Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics

Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field are studied using the method of relativistic quantum mechanics. Using the exact solution of the wave equation for a massive neutrino, taking into account external fields, the effective Hamiltonian governing neutrino spin-flavor oscillations is derived. Then the The consistency of our approach with the commonly used quantum mechanical method is demonstrated. The obtained correction to the usual effective Hamiltonian results in the appearance of the new resonance in neutrino oscillations. Applications to spin-flavor neutrino oscillations in an expanding envelope of a supernova are discussed. In particular, transitions between right-polarized electron neutrinos and additional sterile neutrinos are studied for realistic background matter and magnetic field distributions. The influence of other factors such as the longitudinal magnetic field, the matter polarization, and the non-standard contributions to the neutrino effective potential, is also analyzed.     

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrödinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.     

Neutrinos in matter and external fields

A brief survey of effects generated by the influence of the environment on neutrinos is presented. The issues considered here include flavor and spin oscillations of neutrinos in matter, in electromagnetic fields of various configurations, and in gravitational fields; the electromagnetic properties of the neutrinos and the environment-induced change in these properties; photoneutrino processes generated by the environment; urca processes in magnetic fields; various mechanisms that may be responsible for the asymmetry of neutrino radiation from neutron stars; quantum states of neutrinos in matter and the spin light of neutrinos in matter and external fields; and astrophysical and cosmological applications of the above processes and phenomena. The method that is employed to describe the effect of the environment on neutrinos (as well as on electrons) and which is based on the application of exact solutions to the corresponding modified Dirac equations for particles in matter is briefly discussed.     

Neutrino electromagnetic properties

The main goal of the paper is to give a short review on neutrino electromagnetic properties. In the introductory part of the paper a summary on what we really know about neutrinos is given: we discuss the basics of neutrino mass and mixing as well as the phenomenology of neutrino oscillations. This is important for the following discussion on neutrino electromagnetic properties that starts with a derivation of the neutrino electromagnetic vertex function in the most general form, that follows from the requirement of Lorentz invariance, for both the Dirac and Majorana cases. Then, the problem of the neutrino form factor definition and calculation within gauge models is considered. In particular, we discuss the neutrino electric charge form factor and charge radius, dipole magnetic and electric and anapole form factors. Available experimental constraints on neutrino electromagnetic properties are also discussed, and the recently obtained experimental limits on neutrino magnetic moments are reviewed. The most important neutrino electromagnetic processes involving a direct neutrino coupling with photons (such as neutrino radiative decay, neutrino Cherenkov radiation, spin light of neutrino and plasmon decay into neutrino-antineutrino pair in media) and neutrino resonant spin-flavor precession in a magnetic field are discussed at the end of the paper.     

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.     

Nonlinear propagation of neutrinos in a strongly magnetized medium

The nonlinear propagation of an intense neutrino flux in an electron-positron plasma with equilibrium density and magnetic field inhomogeneities is considered. It is found that the neutrinos are nonlinearly coupled with electrostatic and electromagnetic disturbances due to weak Fermi interaction and ponderomotive forces. The process is governed by a Klein-Gordon equation for the neutrino flux and a wave equation for the plasma oscillations in the presence of the ponderomotive force of the neutrinos. This pair of equations is then used to derive a nonlinear dispersion relation which exhibits that nonthermal electrostatic and electromagnetic fluctuations are created on account of the energy density of the neutrinos. The relevance of our investigation to the anomalous absorption of neutrinos in a nonuniform magnetized medium is pointed out.     

Electromagnetic properties of massive neutrinos

The vertex function for a virtual massive neutrino is calculated in the limit of soft real photons. A method based on employing the neutrino self-energy operator in a weak external electromagnetic field in the approximation linear in the field is developed in order to render this calculation of the vertex function convenient. It is shown that the electric charge and the electric dipole moment of the real neutrino are zero; only the magnetic moment is nonzero for massive neutrinos. A fourth-generation heavy neutrino of mass not less than half of the Z-boson mass is considered as a massive neutrino.     

