Neutrino eigenstates and flavour, spin and spin-flavour oscillations in a constant magnetic field

TL;DR

This paper extends a theoretical framework for neutrino oscillations in magnetic fields to three generations, providing analytic expressions for probabilities that include spin, flavour, and spin-flavour oscillations, with implications for astrophysical environments.

Contribution

It introduces a comprehensive approach to compute neutrino oscillation probabilities considering three generations and magnetic fields, including CP violation effects, which was not previously available.

Findings

Analytic expressions for neutrino oscillation probabilities in magnetic fields.

Entanglement between neutrino flavour and spin oscillations.

CP violation affects certain neutrino conversion probabilities.

Abstract

We develop the approach to the problem of neutrino oscillations in a magnetic field introduced in \cite{Popov:2019nkr} and extend it to the case of three neutrino generations. The theoretical framework suitable for computation of the Dirac neutrino spin, flavour and spin-flavour oscillations probabilities in a magnetic field is given. It is shown that there is an entanglement between neutrino flavour and spin oscillations and in the general case it is not possible to consider these two types of neutrino oscillations separately. The closed analytic expressions for the probabilities of oscillations are obtained accounting for the normal and inverted hierarchies and the possible effect of CP violation. In particular, it is shown that the probabilities of the conversions without neutrino flavor change, i.e. $\nu_e^L \rightarrow \nu_e^L$ and $\nu_e^L \rightarrow \nu_e^R$, do not exhibit the dependence on the CP phase, while the other neutrino conversions are affected by the CP phase. In general, the neutrino oscillation probabilities exhibit quite a complicated interplay of oscillations on the magnetic $\mu_{\nu} B$ and vacuum frequencies. The obtained results are of interest in applications to neutrino oscillations under the influence of extreme astrophysical environments, for example peculiar to magnetars and supernovas, as well as in studying neutrino propagation in interstellar magnetic fields.