On the theory of neutrino mixing and oscillations

A brief review of the status of neutrino oscillations is given. The phenomenology of neutrino mixing and the standard seesaw mechanism of neutrino mass generation is discussed. Different approaches to neutrino oscillations are considered and compared. The role of the Heisenberg space-momentum uncertainty relation and the Mandelstam-Tamm time-energy uncertainty relation in neutrino oscillations is discussed in some detail.     

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.     

Neutrino oscillations and the early universe

The observational and theoretical status of neutrino oscillations in connection with solar and atmospheric neutrino anomalies is presented briefly. The effect of neutrino oscillations on the evolution of the early Universe is discussed in detail. A short review is given of the standard Big Bang Nucleosynthesis (BBN) and the influence of resonant and non-resonant neutrino oscillations on active neutrinos and on primordial synthesis of He-4. BBN cosmological constraints on neutrino oscillation parameters are discussed.     

Solar neutrino problem and gravitationally induced long-wavelength neutrino oscillation

We have reexamined the possibility of explaining the solar neutrino data through long-wavelength neutrino oscillations induced by a tiny breakdown of the weak equivalence principle of general relativity. We have found that such gravitationally induced oscillations can provide a viable solution to the solar neutrino problem.     

Classification of neutrino oscillations in the presence of mirror fermions

We extend the classification of neutrino oscillations to include mirror neutrinos. Besides the traditional first- and second- class oscillations we define a third class: lepton number conserving oscillations within one flavour, or neutrino/mirror-neutrino oscillations. Signatures for different oscillation schemes in charged and neutral current processes of the oscillated neutrinos are described.     

Physics opportunities with supernova neutrinos

The high-statistics neutrino signal from the next nearby supernova (SN) would provide a bonanza of astrophysical and particle-physics information. In particular, there are two new developments in this field: (i) The SASI instability can imprint potentially detectable short-time variations on the neutrino signal. (ii) Collective neutrino oscillations strongly modify the previous paradigm of SN neutrino oscillations with potentially detectable consequences.     

Remarks to the standard scheme (theory) of neutrino oscillations. Corrected scheme of neutrino oscillations

In the standard theory of neutrino oscillations, it is supposed that physically observed neutrino states ν _e , ν_μ, ν_τ, have no definite masses, that they are initially produced as a mixture of the ν₁, ν₂, ν₃ neutrino states (i.e., they are produced as a wave packet), and that neutrino oscillations are the real ones. Then, this wave packet must decompose at a definite distance into constituent parts and neutrino oscillations must disappear. It was shown that these suppositions lead to violation of the law of energy and momentum conservation. An alternative scheme of neutrino oscillations obtained within the framework of particle physics has been considered, where the above mentioned shortcomings are absent, the oscillations of neutrinos with equal masses are the real ones, and the oscillations of neutrinos with different masses are the virtual ones. Expressions for probabilities of neutrino transitions (oscillations) in the alternative (corrected) scheme are given. The text was submitted by the author in English.     

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.     

On the oscillations of neutrinos with Dirac and Majorana masses

Pontecorvo neutrino oscillations are discussed in the case of Dirac as well as Majorana neutrino mass terms. We prove that none of the possible experiments on neutrino oscillations including those on CP nonconservation, can distinguish between these two possibilities. Oscillations of neutrinos having both Dirac and Majorana mass terms also considered.     

Addendum to: Gen. Rel. Grav. 28 (1996) 1161, First Prize Essay for 1996: Neutrino Oscillations and Supernovae

In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscillations may provide a powerful indirect energy transport mechanism to supernovae explosions. The principal aim of this addendum is to present the relevant unedited text of Section 1 of that proposal. We then briefly remind, (a) of an early suggestion of Mazurek on vacuum neutrino oscillations and their relevance to supernovae explosion, and (b) Wolfenstein's result on suppression of the effect by matter effects. We conclude that whether or not neutrino oscillations play a significant role in supernovae explosions shall depend if there are shells/regions of space in stellar collapse where matter effects play no essential role. Should such regions exist in actual astrophysical situations, the final outcome of neutrino oscillations on supernovae explosions shall depend, in part, on whether or not the LNSD signal is confirmed. Importantly, the reader is reminded that neutrino oscillations form a set of flavor-oscillation clocks and these clock suffer gravitational redshift which can be as large as 20 percent. This effect must be incorporated fully into any calculation of supernova explosion.     

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.     

Results from atmospheric neutrinos

With the announcement of new evidence for muon neutrino disappearance observed by the super-Kamiokande experiment, the more than a decade old atmospheric neutrino anomaly moved from a possible indication for neutrino oscillations to an apparently inescapable fact. The evidence is reviewed, and new indications are presented that the oscillations are probably between muon and tau neutrinos. Implications and future directions are discussed.     

Neutrino oscillations: Recent results and future directions

A brief introduction to the phenomena of vacuum neutrino oscillations and resonant flavour conversion is presented with a heavy pedagogic leaning. Variants of these ideas, e.g., neutrino helicity flip in a magnetic field, violation of the equivalence principle, etc. are outlined. A few vexing issues pertaining to the quantum mechanics of neutrino oscillations are discussed. Expectations from some of the future experiments are summarized.     

Paradoxes of neutrino oscillations

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations. The text was submitted by the authors in English.     

No collective neutrino flavor conversions during the supernova accretion phase

We perform a dedicated study of the supernova (SN) neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what was expected in the presence of only neutrino-neutrino interactions, we find that the multiangle effects associated with the dense ordinary matter suppress collective oscillations. The matter suppression implies that neutrino oscillations will start outside the neutrino decoupling region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev-Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle θ(13) is not very small.     

在中微子振荡中的CP破坏

讨论了中微子味混合与中微子振荡的理论,定量地研究了在中微子振荡中的CP破坏效应.在一类超对称模型中,计算了真空中中微子振荡几率和 CP破坏效应.     

Floquet theory of neutrino oscillations in the earth

We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider a parametric resonance in neutrino oscillations that is possible in such media and discuss its implications for the oscillations of neutrinos traversing the Earth and passing through the Earth’s core.     

Introduction to a field-theoretical treatment of neutrino oscillations

We discuss the main features of the field-theoretical approach to neutrino oscillations where one combines neutrino production and detection processes in a single Feynman graph. The ‘oscillating neutrinos’ are represented by inner lines of this graph and appear in the calculation of the cross section of the total process as propagators of the neutrino mass eigenfields. We show that this field-theoretical approach leads to a transparent treatment of neutrino oscillations without ambiguities and provides the correct answer in cases where the standard approach fails.     

Matter effects in active-sterile solar neutrino oscillations

We study the matter effects for solar neutrino oscillations in a general scheme, without any constraint on the number of sterile neutrinos and the mixing matrix elements, only assuming a realistic hierarchy of neutrino squared-mass differences in which the smallest squared-mass difference is effective in solar neutrino oscillations. The validity of the analytic results is illustrated with a numerical solution of the evolution equation in the simplest case of four-neutrino mixing with the realistic matter density profile inside the Sun.