We comment on the paper "On application of the time-energy uncertainty relation to Mössbauer neutrino experiments" (see arXiv: 0803.1424) in which our paper "Time-energy uncertainty relations for neutrino oscillation and Mössbauer neutrino experiment" (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress that a recently proposed Mössbauer neutrino experiment provides the unique possibility to discriminate basically different approaches to oscillations of flavor neutrinos.
We present one point of contact between the standard theory of neutrino oscillations and the alternative one, in which flavor neutrinos are described by states with definite masses. We show that both theories give the same results for static neutrinos only.
It is shown that we cannot put Majorana neutrinos in the standard Dirac theory without violation of the gauge invariance. Experiments on $ν_l \to l (l = e, μ, τ)$ transitions do not confirm this supposition. It means that on neutrino oscillation experiments, the Majorana neutrino oscillations cannot be observed.
In the Standard theory of neutrino oscillations it is supposed that physical observed neutrino states $ν_{e}, ν_μ, ν_τ$ have no definite masses and that neutrinos are initially created as mixture of $ν_{1}, ν_{2}, ν_{3}$ neutrino states and that neutrino oscillations are the real ones even when neutrino masses are different. It is shown that these suppositions lead to violation of the law of energy and momentum conservation and then the neutrino states are unstable ones and they must disintegrate. Then the development of the standard theory of neutrino oscillations in the framework of particle…
In the standard theory of neutrino oscillations it is supposed that physical observed neutrino states $ν_{e}, ν_μ, ν_τ$ have no definite masses, that they are initially produced as a mixture of the $ν_{1}, ν_{2}, ν_{3}$ neutrino states (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 obtain…
We review the current status of the solar neutrino oscillation parameters. We discuss the conditions under which measurements from future solar neutrino experiments would determine the oscillation parameters precisely. Finally we expound the potential of long baseline reactor anti-neutrino experiments in measuring the solar neutrino oscillation parameters.
An analysis of 3-flavour neutrino oscillations inside the Earth is presented in terms of the oscillograms -- contour plots of oscillation probabilities in the plane neutrino energy -- nadir angle. Special attention is paid to CP violation in neutrino oscillations in the Earth.
A brief review of the problem of neutrino masses and oscillations is given. In the beginning we present an early history of neutrino masses, mixing and oscillations. Then we discuss all possibilities of neutrino masses and mixing (neutrino mass terms). The phenomenology of neutrino oscillations in vacuum is considered in some details. We present also the neutrino oscillation data and the seesaw mechanism of the neutrino mass generation.
The three neutrino mass matrices in the $SU(5)\times U(2)$ model are studied focusing on the neutrino oscillation experiments. The atmospheric neutrino anomaly could be explained by the large $ν_μ - ν_τ$ oscillation. The long baseline experiments are expected to detect signatures of the neutrino oscillation even if the atmospheric neutrino anomaly is not due to the neutrino oscillation. However, the model cannot solve the solar neutrino deficit while it could be reconciled with the LSND data.
In the Standard theory of neutrino oscillations is used scheme of mass mixings, i.e., oscillation parameters are expressed via terms of mass matrix. In this work neutrino oscillations generated by charge (the weak interaction couple constants) mixings are considered. Expressions for angle mixings and lengths of oscillations are obtained. The expressions of the probability for three neutrino oscillations are given. Neutrino oscillations in this scheme (mechanism) are virtual if neutrino masses are not equal and real if neutrino masses are equal.
It is shown that in the two schemes with four massive neutrinos which are compatible with the results of all neutrino oscillation experiments, the probabilities of nu_e disappearance and nu_mu->nu_e appearance in long-baseline experiments are severely constrained.
The definition of `lepton flavour eigenstates' introduced in a recent paper hep-ph/0302045 is in disagreement with the Standard Model prediction for the structure of the leptonic charged current and implies the absence of neutrino oscillations following pion decay, in contradiction to experimental data
Neutrino mixing and basics of neutrino oscillations are considered. Recent evidences in favour of neutrino oscillations, obtained in the solar and atmospheric neutrino experiments, are discussed. Neutrino oscillations in the solar and atmospheric ranges of $Δm^{2}$ are considered in the framework of the minimal scheme with the mixing of three massive neutrinos.
This brief report is an extension of a prediction of neutrino oscillation with a sterile neutrino using parameters of the sterile neutrino mass and mixing angle recently extracted from experiment.
This is an extension of estimates of the probability of $ν$ to $e$ neutrino oscillation with one sterile neutrino to three sterile neutrinos, using a 6x6 matrix. Since the mixing angle for only one sterile neutrino has been experimentally determined, we estimate the $ν$ to $e$ neutrino oscillation probability with different mixing angles for two of the sterile neutrinos.
