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.     

Neutrino oscillations in the field of a linearly polarized electromagnetic wave

Neutrino oscillations ν _iL ? ν _jR in the field of a linearly polarized electromagnetic wave are studied on the basis of a recently proposed effective Hamiltonian that describes the evolution of a spin in an arbitrary electromagnetic field. The condition of resonance amplification of the oscillations is analyzed in detail. A method is developed for qualitatively studying solutions to the equation of neutrino evolution in the resonance region. This method can be used to explore neutrino oscillations in fields of various configurations.     

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.     

Atmospheric neutrinos and discovery of neutrino oscillations

Neutrino oscillation was discovered through studies of neutrinos produced by cosmic-ray interactions in the atmosphere. These neutrinos are called atmospheric neutrinos. They are produced as decay products in hadronic showers resulting from collisions of cosmic rays with nuclei in the atmosphere. Electron-neutrinos and muon-neutrinos are produced mainly by the decay chain of charged pions to muons to electrons. Atmospheric neutrino experiments observed zenith-angle and energy dependent deficit of muon-neutrino events. Neutrino oscillations between muon-neutrinos and tau-neutrinos explain these data well. Neutrino oscillations imply that neutrinos have small but non-zero masses. The small neutrino masses have profound implications to our understanding of elementary particle physics and the Universe. This article discusses the experimental discovery of neutrino oscillations.     

Neutrino oscillations in non-inertial frames and the violation of the equivalence principle Neutrino mixing induced by the equivalence principle violation

Neutrino oscillations are analyzed in an accelerating and rotating reference frame, assuming that the gravitational coupling of neutrinos is flavor dependent, which implies a violation of the equivalence principle. Unlike the usual studies in which a constant gravitational field is considered, such frames could represent a more suitable framework for testing if a breakdown of the equivalence principle occurs, due to the possibility to modulate the (simulated) gravitational field. The violation of the equivalence principle implies, for the case of a maximal gravitational mixing angle, the presence of an off-diagonal term in the mass matrix. The consequences on the evolution of flavor (mass) eigenstates of such a term are analyzed for solar (oscillations in the vacuum) and atmospheric neutrinos. We calculate the flavor oscillation probability in the non-inertial frame, which does depend on its angular velocity and linear acceleration, as well as on the energy of neutrinos, the mass-squared difference between two mass eigenstates, and on the measure of the degree of violation of the equivalence principle (). In particular, we find that the energy dependence disappears for vanishing mass-squared difference, unlike the result obtained by Gasperini, Halprin, Leung, and other physical mechanisms proposed as a viable explanation of neutrino oscillations. Estimations on the upper values of are inferred for a rotating observer (with vanishing linear acceleration) comoving with the earth, hence rad/sec, and all other alternative mechanisms generating the oscillation phenomena have been neglected. In this case we find that the constraints on are given by for solar neutrinos and for atmospheric neutrinos. Received: 14 December 2000 / Published online: 15 March 2001     

Solar neutrino experiments: Status and prospects

Solar neutrino experiments were originally conceived as a way to demonstrate that nuclear reactions are responsible for energy generation in stars. When solar neutrinos were first detected the measured flux was much less than what solar models predicted. The Solar Neutrino Problem thus came to be and it persisted for over thirty years. It is now known that the deficit in solar neutrinos (of electron neutrino flavour) was due to neutrino oscillations and that matter effects are important. Solar neutrino experiments played a key part in these discoveries and in recent developments in neutrino physics. This report summarizes Pontecorvo Neutrino Physics School lectures that explored the physics of solar neutrinos and the experiments that detected them. The lectures also included a look forward to future solar neutrino experiments and their physics goals and these are also discussed here.     

