Interplay of neutrino spin and three-flavour oscillations in a magnetic field

Abstract

We develop the approach to the problem of neutrino oscillations in a magnetic field introduced in [1] 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. 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 general, the neutrino oscillation probabilities exhibit quite a complicated interplay of oscillations on the magnetic $\omega_B=\mu_{\nu} B$ and vacuum $\omega_{vac}=\frac{\Delta m^2_{ik}}{4p}$ 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 (see [2]).