Resonant amplification of neutrino spin rotation in matter and the solar-neutrino problem

It is shown that in the presence of matter there can occur resonant amplification of the flavor-changing neutrino spin rotation in transverse magnetic fields, which is roughly analogous to the Mikheyev-Smirnov-Wolfenstein effect in neutrino oscillations. Possible consequences for solar neutrinos are briefly discussed.     

Mimicking diffuse supernova antineutrinos with the sun as a source

Measuring the $ \bar \nu _e $ \bar \nu _e component of the cosmic diffuse supernova neutrino background (DSNB) is the next ambitious goal for low-energy neutrino astronomy. The largest flux is expected in the lowest accessible energy bin. However, for E ≲ 15 MeV a possible signal can be mimicked by a solar $ \bar \nu _e $ \bar \nu _e flux that originates from the usual ⁸B neutrinos by spin-flavor oscillations. We show that such an interpretation is possible within the allowed range of neutrino electromagnetic transition moments and solar turbulent field strengths and distributions. Therefore, an unambiguous detection of the DSNB requires a significant number of events at E ≳ 15 MeV.     

Behavior of neutrinos in stochastic magnetic fields

If massive neutrinos possess magnetic moments, they can undergo spin flip in a magnetic field. The magnetic fields needed for a meaningful measurement of neutrino moments could be very high and may occur in astronomical objects such as some supernovae or active galactic nuclei: they are typically chaotic ones. We develop the general theory of the passage of neutrinos through such fields. We also develop a simple model which becomes solvable in the high energy limit. Both helicities occur with equal probability, independently of the initial distribution. Observational consequences are discussed.     

Neutrino–Electron Processes in a Magnetic Field and Their Crossing Symmetry

We have studied the neutrino–electron processes in a matter with an external magnetic field of an arbitrary strength. Invariant squares of S-matrix elements, which have been obtained for such reactions using the technique based on the density matrix of a particle propagating in an external magnetic field, are valid in an arbitrary frame of reference moving along the magnetic field lines. The transition probabilities obtained can easily be generalized to the processes of interaction of a neutrino with other charged leptons and protons. The probabilities of the processes have been integrated over the transverse momenta of charged particles for the rates of neutrino–electron reactions as well as the energy and momentum transferred in them from the medium to neutrinos. The expressions obtained are written in the unified form for all neutrino–electron processes.     

Neutrino oscillations in a homogeneous moving medium

The quasi-classical equation that describes both neutrino flavor oscillations and spin rotation in dense matter is obtained in the framework of quantum field theory. The solution of this equation for homogeneous medium is found. The probabilities of the spin-flavor transitions in unpolarized moving matter are calculated in the two-flavor model. We show that if the medium is at rest the neutrino helicity is conserved and the flavor transition probabilities are equal to those obtained using the phenomenological approach.     

Third-order equation for two-component spinors

We present the properties of a two-component spinor field that obeys a third-order equation. It is separated into a massive part that corresponds closely to a Dirac field, and a massless part that obeys the Weyl equation. We discuss the interaction of such a field with an external electromagnetic field and the (weak) interactions of two such fields. They can be considered both in terms of relativistic quantum mechanics and quantum field theory. We conclude that this formulation has some attractive features, such as a unified treatment of electrons and muons with their neutrinos, a special role of thePC transformation, a more convergent propagator and a new approach to interactions. It also has some serious difficulties, aside from those generally associated with higher-order equations. These are mainly related to inconsistencies in the simultaneous considerations of electromagnetic and weak interactions. The approach also suggests a further unification of the electron and muon fields into a single bispinor field.     

