On the existence of quaternion-handedness for the spinor solutions of the Dirac and Majorana neutrinos

This study explores the application of quaternionic left- and right-handed algebraic frameworks to discuss the neutrino-handedness behavior. The generalized left- and right-handed Dirac equations are expressed in terms of quaternionic four-dimensional non-commutative algebra, which yields helicity eigenspinors with definite spin states for Dirac neutrino eigenstates. We establish the spinor states of energy and momentum solutions for Dirac neutrinos and antineutrinos revealed by the non-commutative nature of quaternionic algebra. Furthermore, we expand the quaternionic Dirac spinor solutions to Majorana-like spinor solutions, which represent the mass eigenstates for Majorana neutrinos. By examining two-flavor neutrino oscillation, we express the quaternionic energy and momentum eigenstates of Dirac and Majorana neutrinos, as well as their oscillation probabilities. The estimated quaternionic-based probability supports neutrinos' massive nature and the presence of their right chiral components. The current quaternionic theory has the benefit of identifying the distinct properties of left- and right-handed neutrinos, as well as anti-neutrinos, within a unified framework.