After some generalities on neutrino oscillations and on neutrinos, the recent experimental results presented by Soudan 2, MACRO and SuperKamiokande at the Neutrino'98 conference are summarized and discussed.
We explain the physics of neutrino oscillation in vacuum and in matter. We attempt to clarify several features of oscillation that can be puzzling when neutrinos are their own antiparticles.
Recently neutrino oscillation experiments have shown that it is very likely that there are one or two sterile neutrinos. In this review neutrino oscillations with one, two, three sterile and three active neutrinos, and parameters that are consistent with experiments, are reviewed.
Recent Super-Kamiokande data on the atmospheric neutrino anomaly are used to test various mechanisms for neutrino oscillations. It is found that the current atmospheric neutrino data alone cannot rule out any particular mechanism. Future long-baseline experiments should play an important role in identifying the underlying neutrino oscillation mechanism.
The history of neutrino mixing and oscillations is briefly presented. Basics of neutrino mixing and oscillations and convenient formalism of neutrino oscillations in vacuum is given. The role of neutrino in the Standard Model and the Weinberg mechanism of the generation of the Majorana neutrino masses are discussed.
On the basis of quantum field theory, we consider a unified description of various processes accompanied by neutrinos, namely weak decays and oscillation processes. The structures of the expectation values of flavor-neutrino numbers with respect to neutrino-source hadron state are investigated. Due to the smallness of neutrino masses, we naturally obtain the old (i.e. pre-mixing) formulas of decay probabilities. Together, it is shown that the oscillation formulas, similar to the usual ones, are applied irrespectively of the details of neutrino-producing processes. The derived oscillation formu…
The basics of neutrino oscillations is presented. Existing evidences of neutrino oscillations, obtained in the atmospheric and solar neutrino experiments, are considered. The new CHOOZ bound on the element $|U_{e3}|^{2}$, obtained from the three-neutrino analysis of the data, is discussed. Decoupling of neutrino oscillations in the solar neutrino range of $Δm^{2}$ is considered.
A consistent description of the results of the neutrino oscillation experiments carried out so far can be obtained from three basic properties of neutrinos and the parameters of the Hamiltonian matrix. Using these basic neutrino properties, an exact relation for the oscillation amplitudes of moving neutrinos is derived.
This work estimates the probability of $μ$ to $e$ neutrino oscillation with two sterile neutrinos using a 5x5 U-matrix, an extension of the previous estimate with one sterile neutrino and a 4x4 U-matrix. The sterile neutrino-active neutrino mass differences and the mixing angles of the two sterile neutrinos with the three active neutrinos are taken from recent publications, and the oscillation probability for one sterile neutrino is compared to the previous estimate.
The bicycle model of Lorentz noninvariant neutrino oscillations without neutrino masses naturally predicts maximal mixing and a 1/E dependence of the oscillation argument for $ν_μ\to ν_τ$ oscillations of atmospheric and long-baseline neutrinos, but cannot also simultaneously fit the data for solar neutrinos and KamLAND. We examine all nineteen possible structures of the Standard Model Extension for Lorentz noninvariant oscillations of massless neutrinos that naturally have a 1/E dependence at high neutrino energy. Due to the lack of any evidence for direction dependence, we consider only direc…
Using the Mandelstam-Tamm method we derive time-energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant (Mössbauer) production and absorption of tritium antineutrinos is in conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. A Mössbauer neutrino experiment could provide a unique possibility to test the applicability of the time-energy uncertainty relation to neutrino oscillatio…
Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos $ν_{e}$, $ν_μ$ and $ν_τ$, translational invariance does not take place.
We consider neutrino oscillations as non stationary phenomenon based on Schrodinger evolution equation and mixed states of neutrinos with definite flavors. We show that time-energy uncertainty relation plays a crucial role in neutrino oscillations. We compare neutrino oscillations with $B_{d}^{0}\leftrightarrows\bar B_{d}^{0}$ oscillations.
Predictions are presented for the oscillation phase in neutrino oscillations following pion decay at rest and in flight, muon decay and nuclear $β-$decay at rest as well as for muon oscillations following pion decay at rest and in flight. The neutrino oscillation phases found disagree with the conventionally used value: $ϕ_{12} = Δm^2 L/(2P)$. The same oscillation phase is found for neutrino and muon oscillations following pion decay at rest. Shortcomings of previous treatments of the quantum mechanics of neutrino oscillations are commented on.
