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

Artem Popov,Alexander Studenikin

doi:10.1140/epjc/s10052-019-6657-z

Abstract

We further develop a recently proposed new approach to the description of the relativistic neutrino flavour nu _e^L leftrightarrow nu _{mu }^L, spin nu _e^L leftrightarrow nu _{e}^R and spin-flavour nu _e^L leftrightarrow nu _{mu }^R oscillations in a constant magnetic field that is based on the use of the exact neutrino stationary states in the magnetic field. The neutrino flavour, spin and spin-flavour oscillations probabilities are calculated accounting for the whole set of possible conversions between four neutrino states. In general, the obtained expressions for the neutrino oscillations probabilities exhibit new inherent features in the oscillation patterns. It is shown, in particular, that: (1) in the presence of the transversal magnetic field for a given choice of parameters (the energy and magnetic moments of neutrinos and the strength of the magnetic field) the amplitude of the flavour oscillations nu _e^L leftrightarrow nu _{mu }^L at the vacuum frequency is modulated by the magnetic field frequency, (2) the neutrino spin oscillation probability (without change of the neutrino flavour) exhibits the dependence on the mass square difference varDelta m^2. It is shown that the discussed interplay of neutrino oscillations in magnetic fields on different frequencies can have important consequences in astrophysical environments, in particular in those peculiar for magnetars.

Highlights

The best terrestrial upper bounds on the level of μν < 2.9 ÷ 2.8 × 10−11μB on neutrino magnetic moments are obtained by the GEMMA reactor neutrino experiment [5] and recently by the Borexino collaboration [6] from solar neutrino fluxes
In a series of papers [19–22] the solution of the solar neutrino problem was discussed on the basis of neutrino oscillations with a subdominant effect from the neutrino transition magnetic moments conversion in the solar magnetic field
Following to the general idea first implemented in [23,24], we further develop a new approach to the description of the relativistic neutrino flavour νeL ↔ νμL, spin νeL ↔ νeR and spin-flavour νeL ↔ νμR oscillations in the presence of an arbitrary constant magnetic field

Summary

Introduction

Massive neutrinos have nontrivial electromagnetic properties (see [1] for a review, the update can be found in [2]). The helicity operator does not commute with the neutrino evolution Hamiltonian in an arbitrary constant magnetic field and the helicity states are not stationary in this case. This resembles situation of the flavour neutrino oscillations. The proposed alternative approach to the problem of neutrino oscillations in a magnetic field is based on the use of the exact solutions of the corresponding Dirac equation for a massive neutrino wave function in the presence of a magnetic field that stipulates the description of the neutrino spin states with the corresponding spin operator that commutes with the neutrino dynamic Hamiltonian in the magnetic field. The spin operator that commutes with the Hamiltonian (5) can be chosen in the form

Massive neutrino in a magnetic field

Conclusions