Particle quantum states with indefinite mass and neutrino oscillations

TL;DR

This paper introduces a new mathematical formalism for neutrino oscillations applicable to any energy, unifying the description of neutrino states with indefinite mass within quantum field theory.

Contribution

It develops a formalism that constructs neutrino states as multiplets with indefinite mass, extending oscillation formulas beyond the ultra-relativistic limit.

Findings

Formalism agrees with existing theory in the ultra-relativistic limit

Neutrino states can be described as superpositions with different masses and identical momenta

Oscillation phenomena emerge naturally from the modified quantum field theory framework

Abstract

In this work we develop a mathematical formalism which allows obtaining oscillation formula for neutrino of any energy. We demonstrate that in the ultra-relativistic limit the results obtained in this new approach agree with the previously used phenomenological theory which is only applicable to ultra-relativistic neutrinos. To this end we do the following. The Hilbert spaces of particle states are constructed in such a way that the neutrinos are combined in a multiplet with its components being considered as different quantum states of a single particle. The same is done for the charged leptons and the down- and up-type quarks. In the theory based on the Lagrangian of the fermion sector of the Standard Model modified in accordance with this construction, the phenomenon of neutrino oscillations arises as a direct consequence of the general principles of quantum field theory. Using the example of the pion decay, when the resulting neutrino has to be ultra-relativistic, it is shown that the neutrino states produced in the decay process can be described by a superposition of states with different masses and identical canonical momenta with very high accuracy.