MHD origin of density fluctuations deep within the Sun and their influence on neutrino oscillation parameters in LMA MSW scenario

We analyze helioseismic waves near the solar equator in the presence of magnetic fields deep within the solar radiative zone. We find that reasonable magnetic fields can significantly alter the shapes of the wave profiles for helioseismic g modes. They can do so because the existence of density gradients allows g modes to resonantly excite Alfvén waves, causing mode energy to be funneled along magnetic field lines, away from the solar equatorial plane. The resulting waveforms show comparatively sharp spikes in the density profiles at radii where these resonances take place. Such matter density waves with known spatial structure are substituted as a matter density noise into the 2×2 Schrödinger equation for ν _e,π neutrinos oscillating within the Sun. Then we reexamine the sensitivity of solar neutrino oscillations to noise in the solar interior using the best current estimates of neutrino properties. Our results show that the measurement of neutrino properties at KamLAND provides new information about fluctuations in the solar environment on scales to which standard helioseismology constraints are largely insensitive. We also show how the determination of neutrino oscillation parameters from a combined fit of KamLAND and solar data depends strongly on the magnitude of solar density fluctuations.     

Parametric resonance in neutrino oscillations in periodically varying electromagnetic fields

It is shown that a parametric resonance may arise in neutrino oscillations in varying electromagnetic fields. For two types of electromagnetic fields—an amplitude-modulated electromagnetic wave and a transverse magnetic field that is constant in time, but which has an amplitude periodically varying in space—the probabilities of the ν _i ? ν _j neutrino transitions are found, and it is shown that the probability amplitudes increase with time for a specific choice of the parameters of external electromagnetic fields.     

Neutrino flavor conversion in random magnetic fields

If massive neutrinos possess magnetic moments, a magnetic field can cause a spin flip. In the case of Dirac neutrinos the spin flip converts an active neutrino into a sterile one and vice versa. By constrast, if neutrinos are Majorana particles, a spin flip converts them to a neutrino of a different flavor. We examine the behavior of neutrinos in a random magnetic field as it occurs, for instance, in certain astronomical objects, such as an active galactic nucleus. Both Dirac and Majorana neutrinos behave ergodically: independently of their initial density matrix, they tend towards an equipartition of the helicity states. As a result, about half of the Dirac neutrinos produced becomes sterile. For Majorana neutrinos, there will be an approximate equipartition of flavors, independently of the production mechanism.     

Neutrino oscillations as a probe of dark energy

We consider a class of theories in which neutrino masses depend significantly on environment, as a result of interactions with the dark sector. Such theories of mass varying neutrinos were recently introduced to explain the origin of the cosmological dark energy density and why its magnitude is apparently coincidental with that of neutrino mass splittings. In this Letter we argue that in such theories neutrinos can exhibit different masses in matter and in vacuum, dramatically affecting neutrino oscillations. As an example of modifications to the standard picture, we consider simple models that may simultaneously account for the LSND anomaly, KamLAND, K2K, and studies of solar and atmospheric neutrinos, while providing motivation to continue to search for neutrino oscillations in short baseline experiments such as BooNE.     

Testing a new sterile neutrino dark matter candidate

A new class of sterile neutrino dark matter is suggested by an explanation for time variations in the solar neutrino flux in which coupling of sterile neutrinos to other matter is via a very small flavor off-diagonal transition magnetic moment, TMM. The dark matter sterile neutrino’s decay in the radiative channel then depends on the local magnetic field and the unknown value of the TMM. An interesting application of this model uses the DAMA/LIBRA claimed detection of dark matter (assuming they are observing the electromagnetic signal) to provide the decay rate in the Earth’s field, and hence the TMM value. That version of the model is then examined to see if it can be falsified by cosmic X-ray observations or by other direct detection experiments. Particularly the latter could provide a simple, definitive test of this dark matter candidate, which would bring concordance to these experiments.     

Flavour transitions of Dirac-Majorana neutrinos

From a phenomenological point of view, we study active-active and active-sterile flavour-changing (and flavour-conserving) oscillations of Dirac-Majorana neutrinos both in vacuum and in matter. The general expressions for the transition probabilities in vacuum are reported. We then investigate some interesting consequences following from particular simple forms of the neutrino mass matrices, and for the envisaged scenarios we discuss in detail neutrino propagation in matter. Special emphasis is given to the problem of occurrence of resonant enhancement of active-active and active-sterile neutrino oscillations in a medium. The peculiar novel features related to the Dirac-Majorana nature of neutrinos are particularly pointed out. Received: 20 February 1998 / Published online: 5 June 1998