Little group generators for Dirac neutrino one-particle states

Assuming neutrinos to be of the Dirac type, the little group generators for the one-particle states, created off the vacuum by the field operator, are obtained, both in terms of the one-particle states themselves and in terms of creation/annihilation operators. It is shown that these generators act also as rotation operators in the Hilbert space of the states, providing three types of transformations: a helicity flip, the standard charge conjugation, and a combination of the two, up to phases. The transformations’ properties are provided in detail and their physical implications discussed. It is also shown that one of the transformations continues to hold for chiral fields without mixing them. It is argued that these results provide support for the Majorana nature of massive neutrinos.

Three Flavor Quasi-Dirac Neutrino Mixing, Oscillations and Neutrinoless Double Beta Decay

The extension of the Standard model by three right-handed neutrino fields exhibit appealing symmetry between left-handed and right-handed sectors, which is only violated by interactions. It can accommodate three flavor quasi-Dirac neutrino mixing scheme, which allows processes with violation of both lepton flavor and total lepton number symmetries. We propose a 6×6 unitary matrix for parameterizing the mixing among three flavors of quasi-Dirac neutrino. This mixing matrix is constructed by two 3×3 unitary matrices that diagonalizes the Dirac mass term in the Lagrangian. By only assuming the Standard Model V−A weak interaction, it is found that probabilities of neutrino oscillations among active flavor states and effective masses measured by single beta decay, by neutrinoless double-beta decay and by cosmology only depend on single 3×3 unitary matrix relevant to mixing of active neutrino flavors. Further, by considering 1σ and 3σ uncertainties in the measured oscillation probability of electron antineutrino from reactor, derivation of the constraint on the Majorana neutrino mass component is demonstrated. The consequence for effective Majorana neutrino mass governing the neutrinoless double-beta decay is discussed.