Neutrino Oscillations in Caianiello's Quantum Geometry Model

Neutrino flavor oscillations are analyzed in the framework of Quantum Geometry model proposed by Caianiello. In particular, we analyze the consequences of the model for accelerated neutrino particles that experience an effective Schwarzschild geometry modified by the existence of an upper limit on the acceleration, which implies a violation of the equivalence principle. We find a shift of quantum-mechanical phase of neutrino oscillations, which depends on the energy of neutrinos as E³. Implications on atmospheric and solar neutrinos are discussed.     

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 the massive dirac neutrino in an external electromagnetic field

An interpretation of the anomalous magnetic moment of the neutrino is given; we derive an effective Hamiltonian which describes the motion of the neutrino in a weak external magnetic field and calculate the radiation intensity due to the anomalous magnetic moment of the neutrino in a constant magnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 64–70, March, 1988.     

Parametric resonance in neutrino oscillations in matter

Neutrino oscillations in matter can exhibit a specific resonance enhancement — parametric resonance, which is different from the MSW resonance. Oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we review the parametric resonance of neutrino oscillations in matter. In particular, physical interpretation of the effect and the prospects of its experimental observation in oscillations of solar and atmospheric neutrinos in the earth are discussed. On leave from National Research Centre, Kurchatov Institute, Moscow 123182, Russia     

The Mass Operator and Neutrino Oscillations

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different concepts of temporal evolution.     

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.     

Solar neutrino oscillation diagnostics at SuperKamiokande and Sudbury Neutrino Observatory

Results for solar neutrino detection from the SuperKamiokande collaboration have been presented recently while those from the Sudbury Neutrino Observatory are expected in the near future. These experiments are sensitive to the⁸B neutrinos from the sun, the shape of whose spectrum is well-known but the normalization is less certain. We propose several variables, insensitive to the absolute flux of the incident beam, which probe the shape of the observed spectrum and can sensitively signal neutrino oscillations. They provide methods to extract the neutrino mixing angle and mass splitting from the data and also to distinguish oscillation to sequential neutrinos from those to a sterile neutrino.     

Neutrino masses in astrophysics and cosmology

Cosmology yields the most restrictive limits on neutrino masses and conversely, massive neutrinos would contribute to the cosmic dark-matter density and would play an important role for the formation of structure in the universe. Neutrino oscillations may well solve the solar neutrino problem and can have a significant impact on supernova physics. The neutrino signal from a future galactic supernova could provide evidence for cosmologically interesting neutrino masses or set interesting limits.     

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.     

Status of the Sudbury Neutrino Observatory

Solar neutrinos from the decay of ⁸B have been detected at the Sudbury Neutrino Observatory via the charged-current (CC) and neutral-current (NC) reactions on deuterium and by the elastic scattering (ES) of electrons. The CCr eaction is sensitive exclusively to electron neutrinos, the NCr eaction is sensitive to all neutrino species, and the ES reaction also has a small sensitivity to muon and tau neutrinos. These measurements provided strong evidence that neutrinos change flavor as they propagate from the center of the Sun to the Earth at the 5.3σ level. It will also be shown that a global solar neutrino analysis of matter-enhanced neutrino oscillations of two active flavors strongly favors the large mixing angle solution.     

Neutrino oscillations in the sun and the205Tl solar neutrino experiment

Neutrino induced transition rates from²⁰⁵Tl to excited states in²⁰⁵Pb were calculated for neutrino fluxes from the different hydrogen burning reactions in the sun. Suppression factors for electron neutrinos due to flavor oscillations in the sun were obtained. The influence of neutrino oscillations on the neutrino capture rate of²⁰⁵Tl in dependence of the mixing angle and neutrino mass difference is discussed.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Ultra-light neutrinos and R-parity in superstring models

A mechanism is suggested for generating ultra-light neutrinos in intermediate scale superstring models as a consequence of R-parity conservation. Neutrino masses are suppressed by four powers of the intermediate scale and could be appropriate to explain the reduced solar neutrino flux in terms of resonant oscillations of the electron- to the muon-neutrino.