Beyond the new standard model in neutrino oscillations

We discuss effects of new physics (NP) in neutrino oscillation experiments. Such effects can modify a production neutrino flux, a detection cross-section and a matter transition. As a result, the NP effects change neutrino oscillations both in vacuum and in matter. A relation between the small effects of NP and the oscillation parameters is discussed. It is shown for which parameters the NP effects are suppressed and when they are potentially large. Oscillations of non-unitary mixed neutrinos are presented in more details.     

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.     

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.     

Associated neutrino mixing and neutrino oscillations in left-right electro weak gauge theory

The rare electromagnetic decay of a neutral pseudoscalar meson into a lepton pair is calculated in a bound state quark model. For heavy mesons, the leading QCD diagram is argued to be dominant allowing higher order QCD corrections to be neglected for the branching ratio of this decay to the two-photon decay. The experimentally interesting case of pion decay is treated separately, and the rates for competing processes (weak neutral currents, axions, technicolour ...) are estimated. We conclude that existing data may well allow for such contributions.     

Relativistic wave packets in the quantum field approach to the theory of neutrino oscillations

A covariant theory of wave packets and its application to the quantum field method of calculation of the probabilities of neutrino oscillations in vacuum that is based on the technique of macroscopic Feynman diagrams, which describe the processes of emission and absorption of virtual massive neutrinos ν _i (i = 1, 2, 3) at macroscopicly separated space-time points, is considered. The effect of flavor oscillations is reduced to an interference of amplitudes with different vi in an intermediate state. A macroscopic amplitude is calculated that describes a class of processes which go with nonconservation of leptonic numbers, and statistical averaging of the squared modulus of this amplitude is performed. The averaged probability of a process with ultrarelativistic neutrino exchange is representable in the form of an integral of the product of three factors: the flux of massless neutrinos from the source, the differential cross-section for the interaction of a neutrino with the detector, and a dimensionless factor that describes the flavor transition. The conditions under which the last factor can be interpreted as the probability of the flavor transition in the conventional quantummechanical sense are analyzed.     

Non-cyclic phases for neutrino oscillations in quantum field theory

We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.     

Quantum theory of neutrino oscillations for pedestrians: simple answers to confusing questions

A simple rigorous calculation confirms the standard formula and clarifies some confusing difficulties arising in the standard textbook recipe converting the unobserved frequency of time oscillations between neutrino states with different energies to the observed oscillation wave length in space. Including the quantum fluctuations in the position of the detector and in the transit time between source and detector enables the treatment of: (1) The difference in velocity and transit time between neutrinos with different energies. (2) The destruction of all phases between states with different masses by an ideal detector which measures the energy and momentum of the neutrino. (3) The destruction of all phases between states with different energies by a realistic detector in thermal equilibrium with its macroscopic environment. (4) The difficulty for relativistic treatments and relativistic field theory to treat the crucial quantum mechanics of a macroscopic detector at rest in the laboratory.     

Perturbation theory of neutrino oscillations with and without nonstandard interactions

After making brief comments on the Kamioka-Korea two-detector setting, I delivered a pedagogical seminar on perturbation theory of neutrino oscillations with and without nonstandard interactions. I also described a general property of neutrino flavor transformation of such a system which includes useful relationships between S matrix elements and a phase reduction theorem.     

Energy spectrum of photons produced by neutrino (antineutrino) scattering on electrons. Effect of possible neutrino oscillations

The energy spectrum of photons emitted in neutrino (antineutrino) scattering on electrons at E_v ? m_v is calculated with the assumption that the neutral electron flow has an arbitrary (V, A) structure. The result obtained is generalized to the case of possible neutrino oscillations, \(v_e \begin{array}{*{20}c} { - \to } \\ { \leftarrow - } \\ \end{array} v_\mu , \overline v _e \begin{array}{*{20}c} { - \to } \\ { \leftarrow - } \\ \end{array} \overline v _\mu \) , at an arbitrary neutrino mixing angle. Using the Weinberg-Salam model (sin²θ_W = 0.23) estimates of the sections dσ_γ/dω and σ_γ are obtained with consideration of the reactor antineutrino flux \(\bar v_e \) . The contributions from charged and neutral lepton fluxes and their interference to dσ_γ/dω are compared.     

Resonant neutrino oscillations and the neutrino signature of supernovae

We examine the effects of resonant neutrino oscillations, proposed as a solution to the solar neutrino puzzle, on the neutrino signature of a Type II supernova. We find that, for parameters corresponding to an adiabatic conversion of most of the ⁸B neutrino flux, the supernova neutrino signal in a water-Čerenkov detector is altered in the following way: (1) The isotropic-to-directional event ratio increases; (2) The short time scale neutronization burst signal decreases by a factor 7, perhaps rendering it unobservable. Detection of these changes would allow one to distinguish between neutrino oscillations and solar model alterations as solutions to the solar neutrino problem. We also note that mixing of the higher energy ν_μ and ν_r's to ν_e's will enhance detection of the thermally produced ν-flux.     

Phenomenology of neutrino oscillations

The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.     

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.     

MiniBooNE and LSND data: non-standard neutrino interactions in a (3+1) scheme versus (3+2) oscillations

Journal of High Energy Physics - We consider the cosmology of a model in which the dark matter is part of a nonminimal hidden sector which is not in thermal equilibrium with the standard model...     

Search for muon to electron neutrino oscillations

A search for _e and oscillations has been carried out with the CHARM II detector exposed to the CERN wide band neutrino beam. The data were collected over five years, alternating beams mainly composed of muon-neutrinos and muon-antineutrinos. The number of interactions of _e and observed is comparable with the number of events expected from flux calculations. For large squared mass differences the upper limits obtained on the mixing angle aresin ²2 < 9.4=" ·=">^–3 for oscillating to _e andsin ²2 < 4.8=" ·=">^–3 for to , at the 90% confidence level. Combining neutrino and antineutrino data the upper limit is 5.6 · 10^–3.On leave of absence from ITEP (Moscow)     

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.     

Supernova neutrino nucleosynthesis of light elements with neutrino oscillations

Light element synthesis in supernovae through neutrino-nucleus interactions, i.e., the v process, is affected by neutrino oscillations in the supernova environment. There is a resonance of 13-mixing in the O/C layer, which increases the rates of charged-current -process reactions in the outer He-rich layer. The yields of 7Li and 11B increase by about a factor of 1.9 and 1.3, respectively, for a normal mass hierarchy and an adiabatic 13-mixing resonance, compared to those without neutrino oscillations. In the case of an inverted mass hierarchy and a nonadiabatic 13-mixing resonance, the increase in the 7Li and 11B yields is much smaller. Observations of the 7Li/11B ratio in stars showing signs of supernova enrichment could thus provide a unique test of neutrino oscillations and constrain their parameters and the mass hierarchy.     

The discovery of neutrino oscillations

The Nobel Prize for physics 2015 was awarded to Takaaki Kajita and Arthur McDonald for the discovery of neutrino oscillations, showing that neutrinos have a mass. This article describes the two areas of research namely the atmospheric neutrino anomaly and the problem of missing solar neutrinos which lead to these groundbreaking discoveries.