Neutrinos with Mixing in Twisting Magnetic Fields

Transitions in a system of neutrinos with vacuum mixing and magnetic moments, propagating in matter and transverse magnetic field, are considered. It is shown that in the realistic case of magnetic field direction varying along the neutrino path qualitatively new phenomena become possible: permutation of neutrino conversion resonances, appearance of resonances in the neutrino-antineutrino ($\nu_{lL}\leftrightarrow\bar{\nu}_{lR}$) transition channels, neutrino-antineutrino resonant conversion, large amplitude $\nu_{lL}\leftrightarrow\bar{\nu}_{lR}$ oscillations, merging of different resonances (triple resonances). Possible phenomenological implications of these effects are briefly discussed.Comment: LaTeX, 35 pages, 4 figures (not included but available upon request). In memoriam of Ya.A. Smorodinsky. SISSA-170/92/E

Neutrino oscillations: Entanglement, energy-momentum conservation and QFT

We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the $S$-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct physics conditions are imposed. This includes space-time localization of the neutrino production and detection processes. Space-time diagrams are introduced, which characterize this localization and illustrate the coherence issues of neutrino oscillations. We discuss two approaches to calculations of the transition amplitudes, which allow different physics interpretations: (i) using configuration-space wave packets for the involved particles, which leads to approximate conservation laws for their mean energies and momenta; (ii) calculating first a plane-wave amplitude of the process, which exhibits exact energy-momentum conservation, and then convoluting it with the momentum-space wave packets of the involved particles. We show that these two approaches are equivalent. Kinematic entanglement (which is invoked to ensure exact energy-momentum conservation in neutrino oscillations) and subsequent disentanglement of the neutrinos and recoiling states are in fact irrelevant when the wave packets are considered. We demonstrate that the contribution of the recoil particle to the oscillation phase is negligible provided that the coherence conditions for neutrino production and detection are satisfied. Unlike in the previous situation, the phases of both neutrinos from $Z^0$ decay are important, leading to a realization of the Einstein-Podolsky-Rosen paradox.Comment: 30 pages, 3 eps figures; presentation improved, clarifications added. To the memory of G.T. Zatsepi

Neutrino Physics: Open Theoretical Questions

We know that neutrino mass and mixing provide a window to physics beyond the Standard Model. Now this window is open, at least partly. And the questions are: what do we see, which kind of new physics, and how far "beyond"? I summarize the present knowledge of neutrino mass and mixing, and then formulate the main open questions. Following the bottom-up approach, properties of the neutrino mass matrix are considered. Then different possible ways to uncover the underlying physics are discussed. Some results along the line of: see-saw, GUT and SUSY GUT are reviewed.Comment: 17 pages, latex, 12 figures. Talk given at the XXI International Symposium on Lepton and Photon Interactions at High Energies, ``Lepton Photon 2003", August 11-16, 2003 - Fermilab, Batavia, IL US

The MSW effect and Matter Effects in Neutrino Oscillations

The MSW (Mikheyev-Smirnov-Wolfenstein) effect is the adiabatic or partially adiabatic neutrino flavor conversion in medium with varying density. The main notions related to the effect, its dynamics and physical picture are reviewed. The large mixing MSW effect is realized inside the Sun providing the solution of the solar neutrino problem. The small mixing MSW effect driven by the 1-3 mixing can be realized for the supernova (SN) neutrinos. Inside the collapsing stars new elements of the MSW dynamics may show up: the non-oscillatory transition, non-adiabatic conversion, time dependent adiabaticity violation induced by shock waves. Effects of the resonance enhancement and the parametric enhancement of oscillations can be realized for the atmospheric and accelerator neutrinos in the Earth. Precise results for neutrino oscillations in the low density medium with arbitrary density profile are presented and the attenuation effect is described. The area of applications is the solar and SN neutrinos inside the Earth, and the results are crucial for the neutrino oscillation tomography.Comment: 18 pages, latex, 6 figures, talk given at the Nobel Symposium 129, ``Neutrino Physics'', Haga Slott, August 19 - 24, 200

