. With the Bogoliubov transformation, we successfully relate the lepton number eigenstates at different times. This method enables us to understand the time variation of the lepton number induced by chiral oscillations in terms of transition probabilities. We also present the physical picture that emerges through the Bogoliubov transformation.