We analyze the consequences of Lorentz violation (LV) to three-generation neutrino oscillation in the massless neutrino sector. We present a general formalism of three-family neutrino oscillation with neutrino flavor states being mixing states of energy eigenstates. It is also found that the mixing parts could strongly depend on neutrino energy by special choices of Lorentz violation parameters. By confronting with the existing experimental data on neutrino oscillation, the upper bounds on LV parameters are derived. Because the oscillation amplitude could vary with the neutrino energy, neutrin…
In the framework of the three-neutrino mixing the neutrino oscillations in the atmospheric and solar ranges of neutrino mass-squared differences are considered in the leading approximation. Neutrinoless double $β$- decay is also discussed.
Existing experimental data for neutrino oscillations are consistent with Lorentz-violating massless neutrinos. This talk summarizes some aspects of neutrino oscillations from the perspective of Lorentz and CPT violation in effective quantum field theory.
In analyzing neutrino oscillation experiments it is often assumed that while new physics contributes to neutrino masses, neutrino interactions are given by the Standard Model. We develop a formalism to study new physics effects in neutrino interactions using oscillation experiments. We argue that the notion of branching ratio is not appropriate in this case. We show that a neutrino appearance experiment with sensitivity to oscillation probability $P_{ij}^{exp}$ can detect new physics in neutrino interactions if its strength $G_N$ satisfies $(G_N/G_F)^2 \sim P_{ij}^{exp}$. Using our formalism w…
We present the results of an analysis of the data of reactor and accelerator neutrino oscillation experiments in the framework of a model with mixing of three massive neutrino fields and a neutrino mass hierarchy. The results of the LSND experiment are commented. Taking into account future long-baseline neutrino oscillation experiments, we have also analyzed the atmospheric neutrino data in the framework of the model.
We present an analysis of the global neutrino oscillation data in terms of four-neutrino mass schemes. We find that the strong preference of oscillations into active neutrinos implied by the latest solar as well as atmospheric neutrino data allows to rule out (2+2) mass schemes, whereas (3+1) schemes are strongly disfavoured by short-baseline experiments. Our analysis shows that four-neutrino oscillations do not provide a satisfactory description of the global neutrino oscillation data including the LSND result.
Basics of neutrino oscillations is discussed. Importance of time-energy uncertainty relation is stressed. Neutrino oscillations in the leading approximation and evidence for neutrino oscillations are briefly summarized.
Developing neutrino astronomy requires a good understanding of the neutrino oscillations mechanism. The European strategy for neutrino oscillation physics sets a high priority on future long baseline neutrino experiments with the aim to measure the intrinsic parameters that govern the neutrino oscillations. In this work we take a look at the next generation of long baseline experiments and discuss their prospects in future research.
We write the probabilities for neutrino oscillations in uniform-density matter exactly in terms of convention-independent vacuum neutrino oscillation parameters and the matter density. This extends earlier results formulating neutrino oscillations in terms of matter-, phase-, and trace-invariant quantities.
We introduce the representation on one unitarity triangle of the constraints resulting (1) from the interpretation of solar and atmospheric neutrino data in terms of oscillations, and (2) from the search for neutrinoless double beta decay. We show its use for the study of a nearly degenerate neutrino spectrum. The representation shows clearly the particular cases when the neutrinoless double beta decay rate can (or cannot) be small, that is: when the connection of the decay rate with the neutrino spectrum is less (or more) direct. These cases turn out to depend crucially on the scenario of osc…
The relation between neutrino oscillation parameters and neutrinoless double beta decay is studied, assuming normal and inverse hierarchies for Majorana neutrino masses. For normal hierarchy the crucial dependence on U_{e3} is explored. The link with tritium beta decay is also briefly discussed.
This is a brief presentation of historical introduction to the theoretical concept of neutrino oscillation during the early stage up to 60's. (Openig address at the Europhysics NEUTRINO OSCILLATION WORKSHOP (NOW' 98), 7-9 Sept. 1998, Amsterdam.
I discuss how a 1 KM3 neutrino detector can be used to study $ν_τ$ oscillations at PeV energies with neutrinos from AGN's and to study neutrinos from GRB's.
We generalise our previous observation on the invariance of the Jarlskog determinant to matter effects in neutrino oscillations. Within the context of standard neutrino oscillation theory with matter effects, we present the complete set of (five) matter invariant observables for neutrino propagation in matter. We give some examples of their application.
