Chiral interactions, chiral states and "chiral neutrino oscillations"

TL;DR

The paper resolves the long-standing question of vacuum chiral neutrino oscillations by showing that the neutrino state produced in chiral weak interactions is not the chiral spinor $P_L u_h$ but a coherent superposition of propagation eigenstates with the same energy, eliminating any time-dependent phase responsible for vacuum oscillations. It develops a production–detection amplitude formalism, corroborated by a neutrino propagator treatment, to describe oscillations in a process- and kinematics-dependent way. It demonstrates that genuine oscillations arise only in the presence of a medium (matter or magnetic fields) where the matter potential creates a phase difference between helicity components, with a frequency set by the potential and a depth controlled by $(m_ u/2E_ u)^2$. The work also extends to Majorana neutrinos and relic neutrinos, showing that zero-distance effects can appear under certain production/detection conditions, but vacuum chiral oscillations remain absent. Overall, the paper clarifies foundational aspects of neutrino chirality, provides a robust framework for neutrino oscillations via production/detection amplitudes, and delineates when and how chiral effects can manifest in matter or cosmological settings.

Abstract

In vacuum the ``chiral neutrino oscillations'', i.e. the periodic transitions between the left- and right-handed states do not occur. The produced state differs from the chiral component that appear in the Lagrangian of interactions and should be computed for each specific process. The phase difference between components of a produced neutrino is space-time independent. This neutrino state consists of only positive energy solutions of the Dirac equation and therefore the energy splitting $2E_ν$ between the components with different helicities that would drive the chiral oscillations does not exist. Consideration in terms of neutrino propagators leads to the same conclusion. The situation is similar for the Majorana neutrinos and in the presence of flavor mixing. However, oscillations of the neutrino states produced in the chiral interactions are possible in matter with the length determined by the matter potential. Description of oscillations in terms of amplitudes of production and detection is elaborated that does not lead to any misconception. In the expanding Universe the relic neutrinos adiabatically convert to equal number densities of the left and right handed components.