Estimation of Neutrino Masses Without Using Seesaw Mechanism

Abstract

We propose the Bethe-Salpeter-like amplitude of spin operator in spin space and consider that the vibration of this spin operator amplitude causes the vibration in azimuthal angle space, which causes the anomalous magnetic moment of leptons and generates masses of flavor state neutrino. Under this consideration, we can estimate neutrino masses using anomalous magnetic moment of leptons instead of using conventional seesaw mechanism. Electron anomalous magnetic moment and muon anomalous magnetic moment have been measured precisely so that we can estimate the masses of electron and muon neutrino systemically in our consideration. For tau neutrino mass case, we cannot estimate it in our consideration because tauon anomalous magnetic moment has not been measured. Instead, we use the squared mass splitting data to estimate tau neutrino mass in this paper. These are not mass eigenstates masses but flavor states masses, however, the sum of these masses, which should be equal to the sum of mass eigen states masses, is consistent to the current upper and lower bound of the sum of neutrino masses for both cases of normal hierarchy and inverted hierarchy.