Three-flavour neutrino oscillations in a magnetic field

In this paper we study Dirac and Majorana neutrino oscillations in a magnetic field in the three-flavour case. A theoretical framework developed in \cite{Popov:2019} is extended to the case of three neutrino species, as well as to the Majorana neutrinos case. The closed expression for the Dirac neutrinos flavour and spin oscillations are given. Majorana neutrino oscillations are studied numerically. We show that the probabilities exhibit a complicated interplay of oscillation on magnetic $\mu_\nu B$ and vacuum $\Delta m^2_{ij}/2p$ frequencies. It is also shown that neutrino oscillations in an interstellar magnetic field can modify neutrino fluxes observed in neutrino telescopes.