In this lecture we review some of the basic properties of neutrinos, in particular their mass and the oscillation behavior. First we discuss how to describe the neutrino mass. Then, under the assumption that neutrinos are massive and mixed, the fundamentals of the neutrino oscillations are discussed with emphasis on subtle aspects which have been overlooked in the past. We then review the terrestrial neutrino oscillation experiments in the framework of three generations of neutrinos with the standard mass hierarchy. Finally, a brief summary of the current status of the solar and atmospheric ne…
What information about the neutrino mass spectrum and mixing matrix can be inferred from the existing neutrino oscillation data? We discuss here the answer to this question in the case of mixing of three and four neutrinos. We present the constraints on the effective Majorana mass <m> that can be obtained from the results of reactor neutrino oscillation experiments and from atmospheric neutrino data. We discuss the bounds on the oscillation probabilities in long-baseline neutrino oscillation experiments that follow from the results of short-baseline experiments. Some remarks on a model-indepen…
The current status of neutrino oscillation searches with reactors and accelerators is reviewed. An outlook, especially on future long baseline neutrino oscillation projects, is given.
On basis of effective interactions of charged lepton and hadron currents, we obtain an effective interacting Hamiltonian of neutrinos in nuclear media up to the leading order. Using this effective Hamiltonian, we study neutrino mixing and oscillations in nuclear media and strong magnetic fields. We compute neutrino mixing angle and mass squared difference, and find the pattern of vacuum neutrino oscillations is modified in magnetized nuclear media. Comparing with the vacuum neutrino oscillation, we find that for high-energy neutrinos, neutrino oscillations are suppressed in the presence of nuc…
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.
We consider neutrino oscillations as non stationary phenomenon based on Schrodinger evolution equation and mixed neutrino states with definite flavor. We demonstrate that for such states invariance under translations in time does not take place. We show that time-energy uncertainty relation plays a crucial role in neutrino oscillations. We compare neutrino oscillations with $K^{0}\leftrightarrows\bar K^{0}$, $B_{d}^{0}\leftrightarrows\bar B_{d}^{0}$ etc oscillations.
The complete description of neutrino oscillations require the wave packet treatment. For terrestrial experiments the contribution from the interaction of neutrino with the Earth matter would modify oscillation pattern, i.e., the dependence of the flavor transition probability on baseline $L$ and energy $E$. We thus combine the wave packet approach and the matter effects, in order to have more accurate descriptions of neutrino oscillation. The general expression for the transition probability of oscillations with arbitrary numbers of neutrinos are derived. As an example the two-neutrino oscilla…
It is shown that the experiment on recoilless resonant emission and absorption of $\bar ν_{e}$, proposed recently by Raghavan, could have an important impact on our understanding of the physics of neutrino oscillations.
If the three types of active neutrinos possess different maximum attainable velocities and the neutrino eigenstates in the velocity basis are different from those in the flavour (and mass) basis then this will induce a flavour oscillation in addition to the normal mass flavour oscillation. Here we study such an oscillation scenario in three neutrino framework including also the matter effect and apply our results to demonstrate its consequences for long baseline neutrinos. We also predict the possible signatures in terms of yields in a possible long baseline neutrino experiment.
We consider long-baseline neutrino oscillations in the framework of two schemes with mixing of four massive neutrinos which can accommodate all the existing indications in favour of neutrino mixing. Within these schemes, we derive bounds on the oscillation probabilities and the CP-odd neutrino-antineutrino asymmetries in long-baseline experiments. Using the results of short-baseline neutrino oscillation experiments, we obtain rather strong upper bounds on the long-baseline probabilities 1-P(nu_e->nu_e) and P(nu_mu->nu_e). Nevertheless, the projected sensitivities of the MINOS and ICARUS experi…
The theory of neutrino flavor rotations is discussed in terms of wave function solutions to the Dirac equation with a neutrino mass matrix. We give a critical review of the nature of neutrino oscillations.
The quantum field theoretical treatment of neutrino oscillations is formulated. The procedure how to calculate the transition probability of one type neutrino into another is briefly outlined.
Evidences in favor of neutrino oscillations, obtained in the solar and atmospheric neutrino experiments, are discussed. Neutrino oscillations in the solar and atmospheric ranges of the neutrino mass-squared differences are considered in the framework of the minimal scheme with the mixing of three massive neutrinos.
We review the status of several phenomenological topics of current interest in neutrino oscillations: (i) Solar neutrino oscillations after the first Sudbury Neutrino Observatory measurements, including both model-independent and model-dependent results; (ii) Dominant nu_mu-->nu_tau oscillations of atmospheric and K2K neutrinos, and possible subdominant oscillations induced by either extra states or extra interactions; and (iii) Four-neutrino scenarios embedding the controversial LSND evidence for oscillations.