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, in the framework of the wave packet approach, 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 production/detection and propagation coherence 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, the applicability limits of the stationary source approximation, and Lorentz invariance of the oscillation probability. We also develop a novel approach to calculation of the oscillation probability in the wave packet picture, based on the summation/integration conventions different from the standard one, which gives a new insight into the oscillation phenomenology. We discuss a number of apparently paradoxical features of the theory of neutrino oscillations.Comment: LaTeX, 45 pages, no figures. v2: references adde

Relativistic quantum theories and neutrino oscillations

Neutrino oscillations are examined under the broad requirements of Poincar\'e-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable, and how many factors that are important in principle end up being negligible in practice.Comment: 21 pages, no figure

Seesaw mechanism in three flavors

We advance a method used to analyse the neutrino properties (masses and mixing) in the seesaw mechanism. Assuming the hierarchical Dirac and light neutrino masses we establish rather simple relations between the light and the heavy neutrino parameters in the favored region of the solar and the atmospheric neutrino experiments. A empirical condition satisfied by the RH mixing angles is obtained.Comment: 19 pages. Acceptted by Phys. Rev. D The part about the neutrino experiments is selected as a single section. The mistakes in spelling and grammer are corrected. Also, some equations are neewly numbere

Mass Hierarchies and the Seesaw Neutrino Mixing

We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. They are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.Comment: 11 pages, no figures, replaced with final version. Minor corrections and one typo corrected. Added one referenc

Solar neutrinos and grand unification

We consider the Grand Unification (GU) scenario for neutrino masses which is based on the see-saw mechanism with the mass of the heaviest right handed (RH) neutrino at the GU-scale: $M_3 \sim \Lambda_{GU}$, and on the quark-lepton symmetry for fermions from the third generation. The scenario predicts for the light neutrinos: $m_3 \sim (2 - 4) \cdot 10^{-3}$ eV and $m_2 \sim (0.3 - 3) \cdot 10^{-5}$ eV (in the case of a linear mass hierarchy of the RH neutrinos or/and in presence of the Planck scale suppressed non-renormalizable operators). It also predicts large $\nu_e - \nu_{\mu}$ mixing: $~\sin^2 2\theta_{e\mu} \stackrel{_>}{_\sim} 0.2$. In this scenario the solar neutrinos ($\nu_{\odot}$) undergo both the \nue $\to$ \nutau resonance conversion in the Sun and substantial \nue $\to$ \numu vacuum oscillations on the way from the Sun to the Earth. The interplay of both effects enlarges the range of neutrino parameters which solve the $\nu_{\odot}$-problem. In particular, $\nu_e - \nu_{\tau}$ mixing angle can be as small as the corresponding quark mixing: $\sin^2 2\theta_{e\tau} \geq (2~-~5) \cdot 10^{-4}$. The scenario predicts peculiar (oscillatory) distortion of the boron neutrino energy spectrum and seasonal variations of signals. Manifestations of these effects in the Super-Kamiokande and SNO experiments are studied.Comment: 36 pages, LaTeX, includes 14 figures, revised and expande

Neutrino spin-flip effects in collapsing stars

We study the spin-flavor transitions of neutrinos in the magnetic fields of a collapsing star. For the neutrino mass squared difference (10^{-10} - 10) eV^2 the transitions take place in almost isotopically neutral region of the star, where the effective matter density is suppressed up to 3 - 4 orders of magnitude. This suppression is shown to increase the sensitivity of the neutrino bursts studies to the magnetic moment of neutrino by 1.5 - 2 orders of magnitude, and for realistic magnetic field the observable effects may exist for (2 - 3)10^{-14} Bohr magneton. In the isotopically neutral region the jumps of the effective potential exist which influence the probabilities of transitions. The experimental signatures of the spin-flavor transitions are discussed. In particular, in the case of direct mass hierarchy, the spin-flip effects result in a variety of modifications of the electron antineutrino spectrum. Taking this into account, we estimated the upper bounds on the magnetic moment from the SN1987A data. In the isotopically neutral region the effects of possible twist of the magnetic field on the way of neutrinos can be important, inducing distortion of the neutrino energy spectra and further increasing the sensitivity. However, if the total rotation angle is restricted the absolute change of probabilities is small.Comment: Standard LaTeX file, 30 pages + 10 figures as separate compressed PostScript file